SYSTEMS USING A LEVITATING, ROTATING PUMPING OR MIXING ELEMENT AND RELATED METHODS

Abstract: A system for pumping or mixing a fluid F using a levitating, rotating pumping or mixing element 812 and various other components for use in a pumping or mixing system are disclosed. The pumping or mixing element 812 is placed in a fluid-containing vessel 810 in close proximity to a superconducting element 818. A cooling source thermally linked to the superconducting element 818 provides the necessary cooling to induce levitation in the pumping or mixing element 812. The superconducting element 818 may be thermally isolated, such that the pumping or mixing element 812, the vessel 810, and any fluid F contained therein are not exposed to the cold temperatures required to produce the desired superconductive effects and the resulting levitation. By using means external to the vessel to rotate and/or stabilize the pumping or mixing element 812 levitating in the fluid F, including possibly rotating the superconducting elements 818 itself or moving it relative to the vessel 810, the desired effective pumping or mixing action may be provided.

Description: SYSTEMS USING A LEVITATING, ROTATING PUMPING OR MIXING ELEMENT AND RELATED METHODS This application claims the benefit of the following U.S. Provisional Patent Applications: (1) Ser. No. 60/239,187, filed October 9, 2000, entitled "Pumping or Mixing System Using a Levitating Magnetic Bearing"; (2) Ser. No. 60/282,927, filed April 10, 2001, entitled "Systems Using a Levitating, Rotating Pumping or Mixing Element and Related Methods"; and (3) Ser. No. 60/318,579, filed September 11 , 2001 , entitled "Systems for Levitating and Rotating a Pumping or Mixing Element Including Assist Magnets." Technical Field The present invention relates generally to the levitation of magnets using superconductivity and, more particularly, to a system, related components, and related method for pumping or mixing fluids using a rotatable magnetic element levitated in a vessel by a superconducting element. Background of the Invention Most pharmaceutical solutions and suspensions manufactured on an industrial scale require highly controlled, thorough mixing to achieve a satisfactory yield and ensure a uniform distribution of ingredients in the final product. Agitator tanks are frequently used to complete the mixing process, but a better degree of mixing is normally achieved by using a mechanical stirrer or impeller (e.g., a set of mixing blades attached to a metal rod). Typically, the mechanical stirrer or impeller is simply lowered into the fluid through an opening in the top of the vessel and rotated by an external motor to create the desired mixing action. One significant limitation or shortcoming of such an arrangement is the danger of contamination or leakage during mixing. The rod carrying the mixing blades or impeller is typically introduced into the vessel through a dynamic seal or bearing. This opening provides an opportunity for bacteria or other contaminants to enter, which of course can lead to the degradation of the product. A corresponding danger of environmental contamination exists in applications involving hazardous or toxic fluids, or suspensions of pathogenic organisms, since dynamic seals or bearings are prone to leakage. Cleanup and sterilization are also made difficult by the dynamic bearings or seals, since these structures typically include folds and crevices that are difficult to reach. Since these problems are faced by all manufacturers of sterile solutions, pharmaceuticals, or the like, the U.S. Food and Drug Administration (FDA) has consequently promulgated strict processing requirements for such fluids, and especially those slated for intravenous use. Recently, there has also been an extraordinary increase in the use of biosynthetic pathways in the production of pharmaceutical materials, but problems plague those involved in this rapidly advancing industry. The primary problem is that suspensions of genetically altered bacterial cells frequently used to produce protein pharmaceuticals (insulin is a well-known example) require gentle mixing to circulate nutrients. If overly vigorous mixing or contact between the impeller and the vessel wall occurs, the resultant forces and shear stresses may damage or destroy a significant fraction of the cells, as well as protein molecules that are sensitive to shear stresses. This not only reduces the beneficial yield of the process, but also creates deleterious debris in the fluid suspension that requires further processing to remove. In an effort to overcome this problem, others have proposed alternative mixing technologies. The most common proposal for stirring fluids under sterile conditions is to use a rotating, permanent magnet bar covered by an inert layer of TEFLON, glass, or the like. The magnetic bar is placed on the bottom of the agitator vessel and rotated by a driving magnet positioned external to the vessel. Of course, the use of such an externally driven magnetic bar avoids the need for a dynamic bearing, seal or other opening in the vessel to transfer the rotational force from the driving magnet to the stirring magnet. Therefore, a completely enclosed system is provided. This of course prevents leakage and the potential for contamination created by hazardous materials (e.g., cytotoxic agents, solvents with low flash points, blood products, etc.), eases clean up, and allows for the desirable sterile interior environment to be maintained. However, several well-recognized drawbacks are associated with this mixing technology, making it unacceptable for use in many applications. For example, the driving magnet produces not only torque on the stirring magnetic bar, but also an attractive axial thrust force tending to drive the bar into contact with the bottom wall of the vessel. This of course generates substantial friction at the interface between the bar and the bottom wall of the vessel. This uncontrolled friction generates unwanted heat and may also introduce an undesirable shear stress in the fluid. Consequently, fragile biological molecules, such as proteins and living cells that are highly sensitive to temperature and shear stress, are easily damaged during the mixing process, and the resultant debris may contaminate the product. Moreover, the magnetic bar stirrer may not generate the level of circulation provided by an impeller, and thus cannot be scaled up to provide effective mixing throughout the entire volume of large agitation tanks of the type preferred in commercial production operations. In yet another effort to eliminate the need for dynamic bearings or shaft seals, some have proposed mixing vessels having external magnets that remotely couple the mixing impeller to a motor located externally to the vessel. A typical magnetic coupler comprises a drive magnet attached to the motor and a stirring magnet carrying an impeller. Similar to the magnetic bar technology described above, the driver and stirrer magnets are kept in close proximity to ensure that the coupling between the two is strong enough to provide sufficient torque. An example of one such proposal is found in U.S. Patent No. 5,470,152 to Rains. As described above, the high torque generated can drive the impeller into the walls of the vessel creating significant friction. By strategically positioning roller bearings inside the vessel, the effects of friction between the impeller and the vessel wall can be substantially reduced. Of course, high stresses at the interfaces between the ball bearings and the vessel wall or impeller result in a grinding of the mixing proteins and living cells, and loss of yield. Further, the bearings may be sensitive to corrosive reactions with water-based solutions and other media and will eventually deteriorate, resulting in frictional losses that slow the impeller, reduce the mixing action, and eventually also lead to undesirable contamination of the product. Mechanical bearings also add to the cleanup problems. In an effort to address and overcome the limitations described above, still others have proposed levitated pumping or mixing elements designed to reduce the deleterious effects of friction resulting from magnetically coupled mixers. By using a specially configured magnetic coupler to maintain only a repulsive levitation force in the vertical direction, the large thrust force between the stirring and driving magnets can be eliminated, along with the resultant shear stress and frictional heating. An example of one such arrangement is shown in U.S. Patent No.5,478, 149 to Quigg. However, one limitation remaining from this approach is that only magnet-magnet interactions provide the levitation. This leads to intrinsically unstable systems that produce the desired levitation in the vertical direction, but are unable to control side-to-side movement. As a result, external contact bearings in the form of bearing rings are necessary to laterally stabilize the impeller. Although this "partial" levitation reduces the friction between the impeller and the vessel walls, it does not totally eliminate the drawbacks of the magnetically coupled, roller bearing mixers previously mentioned. In an attempt to eliminate the need for contact or other types of mechanical roller bearings, complex feedback control has been proposed to stabilize the impeller. Typical arrangements use electromagnets positioned alongside the levitating magnet. However, the high power level required to attain only sub- millimeter separations between the levitating magnet and the stabilizing magnets constitutes a major disadvantage of this approach. Furthermore, this solution is quite complex, since the stabilizing magnets must be actively monitored and precisely controlled by complex computer-implemented software routines to achieve even a moderate degree of stability. As a consequence of this complexity and the associated maintenance expense, this ostensible solution has not been accepted in the commercial arena, and it is doubtful that it can be successfully scaled up for use in mixing industrial or commercial scale process volumes. Still others have proposed the use of superconductive materials to levitate objects, such as bearings or flywheels in motors, where the relatively cold temperatures required to induce superconductivity are not a great concern. However, despite recent advances in the art, significant limitation on the application of this technology to non-cryogenic fluid pumping or mixing systems results from the cold temperatures required to create the desired superconductive effects. Even the recently discovered "high temperature" superconductors require temperatures on the order of 77 to 130 Kelvin to induce reliable, stable levitation in a pumping or mixing element. Hence, to date, applications of this technology to fluids have been primarily in the pumping of cryogens or the like, such as those typically used in cold fusion experiments, in flywheels or other energy storage devices, or for space travel (see representative U.S. Patent No. 5,747,426 to Abboud or U.S. Patent No. 4,365,942 to Schmidt), where there is of course little concern for the inevitable cooling effect created. My prior U.S. Patent No. 5,567,672 discloses levitating a magnet above a superconducting element that is thermally separated by the entirety of the double- walled vacuum jacket of the cryostat containing the cooling source used to cool the superconducting element. This increased separation reduces the thermal transfer between the cold superconducting element and the levitating element, so that it could possibly be used in mixing temperature sensitive fluids, such as cell suspensions or blood, as disclosed herein. Hence, while this technology could be employed in the pumping or mixing of fluids, the increased separation distance between the superconducting element and the levitating element created by the double wall vacuum gap may significantly decrease the stability and the load capacity. This could limit the applications in which this arrangement is useful, and may especially preclude use with pumping or mixing particularly viscous fluids or with the large volumes of fluid typically present in commercial scale operations. However, it may still have utility in other applications. Another well-recognized need is for systems that are capable of mixing fluids in vessels that are frequently subjected to high internal pressures. Such vessels are widely used in the biotechnology and food processing industries, where periodic sterilization by high pressure steam is required. To withstand the forces created by the internal pressurization, the vessel must have relatively thick sidewalls, which are usually formed of non-magnetic stainless steel (e.g, at least seven millimeters of thickness to hold an internal pressure on the order of seven bar). This increased thickness is deleterious, since it makes the application of external levitation systems relying on magnet-magnet interactions alone difficult. In particular, the interaction (attractive) forces between the magnets drop significantly as the separation distance increases as a result of the increased wall thickness necessary to withstand the higher internal pressures. As a result, achieving stable levitation is difficult, it not impossible. In an effort to solve this problem, others in the past have proposed special vessels having a thin-walled cavity, usually cylindrical in form. Of course, this arrangement reduces the gap created between a driving magnet positioned in the cavity external to the vessel and a non-levitating magnet, such as a stirrer, internal to the vessel adjacent to the cavity. Also, the high internal pressure serves to contract the thin sidewalls of the cylindrical cavity, while the area of the upper wall of the cavity acted upon by the pressure forces is ' minimized. However, even with the improvement afforded, the use of a non-levitating magnetic stripper is deleterious in many applications for the reasons previously explained (e.g., frictional contact with the walls of the vessel, the need for mechanical bearings or the like, etc.). Thus, a need is identified for an improved system having a levitating magnetic element for pumping or mixing fluids, and especially ultra-pure, hazardous, or delicate fluid solutions or suspensions, including those which may be processed in vessels capable of withstanding high pressurization. The system would preferably employ a magnetic element capable of pumping or mixing a fluid that levitates in a stable fashion in the vessel to avoid contact with the bottom or side walls thereof when in use, including any portion of the cavity in the case of the special high pressure vessel described above. Since the magnetic element would levitate in the fluid, no mixing rod or other structure penetrating the mixing vessel would be required, which of course eliminates the need for dynamic bearings or seals and all potentially deleterious effects associated therewith. Also, the use of a levitating magnetic element would eliminate the need for mechanical bearings or the deleterious magnet-wall interactions that create undesirable shear stresses and unwanted friction in the fluid. Since penetration is unnecessary, the vessel could be completely sealed prior to mixing, and possibly even pressurized. This would reduce the chance for external exposure in the case of hazardous or biological fluids, such as blood or the like, or contamination, in the case of biologically active or sensitive products. The vessel and pumping or mixing element could also possibly be made of disposable materials, such as inexpensive, flexible plastic materials, and discarded after each use to eliminate the need for cleaning or sterilization. In the case of warm or temperature-sensitive fluids, the use of superconductivity to provide the desired levitation would be possible by thermally isolating and separating the cold superconducting element from the pumping or mixing element. This combined thermal isolation and separation would avoid creating any significant cooling in the vessel, the pumping or mixing element or the fluid being mixed or pumped. The use of a superconductor would also eliminate the sole reliance on magnet-magnet repulsion to provide the levitation force and the concomitant need for active electronic control systems to ensure stable levitation. Overall, the proposed system would have superior characteristics over existing mixing or pumping technologies, especially in terms of sterility, mixing quality, safety and reliability, and would be readily adaptable for use in larger, industrial scale operations. Summary of the Invention In accordance with a first aspect of the invention, a system for pumping or mixing a fluid is disclosed. The system comprises a vessel for holding the fluid, the vessel having a cavity formed in at least one side thereof; a magnetic pumping or mixing element positioned in the vessel concentric with the cavity; at least one superconducting element positioned in or adjacent to the cavity for levitating the pumping or mixing element; a wall defining a chamber around the superconducting element, the chamber thermally isolating and/or separating the superconducting element from the vessel; a cooling source thermally linked to the superconducting element; and a motive device for rotating the pumping or mixing element or the superconducting element and the pumping or mixing element together relative to the cavity. In one embodiment, a first wall of the vessel defines a portion of the cavity, the wall being formed of a material having a first thickness that is less than the thickness of the material forming a remainder of the vessel. Preferably, the first wall of the vessel is circular in cross-section. The wall defining a chamber around the superconducting element may be the outer wall of a cryostat adapted for insertion into the cavity. The pumping or mixing element may include a levitation magnet concentric with the superconducting element in the cryostat. The superconducting element may be annular, in which case and a corresponding portion of the chamber defined by the wall is also annular for receiving the superconducting element. In one possible embodiment, the motive device includes a shaft carrying a plurality of alternating polarity driving magnets at one end, with the driving magnets being inserted in a thermally separated or isolated bore in the cryostat. The bore is concentric with the annular chamber for housing the superconducting element. Preferably, the levitation magnet corresponds in at least one dimension to the superconducting element and further includes a plurality of driven magnets having alternating polarities. In operation, the driven magnets are aligned with the driving magnets and rotated by the motive device such that the levitation magnet levitates the pumping or mixing element while the driven magnets transmit driving torque to the pumping or mixing element from the driving magnets. A platform thermally linked to the cooling source may be provided in the chamber for supporting the superconducting element. Preferably, the thermal linking is provided by either a rod extending from the cooling source to the platform for supporting the superconducting element or a cryocooler serving as the cooling source in thermal engagement with the platform. To eliminate deleterious thermal transfer, the chamber surrounding the superconducting element is evacuated or insulated. In a particularly preferred version, the pumping or mixing element includes a levitation magnet having a magnetization vector, and the at least one superconducting element is comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis. Preferably, the A-B planes are parallel to the magnetization vector and the C-axis is peφendicular to the magnetization vector. In addition, at least two superconducting elements may be provided, with each comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis. Preferably, the A-B planes of each segment are parallel to the magnetization vector and the C-axis of each segment is peφendicular to the magnetization vector. Another option is for orienting: (1) the A-B planes of each segment comprising the first superconducting element parallel to the magnetization vector and the C-axis of each segment comprising the first superconducting element peφendicular to the magnetization vector; and (2) the A-B planes of each segment comprising the second superconducting element peφendicular to the magnetization vector and the C-axis of each segment comprising the second superconducting element parallel to the magnetization vector. In a most preferred embodiment, the arrangement includes first, second, and third superconducting elements, each comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis. In this case, the A-B planes of the segments of the first and third superconducting elements are preferably parallel to the magnetization vector, and the C-axes of the segments of the first and third superconducting elements are peφendicular to the magnetization vector. The A-B planes of the segments of the second superconducting element are peφendicular to the magnetization vector and the C-axis of the segments of the second superconducting element are parallel to the magnetization vector. The three superconducting elements may each be arranged in an annular or polygonal configuration, and the pumping or mixing element may include an annular levitation magnet that is positioned in the vessel such that each of three of the four sides of the levitation magnet are juxtaposed to one of the three superconducting elements. Each superconducting element may be comprised of a plurality of contiguous or noncontiguous segments. In another embodiment, the pumping or mixing element includes a disc-shaped body for overlying an upper wall of the cavity. The body carries an annular levitation magnet surrounding a cylindrical sidewall defining the cavity in the vessel. The superconducting element is annular and positioned in or adjacent to the cavity for interacting with the annular levitation magnet. In accordance with a second aspect of the invention, a system for levitating a permanent magnet having a magnetization vector is provided. The system comprises at least two superconducting elements, each positioned on a different side of the magnet and comprised of a plurality of segments of a superconducting material in a superconducting state. Each superconducting element has a crystallographic structure comprising A-B planes and a C-axis. Preferably, the A-B planes of each segment are substantially parallel to the magnetization vector and the C-axes of each segment are substantially peφendicular to the magnetization vector. Preferably, the levitation magnet: (1) forms a part of a rotor, impeller, or other type of pumping or mixing element; and (2) is annular. A first of the two superconducting elements is positioned adjacent to the inner surface of the opening in the annular levitation magnet, and a second superconducting element is positioned opposite the first superconducting element. The system may further include a third superconducting element comprised of a plurality of segments of a superconducting material, each having a crystallographic structure comprising A-B planes and a C-axis. In that case, the A-B planes of each segment comprising the third superconducting element are substantially peφendicular to the magnetization vector and the C-axis of each segment comprising the third superconducting element is substantially parallel to the magnetization vector. Preferably, the third superconducting element is positioned adjacent to an upper or lower surface of the annular levitation magnet. In accordance with a third aspect of the invention, a system for pumping or mixing a fluid is disclosed. The system comprises a vessel for holding the fluid, a magnetic pumping or mixing element positioned in the vessel, at least one superconducting element positioned adj acent to the vessel for levitating the pumping or mixing element, a cryostat including a chamber thermally isolating and/or separating the superconducting element from the vessel and a cooling source thermally linked to the superconducting element, and a motive device for rotating the cryostat, including the cooling source and superconducting element. Preferably, the cooling source in the rotating cryostat is a Stirling-cycle cryocooler and the system further includes a power source for supplying power to the rotating cryocooler by way of a dynamic electrical connection, such as a slip ring. At least one bearing may be provided to support the cryostat and permit low-friction rotational motion. The motive device may include a motor for rotating a pulley that is coupled to the cryostat by an endless belt or a driven shaft that is coupled to the cryostat. In accordance with a fourth aspect of the invention, a system for levitating a magnet having a magnetization vector is disclosed. The system comprises first and second superconducting elements, each positioned on a different side of the levitation magnet and comprising a plurality of segments of a superconducting material in a superconducting state, with each segment having a crystallographic structure comprising A-B planes and a C-axis. Preferably, the A-B planes of the segments comprising the first superconducting element are substantially parallel to the magnetization vector and the C-axes of the segments comprising the first superconducting element are substantially peφendicular to the magnetization vector. The A-B planes of the segments comprising the second superconducting elements are substantially peφendicular to the magnetization vector and the C-axes of the segments comprising the second superconducting element are substantially parallel to the magnetization vector. Preferably, the levitation magnet is annular and forms a part of a rotor, impeller, or other type of pumping or mixing element. In that case, the first superconducting element is positioned adjacent to the inside surface of the opening in the annular levitation magnet or an opposite outside surface thereof, and the second superconducting element is positioned adjacent to the upper or lower outer surface of the levitation magnet. The system may further include a third superconducting element comprised of a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C-axis. Preferably, the A-B planes of the segments comprising the third superconducting element are substantially parallel to the magnetization vector and the C-axes of the segments comprising the third superconducting element are substantially peφendicular to the magnetization vector. The third superconducting element may be positioned opposite the first superconducting element. In accordance with a fifth aspect of the invention, a system for levitating a magnet having a magnetization vector is disclosed. The system comprises first, second, and third superconducting elements, each positioned on a different side of the levitation magnet and comprised of a plurality of segments of a superconducting material in a superconducting state. Each segment has a crystallographic structure comprising A-B planes and a C-axis. The A-B planes of the segments comprising the first and third superconducting elements are substantially parallel to the magnetization vector and the C-axes of the segments comprising the first and third superconducting elements are substantially peφendicular to the magnetization vector. The A-B planes of the segments comprising the second superconducting element are substantially peφendicular to the magnetization vector and the C-axes of the segments comprising the second superconducting element are substantially parallel to the magnetization vector. As a result of this arrangement, levitation of the magnet is both stabilized and enhanced by the orientation of the planes and axes of the superconducting element relative to the magnetization vector. Preferably, each superconducting element is positioned such that the C-axis passes substantially through the center of the levitation magnet, which is preferably annular. In accordance with a sixth aspect of the invention, a method of levitating and rotating a magnetic element in a vessel having a cavity, such as for pumping or mixing a fluid, is disclosed. The method comprises placing the magnetic element in a vessel concentric with the cavity; levitating the magnetic element above a superconducting element maintained in a superconducting state in accordance with a field cooling protocol and held in an evacuated or insulated chamber positioned adjacent to the cavity in the vessel; and rotating the magnetic element. In accordance with a seventh aspect of the invention, a method of levitating a magnet having a magnetization vector is disclosed. The method comprises providing first and second elements in a superconducting state in accordance with a field cooling protocol for levitating the magnet, each superconducting element being positioned on a different side of the magnet and comprising a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C-axis; orienting the A-B planes of the segments comprising the first superconducting element to be substantially parallel to the magnetization vector; orienting the C-axes of the segments comprising the first superconducting element to be substantially peφendicular to the magnetization vector; orienting the A-B planes of the segments comprising the second superconducting elements to be substantially peφendicular to the magnetization vector; and orienting the C-axes of the segments comprising the second superconducting element to be substantially parallel to the magnetization vector. In accordance with an eighth aspect of the invention, a method of levitating a magnet having a magnetization vector is disclosed. The method comprises providing first and second superconducting elements in a superconducting state in accordance with a field cooling protocol for levitating the levitation magnet, each superconducting element being positioned on a different side of the levitation magnet and comprising a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C- axis; orienting the A-B planes of the segments comprising the first superconducting element to be substantially parallel to the magnetization vector; orienting the C-axes of the segments comprising the first superconducting element to be substantially peφendicular to the magnetization vector; orienting the A-B planes of the segments comprising the second superconducting elements to be substantially parallel to the magnetization vector; and orienting the C-axes of the segments comprising the second superconducting element to be substantially peφendicular to the magnetization vector. In accordance with a ninth aspect of the invention, a method for levitating a magnet having a magnetization vector is disclosed. The method comprises providing first, second, and third superconducting elements in a superconducting state in accordance with a field cooling protocol for levitating the magnet, each positioned on a different side of the magnet and comprised of a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C-axis; orienting the A-B planes of the segments comprising the first and third superconducting elements to be substantially parallel to the magnetization vector; orienting the C-axes of the segments comprising the first and third superconducting elements to be substantially peφendicular to the magnetization vector; orienting the A-B planes of the segments comprising second superconducting element to be substantially peφendicular to the magnetization vector; and orienting the C-axes of the segments comprising the second superconducting element to be substantially parallel to the magnetization vector. As a result, the levitation of the magnet is both stabilized and enhanced by the orientation of the planes and axes of the superconducting elements relative to the magnetization vector. In accordance with a tenth aspect of the invention, a pumping or mixing element for a system including a superconducting element for levitating the pumping or mixing element and a plurality of alternating polarity driving magnets for rotating the pumping or mixing element is disclosed. The system comprises a body carrying an annular levitation magnet and a plurality of alternating polarity driven magnets corresponding to the alternating polarity driving magnets. The body is preferably disc-shaped and the annular levitation magnet depends from the body. The driven magnets may be'embedded in the body in a circular configuration inside of the periphery of the opening in the annular levitation magnet. In accordance with an eleventh aspect of the invention, a cryostat for keeping one or more annular superconducting elements in a superconducting state thermally isolated from a vessel having a cavity formed in a sidewall thereof defining an annular outer portion for receiving a portion of a pumping or mixing element including a levitation magnet is disclosed. The cryostat comprises an outer wall defining an annular chamber for housing the one or more annular superconducting elements. The annular chamber is evacuated or insulated to thermally isolate the superconducting element from the wall, which includes an annular channel for receiving the annular outer portion of the vessel with the portion of the pumping or mixing element. In one embodiment, a bore or opening is provided concentric with the annular chamber and exposed to the ambient environment for receiving a portion of a motive device for rotating the pumping or mixing element. In accordance with a twelfth aspect of the invention, a system for pumping or mixing a fluid in a vessel positioned on a stable support structure is disclosed. The system comprises a magnetic pumping or mixing element for placement in the vessel, at least one superconducting element for levitating the pumping or mixing element, a cooling source thermally linked to the superconducting element, and a motive device for rotating the superconducting element and the cooling source together. The system may further include a cryostat having a wall defining a chamber for thermally isolating the superconducting element, wherein the cryostat is rotated with the superconducting element and the cooling source. Preferably, the cryostat is supported by a bearing permitting rotational motion, the motive device is a motor, and an endless belt is provided for transmitting the rotary motion produced by the motor to the cryostat to rotate the superconducting element. The cooling source may be an electric cryocooler that is coupled to a power source by a dynamic electrical connection. Preferably, the dynamic electrical connection comprises either a pair of electrical contacts on the rotating cryocooler for engaging a corresponding pair of stationary electrical contacts in communication with the power source or a slip ring. The vessel may be supported by a stable support structure positioned between the superconducting element and the magnetic pumping or mixing element. The magnetic pumping or mixing element includes a levitation magnet comprised of plurality of alternating polarity segments and the superconducting element is comprised of a plurality of segments, each having a crystallographic C-axis oriented in the radial direction. The vessel may include a cavity, with the pumping or mixing element being concentric with the cavity. The superconducting element is preferably housed in a vacuum jacket of a cryostat. Prior to or during operation of the system, the cryostat is at least partially introduced into the cavity such that the superconducting element induces levitation in the pumping or mixing element. As a result of this arrangement, the cavity acts as a centering or support post for the concentric pumping or mixing element when in a non-levitated position. The vessel with the cavity may also be a flexible bag. In accordance with a thirteenth aspect of the invention, a system for pumping or mixing a fluid is disclosed. The system comprises a vessel for holding the fluid, a magnetic pumping or mixing element positioned in the vessel, at least one superconducting element positioned adjacent to the vessel for levitating the pumping or mixing element, a cryostat having a wall defining a chamber around the superconducting element, the chamber thermally isolating and/or separating the superconducting element from the vessel, and a cooling source thermally linked to the superconducting element; and a motive device for rotating the cryostat. In one embodiment, a first wall of the vessel defines a cavity. The wall is preferably formed of a material having a first thickness that is less than the thickness of the material forming a remainder of the vessel and is cylindrical in shape. The cryostat is adapted for insertion into the cavity, and the pumping or mixing element includes a combined levitation and driven magnet that is concentric with the superconducting element in the cryostat. Accordingly, the superconducting element is preferably annular. In one version of this embodiment, the cryostat is rotatably supported and the motive device is a motor. An endless belt transfers the rotary motion produced by the motor to the cryostat to cause the superconducting element to rotate. The cryostat is preferably rotatably supported by one or more bearings or bearing assemblies, each of which is in turn supported by a stable support structure. A platform is also preferably provided in the chamber for supporting the superconducting element, wherein the platform is thermally linked to the cooling source. The chamber around the superconducting element is preferably evacuated or insulated. In accordance with a fourteenth aspect of the invention, a container for use in a pumping or mixing system using a levitating pumping or mixing element having an opening, the pumping or mixing element being driven by way of magnetic coupling, is disclosed. The container comprises a flexible body for holding a fluid and a cavity defined by a cylindrical wall adjacent to the body. The wall passes through the opening to loosely hold the pumping or mixing element in place, such as when transporting the container or in the event of accidental decoupling of the pumping or mixing element. The wall preferably has an oversized portion. This portion prevents the pumping or mixing element from inadvertently lifting from the wall. In accordance with a fifteenth aspect of the invention, a method of levitating and rotating a magnetic element, such as for pumping or mixing a fluid, is disclosed. The method comprises placing the magnetic element in a vessel having a cavity; levitating the magnetic element using a superconducting element; and rotating the magnetic element in the vessel about the cavity in a non-contact fashion. In accordance with a sixteenth aspect of the invention, a system for pumping or mixing a fluid is disclosed. The system comprises a vessel for holding the fluid, the vessel having a cavity formed therein; a magnetic pumping or mixing element positioned in the vessel at a position concentric with the cavity; at least one superconducting element positioned in or adjacent to the cavity for levitating the pumping or mixing element relative to the vessel; a wall defining a chamber around the superconducting element, the chamber thermally isolating and/or separating the superconducting element from the vessel; a cooling source thermally linked to the superconducting element, a motive device for rotating the pumping or mixing element or the superconducting element and the pumping or mixing element, and means for assisting in maintaining a proper position of the levitating pumping or mixing element relative to the cavity. In one embodiment, the assisting means includes a first magnetic structure positioned on the pumping or mixing element and a second magnetic structure positioned in or on one of the wall defining the chamber around the superconducting element or the vessel in juxtaposition to the first magnetic structure, wherein the adjacent surfaces of the first and second magnetic structures have like polarities and thus repel each other. In a second embodiment, the assisting means includes a first magnetic structure positioned on the pumping or mixing element and a second magnetic structure positioned in or on one of the wall defining the chamber around the superconducting element or the vessel in juxtaposition to the first magnetic structure, wherein the adjacent surfaces of the first and second magnetic structures have like polarities. Preferably, the first and second magnetic structures are each ring magnets, but instead may be comprised of arrays of magnets. The pumping or mixing structure may also include an opening and create an annulus with the cavity, whereby upon rotating about the cavity, fluid is drawn through the annulus and out the opening to enhance the pumping or mixing action provided. The superconducting element may be comprised of a pair of spaced arrays of superconducting elements and the pumping or mixing element includes spaced arrays of alternating polarity levitation magnets. In accordance with a seventeenth aspect of the invention, a system for pumping or mixing a fluid is disclosed. The system comprises a vessel for holding the fluid, the vessel having a cavity formed in at least one side thereof; a magnetic pumping or mixing element positioned in the vessel at a position concentric with the cavity and including at least one levitation magnet structure; at least one superconducting element positioned in or adjacent to the cavity for levitating the pumping or mixing element; a wall defining a chamber around the superconducting element, the chamber thermally isolating and/or separating the superconducting element from the vessel; a cooling source thermally linked to the superconducting element, a motive device for rotating either the pumping or mixing element alone or the superconducting element and the pumping or mixing element; a first magnetic levitation-assist structure positioned on the pumping or mixing element; and a second magnetic structure positioned in, inside or on one of the wall defining the chamber around the superconducting element or in, inside, or on the vessel in juxtaposition to the first magnetic levitation-assist structure, wherein the adjacent ends of the first and second magnetic structures have like polarities. In accordance with an eighteenth aspect of the invention, a system for pumping or mixing a fluid is disclosed. The system comprises a vessel for holding the fluid, the vessel having a cavity formed in at least one side thereof; a magnetic pumping or mixing element positioned in the vessel at a position concentric with the cavity and including first and second arrays of alternating polarity levitation magnets; at least two spaced arrays of superconducting elements positioned in or adjacent to the cavity in juxtaposition to the first and second arrays of alternating polarity levitation magnets; a wall defining a chamber around the superconducting element, the chamber being evacuated or insulated to thermally isolate and/or separate the superconducting element from the vessel; a cooling source thermally linked to the superconducting element, and a motive device for rotating the pumping or mixing element or the superconducting element. Means for assisting in maintaining the proper positioning of the levitating pumping or mixing element relative to the cavity may also be included in the system. In accordance with a nineteenth aspect of the invention, a method of pumping or mixing a fluid is disclosed. The method comprises positioning a pumping or mixing element in a vessel; levitating the pumping or mixing element using a superconducting element positioned in an evacuated or insulated chamber adjacent to the vessel; rotating the pumping or mixing element; and using one or more pairs of assist magnets to separately or simultaneously attract or repel the pumping or mixing element to maintain a proper position relative to the vessel. The vessel may include a cavity, in which case the pumping or mixing element is adj acent to and concentric with the cavity and the step of levitating includes inserting the chamber in which the superconducting element is positioned into the cavity in juxtaposition with the adjacent pumping or mixing element. The method may further include simultaneously attracting and repelling the pumping or mixing element to maintain a proper position relative to the vessel. In accordance with a twenty-first aspect of the invention, a system for pumping or mixing a fluid in a vessel capable of holding the fluid, the vessel having a cavity, using a magnetic pumping or mixing element positioned in the vessel concentric with the cavity, is disclosed. The system comprises a cryostat including a cooling source thermally linked to a superconducting element and capable of selectively holding the superconducting element below a transition temperature and a chamber that is evacuated or insulated to thermally isolate and/or separate the superconducting element from the vessel, wherein the cryostat is positioned in the cavity but external to the vessel; a first motive device for rotating the cryostat, including the cooling source and superconducting element; and a second motive device for moving the cryostat and hence the superconducting element therein relative to the cavity. In one embodiment, the vessel includes an engagement structure having a surface that corresponds to a matching surface on the pumping or mixing element and these surfaces are in engagement when the pumping or mixing element is in a non-levitated or resting position. The cryostat is moved to a first position adjacent to the magnetic pumping or mixing element in the non-levitated position, the superconducting element is cooled to below the transition temperature to form a magnetic coupling with the magnetic pumping or mixing element, and the cryostat is moved to a second position to separate the matching surfaces and levitate the pumping or mixing element. The cryostat is rotated once in the second position such that the levitating pumping or mixing element is rotated as a result of the magnetic coupling formed. When pumping or mixing is complete, the superconducting element is warmed or allowed to warm to above the transition temperature to allow the matching surface of the pumping or mixing element to rest on or engage the support surface. In accordance with a twenty-first aspect of the invention, a system for pumping or mixing a fluid is disclosed. The method comprises a vessel for holding the fluid having a cavity, with the vessel including a tapered or frusto-conical engagement surface. A magnetic pumping or mixing element positioned in the vessel concentric with the cavity includes a surface matching the engagement surface. A device is provided for levitating the pumping or mixing element in the vessel such that the matching surface is separated from the engagement surface, and a device for rotating the pumping or mixing element once levitated is also provided. In one embodiment, the device for levitating the pumping or mixing element comprises a cryostat including a cooling source thermally linked to a superconducting element and capable of selectively holding the superconducting element below a transition temperature and a chamber that is evacuated or insulated to thermally isolate and/or separate the superconducting element from the vessel. The cryostat is positioned in the cavity but external to the vessel and the device for rotating the pumping or mixing element further includes a first motive device for rotating the cryostat, including the cooling source and superconducting element. A second motive device may also be provided for moving the cryostat and hence the superconducting element therein relative to the cavity. In accordance with a twenty-second aspect of the invention, an assembly for use in pumping or mixing a fluid using a pumping or mixing element that is selectively levitated is disclosed. The assembly comprises a vessel for holding the fluid having a cavity, the vessel including a tapered or frusto-conical engagement surface. The magnetic pumping or mixing element positioned in the vessel concentric with the cavity and having a surface matching the tapered or frusto- conical engagement surface. Hence, in a non-levitated position, the pumping or mixing elements rests on and is centered relative to the cavity by the engagement established between the matching surfaces, but in a levitated position, the surfaces are separated. In accordance with a twenty-third aspect of the invention, a method for levitating a magnetic pumping or mixing element in a vessel for holding a fluid having at least one cavity formed therein, with the pumping or mixing element being generally concentric with the cavity and initially in a non-levitated or resting position, is disclosed. The method comprises positioning a superconducting element at a first position in the cavity, but external to the vessel, in alignment with the magnetic pumping or mixing element in the vessel; cooling the superconducting element to below a transition temperature to form a magnetic coupling with the magnetic pumping or mixing element; and moving the superconducting element to a second position in the cavity to induce levitation in the pumping or mixing element. The method may further include the step of thermally isolating or separating the superconducting element from the vessel, as well as the step of centering the pumping or mixing element in the non-levitated position. The step of centering may comprise: (1) providing a first alignment structure on or adjacent to the vessel; and (2) providing a second matching alignment structure on the pumping or mixing element. The first and second alignment structures are in contact when the pumping or mixing element is at a non-levitated position and are separated when the pumping or mixing element is levitated. In accordance with a twenty-fourth aspect of the invention, a system for pumping or mixing a fluid by levitating and rotating a magnetic pumping or mixing element in a vessel is disclosed. The system comprises at least one superconducting element for levitating the pumping or mixing element and a cryostat thermally isolating the superconducting element from the ambient environment. The cryostat includes a portable Stirling-cycle cryocooler for cooling the superconducting element to below a transition temperature. A motive device may also be provided for rotating the cryostat, including the cryocooler and the superconducting element, to induce rotation in the pumping or mixing element. Brief Description of the Drawings The accompanying drawings incoφorated in and forming apart of the specification illustrate several aspects of the present invention and, together with the description, assist in explaining the principles of the invention. In the drawings: Figure 1 is a partially cross-sectional, partially cutaway, partially schematic view of one embodiment of the system of the present invention wherein the levitating pumping or mixing element is rotated by an external drive or driving magnet to mix a fluid in a vessel and the cooling source is a separate cooling chamber defined by the outer wall of a cryostat holding a cryogen; Figure 2 is an enlarged cross-sectional, partially cutaway, partially schematic view of an embodiment wherein the rotating, levitating pumping or mixing element is used to pump a fluid through a vessel positioned adjacent to the housing for the superconducting element and the cooling source is a closed cycle refrigerator; Figure 3 is a partially cross-sectional, partially cutaway, partially schematic view of the system of the first embodiment wherein the superconducting element, vessel, pumping or mixing element, and drive magnet are axially aligned, but moved off-center relative to the vertical center axis of the vessel; Figure 4a is a bottom view of the drive magnet used in situations where exceptional rotational stability of the pumping or mixing element of the preferred embodiment is required; Figure 4b is a partially cross-sectional, partially cutaway side view of the system showing the drive magnet of Figure 4a magnetically coupled to a similarly constructed second permanent magnet forming a part of the pumping or mixing element; Figure 4c is one possible embodiment of the pumping or mixing system including a pumping or mixing element having a chamber for holding a substance that is lighter than the surrounding fluid, such as air, that assists in levitating the pumping or mixing element; Figure 5 is a partially cross-sectional, partially schematic side view of a second possible embodiment of a pumping or mixing system using a pumping or mixing element levitated by a thermally isolated cold superconducting element wherein the motive force for rotating the pumping or mixing element in the vessel is provided by rotating the superconducting element itself; Figure 6a is a top schematic view of one possible arrangement of the levitating pumping or mixing element that may be driven by a rotating superconducting element; Figure 6b shows the pumping or mixing element of Figure 6a levitating above a rotating superconducting element formed of two component parts; Figure 7 is a partially cutaway, partially cross-sectional schematic side view of a vessel in the form of a centrifugal pumping head, including a levitating, rotating pumping or mixing element for pumping fluid from the inlet to the outlet of the centrifugal pumping head; Figure 8a shows an alternate embodiment of a pumping or mixing element especially adapted for levitation in a vessel or container having a relatively narrow opening; Figure 8b shows another alternate embodiment of a pumping or mixing element adapted especially for use in a vessel or container having a relatively narrow opening; Figure 8 c illustrates the pumping or mixing element of Figure 8b in a partially folded state for insertion in the narrow opening of a vessel or container; Figure 9 is a partially cross-sectional, partially schematic side view of a second embodiment of a pumping or mixing system wherein separate levitating and driven magnets are carried on the same, low-profile pumping or mixing element, with the levitation being supplied by a thermally isolated superconducting element and the rotary motion being supplied a motive device including driving magnets coupled to a rotating shaft and positioned in an opening in the evacuated or insulated chamber surrounding the superconducting element; Figure 9a is a top or bottom view of one possible embodiment of a pumping or mixing element for use in the system of Figure 9; Figure 9b is a partially cross-sectional side view of the pumping or mixing element of Figures 9 and 9a levitating above the superconducting element, and illustrating the manner in which the driven magnets are coupled to the corresponding driving magnets to create the desired rotational motion; Figure 10 is a top view of a most preferred version of a cryostat for use with the pumping and mixing system of the embodiment of Figure 9; Figure 11 is a partially cutaway, partially cross-sectional side schematic view of a centrifugal pumping head for use with the system of Figure 9; Figure 12 is a cross-sectional side view of another possible embodiment of a pumping or mixing system of the present invention; Figure 12a is a cross-sectional view taken along line 12a- 12a of Figure 12; Figure 12b is a cross-sectional view taken along line 12b- 12b of Figure 12; Figure 12c is a cross-sectional view of the embodiment of Figure 12, but wherein the motive device is in the form of a winding around the vessel for receiving an electrical current that creates an electrical field and causes the pumping or mixing element to rotate; Figure 13 is an alternate embodiment of an inline levitating pumping or mixing element, similar in some respects to the embodiment of Figure 9; Figure 14 is an enlarged partially cross-sectional, partially cutaway side view showing the manner in which a sealed flexible bag carrying a pumping or mixing element may be used for mixing a fluid, and also showing one example of how a transmitter and receiver may be used to ensure that the proper pumping or mixing element is used with the system; Figure 14a is an enlarged, partially cross-sectional, partially cutaway side view showing an attachment including a coupler for coupling with the pumping or mixing element; Figure 14b is an enlarged, partially cross-sectional, partially cutaway side view showing a mixing vessel having centering and alignment structures; Figure 14c is an enlarged, partially cross-sectional, partially cutaway side view showing an alternate orientation of the vessel with centering and alignment structures; Figure 14d is an enlarged, partially cross-sectional, partially cutaway side view showing the use of a second motive device in the system of Figure 14, such as a linear motion device, for moving the superconducting element, and hence, the pumping or mixing element to and fro inside of the vessel; Figure 15 illustrates one charging magnet including a spacer that may form part of a kit for use in charging the superconducting element as it is cooled to the transition temperature, as well as a heater for warming the superconducting element to above the transition temperature for recharging; Figure 16 is as partially cross-sectional, mainly schematic view of an embodiment of the system for use with a vessel having a thin- walled cavity; Figure 16a is a partially cutaway, partially cross-sectional top view of the cryostat of Figure 16; Figure 17 is an enlarged, schematic view showing a superconductor or superconducting element comprised of a plurality of segments of a superconducting material having crystallographic planes for levitating a concentric annular levitation magnet, and showing in particular a desired orientation of the crystallographic C-axis of each segment relative to the magnetization vector of the levitation magnet; Figure 18 is a cross-sectional view taken along line 18-18 of Figure 17; Figure 19 is an embodiment wherein a plurality of superconductors or superconducting elements are used to levitate a pumping or mixing element in a fluid containing vessel, and again showing in particular a desired orientation of the crystallographic C-axis of each segment relative to the magnetization vector of the levitation magnet; Figure 19a is a top view of the cryostat and a portion of the motive device in the system of Figure 19; Figure 20 illustrates an embodiment where the cryostat includes a cryocooler which rotates along with the superconducting element to both levitate and rotate the pumping or mixing element in a vessel, which is shown as having a cavity formed therein; Figure 21 is a schematic view showing one possible orientation of the magnets and superconductors in the embodiment of Figure 20; Figure 22 illustrates a flexible bag or container having a cavity formed therein, which in addition to receiving the head end of the cryostat may also act as a centering post for a concentric pumping or mixing element; and Figure 23 illustrates an embodiment where permanent magnets are used to provide a levitation-assist function to prevent the pumping or mixing element from contacting the adjacent vessel; Figure 24 is another embodiment where permanent magnets are used to provide a levitation-assist function to prevent the pumping or mixing element from contacting the adjacent vessel; Figure 25 is yet another embodiment where permanent magnets are used to provide a levitation-assist function to prevent the pumping or mixing element from contacting the adjacent vessel; Figure 26 is a partially cross-sectional view showing a vessel including an engagement structure for engaging and supporting the pumping or mixing element when in a non-levitating condition; and Figure 27 is a partially cross-sectional view showing the moving of the cryostat to in turn move the magnetically coupled pumping or mixing element of Figure 26 to a levitated position. Detailed Description of the Invention Reference is now made to Figure 1, which shows a first possible embodiment of the mixing or pumping system 10 of the present invention. In this embodiment, a cryostat 12 is used to hold the cooling source for the superconducting element that produces the desired levitation in a pumping or mixing element 14. This element 14 is placed in a vessel 16 positioned external to the cryostat 12. The vessel 16 may already contain a fluid F or may be filled after the pumping or mixing element 14 is in place. It should be appreciated at the outset that the term "fluid" is used herein to denote any substance that is capable of flowing, as may include fluid suspensions, gases, gaseous suspensions, or the like, without limitation. The vessel 16 for holding the fluid is shown as being cylindrical in shape and may have an open top. Alternatively, it may be completely sealed from the ambient environment to avoid the potential for fluid contamination or leakage during mixing, or adapted to pump the fluid F from an inlet to an outlet in the vessel 16 (see Figure 2). In any case, the vessel 16 may be fabricated of any material suitable for containing fluids, including glass, plastic, metal, or the like. Of course, the use of lightweight plastic or other high density polymers is particularly desirable if the vessel 16 is going to be discarded after mixing or pumping is complete, as set forth in more detail in the description that follows. As illustrated in Figure 1 , the vessel 16 rests atop the outer wall 18 of the cryostat 12. Preferably, this outer wall 18 is fabricated of non-magnetic stainless steel, but the use of other materials is of course possible, as long as the ability of the pumping or mixing element 14 to levitate and rotate remains substantially unaffected. Positioned inside of and juxtaposed to this wall 18 is a superconducting element 20. The superconducting element 20 is supported by a rod 22 that serves as the thermal link to a cooling source 24. The outer wall 18 of the cryostat 12 thus defines a chamber 25 that is preferably evacuated to thermally isolate the cold superconducting element 20 from the relatively warm vessel 16, pumping or mixing element 14, and fluid F. Positioning of the superconducting element 20 in this vacuum chamber 25 may be possible by virtue of the thermal link provided by the rod 22. The thermal isolation and separation provided by the chamber 25 allows for the superconducting element 20 to be placed in very close proximity to the outer wall 18 without affecting its temperature, or the temperature of the vessel 16. This allows the separation distance from the superconducting element 20 to the inner surface of the wall 18 to be narrowed significantly, such that in the preferred embodiment, the gap G between the two is preferably under 10 millimeters, and can be as narrow as approximately 0.01 millimeters. This substantial reduction in the separation distance enhances the levitational stability, magnetic stiffness, and loading capacity of the pumping or mixing element 14. In this first illustrated embodiment, the cooling source 24 is a separate, substantially contained cooling chamber 26 holding a cryogen C, such as liquid nitrogen. The chamber 26 is defined by an outer wall 28 that is substantially thermally separated from the outer wall 18 of the cryostat 12 to minimize heat transfer. An inlet I is provided through this wall 28 for introducing the cryogen into the cooling chamber 26. To permit any vapor P to escape from the chamber 26 as the cryogen C warms, an exhaust outlet O is also provided (see action arrows in Figure 1 also designating the inlet and outlet). In the illustrated embodiment, the inlet I and outlet O lines may formed of a material having a low thermal conductivity, such as an elongate, thin walled tube formed of non-magnetic stainless steel, and are sealed or welded in place to suspend the cooling chamber 26 in the cryostat 12. As should be appreciated by one of ordinary skill in the art, the use of a thin walled tube formed of a material having a low thermal conductivity, such as stainless steel, results in a negligible amount of thermal transfer from the inlet or outlet to the wall 18. The sealing or welding method employed should allow for the chamber 25 to be maintained in an evacuated state, if desired. Despite this illustration of one possible support arrangement, it should be appreciated that the use of any other support arrangement that minimizes thermal transfer between the cooling chamber 26 and the cryostat wall or other housing 18 is also possible (see, e.g., my '672 patent). The rod 22 serving as the thermal link between the cooling source 24 and the superconducting element 20 may be cylindrical and may extend through the outer wall 28 of the cooling chamber 26. The entire surface area of the superconducting element 20 should contact the upper surface of the cylindrical rod 22 to ensure that thermal transfer is maximized. The rod 22 may be formed of materials having low thermal resistance/high thermal conductance, such as brass, copper, or aluminum. As should be appreciated from viewing Figure 1 , and as briefly noted in the foregoing description, the combination of the outer wall 18 and the inner cooling chamber 26 in this first embodiment defines the chamber 25 around the superconducting element 20. Preferably, this chamber 25 is evacuated to minimize heat transfer from the cooling chamber walls 28 and the superconducting element 20 to the outer wall 18 of the cryostat 12. The evacuation pressure is preferably at least 10 "3 torr, and most preferably on the order of 10 "5 torr, but of course may vary depending upon the requirements of a particular application. The important factor is that thermal transfer from the cooling source 24, which in this case is the cooling chamber 26 holding a cryogen C, and the superconducting element 20 to the outer wall 18 is minimized to avoid cooling the vessel 16 or fluid F held therein. Although a vacuum chamber 25 is proposed as one preferred manner of minimizing this thermal transfer, the use of other means to provide the desired thermal isolation is possible, such as by placing insulating materials or the like in the chamber 25. As is known in the art, by cooling the superconducting element 20 in the presence of a magnetic field, it becomes capable of distributing the current induced by a permanent magnet such that the magnet levitates a certain distance above the superconducting element, depending primarily upon the intensity and the direction of the magnetic field generated by the levitating magnet. Although basically a repulsive force is created, the peculiar nature of the pinning forces generated actually tie the levitating magnet to the superconducting element as if the two were connected by an invisible spring. As should be appreciated, this form of attachment cannot be achieved in conventional levitation schemes for pumping or mixing elements that employ two opposed permanent magnets that merely repel each other, since no pinning forces act to tie the two magnets together, while at the same time provide a balancing repulsive force. In the preferred embodiment of the present system 10, the element 20 providing the superconductive effects is a "high temperature" or "type II" superconductor. Most preferably, the superconducting element 20 is formed of a relatively thin cylindrical pellet of melt-textured Yttrium-Barium Copper Oxide (YBCO) that, upon being cooled to a temperature of approximately 77-78 Kelvin using a cooling source 24, such as the illustrated liquid nitrogen chamber 26, exhibits the desired levitational properties in a permanent magnet. Of course, the use of other known superconducting materials having higher or lower operating temperatures is also possible, and my prior U.S. Patent No. 5,567,672 is incoφorated herein by reference for, among other things, the other high-temperature superconducting materials referenced therein. The pumping or mixing element 14 in the preferred embodiment includes a first permanent magnet 32 for positioning in the vessel 16 adjacent to the superconducting element 20 such that it levitates in the fluid F. Although the polarity of this first magnet 32 is not critical to creating the desired levitation, the magnet 32 is preferably disk-shaped and polarized in the vertical direction. This ensures that a symmetrical magnetic field is created by the magnet 32 and stable levitation results above the superconducting element 20, while at the same time free rotation relative to the vertical axis is possible. In a version of the pumping or mixing element 14 particularly adapted for use in relatively deep fluid vessels, a support shaft 34 is connected to and extends vertically from the first permanent magnet 32. Along the shaft 34, at least one, and preferably two, impellers 36 are carried that serve to provide the desired pumping, or in the case of Figure 1, mixing action when the pumping or mixing element 14 is rotated. Rotation of the levitating pumping or mixing element 14 in the vessel 16 is achieved by a magnetic coupling formed between a second permanent magnet 38 (shown in dashed line outline in Figure 1, but see also Figure 2) and a drive magnet 40 positioned externally of the vessel 16. The drive magnet 40 is rotated by a drive means, such as an electric motor 42 or the like, and the magnetic coupling formed with the second permanent magnet 38 serves to transmit the driving torque to the pumping or mixing element 14 to provide the desired pumping or mixing action. The direction of rotation is indicated by the action arrows shown in Figures 1 and 2 as being in the counterclockwise direction, but it should be appreciated that this direction is easily reversed by simply reversing the direction in which the drive magnet 40 is rotated. In operation, and in practicing one possible method of pumping or mixing a fluid disclosed herein, the vessel 16 containing the fluid F and pumping or mixing element 14 are together placed external to the wall 18 of the cryostat 12 adjacent to the superconducting element 20, which is placed in the evacuated or insulated chamber 25. When the first disk-shaped permanent magnet 32 is brought into the proximity of the superconducting element 20, the symmetrical magnetic field generated causes the entire pumping or mixing element 14 to levitate in a stable fashion above the bottom wall of the vessel 16. This levitation brings the second permanent magnet 38 into engagement with the drive magnet 40 to form the desired magnetic coupling. In addition to transmitting the driving torque, this magnetic coupling also serves to stabilize rotation of the pumping or mixing element 14. The motor 42 or other motive device is then activated to cause the drive magnet 40 to rotate, which in turn induces a steady, stable rotation in the pumping or mixing element 14. Rotating impellers 36 then serve to mix or pump the fluid F in a gentle, yet thorough fashion. Since the pumping or mixing element 14 fully levitates and can be completely submerged in the fluid, the need for mixing or stirring rods penetrating through the vessel 16 in any fashion is eliminated. The concomitant need for dynamic shaft seals or support bearings in the vessel walls is also eliminated. Deleterious friction is also not a concern. A related advantage is that the vessel 16 containing the fluid F and the pumping or mixing element 14 can be completely sealed from the outside environment before mixing to provide further assurances against leakage or contamination. Yet another related advantage discussed in detail below is that the vessel 16 and pumping or mixing element 14 can be formed of relatively inexpensive, disposable materials and simply discarded once mixing is complete. As should be appreciated, this advantageously eliminates the need for cleanup and sterilization of the pumping or mixing element 14 and vessel 16. Thus, by completely sealing a disposable vessel, such as a plastic container or flexible bag containing the pumping or mixing element and fluid prior to mixing, the entire assembly can simply be discarded once the fluid contents are recovered. This reduces the risk of exposure both during and after mixing in the case of hazardous fluids, and also serves to protect the fluid from contamination prior to or during the pumping or mixing operation. An alternative version of this first possible embodiment of the system 10 of the present invention particularly adapted for pumping a fluid F is shown in Figure 2. In this version, the vessel 16 includes at least one fluid inlet 44 and at least one outlet 46. The pumping or mixing element 14 preferably carries rotating impellers 36 that serve to provide the desired pumping action by forcing fluid F from the inlet 44 to the outlet 46 (see action arrows). By increasing or decreasing the rotational speed of the motor 42 or other motive device, or adjusting the size, shape or style of the pumping or mixing element 14, impeller blades 36, or substituting a different design altogether, a precise level of pumping action may be provided. Another possible modification shown in Figure 2 is to use a closed cycle refrigerator 48 to provide the necessary cooling for the superconducting element 20 instead of a cryostat with a liquid cryogen as the cooling source. The refrigerator 48 can be positioned externally to a housing 18 containing the superconducting element 20, which may be the equivalent of the cryostat outer wall 18 previously described. As with the first embodiment, a chamber 25 is defined by the housing 18. This chamber 25 is preferably evacuated or filled with other insulating materials to minimize thermal transfer from the superconducting element 20 to the housing 18. However, since no cooling source 24 is contained within the housing 18, it is not actually a "cryostat" as that term is commonly defined. Nevertheless, the desired dual levels of thermal separation are still possible, and the concomitant advantages provided, since: (1) the cooling source 24, 48 is positioned away from the housing 18 and, thus, the vessel 16, pumping or mixing element 14, and fluid F; and (2) the housing 18 still separates and defines a chamber 25 that thermally isolates the superconducting element 20 and the vessel 16. In yet another alternate arrangement, the refrigerator 48 can be used as a primary cooling source, with the cryogenic chamber (not shown) serving as a secondary or "backup" cooling source in the event of a power outage or mechanical failure. In accordance with another of the many important aspects of the present system 10, the absence of a mixing rod or other mechanical stirrer extending through a wall of the vessel 16 also allows for placement of the pumping or mixing element 14 at an off-axis position, as shown in Figure 3. Specifically, the superconducting element 20, pumping or mixing element 14, and drive magnet 40 are all axially aligned away from the vertical center axis of the vessel 16. One particular advantage of using this approach is that the pumping or mixing element 14 may be rotated at a very low speed while the vessel 16 is also rotated about its center axis. This advantageously ensures that gentle, yet thorough mixing, is achieved, which is particularly advantageous for use with fluids that are sensitive to shear stress. As should be appreciated, this arrangement can be used both whether the vessel 16 is completely sealed, provided with an inlet 44 and an outlet 46 for pumping as shown in Figure 2, or open to the ambient enviromnent. For puφoses of illustration only, Figure 3 shows the cryostat 12 of the embodiment shown in Figure 1 having an outer wall 18 and a cooling chamber 26 defined by a wall 28. However, it should be appreciated that use of the housing 18 and closed-cycle refrigerator 48 of the second embodiment of Figure 2 as part of the "cryostat" is also possible with this arrangement. Through experimentation, it has been discovered that when the pumping or mixing element 14 of the type described for use in this first possible embodiment is employed, providing the requisite degree of stability to ensure that all contact with the side walls of the container 16 is avoided may in some instances be a concern. Thus, to ensure that the pumping or mixing element 14 rotates with exceptional stability and such deleterious contact is completely avoided, the second permanent magnet 38 and the drive magnet 40 are each provided with at least two pairs, and preferably four pairs of cooperating sub-magnets 50a, 50b. As shown in Figures 4a and 4b, these magnets 50a, 50b have opposite polarities and thereby serve to attract each other and prevent the levitating pumping or mixing element 14 from moving from side-to-side to any substantial degree. However, the attractive force is counterbalanced by the combined spring-like attractive and repulsive levitational/pinning forces created between the first permanent magnet 32 and the superconducting element 20 when cooled. This avoids the potential for contact with the upper wall of the vessel 16, if present. Overall, the pumping or mixing element 14 is capable of exceptionally stable rotation using this arrangement, which further guards against the undesirable frictional heating or shear stress created if the rotating pumping or mixing element 14, or more particularly, the first and second permanent magnets 32, 38 or the blades of the impellers 36 could move into close proximity with the bottom or side walls of the vessel 16. As should be appreciated, it is possible to rearrange the components of the system 10 such that the levitation and driving forces are provided from other areas of the vessel, rather than from the top and bottom of the vessel. Thus, as shown in Figure 4c, the cryostat 12 or other housing for containing the superconducting element 20 may be positioned adjacent to one side of the vessel 16, while the drive magnet 40 is positioned adjacent to the opposite side. In that case, the pumping or mixing element 14 may be turned on its side and supported by a separate stable support structure, such as a table T or the like. The vessel 14 is shown as being sealed, but it should be appreciated that any of the vessels disclosed herein may be employed instead, including even a straight or L-shaped pipe. To assist in levitating the pumping or mixing element 14 in either the embodiment of Figures 1 or 2 or the other embodiments disclosed herein, at least one, and preferably a plurality of chambers 60 are provided for containing a substance lighter than the surrounding fluid F. The chambers 60 may be provided adjacent to each magnet 32, 38 in the pumping or mixing element 14, as well as around the shaft 34, if desired. In the preferred embodiment where the fluid F is or has a specific gravity similar to that of water, the substance contained in the chambers 60 may be air. However, in more viscous fluids, such as those having a specific gravity more like glycerin, it may be possible to use lighter fluids, such as water, even lighter gases, or combinations thereof. These chambers 60 thus serve to assist in levitating the pumping or mixing element 14 by helping it "float" in the fluid F. However, the "pinning" force created by the superconducting element 20, plus the levitating and aligning force created between the second permanent magnet 38 and the driving magnet 40, both also serve to assist in keeping the pumping or mixing element 14 in the proper position as it rotates. In the case of disk or pancake shaped permanent first and second magnets 32, 38 and a cylindrical shaft 34, annular chambers 60 may be used. Instead of fluid or gas filled chambers, the use of other buoyant materials is also possible to provide the levitation-assist function. As previously mentioned, one of the many advantages of the system 10 of the present invention is that, since the pumping or mixing element 14 levitates in the fluid F and no mixing or stirring rods are required for rotation, the vessel 16 can be completely sealed from the outside ambient environment. Thus, by forming the pumping or mixing element 14 and vessel 16 of relatively inexpensive or disposable materials, both can simply be discarded after mixing is completed and the fluid F is recovered. Of course, such disposable materials can also be used to form the vessel 16 designed for pumping fluids (Figure 2), or to form the open-top container for mixing fluids to avoid the need for clean up or sterilization once the operation is complete. It should also be appreciated that the pumping or mixing element 14 illustrated is an example of one preferred arrangement only, and that other possible configurations are possible. For instance, impeller blades are not required, since a smooth-walled, disk-shaped pumping or mixing element alone creates some gentle mixing action simply by rotating. If present, the blade or blades could simply be placed circumferentially around the disk-shaped first permanent magnet 32 to reduce the length of the shaft 34, or eliminate it altogether, especially if the vessel 16 has a relatively small vertical dimension. Instead of a bladed impeller assembly 36, the use of other structural arrangements is also possible, such as disk-shaped wheels having vanes or like structures designed to create more or less efficient rotation, and a concomitant increase in the desired mixing or pumping action when rotated. Depending on the depth of the vessel 16, the length of the shaft 34, if present, can also be increased or decreased as necessary. All components forming the pumping or mixing element in any embodiment described above may be coated with TEFLON or other inert materials to reduce the chances of contamination or corrosion, as well as to facilitate clean up, if required. Of course, besides use in the mixing or pumping of small batches of fluid solutions or suspensions used during experimentation and research in the laboratory setting, all components are also easily scaled up for use in industrial or commercial pumping or mixing operation, such as those commonly used in the manufacture of large batches pharmaceuticals or food products. The stable, reliable levitation of the magnetic pumping or mixing element can still be readily achieved in systems of much greater capacity than the one shown for puφoses of illustration in the drawings, thus making the present arrangement particularly well-suited for the commercial production of pharmaceuticals or any other solutions or suspensions that require gentle, yet thorough mixing during processing. Experiments conducted to date have demonstrated the efficacy of the system 10 described above. The set-up utilized in conducting these experiments included a pumping or mixing element having axially aligned upper and lower magnets and an impeller assembly mounted on a vertically extending support shaft, as shown in Figure 1. A cylindrical pellet of melt-textured YBa 2 Cu 3 O 7+x having a diameter of 30 millimeters and a thickness of 25 millimeters was used as the superconducting element and placed in a cryostat having a configuration similar to the one shown in Figure 1. The cryostat included a cooling chamber filled with approximately 1 liter of liquid nitrogen. A Nd-Fe-B permanent magnet with a surface field intensity of 0.4 Tesla was used as the lower, first permanent magnet. Using this set-up, the experiments demonstrated that the desired exceptionally stable levitation of the pumping or mixing element above the top surface of the cryostat in a vessel filled with a relatively warm fluid was possible. A separation distance of up to seven millimeters was achieved, and the levitation was stable for up to five hours using just a liter of liquid nitrogen as the cryogen. In the first experiment using this set up, water was selected as a model low viscosity fluid. Rotational speeds of up to 600 φm were achieved - this upper limit being defined by only the limited capabilities of the motor used to rotate the drive magnet in this experiment. No decoupling or instability in the pumping or mixing element was observed at any speed. In the case of glycerin, a model high viscosity fluid, a maximum rotational speed of 60 φm was achieved before some decoupling of the pumping or mixing element was observed. To further demonstrate the mixing capabilities using the proposed system, SEPHADEX powder (dry bead, 50-150 micron diameter) was placed on the bottom of a water-filled vessel and the levitating pumping or mixing element rotated. A uniform suspension was achieved after approximately five minutes of mixing. As should be appreciated, the system 10 described above and shown in Figures 1-4 is based on the use of a stationary superconducting element 20 and a pumping or mixing element 14 that, in addition to a "levitation" magnet, includes one or more separate driven magnets for coupling with a drive mechanism, such as one positioned at the opposite end of the vessel or container relative to the superconducting element. However, other embodiments of the pumping or mixing system may include a levitating, rotating pumping or mixing element with magnets that are simultaneously used not only for levitation, but also for transmitting driving torque. In one embodiment, this driving torque is simultaneously provided by the pinning forces that couple the pumping or mixing element with a rotating superconducting element. Thus, the superconducting element causes the pumping or mixing element to both levitate and rotate, even though there is no physical contact between the two elements. More specifically, and in accordance with this second possible embodiment of the present invention illustrated in Figure 5, the pumping or mixing system 100 includes a cryostat 102, which may be formed of two separate components: a first component 102a including an outer wall 104 that surrounds a relatively thin, disk-shaped superconducting element 106 to define a chamber 108, and a second component 102b including the cooling source 110. Preferably, the outer wall 104 is formed of thin, non-magnetic material, such as non-magnetic stainless steel or the like, but the use of other materials is possible, as long as they do not interfere with the operation of the system 100 and have relatively poor thermal conductivity. The chamber 108 surrounding the superconducting element 106 may be evacuated or insulated as described above to thermally isolate and separate it from the wall 104. However, in this embodiment, and as noted further below, it is possible to eliminate the chamber 108 entirely in the case where a non-temperature sensitive fluid is being pumped or mixed. In the case where the chamber 108 is evacuated, a valve 112 may be provided in the outer wall 104 for coupling to a vacuum source. An optional getter 114 (such as an activated carbon insert or the like) may be positioned in the chamber 108 for absorbing any residual gases and ensuring that the desired evacuation pressure is maintained. As with the embodiments described above, the evacuation pressure is preferably on the order of 10 "3 torr or greater, but may vary depending on the particular application. The superconducting element 106 is supported in the chamber 108 independent of the outer wall 104 of the first portion 102a of the cryostat 102. The support may be provided by a platform 116 that is enclosed by wall 104 and supported at one end of an elongated thermal link 118, preferably foπned of metal or another material having a high degree of thermal conductivity (e.g., 50 Watts/Kelvin or higher). To supply the necessary cooling to the superconducting element, the opposite end of the elongated thermal link 118 is positioned in contact with the cooling source 110, which as described above forms a part of the second component 102b of the "cryostat" 102 (the term cryostat being used throughout to denote a structure or combination of structures that are capable of maintaining a superconducting element in a cold state, whether forming a single unit or not). The cooling source 110 is illustrated schematically as an open-top container 119, such as a Dewar flask, containing a liquid cryogen C, such as nitrogen. However, it is also possible to use a closed-cycle refrigerator or any other device capable of supplying the cooling necessary to levitate a magnet above a superconducting element after field cooling is complete. In the case where the wall 104 of the first portion 102a of the cryostat 102 makes contact with the cryogenic fluid C, as illustrated, it should be appreciated that there is only negligible thermal transfer to the portion of the wall 104 adjacent the vessel, since: (1) the wall 104 may be formed of a thin material having low thermal conductivity; and (2) the portion of the wall 104 adjacent to the vessel is surrounded by the ambient, room-temperature environment. To permit the superconducting element 106 to rotate, a roller bearing assembly 120 comprising one or more annular roller bearings 122 supports the first portion of the cryostat 102a, including the wall 104 defining the chamber 108. As should be appreciated from viewing Figure 5, these roller bearings 122 permit the first portion of the cryostat 102a housing the superconducting element 102 to rotate about an axis, which is defined as the axis of rotation. A bearing housing 124 or the like structure for supporting the bearing(s) 122 is secured to an adjacent stable support structure 126. In the illustrated embodiment, a motive device includes an endless belt 128 that serves to transmit rotational motion from the pulley 129 keyed or attached to the shaft 130 of a motor 131 to the first portion of the cryostat 102a. The motor 131 may be a variable speed, reversible electric motor, but the use of other types of motors to create the rotary motion necessary to cause the superconducting element 106, and more particularly, the first portion of the cryostat 102a housing the superconducting element 106, to rotate is possible. The vessel 132 containing the fluid to be mixed (which as described below can also be in the form of a centrifugal pumping head for transmitting a fluid) is positioned adjacent to the rotating superconducting element 106, preferably on a stable support surface T fabricated of a material that does not interfere with the magnetic field created by the pumping or mixing element 134. As previously noted, the vessel 132 can be a rigid vessel of any shape (open top, sealed having an inlet or outlet, cylindrical with a hollow center, such as a pipe, or even a flexible plastic bag (by itself, with rigid inserts, or inserted into a rigid or semi-rigid vessel)). The only requirement is that the vessel 132 employed is capable of at least temporarily holding the fluid F (or gas) being mixed or pumped. To create the desired mixing action in this embodiment, a pumping or mixing element 134 is positioned in the vessel 132 and simultaneously levitated and rotated by the superconducting element 106. More specifically, the first portion of the cryostat 102a containing the superconducting element 106, thermal link 118, and the evacuated chamber 108 is rotated as a result of the rotational motion transmitted by the endless belt 128. This rotation causes the pumping or mixing element 134 in the vessel 124 to rotate and either pump or mix the fluid F held therein. In the case where the chamber 104 is evacuated or insulated, the pumping or mixing element 134 is rotated in a stable, reliable fashion while the desired thermal separation between the cold superconducting element 106 supplying the levitation force, ,the vessel 124, and hence the fluid F, is achieved. The pumping or mixing element 134 may include a plurality of mixing blades B (see Figures 6a and 6b), vanes N (not shown, but see Figure 7), or like structures to create an impeller. However, again referring back to Figure 5, a low-profile, disk-shaped pumping or mixing element 134 may also be used to provide the desired mixing action, especially for particularly delicate fluids, such as blood or other types of cell suspensions. As perhaps best understood by viewing Figures 6a and 6b together, the pumping or mixing element 134 may include at least two magnets 135a, 135b, and possibly more than two (see Fig.20). These magnets 135a, 135b not only serve to generate the magnetic field that causes the pumping or mixing element 134 to levitate above the superconducting element 106, but also transmit rotational motion to the pumping or mixing element. As should be appreciated by one of ordinary skill in the art, the magnetic field generated by the magnets 135a, 135b should be axially non-symmetrical relative to the axis of rotation of the superconducting element 106 in order to create the magnetic coupling necessary to efficiently transmit the rotary motion. In one embodiment, the magnets 135a, 135b are disk-shaped and polarized along a center vertical axis (see Figure 6b, showing permanent magnets 135a, 135b of alternating polarities (N-North; S- South) levitating above a pair of superconducting elements 106a, 106b, with the corresponding action arrows denoting the direction and axis of polarity). These magnets 135a, 135b can be fabricated from a variety of known materials exhibiting permanent magnetic properties, including, but not limited to, Neodymium-Iron-Boron (NdFeB), Samarium Cobalt (SmCo), the composition of aluminum, nickel, and cobalt (Alnico), ceramics, or combinations thereof. The magnets 135a, 135b may be interconnected by a piece ofan inert matrix material M, such as plastic or inert, non-corrosive metals. Alternatively, the magnets 135 a, 135b may each be embedded in separate pieces of a matrix material M, or may be embedded in a single unitary piece of material (not shown). Also, as previously mentioned, the pumping or mixing element 134 may carry one or more optional blades B, vanes or like structures to enhance the degree of pumping or mixing action created. In another possible embodiment, the second portion of the cryostat 102b including the cooling source (either a liquid cryogen container (open top, sealed with inlet/outlet ports, or a refrigerator (preferably a "cryocooler," as described further below)) may be rigidly attached to the first portion 102a and both components may be simultaneously rotated together (see the dashed lines at the top of the open cooling container 119 in Figure 5, and see also the embodiment described below and shown in Figures 20-21). The rotational motion may be supplied by an endless belt/motor combination, as described above, or alternatively may be provided through a direct coupling between the second portion of the cryostat 102b (comprising any type of cooling source) and an inline shaft extending from or coupled to a motor or similar motive device (not shown). As briefly mentioned above, it is possible to use this embodiment of the system 100 without evacuating, insulating, or otherwise thermally separating the superconducting element 106 from the ambient environment, such as for mixing or pumping cold (cryogenic) or non-temperature sensitive fluids. In that case, there is no specific need for a wall 104 or chamber 108 surrounding the superconducting element 106, since thermally separating it from the structure supporting the vessel 132 (e.g., a table, stand or the like) is unnecessary. Even with this modification, reliable and stable levitation of the pumping or mixing element 134 is still achieved. From the foregoing, it should be appreciated that the same driving mechanism and cryostat shown in Figure 5 can be used for pumping a fluid instead of mixing it. One version of a vessel 132 in the form of a centrifugal pumping head 150 is shown in Figure 7. This pumping head 150 includes a pumping chamber 152 having an inlet 154 and an outlet 156 (which of course, could be reversed, such as in a non-centrifugal pumping head (see Figure 2)). The chamber 150 contains the levitating pumping or mixing element 158, which as shown may include a plurality of vanes N, or may alternatively carry a plurality of blades (not shown). At least two permanent magnets 160a, 160b having different polarities are embedded or otherwise included in the pumping or mixing element 158, which may be substantially comprised of an inert matrix material M having any desired shape to facilitate the pumping or mixing action. As described above, these magnets 160a, 160b provide both levitation and torque transmission as a result of the adjacent rotating superconducting element 106. As should be appreciated, one advantage of providing the driving force for the levitating pumping or mixing element 158 from the same side of the vessel/pumping head 150 from which the levitating force originates is that the fluid inlet 154 (or outlet 156, in the case where the two are reversed) may be placed at any location along the opposite side of the vessel/pumping head 150, including even the center, without interfering with the pumping or mixing operation. Also, this same side of the vessel/pumping head 150 may be frusto-conical or otherwise project outwardly, as illustrated, without interfering with the rotation or necessitating a change in the design of the pumping or mixing element 134, 158. As briefly noted above, in some instances the opening in a vessel may be too small to permit an even moderately sized pumping or mixing element 134 to be inserted into the fluid F. In such a case, alternate versions of a pumping or mixing element 134 meeting this particular need are shown in Figures 8a-8c. In the first alternate version, the pumping or mixing element 134a is in the form of a slender rod formed of an inert matrix material M carrying one of the levitating/driven magnets 135a, 135b at or near each end. As should be appreciated, this pumping or mixing element 134a may be easily turned to an upstanding position and inserted in the opening. Upon then coming into engagement with the rotating superconducting element 106, the pumping or mixing element 134a would simultaneously levitate and rotate to pump or mix a fluid held in the vessel. To further facilitate insertion in the narrow opening, the matrix material M may be an elastomeric material or another material having the ability to freely flex or bend. A second version of a pumping or mixing element 134b for use with a vessel having a narrow opening is shown in Figure 8b. The pumping or mixing element 134b includes first and second thin rods 180 formed of a matrix material M. The rods 180 each carry the levitating/driven magnets 135a, 135b at each end thereof, with at least two magnets having the identical polarity being held on each different rod. In one version, the rods 180 are pinned about their centers (note connecting pin 182) and are thus capable of folding in a scissor-like fashion. As should be appreciated from Figure 8c, this allows the pumping or mixing element 134b to be folded to a low-profile position for passing through the opening of the vessel 132. The rods 180 of the pumping or mixing element 134b may then separate upon coming into engagement with an appropriately field cooled superconducting element 106 positioned adjacent to the bottom of the vessel 132. Since magnets 135a or 135b having the same polarity are positioned adjacent to each other, the corresponding ends of the rods 180 repel each other as the pumping or mixing element 132b rotates. This prevents the rods 180 from assuming an aligned position once in the vessel 132. As should be appreciated, instead of pinning two separate rods 180 together to form the pumping or mixing element 134b, it is also possible to integrally mold the rods 180 of a flexible material tσ orm a cross. This would permit the rods 180 of the pumping or mixing element 134b to flex for passing through any narrow opening, but then snap-back to the desired configuration for levitating above the superconducting element 106. In accordance with yet another aspect of the present invention, a third version of a pumping or mixing system 200 is disclosed. In this third embodiment, which is illustrated in Figures 9, 9a, 9b, and 10, the forces for driving and levitating the pumping or mixing element 204 are supplied from the same side of a fluid vessel 202 (which is shown as an open-top container, but as described above, could be a sealed container, a pumping chamber or head, a flexible bag, a pipe, or the like). In this system 200, the pumping or mixing element 204 actually includes two magnetic subsystems: a first one that serves to levitate the pumping or mixing element 204, which includes a first magnet 206, preferably in the form of a ring, and a second magnetic subsystem that includes at least two alternating polarity driven magnets 208a, 208b, preferably positioned inside of the first, ring-shaped magnet 206, to transmit driving torque to the pumping or mixing element (see Figures 9a and 9b). Figure 9 shows one embodiment of the overall system 200 in which the ring-shaped permanent magnet 206 or array of magnets (not shown) provides the levitation for the pumping or mixing element 204. Polarization of the ring magnet 206 is vertical (as shown by the long vertical arrows in Figure 9b). The driven magnets 208a, 208b are shown as being disk-shaped and having opposite or alternating polarities (see corresponding short action arrows in Figure 9b representing the opposite polarities) to form a magnetic coupling and transmit the torque to the levitating pumping or mixing element 204. Levitation magnet 206 and driven magnets 208a, 208b are preferably integrated in one rigid structure such as by embedding or attaching all three to a lightweight, inert matrix material M, such as plastic or the like. To correspond to the ring-shaped levitation magnet, the superconducting element 210 for use in this embodiment is annular, as well. This element 210 can be fabricated of a single unitary piece of a high-temperature superconducting material (YBCO or the like), or may be comprised of a plurality of component parts or segments. Upon being cooled to the transition temperature in the presence of a magnetic field and aligning with the ring-shaped permanent magnet 206 producing the same magnetic field, the superconducting ring 210 thus provides the combined repulsive/attractive, spring-like pinning force that levitates the pumping or mixing element 204 in the vessel 202 in an exceptionally stable and reliable fashion. In Figure 9, the vessel is shown as being supported on the outer surface of a special cryostat 220 designed for use with this system 200, a detailed explanation of which is provided in the description that follows. However, it is within the broadest aspects of the invention to simply support the vessel 202 on any stable support structure, such as a table (not shown), as long as it remains sufficiently close to the superconducting element 210 to induce the desired levitation in the pumping or mixing element 204 held therein. As in the embodiments described above, a motive device is used to impart rotary motion to the pumping or mixing element 204, and is preferably positioned adj acent to and concentric with the annular superconducting element 210. One example of a motive device for use in the system 200 of this third embodiment includes driving magnets 212a, 212b that correspond to the driven magnets 208a, 208b on the pumping or mixing element 204 and have opposite polarities to create a magnetic coupling (see Figure 9b). The driving magnets 212a, 212b are preferably coupled to a shaft 214 also forming part of the motive device. The driving magnets 212a, 212b may be attached directly to the shaft 214, or as illustrated in Figure 9, may be embedded or attached to a matrix material (not numbered in Figure 9, but see Figure 9b). By positioning the driving magnets 212a, 212b close to the pumping or mixing element 204, such as by inserting them in the opening or bore 219 defined by the annular superconducting element 210, and rotating the shaft 214 using a motor 216 also forming a part of the motive device, synchronous rotation of the levitating pumping or mixing element 204 is induced. The pumping or mixing element 204 may include one or more blades B that are rigidly attached to the ring or levitation magnet 206 (or any matrix material forming the periphery of the pumping or mixing element 204). However, it remains within the broadest aspects of the invention to simply use a smooth, low-profile pumping or mixing element (see Figure 5) to provide the desired mixing action. As shown in Figures 9 and 10 and briefly mentioned above, the mixing or pumping system 200 including the pumping or mixing element 204 comprised of the magnetic levitation ring 206 and separate driven magnets 208a, 208b may use a special cryostat 220 to ensure that reliable and stable rotation/levitation is achieved. As perhaps best shown in the cross-sectional side view of Figure 9, the cryostat 220 includes a cooling source 221 for indirectly supplying the necessary cooling to the superconducting element 210, which as described below is supported and contained in a separate portion of the special cryostat 220. In the illustrated embodiment, the cooling source 221 (not necessarily shown to scale in Figure 9) includes a container 222, such as a double- walled Dewar flask, in which a first chamber 224 containing a liquid cryogen C (nitrogen) is suspended. A second chamber 223 defined around the first chamber 224 is preferably evacuated or insulated to minimize thermal transfer to the ambient environment, which is normally at room temperature. A port 226 is also provided for filling the suspended chamber 224 with the chosen liquid cryogen C, as well as for possibly allowing any exhaust gases to escape. As with the first and second embodiments described above, the cooling source 221 may instead take the form of a closed-cycle refrigerator (not shown), in which case the double wall container 222 may be entirely eliminated from the system 200. A thermal link 228 is provided between the cooling source (in the illustrated embodiment, the container 222) and a platform 230 suspended in the cryostat 220 for supporting the superconducting ring 210. The use of the platform 230 is desirable to ensure that the temperature of the superconducting element 210 is kept below the transition temperature, which in the case of a "high temperature" superconducting material (such as YBCO) is most preferably in the range of between 87-93 Kelvin. However, the use of the platform 230 is not critical to the invention or required as part of the special cryostat 220, since the thermal link 228 could extend directly to the superconducting element 210. The thermal link 228 may be a solid rod of material, including copper, brass, or any other material having a relatively high thermal conductivity. Instead of a solid rod, it is also possible to provide an open channel 232 in the thermal link 228, especially when a liquid cryogen C capable of flowing freely, such as nitrogen, is used as the cooling source 221. This channel 232 allows the cryogen C from the suspended container 224 to reach the platform 230 directly. Of course, the direct contact with the cryogen C may provide more efficient and effective cooling for the superconducting element 210, but is not required. The ring-shaped platform 230 that supports the superconducting element(s) 210 and supplies the desired cooling via thermal conduction may be made of copper, brass, aluminum, or another material having good thermal conductivity. It may be in the form of a solid ring, as illustrated, or may be in the form of a hollow ring (such as a substantially circular or elliptical torus, not shown). This would allow the liquid cryogen C to flow completely around the ring to further increase the efficiency with which the cooling is transferred to the superconducting element 210. In any case, where a platform 230 is used, care should be taken to ensure that full contact is made with at least a majority of the corresponding surface of the superconducting element 210, since even cooling helps to ensure that the desired smooth, even, and reliable levitation is achieved. To reduce the thermal transfer to the vessel 202 in the case where a temperature sensitive fluid is being pumped or mixed by the system 200, a ring- shaped wall or enclosure 234 surrounding the platform 230 and the annular superconducting element 210 defines a first chamber 235. In addition, a hollow cylindrical wall or enclosure 236 may also surround the thermal link 232 and define a second chamber 237. Preferably, these first and second chambers 235, 237 are evacuated or insulated to minimize thermal transfer between the ambient environment and the cold elements held therein. In a preferred embodiment, each enclosure 234, 236 is fabricated from non-magnetic stainless steel, but the use of other materials is of course possible, as long as no interference is created with the levitation of the pumping or mixing element 204. As with the second embodiment described above, it is also possible to use the system 200 of the third embodiment to pump or mix cryogenic or non-temperature sensitive fluids, in which case there is no need to evacuate or insulate the enclosures 234, 236, or to even use the special cryostat 220 described herein. As should be appreciated, it is possible to create the chambers 235, 237 defined by the enclosures 234, 236 and the chamber 223 such that all three are in fluid communication and thus represent one integrated vacuum space (not shown) . This facilitates set-up, since all three chambers 223, 235, 237 may be evacuated in a single operation, such as by using a vacuum source coupled to a single valve (not shown) provided in one of the chambers. However, separately evacuating each chamber 223, 235, 237 is of course entirely possible. Also, instead of or in addition to evacuating the chambers 223, 235, 237, some or all may be instead filled with a suitable insulating material (not shown). As should be appreciated, to rotate the pumping or mixing element 204 in this embodiment, it is desirable to place the drive magnets 212a, 212b in close proximity to the pumping or mixing element, but preferably on the same side of the vessel 202 as the superconducting element 210. Accordingly, the special cryostat 220, and more specifically, the wall or enclosure 234 defines a room-temperature cylindrical bore or opening 240 that allows for the introduction of the end of the shaft 214 carrying the driving magnets 212a, 212b, which are at room temperature. As a result of this arrangement, the shaft 214, which is part of the motive device, is concentric with the superconducting element 210. The shaft 214 is also positioned such that the driving magnets 212a, 212b align with the driven magnets 208a, 208b on the pumping or mixing element 204 when the levitating magnet 206 is aligned with the superconducting element 210. Thus, despite being positioned adjacent to and concentric with the superconducting element 210, the shaft 214 and driving magnets 212a, 212b remain at room temperature, as does the vessel 202, the fluid F, and the pumping or mixing element 204. An example of one possible embodiment of a centrifugal pumping head 250 for use with the system 200 of Figure 9 is shown in Figure 11. The head 250 includes a levitating pumping or mixing element 252 that carries one or more optional blades or vanes N (which are upstanding in the side view of Figure 11), a fluid inlet 254 (which as should be appreciated can be in the center at one side of the pumping head 250 in view of the fact that the levitation and driving forces are both supplied from the same side of the vessel 202), a fluid outlet 256, driven magnets 258a, 258b, and a ring-shaped levitation magnet 260. In yet another possible embodiment of the invention, as shown in the cross-sectional view of Figure 12, the system 300 includes a pumping or mixing element 302 adapted for inline use, such as when the vessel is in the form of a hollow pipe 304. The pumping or mixing element 302 includes first and second spaced levitating magnets 305a, 305b, one of which is preferably positioned at each end to ensure that stable levitation is achieved. The magnets 305a, 305b preferably correspond in shape to the vessel, which in the case of a pipe 304, means that they are annular. The magnets 305a, 305b are carried on a shaft 306 forming a part of the pumping or mixing element 302, which further includes a driven magnet 308. The driven magnet 308 may be comprised of a plurality of sub-magnets 308a . . . 308n having different polarities and arranged in an annular configuration to correspond to the shape of the pipe 304 serving as the vessel in this embodiment (see Figure 12b). All three magnets 305a, 305b, and 308 may be embedded or attached to an inert matrix material M, such as plastic, that provides the connection with the shaft 306. The shaft 306 of the bearing 302 may also carry one or more blades B. First and second "cryostats" 310a, 31 Ob are also provided. As perhaps best understood with reference to the cross-sectional view of Figure 12a, the first "cryostat" 310a includes a superconductor for levitating the pumping or mixing element in the form of an annular superconducting element 312a. This superconducting element 312a is suspended in a chamber 314a defined by the cryostat 310a, which may be evacuated or insulated to prevent thermal transfer to the pipe 304 or the passing fluid F. The cryostat 310a may include an inner wall adjacent to the outer surface of the pipe 304 (not shown), but such a wall is not necessary in view of the thermal separation afforded by the evacuated or insulated space surrounding the superconducting element 312a. The superconducting element 312a may be coupled to annular support platform 316a, which in turn is thermally linked to one or more separate cooling sources 318. The connection is only shown schematically in Figure 12, but as should be appreciated from reviewing the foregoing disclosure, may include a rod that serves to thermally link a container holding a liquid cryogen or a closed cycle refrigerator to the superconducting element 312a. While not shown in detail, "cryostat" 310b may be similar or identical to the cryostat 310a just described. With reference now to Figures 12b and 12c, two different motive devices for rotating the pumping or mixing element 302 in the pipe 304 are disclosed. The first motive device includes a driving magnet assembly 320 that is rotatably supported on a bearing 322, such as a mechanical ball or roller bearing, carried on the outer surface of the pipe 304. The magnet assembly 320 includes a plurality of driving magnets 320a . . . 320n, also having different or alternating polarities. As with the driven magnets 308a . . 308n, the driving magnets 320a . . . 320n are embedded or attached to an inert, non-magnetic matrix material M, such as plastic. An endless belt 324 also forming a part of the motive device frictionally engages both the driving magnet assembly 320 and a pulley or wheel W carried on the spindle or shaft of a motor (preferably a reversible, variable speed electric motor, as described above). As should now be appreciated, the pumping or mixing element 302 is caused to levitate in the pipe 304 as a result of the interaction of the levitation magnets 305a, 305b with the adjacent superconducting elements 310a, 310b, which may be thermally separated from the outer surface of the pipe 304 (or the adjacent inner wall of the cryostat 310a, 310b, if present). Upon then rotating the magnetic drive assembly 320, the pumping or mixing element 302 is caused to rotate in the pipe 304 serving as the vessel to provide the desiring pumping or mixing action. Even if the fluid F is flowing past the pumping or mixing element 302, it remains held in place in the desired position in the pipe 304 as a result of the pinning forces created by the superconducting elements 310a, 310b acting on the levitation magnets 305a, 305b. The second version of a motive device is shown in the cross-sectional view of Figure 12c, which is similar to the cross-section taken in Figure 12b. However, instead of a magnetic driving assembly 320, endless belt 324, and motor, rotary motion is imparted to the pumping or mixing element 302 by creating an electrical field around the pipe 304. This may be done by placing a winding 326 around the outer wall of the pipe 304 and supplying it with an electrical current, such as from a power supply 328 or other source of AC current. Since the pumping or mixing element 302 carries magnets 308a . . . 308n having different polarities, the resulting electric field will thus cause it to rotate. Yet another embodiment of an inline pumping or mixing system 400 is shown in Figure 13. The cryostat 402 in this case is essentially positioned directly in the path of fluid flow along the pipe 403, thus creating an annular (or possibly upper and lower) flow channels 404a, 404b. The cryostat 402 has an outer wall 406 that defines a chamber 408 for containing a superconducting element 410. The superconducting element 410 may be annular in shape, in which case the chamber 408 is of a similar shape. The chamber 408 may also be evacuated or insulated to thermally separate the superconducting element 410 from the outer wall 406. The superconducting element 410 is thermally linked to a separate cooling source 412, with both the thermal link and the cooling source being shown schematically in Figure 13. It should be appreciated that this cryostat 402 is similar in many respects to the one described above in discussing the third embodiment illustrated in Figure 9, which employs a similar, but somewhat reoriented, arrangement. The wall 406 creating annular chamber 408 for the superconducting element 410 defines a room temperature bore or opening 414 into which a portion of a motive device may be inserted, such as the end of a shaft 416 carrying at least two driving magnets. Figure 13 illustrates the motive device with three such driving magnets 418a, 418b, 418c, one of which is aligned with the rotational axis of the shaft 416. The opposite end of the shaft 416 is coupled to a motor (not numbered), which rotates the shaft and, hence, the driving magnets 418a, 418b, and 418c. The magnets 418a, 418b, 418c may be coupled directly to the shaft 416, or embedded/attached to an inert matrix material M. The pumping or mixing element 420 is positioned in the pipe 403 adjacent to the outer wall 406 of the cryostat 402. The pumping or mixing element 420 includes a levitation magnet 422 that corresponds in size and shape to the superconducting element 410, as well as driven magnets 424a, 424b, 424c that correspond to the driving magnets 418a, 418b, and 418c. The levitation magnet 422 and driven magnets 424a-424c are attached to or embedded in a matrix material M, which may also support one or more blades B that provide the desired pumping or mixing action. In operation, the motor rotates the shaft 416 to transmit rotary motion to the driving magnets 418a, 418b and 418c. As a result of the magnetic coupling formed between these magnets 418a-c and the opposite polarity driven magnets 424a-c, the pumping or mixing element 420 is caused to rotate in the fluid F. At the same time, the pumping or mixing element 420 remains magnetically suspended in the fluid F as the result of the pinning forces created between the superconducting element 410 and the levitation magnet 422. The operation is substantially the same as that described above with regard to the third embodiment, and thus will not be explained further here. Various optional modifications may in some circumstances enhance the set-up or performance of any of the systems described herein, or instead adapt them for a particular use, puφose, or application. As noted previously, the disposable vessel or container for holding the fluid undergoing pumping or mixing may be in the form of a flexible bag. An example of such a bag 500 is shown in Figure 14, along with the system 100 for levitating the pumping or mixing element 502 of Figure 5. The bag 500 may be sealed with either fluid F or the pumping or mixing element 502 (which may take the form of one of the several pumping or mixing elements disclosed above or an equivalent thereof) inside prior to distribution for use, or may be provided with a sealable (or resealable) opening that allows for the fluid and pumping or mixing element to be introduced and later retrieved. Both the pumping or mixing element 502 and bag 500, whether permanently sealed or resealable, may be fabricated of inexpensive, disposable materials. Accordingly, both can simply be discarded after the pumping or mixing operation is completed and the fluid F is retrieved. It should also be appreciated that the vertical dimension of the bag 500 is defined by the volume of fluid F held therein. Thus, instead of placing the bag 500 containing the pumping or mixing element 502 directly on the surface of the cryostat, table T, or other support structure adjacent to the superconducting element 106, it is possible to place the flexible bag 500 in a separate rigid or semi-rigid container (see, e.g., Figure 22). This helps to ensure that the fluid F provides the bag 500 with a sufficient vertical dimension to permit the pumping or mixing element 502 to freely rotate in a non-contact fashion. Alternatively, the bag 500 may include internal or external reinforcements (not shown) to enhance its rigidity without interfering with the rotation of the pumping or mixing element. In cases where the pumping or mixing element 502 is prepackaged in the bag 500, with or without fluid, it may inadvertently couple to adjacent magnets or other metallic structures. Breaking this coupling may render the bag susceptible to puncturing, tearing, or other forms of damage. Accordingly, as shown in Figures 14a and 14b, it may be desirable to hold the pumping or mixing element 502 place prior to use with any of the systems described herein, especially in cases where it is sealed inside the vessel/bag 500 during manufacturing As shown in Figure 14a, one manner of holding the element 502 in place is to use an attachment 520, cover, or similar device including a coupler 522 formed of a ferromagnetic material or the like adjacent to the bag 500. This coupler 522 is thus attracted to and forms a magnetic coupling with the pumping or mixing element 502 when the attachment 520 is in place. As a result of this coupling, the pumping or mixing element 502 is prevented from coupling with magnets in adj acent bags or other magnetic structures (not shown). The attachment 520 should be fabricated of a non-magnetic material, such as rubber. In the operative position, the coupler 522 shields the magnetic field created by the pumping or mixing element 502. When the assembly including the bag 500 and the pumping or mixing element 502 is ready for use, the attachment 520 may simply be removed from the bag 500 to break the magnetic coupling between the pumping or mixing element 502 and the coupler 522. A second manner of keeping the pumping or mixing element 502 at a desired location to facilitate coupling with the particular levitation/rotation devices used is to provide the bag 500 with a "centering" structure, such as post 528. As shown in the embodiment illustrated in Figure 14b, which includes the basic levitation and rotation system of Figure 5, this post 528 may take the form of a rigid or semi-rigid piece of material projecting into the interior of the bag 500. Preferably, the post 528 is formed of the same material as the bag 500 or other container (plastic) and has an outer diameter that is less than the inner diameter or a bore or opening formed in the pumping or mixing element 502. As should be appreciated, the pumping or mixing element 502 may be held in place on the post 528 by gravity during shipping, prior to use, and even between uses. As illustrated, the upper end of the post 528 could also include a T-shaped or oversized head 529 (which could have a spherical, pyramidal, conic, or cubic shape). Alternatively, the head could have one or more transversely extending, deformable cross-members, an L-shaped hook-like member, or another type of projection for at least temporarily capturing the pumping or mixing element 502 to prevent it from inadvertently falling off when not in use. Of course, the positioning of the head 529 for capturing the pumping or mixing element 502 is preferably selected such that it does not interfere with the free levitation or rotation. As should be appreciated, the post 528 provides not only centering function, but also holds the pumping or mixing element 502 in place in case it accidentally decouples during the pumping or mixing operation. This significantly eases the process of returning the pumping or mixing element 502 to the proper position for initiating or resuming levitation/rotation by the corresponding system (which may be, for example, systems 10, 100, 200, 300, 800 etc.). In Figure 14b, this post 528 is adapted to receive the pumping or mixing element 502, which has a corresponding opening (and thus, may be annular or have any other desired shape or size). Since the post 528 preferably includes an oversized head portion 529 that keeps the pumping or mixing element 502 in place, including before a fluid is introduced, the vessel 500 may be manufactured, sealed (if desired), shipped, and stored prior to use with the pumping or mixing element 502 already in place. The vessel 500 may also be sterilized as necessary for a particular application, and in the case of a flexible bag, may even be folded for compact storage. As should be appreciated, the post 528 also serves the advantageous function of keeping the pumping or mixing element 502 substantially in place (or "centered") should it accidentally become decoupled from the adjacent motive device, which as in this case is a rotating annular superconducting element 106. However, the centering post 528 could also be used in the embodiment of Figure 9 as well by simply forming a center opening in the pumping or mixing element 204. In the illustrated embodiment, the post 528 is shown as being formed by an elongated rod-like structure inserted through one of the nipples 530 typically found in the flexible plastic bags frequently used in the bioprocessing industry (pharmaceuticals, food products, cell cultures, etc.). The oversized head portion 529 is preferably formed of a material that is sufficiently flexible/deformable to easily pass through the opening in the nipple 530. A conventional clamp 531, such as a cable or wire tie, may be used to form a fluid-impervious seal between the nipple 530 and the portion of the post 528 passing therethrough, but other known methods for forming a permanent or semi-permanent seal could be used (e.g., ultrasonic welding in the case of plastic materials, adhesives, etc.). Any other nipples 530 present (shown in phantom in Figure 14b) may be used for introducing the fluid prior to mixing, retrieving a fluid during mixing or after mixing is complete, or circulating the fluid in the case of a pumping operation. Advantageously, the use of the rod/nipple combination allows for easy retrofitting. Nevertheless, instead of using a separate rod, the post 528 may be integrally formed with the material forming the vessel 500, either during the manufacturing process or as part of a retrofit operation. The oversized head portion 529 may be cross-shaped, disc-shaped, L-shaped, Y- shaped, or may have any other desired shape, as long as the corresponding function of capturing the pumping or mixing element 502 is provided. The head portion 529 may be integrally formed, or alternatively may be provided as a separate component that is clamped or fastened (e.g., threaded, welded, or attached using an interference fit) to the post 528. In yet another embodiment, the vessel 500 may also include a structure that helps to ensure that proper alignment is achieved between the centering post 528 and an adjacent structure, such as a device for rotating and/or levitating the pumping or mixing element 502. In the embodiment of Figure 14b, this alignment structure is shown in the form of an alignment post 532 projecting outwardly from the vessel 500 and co-extensive with the centering post 528. The adjacent motive device, which as shown as including a cryostat 102 containing a rotating superconducting element 106, includes a locator bore 533. This bore 533 is concentric with the superconducting element 106 and is sized and shaped for receiving the alignment post 532 (which may have any desired cross-sectional shape, including circular, elliptical, square, polygonal, etc.). As a result of the centering and alignment posts 528, 532, assurance is thus provided that the pumping or mixing element 502 is in the desired position for forming a coupling with an adjacent motive device, such as the cryostat 102 housing the rotating superconducting element 106 (which may both rotate together, as described above). This is particularly helpful for properly aligning the pumping or mixing element 502 with the cryostat, such as cryostat 102, in the case of opaque vessels or adjacent containers, sealed or aseptic containers, large containers, or where the fluid is not clear. Instead of forming the alignment post 532 from an elongated rod inserted into a nipple 530 or the like, it should be appreciated that it may also be integrally formed with the vessel 500 during manufacturing, or later during a retrofit. Figure 14b also shows the centering post 528 projecting upwardly from a bottom wall of the vessel 500, but as should be appreciated, it could extend from any wall or other portion thereof. For example, as illustrated in Figure 14c, the rod serving as both the centering post 528 and the alignment post 532 may be positioned substantially peφendicular to a vertical plane. Specifically, in the particular embodiment shown, the vessel 500 is an empty flexible bag as shown above positioned in a rigid or semi-rigid support container 534 having an opening 536 formed in the lower portion thereof. Once the vessel 500 is inserted in the container 534, but preferably prior to introducing a fluid, the alignment post 532 is positioned in the opening 536 such that it projects therefrom (along with any inlet or outlet hoses present). The proximal end of the alignment post 532 is then inserted into a corresponding receiver in the motive device, such as the locator bore 533 formed in the cryostat 102 (which is easily reoriented, as described herein). This ensures that the pumping or mixing element 502 is in the desired position to form the magnetic coupling with the superconducting once field cooling is complete to achieve levitation and/or rotation without the need for external intervention. As noted above, the coupling may be formed either before or after the introduction of the fluid into the vessel 500. Also, while shown in conjunction with a particular embodiment of the pumping or mixing system, it should be appreciated that the alignment and centering posts 528, 532 may, either together or separately, be used in conjunction with different types of pumping or mixing elements or with any of the pumping or mixing systems disclosed herein. In many of the above-described embodiments, the pumping or mixing action is essentially localized in nature. This may be undesirable in some situations, such as where the vessel is relatively large compared to the pumping or mixing element. To solve this problem, the particular system used to supply the pumping or mixing action may be provided with a motive device for physically moving the superconducting element (which may also be simultaneously rotated). This of course will cause the levitating pumping or mixing element to follow a similar path. With reference to the schematic view of Figure 14d, and by way of example only, the particular arrangement is shown in use on the system 100 of Figure 5, but with the bag 500 of Figure 14. In addition to a motive device 540 for rotating the first portion of the cryostat 102a (which may comprise the bearing(s) 120, endless belt 128, motor 131, shaft, and pulley) and a cooling source 541, the system 100 may include a second motive device 542. In one embodiment, this second motive device 542 (shown schematically in dashed line outline only in Figure 14c) is capable of moving the first portion of the ciyostat 102a, and hence the superconducting element 106, to and fro in a linear fashion (see action arrow L in Figure 14c). Thus, in addition to levitating and rotating the pumping or mixing element 502, the side-to- side motion allows it to move relative to the bag 500 or other vessel containing the fluid. This advantageously permits non-localized pumping or mixing action to be provided. The second motive device 542 may include a support structure, such as a platform (not shown) for supporting all necessary components, such as the first portion of the cryostat 102a (or the entire cryostat, such as in the embodiment of Figure 9), the first motive device 540 for rotating one of the superconducting element 106 (or the pumping or mixing element 502 such as in the embodiment of Figure 9), and the cooling source 541 (which may form part of the cryostat as shown in Figure 9, or may be a separate component altogether, as shown in Figure 2). Instead of using a linear motion device, it should also be appreciated that the second motive device 542 may be capable of moving the superconducting element 106 in a circular or elliptical path relative to the fixed position of the bag 500 or other vessel, or in any other direction that will enhance the overall mixing or pumping action provided by the rotating pumping or mixing element 502. Also, the bag 502 or vessel may be separately rotated or moved to further enhance the operation (see the above- description of the embodiment of Figure 3). Ensuring that the pumping or mixing elements are both proper for a particular system and are of the correct shape and size may also be important. To do so, it is possible to provide a transmitter in one of the pumping or mixing element or the vessel for generating a signal that is received by a receiver in the system (or vice versa), such as one positioned adjacent to the superconducting element or elsewhere. An example of one possible configuration is shown in Figure 14, wherein the transmitter 550 is provided on the pumping or mixing element 502 itself and the receiver 560 is positioned in the cryostat 102 (but see Figure 14a, wherein the transmitter 550 or receiver 560 is provided in the bag 500 serving as the vessel). A controller for the system, such as a computer (not shown) or other logic device, can then be used to maintain the system for rotating the pumping or mixing element 502 in a non-operational, or "lock-out," condition until the receiver and transmitter 550, 560 correspond to each other (that is, until the transmitter 550 generates an appropriate signal that is received by the receiver 560). The transmitter/receiver combination employed may be of any type well known in the art, including electromagnetic, ultrasound, optical, or any other wireless or remote signal transmitting and receiving devices. In accordance with another aspect of the invention, a kit is also provided to assist in the set-up of any of the systems previously described. Specifically, and as briefly noted in both this and my prior applications, it is necessary during field cooling to cool the superconducting element to below its transition temperature in the presence of a magnetic field in order to induce levitation in a permanent magnet producing the same magnetic field. This cooling process causes the superconducting element to "remember" the field, and thus induce the desired levitation in the pumping or mixing element each time it or any other magnet having either a substantially similar or identical magnetic field distribution is placed over the superconducting element. While it is possible to use the pumping or mixing element itself to produce the magnetic field required during field cooling, oftentimes the pumping or mixing element will be sealed in the vessel or container. This makes it difficult, if not impossible, to ensure that the magnets held therein are properly aligned and spaced from the superconducting element during field cooling. One way to overcome this potential problem is to use a set-up kit. As illustrated in Figure 15, the set-up kit may comprise at least one charging magnet 600 having a size, shape, and magnetic field distribution that is identical to the levitation magnet contained in the particular pumping or mixing element slated for use in one of the pumping or mixing systems previously described. The charging magnet 600 is placed adjacent to the superconducting element 602, such as on the upper surface of the cryostat 604, table (not shown), or other structure. As illustrated, the charging magnet 600 may further include a spacer 606. This spacer 606 allows the charging magnet 600 to simulate the spacing of the pumping or mixing element (not shown) above the superconducting element 602 during field cooling. This ensures that the desired levitation height is achieved for the pumping or mixing element (not shown) once the vessel is in position. The spacer 606 is formed of a non-magnetic material to avoid interfering with the charging process. By providing a variety of different sizes, shapes, and configurations of charging magnets in the kit (e.g., annular magnets), it is possible to easily perform field cooling for any corresponding size or shape of levitation magnet in the corresponding pumping or mixing element, and then simply place the vessel containing the pumping or mixing element over the superconducting element 602 to induce the desired stable, reliable levitation. It is also possible to field cool the superconducting element 602 while the cryostat 604 is in one orientation, and then reorient it for forming the coupling with the pumping or mixing element (see, e.g., Figure 14c). During field cooling, and regardless of whether the pumping or mixing element or a separate charging magnet 600 is used to produce the charging magnetic field, it is possible to unintentionally or accidentally induce an undesired magnetic state in the superconducting element 602, such as if the position of the pumping or mixing element (not shown) or charging magnet 600 is not correct. Since improper charging may prevent the pumping or mixing element from levitating in a stable fashion, recharging the superconducting element 602 may be required. To facilitate recharging the superconducting element, it is provided with a heater H, such as an electric heating coil (not shown). By energizing this coil using a power supply P or other source of electrical current (not shown), the superconducting element 602 may be quickly brought up from the transition temperature for recharging. As shown schematically, the power supply P is preferably positioned externally to the cryostat 604. Once the position of the pumping or mixing element or charging magnet 600 is adjusted or corrected, the heater H may be turned off and the superconducting element once again allowed to cool to the transition temperature in the presence of the desired magnetic field. Yet another embodiment of a system 700 is provided for use with a particular type of vessel including a cavity, such as of the type designed to withstand high internal pressures. Even with this cavity, the system 700 permits a strong magnetic coupling to be foπned between an external magnet or superconductor and one or more magnets forming part ofan internal mixing element, such as a rotor or impeller, inside the vessel to ensure that stable, reliable levitation is achieved. As shown in the schematic, partially cross-sectional side elevational view of Figure 16, the vessel 702 includes a cavity 704 formed in one sidewall thereof. As briefly explained above, the shape of this cavity 704 is preferably cylindrical. In the cylindrical case, this shape allows for the outer sidewall of the cavity 704 to be fabricated having a first thickness t, (about 2 millimeters in one possible embodiment, but possibly even less), with the remainder of the vessel 702 being formed from the same or a different material having a second, greater thickness t 2 (e.g., more than 2 millimeters, and preferably about 7 millimeters). To form a unitary vessel, the cavity 704 may be formed as a separate "hat-shaped" section, including an annular flange that is welded (see weld 705 in Figure 16) to a corresponding flange (not numbered). With this construction, the vessel 702 is able to withstand relatively high internal pressures (up to about 7 bar, and possibly greater), yet the relatively thin sidewall of the cavity 704 allows for strong magnet-magnet/magnet- superconductor interactions to be achieved. Of course, the potential reduction in thickness of the sidewalls of the cavity 704 and the upper limit of the internal pressure are directly influenced by the type of material used, with the dimensions provided above corresponding to a vessel 702 formed of conventional non-magnetic stainless steel. Although a cylindrical cavity 704 is shown, it should be appreciated that other equivalent geometric arrangements may also be used, including those having regular or irregular polygonal cross-sections or the like. To adapt the superconducting levitation scheme described immediately above to a vessel 702 having such a cavity 704, a special "cryostat" 706 may be used, which is generally similar in construction to the one shown in Figure 9. In the illustrated embodiment, the cryostat 706 includes an external wall 708 that defines an enclosed space or chamber (not numbered). This space is evacuated, such as by using a vacuum source (not numbered), and together with the wall 708 creates a vacuum "jacket" 710 around a superconductor or superconducting element 712 held therein. The superconducting element 712 is preferably a "high temperature" superconducting element formed of melt-textured ReBa 2 Cu 3 O x , with Re representing a rare earth element (e.g., Yttrium, of which YBCO is a common example), but the use of other such materials either already known or discovered after the filing is of course possible without departing from the broadest aspects of the invention. Also, as is known in the art, the superconducting element 712 may be formed from a single annular or ring shaped piece of material, or as outlined further in the description that follows, may be comprised of a plurality of contiguous or non-contiguous segments or sections, each formed of a piece of superconducting material interconnected or arranged in an annular or substantially polygonal configuration. In the illustrated embodiment, the superconducting element 712 is positioned in a "head" portion of the cryostat 706 sized and/or otherwise adapted for extending or projecting into the cavity 704 formed in the vessel 702. The cryostat 706 also includes or houses a thermal link 714 for supplying the cooling that keeps the element 712 in the desired superconducting state. As described above, the thermal link 714 is preferably formed of a material having a high degree of thermal conductivity/low thermal resistance (metals, such as copper, brass, or the like). Although not critical, the link 714 may include an engagement portion corresponding generally in size and shape to the superconducting element 712 to ensure that the desirable full contact and engagement is established between the corresponding surfaces to improve thermal transfer. As also described above, the thermal link 714 is connected to a cooling source, such as a Dewar flask filled with a liquid cryogen, a closed cycle refrigerator, or the like (see, e.g., Figure 9). It should be appreciated by skilled artisans that the particular cooling source or thermal link used is not important or critical, as long as it is capable of maintaining the element 712 in the desired superconducting state to induce levitation in the mixing element 722. As with the embodiment in Figure 9, the outer wall 708 of the cryostat 706 may be configured to create a bore or opening that allows for a shaft 716 or the like to pass therethrough (see Figure 16a). One end of the shaft 716 is coupled to a motive device, such as a motor 718, while the other carries a plurality or array of drive magnets 720. The drive magnet array 720 is preferably positioned in close proximity to the inside surface of the sidewall of the cavity 704, and is comprised of a plurality of magnets having alternating polarities or polar orientations (with the N-S poles preferably being arranged peφendicular to the vertical plane and spaced sufficiently close to the wall of the cavity 704 to create the strongest possible magnetic coupling, and hence, the most efficient torque transfer). Turning now to the mixing element 722, it is preferably in the form of a rotor or impeller comprised of a hollow, substantially cylindrical or tubular body sized so as to permit a concentric orientation with the cylindrical cavity 704 inside the vessel 702. The mixing element 722 may comprise a levitation magnet 724 generally corresponding in shape and proportional in size to the superconducting element 712, and preferably having its poles oriented in a direction parallel to a vertical plane. Spaced from the levitation magnet 724, and preferably embedded in a matrix material M, is an array of strategically positioned driven magnets 726. The driven magnets 726 correspond generally in size and shape to the array of alternating polarity drive magnets 720 carried on the shaft 716. The driven magnets 726 are also of alternating polarity to create the desired magnetic coupling with the drive magnets 720 for transmitting the drive torque from the motive device, such as the motor, to the shaft 716, and ultimately to the levitating mixing element 722. As shown in Figure 16, the mixing element 722 may also carry one or more blades 728, vanes, or the like to further enhance the mixing action provided (or pumping action, in the case of a pumping chamber having a cavity bottom). Hence, as depicted in Figure 16, it is possible to easily adapt the mixing system 700 for use with a vessel 702 having a thin-walled cavity 704 that is nevertheless capable of withstanding high pressures, such as those possibly created during cleaning or sterilization. As an example of one possible application, the vessel 702 may thus be pre-sealed with the magnetic mixing element 722 (e.g., rotor or impeller) inside, and then simply placed over the cryostat 706, such as by positioning the vessel on an adjacent stable support surface, such as a table, support platform, stand or the like (see reference character T in Figure 16). Assuming that field cooling has previously been completed (such as by using a "kit" for supporting a corresponding "set-up" magnet adj acent to the superconducting element 712 during cooling, which in this case could be an annular set-up magnet, as opposed to the disc- shaped one in Figure 15), the vessel 702 is simply positioned over the cryostat 706, as shown in Figure 16, such that the magnetic field of the permanent levitation magnet 724 creates the desired flow of current through the superconducting element 712 to achieve the simultaneous attraction and repulsion that results in stable levitation. During experimentation using the system 700, it was discovered that it may be advantageous in terms of levitational stability to form the superconducting element 712 of a plurality of segments of the melt-textured/melt-processed rare-earth superconductor described above, with the particular orientation of the crystallographic axis or planes of each segment being selected to significantly enhance the magnetic stiffness of the coupling, as well as the load capacity of the levitating mixing element 722. Specifically, as shown in Figure 17, which is a plan schematic view of the levitation magnet 724 and a plurality of segments 712a . . . 712n formed of a superconducting material having crystallographic planes (see below) and arranged in a non-contiguous polygonal configuration, and Figure 18, which is a cross-sectional view of the same taken along line 18-18 of Figure 17, the crystallographic "C-axis" of each superconducting segment 712a . ..712n is oriented in a radial direction, or in the illustrated embodiment, substantially peφendicular to the magnetization vector of the levitation magnet 724, and preferably passes through the center thereof. Accordingly, the A-B planes are oriented substantially parallel to the polar magnetization axis of the levitation magnet 724. Superconducting materials having these crystallographic planes/axes include those comprised of ReBa 2 Cu 3 O x , formed by a melt-texturing or "melt-processing," as is known in the art (see, e.g.,U.S. Patent No. 5,747,426 to Abboud and U.S. Patent No. 5,763,971, the disclosures of which are incoφorated herein by reference). Using this arrangement, it was found that the levitation force, magnetic stiffness, and concomitant load capacity of the levitation magnet 724 is increased on the order of two to three times without a corresponding change in any other parameter of the system 700 described above. Of course, these increases serve to enhance the rotational stability of the mixing element 722 when such an arrangement is used in a pumping or mixing system, which in turn improves the operational reliability. These increases also advantageously reduce the tendency of the pumping or mixing element 722 to decouple at higher rotational speeds or in pumping or mixing high viscosity fluids or the like. It is also noted that the system 700 is generally described above as a mixing system for use with vessels 702 or containers capable of withstanding high pressures. However, it should also be appreciated that the system 700 could also be used for the mixing or pumping of fluids through a vessel 702 in the form of a flexible, open-top container or any other type of container having the cavity 704 or a similar configuration. Of course, the strategic orientation of the elements of a segmented superconductor could also be used to enhance the levitational and rotational stability of a pumping or mixing element used in any of the systems described herein as well. Yet another embodiment of a pumping or mixing system 800 is proposed in Figure 19. Perhaps the best way to describe this embodiment is to begin with a description of the vessel 810 and the pumping or mixing element 812. The vessel 810, like vessel 702, is preferably created having a cavity 814 that defines a concentric aimular protruding portion 815. Preferably, the wall defining each side of cavity 814 and each side of the annular portion 815 is fabricated of a relatively thin, non-magnetic material, such as stainless steel. As noted above with regard to vessel 702, by forming the remainder of the vessel 810 having relatively thick sidewalls, it may withstand high pressures, such as those created during sterilization using steam under pressure or the like. However, in the case where the vessel 810 is not subjected to high pressures or is used as a pumping chamber, the walls may be formed of a substantially homogeneous material (disposable plastics, glass, stainless steel, etc.) having substantially the same relative thickness. A description of an embodiment wherein a flexible plastic bag is provided with a cavity is described below and shown in Figure 22. The pumping or mixing element 812 is capable of being positioned in the vessel 810 and includes a levitation magnet 816. In particular, the levitation magnet 816 is sized and shaped for extending into the interior of the annular portion 815 of the vessel 810. In the illustrated embodiment, the levitation magnet 816 is polarized in the vertical direction (the specific orientation of the poles is not critical) to create a vertical magnetization vector. However, the magnetization vector could also be oriented in a horizontal or substantially horizontal plane (although those skilled in the art will recognize that forming a single ring shaped magnet having opposite poles oriented in a horizontal plane is more difficult than forming one having a vertical magnetization vector) . To levitate the pumping or mixing element in the vessel 810, at least one, and preferably a plurality of superconducting elements 818 are positioned in an annular cryostat 802. This cryostat 802 is specially adapted for receiving the annular protruding portion 815 of the vessel 810 (see Figure 19a) and may even support the vessel, as shown in Figure 19. More specifically, in the illustrated embodiment, the cryostat 802 includes an annular channel 806 for receiving the corresponding annular portion 815 of the vessel 810. The outer wall 808 of the cryostat 802 defines a space or chamber that is preferably evacuated to create a vacuum jacket, as described above. Alternatively, the chamber could be filled with an insulating material to reduce the thermal transfer. Regardless of the means used, the important point is that in the case of pumping or mixing non-cryogenic, warm or temperature sensitive fluids, no or only negligible thermal transfer from the cold superconductor to the vessel and hence the fluid results. Preferably, the superconducting elements 818 are comprised of a plurality of segments, each of which is in thermal communication with a cooling source (e.g., a Dewar flask or a closed-cycle refrigerator) via a thermal link 820 positioned and supported in the cryostat 802. The segments comprising each of the one or more superconducting elements 818 are preferably formed of a "high- temperature" superconducting material having crystallographic A-B planes and a C- axis, which as noted above, is a characteristic of melt-textured or melt-processed ReBa 2 Cu 3 O x , with Re representing a rare earth element (e.g., Yttrium, of which YBCO is a common example). In the preferred embodiment, three superconducting elements 818a, 818b, 818c are provided on the thermal link 820, although it should be appreciated from reviewing the description that follows that using only a single superconducting element or two superconducting elements to levitate the pumping or mixing element 812 is entirely possible (see Figure 16). A first of the superconducting elements 818a is positioned adjacent to a first side of the annular channel 806 formed in the cryostat 802 adjacent to a first side of the annular levitation magnet 816. The second superconducting element 818b is also positioned adjacent to a second side of the annular levitation magnet 816. The third superconducting element 818c is positioned adjacent to a third side of the annular levitation magnet 816. Each of the superconducting elements 818a, 818b, 818c may be in thermal communication with the same thermal link 820, as shown in Figure 19 and positioned internal to the corresponding cryostat 802, which by way of insulation or vacuum jacket prevents any thermal transfer to the room temperature vessel 810, the fluid F held therein, or the pumping or mixing element 812. In a most preferred version of this embodiment, the crystallographic planes/axes of the segments forming the superconducting elements 818a, 818b, 818c are oriented so as to significantly improve the levitation force, the resulting loading capacity, and the magnetic stiffness of the coupling formed with the pumping or mixing element 812. Specifically, the first and third superconducting elements 818a, 818c (or more particularly, the segments comprising these elements) are oriented such that the C-axes thereof are peφendicular to the magnetization vector of the levitation magnet 816, while the second superconducting element 818b is oriented such that the C-axis of each segment thereof is aligned with and parallel to the magnetization vector of the levitation magnet 816. Another way to describe the arrangement is that the A-B crystallographic planes of the first and third superconducting elements 818a, 818c are parallel to the axis of polarization of the levitation magnet 816, while the A-B crystallographic planes of the second superconducting element 818b are peφendicular to the polarization axis (note the substantially parallel lines representing the A-B planes drawn on each superconducting element 818a-c in Figure 19). As used herein, the terms "parallel" and "peφendicular" are intended to mean generally or substantially parallel or peφendicular, it being recognized that variations in the orientation of the various crystallographic planes or axes relative to the magnetization vector are either inherent or may be created by slight misalignments of adjacent elements, or may be intentionally varied within a range to adjust or fine tune the levitation force provided or rotational stability. The particular arrangement shown in Figure 19 results in a system 800 in which the pumping or mixing element 812 is levitated in a most stable fashion. This stable levitation results primarily from the interaction between the specially oriented segments forming each superconducting element 818a-c and the annular levitation magnet 816. As a result of this arrangement, the loading capacity of the pumping or mixing element is increased, as it the stiffness of the magnetic coupling. This combination allows for a greater amount of torque to be supplied to the pumping or mixing element 812 without accidental decoupling, which allows for higher angular velocities to be achieved. It also allows for use of the system 800 with fluids having higher viscosities. The drive system for rotating the pumping or mixing element may be substantially as described above. Specifically, a shaft 822 coupled at one end with a motive device, such as a motor 824, is positioned in a room temperature bore or through an opening formed in the cryostat 802. The end of the shaft 822 adjacent to the vessel 810 carries a plurality of drive magnets 824 having alternating polarities. Corresponding driven magnets 826 having alternating polarities are provided on the pumping or mixing element 812. As shown in Figure 19, the pumping or mixing element may also include impeller blades 828, vanes, or like structures to further enhance the pumping or mixing action provided. In accordance with yet another embodiment of the present invention, a specific pumping or mixing system 900 using a rotating superconducting element 901 is shown in Figure 20. The superconducting element 901 may be supported by a plate 902 in thermal engagement with a cooling source forming a part of a cryostat 903 and preferably rotating therewith. The superconducting element 901 is surrounded by a wall 905 defining an evacuated chamber 906, which may together be considered to form a vacuum jacket comprising part of the cryostat 903 (although as described above the chamber 906 could also be insulated or any other known or yet-to-be discovered means for obviating thermal transfer between a cold superconducting element could be used). In the illustrated embodiment, the cooling source is a portable refrigerator or "cryocooler" 904 that also forms part of the cryostat 903. The cryocooler 904 is shown as having a "head" end 905 that extends into the chamber 906 to directly engage and support the plate 907 which in turn supports the superconducting element 901, although the use of a separate thermal link (not shown) is also possible, depending on the relative dimensions of the system. As with the thermal link previously described, both the plate 902 and the head end 907 of the cryocooler are typically formed of a material having a high degree of thermal conductivity/low thermal resistance (e.g., a metal) to ensure that the desirable efficient thermal transfer is established. The plate 902 may also be supported from the wall 905 by one or more connecting members 908, which are preferably thin, but relatively strong, and formed of a material having a low degree of thermal conductivity so as to create only negligible thermal transfer to the wall 905. The cryostat 903 is rotatably supported by at least one, and preferably a pair of bearings or bearing assemblies 909a, 909b, which are in turn supported by a stable support structure, such as an adjacent vertical wall NW or another type of support frame (which may or may not engage the adjacent structure, such as table T, supporting the vessel). For example, one bearing may engage the outer wall 905 of the cryostat 903, while the other engages the outer wall of the cryocooler 904. The use of two bearing assemblies 909a, 909b of course ensures that the cryostat 903 rotates about a vertical center axis in a most stable and reliable fashion and is capable of resisting any skewing forces, and may also allow it to be turned on its side (such as it would appear if Figure 20 is oriented in a landscape view, rather than a portrait view). As shown in Figure 20, the bearing assemblies 909a, 909b may include mechanical roller or ball bearings, or other elements that may provide low-friction, rotatable support the cryostat 903. To transmit the desired rotational motion, an endless belt 910 may be placed in frictional engagement with a first pulley 911 coupled to or carried by the cryostat 903. The belt 910 also engages a second pulley 912 supported by the shaft 914 of a motive device 916, such as a variable speed electric motor. As should be appreciated, the rotation of the shaft 914 thus causes the cryostat 903, and hence, the superconducting element 901 positioned therein to rotate. As noted above, the cryostat 903 could also be mounted "inline" on a shaft that is in turn connected or coupled directly to a motive device, such as an electric motor. One particularly preferred example of a commercially available closed-cycle refrigerator or cryocooler 904 for use in the present invention is a type of substantially self-contained, compact, closed-cycle cryocooler employing the Stirling cycle to produce the desired refrigeration, several models of which are manufactured and distributed by Sunpower, Inc. of Athens, Ohio. As shown schematically in Figure 20, this cryocooler 904 includes a lower portion 904a which serves to house an electric motor and an upper portion 904b adjacent to the head 907 which houses a reciprocating piston (not shown). In light of the commercial availability of several suitable models, the workings of such a cryocooler need not be understood to practice the present invention. However, it is noted that Sunpower, Inc. holds a number of U.S. patents on various types of cryocoolers, each of which is incoφorated herein by reference to the extent deemed necessary to allow a skilled artisan to make or use this invention. Regardless of the type of cooling source used, the important point is that it is fully capable of generating the "high temperatures" (e.g., 77K-90K) necessary to induce a superconducting state in, for example, a YBCO superconducting element (which may be comprised of a plurality of segments, as described below). To supply the necessary power to the cryocooler 904 such that it keeps the superconducting element 901 at the desired temperature, yet allows it to rotate even at high speeds, a dynamic electrical connection is provided. Specifically, contacts 918, which are shown in the form of annular rings surrounding the outer wall of the cryocooler 904, are provided for engaging corresponding "stationary" flexible or pivoting contacts 920 in electrical communication with a power source 922 (120/220N), which may be remote. As should be appreciated, this configuration allows the cryocooler 904 to freely rotate at both high and low speeds while continuously receiving the power necessary to run the motor/drive the piston and keep the head end 907 at the desired cold temperature. Instead of this illustrated configuration, a well-known type of dynamic electrical connection called a "slip ring" may be used, such as those manufactured by Siemens, Litton, and the Kaydon Coφ. A slip ring is also sometimes referred to in the art as a "rotary electrical interface," a "commutator," a "swivel," or a "rotary joint." The system described above can be substituted into the system 100 shown in Figures 5-7 for rotating a pumping or mixing element in the form of a flat, disc-shaped rotor or impeller 134 for pumping or mixing a fluid in a flat-bottomed rigid vessel or bag. In that case, the plate 902 could be eliminated and a disc-shaped superconducting element, such as element 106, used in its place. However, in Figure 20, the vessel 922 is illustrated having a cavity 924, which may of course be similar in construction to the cavity provided in a vessel capable of withstanding high internal pressures, as described above and shown in Figure 16. Alternatively, the cavity 924 could be formed in a conventional open-top vessel, in a flexible bag or container (see Figure 22), or in any other type of vessel used in applications where high pressures are not a concern. In the case where the cavity 924 is formed in a flexible bag or container, as shown in Figure 22, is should also be appreciated that the cavity 924 may serve a function similar to that of centering post 528 shown in Figure 14b (and could even include a peripheral flange, projections, or like structures at the upper end to ensure that the pumping or mixing element 926 remains fully held in place during shipping, storage, or between uses, yet spaced far enough away to avoid creating any interference with the desired levitation/rotation). In any case, in the embodiment in Figure 20, the pumping or mixing element 926 is substantially cylindrical and includes only a levitation magnet 928, since both the levitation force and the driving torque are provided by the superconducting element 901. This levitation magnet 928 may be comprised of a plurality of segments of permanent magnets 928a . . . 928n having alternating polarities and arranged in a substantially annular or polygonal configuration (see the schematic illustration merely showing a preferred orientation/arrangement in Figure 21). As also shown schematically in Figure 21, the superconducting element 901 is concentric with the levitation magnet 928 and is also comprised of a plurality of segments 901a . . . 90 In arranged in an annular or polygonal configuration. Preferably, each segment 901 a . . .90 In is oriented having its crystallographic C-axis aligned in the radial direction (i.e., oriented generally parallel to the magnetization vector of a corresponding segment 928a . . . 928n of the permanent magnet 928, and preferably passing substantially through the center thereof). Accordingly, the A-B planes of the segments 901a . . . 90 In comprising the superconducting element 901 are oriented generally peφendicular to the radial direction, and hence, the magnetization vector. As a result of this arrangement, the rotating superconducting element 901 not only reliably induces stable levitation in the pumping or mixing element 926 via levitation magnet 928, but also forms a magnetic coupling which causes the pumping or mixing element 926 to rotate. As shown in Figure 20, the pumping or mixing element 926 may also carry one or more impeller blades, vanes, wings, or like structures 930 to further enhance the pumping or mixing action. Figure 23 shows an embodiment of the pumping or mixing system 950 for use with a vessel (such as a tank K, but any vessel disclosed herein would also work) having a cavity that is generally similar to the embodiment shown in Figure 20 with a few modifications. The first is that the rotating cryostat 952 includes two superconducting elements 954, 956 (which may be formed of segments) spaced in the vertical direction. The pumping or mixing element 958 includes corresponding arrays of alternating polarity magnets 960, 962 (see, e.g., Figure 21), with each magnet in the array 960 having a neighboring magnet with an alternating polarity. The rotation of the cryostat 952 and, hence, the superconducting elements 954, 956 thus induces both levitation and rotation in the pumping or mixing element 958 (which is shown having a plurality of upstanding blades B). As should be appreciated, the dual arrays enhance the vertical stiffness of the coupling and improve torque transfer. The superconducting element arrays 954, 956 are supported on a thermally conductive platform 963 by an upstanding cylindrical wall 964. The platform 963 in turn is coupled to a rod 965 serving as a theπnal link to a cooling source, such as the Sunpower cryocooler described above or a Dewar flask filled with a liquid cryogen, which is in turn coupled to a motive device (shown in block form only, but see Figure 20 for an example of one possible embodiment). As noted above, insulating or evacuating the chamber 966 in the cryostat 952 prevents the cold superconducting elements 954, 956 from cooling the adjacent tank K to any significant degree, which means that the system is well-adapted for pumping or mixing non-cryogenic fluids, including room-temperature fluids. The embodiment of Figure 23 also differs from the one shown in Figure 20 in that the pumping or mixing element 958 carries a first ring magnet 968 (or an equivalent array of magnets, such as vertically polarized magnetic discs (not shown)). A corresponding ring magnet 970 (or array of magnets) is carried by the rotating cryostat 952 (preferably externally and at the top, as shown in Figure 23). The first ring magnet 968 and the second ring magnet 970 are oriented such that like poles are adjacent to each other. This magnet-magnet interaction thus repels the pumping or mixing element 958 from the cryostat 952. However, the interaction between the superconducting elements 954, 956 and the arrays of magnets 960, 962 together generally levitate and hold the pumping or mixing element 958 in place. The net result is that the pumping or mixing element 958 is levitated, but is able to resist any force tending to move it into contact with the tank K, including the outer surface of the adjacent cavity. Another distinction in the illustrated embodiment is that the pumping or mixing element 958 is generally cylindrical and includes an opening 967. As a result of this construction, when the pumping or mixing element 958 is rotated, fluid is drawn into the gap between it and the adjacent cavity in the tank K (see action arrows F). The fluid then passes through the opening 967, which enhances the fluid agitation created by the rotation of the pumping or mixing element 958, even at relatively low angular velocities. A related embodiment is shown in Figure 24. In this embodiment, the first ring magnet 968 (or array) is again provided on or in the pumping or mixing element 958, but the second ring magnet 970 (or array) is positioned external to the tank K. Again, the rings 968, 970 have like polarities along the adjacent faces to create a repelling force. In this case, this force helps to prevent the pumping or mixing element 958 from "bottoming out" on the adjacent surface of the tank K. Although not preferred for most applications due to the clean-up and sterilization problems possibly created, the second ring magnet 970 could be positioned just inside the tank K as well. Instead of attaching the ring magnet 970 to the tank K, it could also be supported by the cryostat 952, such as a flange (note dashed lines in Figure 24) or a related structure that rotates therewith. Also, the possibility of providing neighboring magnets in each array 960, 962 with like polarities is shown (with the polarities of vertically adjacent magnets in each array still alternating), which is somewhat less preferred than the embodiment of Figure 23 in which the polarities of neighboring magnets in each array alternate. These two approaches could also be combined into the same system, as shown in Figure 25. In particular, first and second ring magnets 968a, 970a are provided in one portion of the pumping or mixing element 958, and third and fourth ring magnets 968b, 970b are provided in another. The repelling forces created thus provide dual levels of protection against the rotating pumping or mixing element 958 inadvertently contacting the vessel or tank K. Also, either or both approaches could be used in the embodiments of Figure 16 or 19 as well. Also note that the polarities of adjacent magnets in the arrays 960, 962 are alike, although each vertically adjacent pair has a different polarity that the next-adjacent pair. This is somewhat less preferred than the arrangement of Figure 23 in terms of stiffness, but would work nevertheless. By switching the polarities, it is also possible to provide one or more sets of magnets like ring magnets 968, 970 that attract, rather than repel each other. The attractive force thus created may help to prevent the pumping or mixing element 958 from moving in a vertical direction relative to the cavity as it rotates (or in the horizontal direction, in the case where the cavity is positioned with its centerline axis parallel to a horizontal plane). The magnets would preferably be sufficiently weak in power to avoid creating any instability in the levitation and/or rotation induced by the superconducting element arrays 954, 956. Figures 26 and 27 show a method and apparatus for centering and setting up a pumping or mixing element 980 that is capable of levitating in a vessel 981, such as in a hermetically sealed tank, in a sterile vessel, such as a flexible bag, or even in an open-top vessel where access to the corresponding surface adjacent to levitating the pumping or mixing element is restricted. The vessel 981 includes a cavity 982, as described above. Inside the vessel 981, the cavity 982 may include along its outer surface an engagement structure for contacting, engaging, or supporting the pumping or mixing element 980 when in a non-levitating or resting position. In the preferred embodiment, this engagement structure comprises a frusto- conical surface 984 that is tapered relative to the horizontal plane. The pumping or mixing element 980, which is of course generally annular, includes a matching surface 986 along at least a portion ofan adjacent inner surface thereof. Preferably, the matching surface 986 is formed in an inert portion of the pumping or mixing element 980, such as the matrix material (e.g., plastic, metal, composites, etc.) used to support the levitation magnet or magnet array 988 (which is shown schematically, but could be any appropriate one of the arrangements described herein). The pumping or mixing element 980 is shown slightly raised in the vertical direction to illustrate the shape of the surfaces 984, 986. However, it should be appreciated that these surfaces 984, 986 would normally be in contact with each other as the result of gravity when the pumping or mixing element 980 is at rest (i.e., non-levitating), such that a radial centering function is inherently provided. A cryostat 989, which may be substantially identical to those described above, is positioned in the cavity 982. In particular, the cryostat 989 contains one or more superconducting elements 990 (which may in turn be formed of segments) that are mounted on a platform 983 that is in turn coupled via thermal link 991 to a cooling source, which in view of the various versions described herein is merely shown in block form. The entire cryostat 989 is preferably coupled to a second motive device 994, also shown in block form, that rotates it along with the superconducting element(s) 990. It may also be coupled to a second motive device for moving it relative to an inner surface of the cavity 982, such as in the vertical direction as shown in Figure 26. As described above, in the case of non-cryogenic fluids, the cryostat 989, or at least the portion housing the superconducting element(s) 990 and any other cryogenic structures, is preferably evacuated or insulated to prevent thermal transfer to the adjacent vessel 981. To form a magnetic coupling between the superconducting element(s) 990 and the levitation magnet 988 of the pumping or mixing element 980, the cryostat 989 is moved to a position within the cavity 982 where these two structures are substantially aligned. In particular, the alignment is such that the superconducting element(s) 990 face the adjacent levitation/driven magnet(s) on the pumping or mixing element 980, which of course is inside of the vessel 981. Once this alignment is achieved, the superconducting element(s) 990 are cooled to below the transition temperature (preferably less than 90K for a YBCO superconductor) in accordance with a field cooling protocol. As a result, a magnetic coupling is established with the levitation/driven magnet 988 and the desired pinning forces are created that permit stable, exceptionally reliable levitation of the pumping or mixing element 980 (and rotation, in the case where the superconducting element 990 is rotated, such as by using the configuration shown in Figure 21). Once the magnetic coupling is formed, the cryostat 989 maybe moved further into the cavity 982, either manually or using a third motive device 996, such as a linear actuator or the like. As a result of the coupling formed between the superconducting element(s) 990 and the levitation magnet 988, this causes the matching surface 986 of the pumping or mixing element 980 to separate from the frusto-conical engagement surface 984 (see Figure 27 and note action arrow Z). Rotation of the cryostat 989 using the second motive device 994 may then be effected as described above to cause the levitating pumping or mixing element 980 to rotate and, hence, pump or mix the fluid in the vessel 981. To return the pumping or mixing element 980 to a resting position such that contact is re-established between surfaces 984, 986, the superconducting element(s) 990 need only be returned to above the transition temperature, at which point the magnetic coupling is lost. To expedite this operation, and as described above, a heater 998 may be used. Once the coupling is no longer formed, it should be appreciated that the pumping or mixing element 980 gently comes to rest such that the surfaces 984, 986 are in engagement and the desired centering function is provided as a result of the matching tapers or slopes. Advantageously, this means that the user of the system need not have access to the pumping or mixing element 980 to ensure that it is properly centered for puφoses of field cooling prior to levitation, and actually avoids the need for the use of a set-up kit, as described above (which in this case could be hat-shaped with a set-up or charging magnet corresponding in magnetic field and polarity to levitation magnet being placed over the head end of the cryostat 989). The use of this "moving cryostat" arrangement with the other embodiments of pumping or mixing systems disclosed herein is also possible, and in particular, with the embodiment shown in Figures 19, 20, 23-25 (which may require adjusting the relative dimensions or adding an annular piece of inert material to the pumping or mixing element to provide the matching surface 986). Also, instead of forming the frusto-conical surface as part of the cavity 982, it could actually be a separate, freestanding structure positioned at the same location or adjacent to the outer surface of the pumping or mixing element 980 (see the phantom depiction of engagement structure 999 in Figure 27), in which case the matching surface 986 would be positioned accordingly (i.e., along the outer surface of the pumping or mixing element 980). The entire arrangement could also be inverted (not shown), with the engagement surface 984 being provided on the upper end of the cavity 982 and the matching surface 986 being on a corresponding surface of the pumping or mixing element 980 (in which case, the cryostat 989 would be withdrawn from the cavity 982 once the desired magnetic coupling is formed). If the vessel 981 is inverted, the cavity 982 would preferably be elongated to avoid interfering with the adjacent wall of the vessel 981. Each of the embodiments of pumping or mixing systems disclosed herein 10, 100, 200, 300, 700, 800, or 900 could also be used for mixing a fluid with a product, such as a bacterial nutrient culture media, eukaryotic cell nutrient culture media, buffer, reagent, or like intermediate product for forming one or more end products. As a result of the levitating nature of the pumping or mixing element, application of these systems to vessels where the product and the pumping or mixing element are sealed in the vessel before use, including in an aseptic environment, is of course possible. In summary, a number of systems 10, 100, 200, 300, 700, 800, 900 as well as variations on these systems and related methods, are disclosed that use or facilitate the use of superconducting technology to levitate a magnetic element that, when rotated, serves to pump or mix a fluid. In one system 10, the magnetic element 14 is placed in a fluid vessel 16 positioned external to a cryostat 12 having an outer wall or other housing 18 for containing a superconducting element 20. A separate cooling source 24 (either a cryogenic chamber 26, Figures 1 and 3 or a refrigerator 48, Figure 2) thermally linked to the superconducting element 20 provides the necessary cooling to create the desired superconductive effects and induce levitation in the magnetic element 14. Since the pumping or mixing element levitates in the fluid F, no penetration of the vessel walls by mixing or stirring rods is necessary, which eliminates the need for dynamic bearings or seals. Additionally, the outer wall 18 of the cryostat 12 or other housing defines a chamber 25 that thermally isolates and separates the superconducting element 20 from the vessel 16 containing the fluid F and pumping or mixing element 14. The thermal isolation may be provided by evacuating the chamber 25, or filling it with an insulating material. By virtue of this thermal isolation and separation, the superconducting element 20 can be positioned in close proximity to the outer wall or housing 18 adjacent to the vessel 16 and pumping or mixing element 14, thereby achieving a significant reduction in the separation distance or gap G between the pumping or mixing element 14 and the superconducting element 20. This enhances the magnetic stiffness and loading capacity of the magnetic levitating pumping or mixing element 14, thus making it suitable for use with viscous fluids or relatively large volumes of fluid. The exceptionally stable levitation provided as a result of the reduced separation distance also significantly reduces the potential for contact between the rotating pumping or mixing element and the bottom or sidewalls of the vessel. This makes this arrangement particularly well-suited for use in fluids that are sensitive to shear stress or the effects of frictional heating. However, since the superconducting element 20 is substantially thermally isolated and separated from the vessel 16, the magnetic element 14, and hence the fluid F contained therein, may be shielded from the cold temperatures generated by the cooling source 24 to produce the desired superconductive effects and the resultant levitation. This allows for temperature sensitive fluids to be mixed or pumped. By using means external to the vessel 16 to rotate and/or stabilize the magnetic element 14 levitating in the fluid F, such as one or more rotating driving magnets coupled to the magnetic element 14, the desired pumping or mixing action is provided. Additional embodiments of systems 100 (900), 200 for pumping or mixing a fluid wherein the necessary motive force is provided from the same side of the vessel at which the superconducting element is positioned are also disclosed, as are systems 300, 400 for rotating an inline pumping or mixing element positioned in a vessel in the form of a pipe or the like in a similar fashion. Alternative systems 700, 800, and 900 are also disclosed, which are particularly well adapted for applications using special vessels having cavities that assist in withstanding high internal pressures. Particular orientations of the crystallographic planes of the material used as the superconductor are also described to enhance the levitation force and magnetic stiffness of the coupling, which in turn increases the stability and load capacity of the pumping or mixing element, as is the use of opposing pairs of permanent magnets to provided a levitation-assist function. A manner of centering and setting up a pumping or mixing element in a hermetically sealed vessel is also disclosed. The foregoing description of various embodiments of the present invention have been presented for puφoses of illustration and description. The description is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obvious modifications or variations are possible in light of the above teachings. For example, while the use of a thermally separated superconducting element is disclosed, the subsequent development of room temperature superconductors would obviate this need. The embodiments described provide the best illustration of the principles of the invention and its practical applications to thereby enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the invention as determined by the appended claims when inteφreted in accordance with the breadth to which they are fairly, legally and equitably entitled.

Claims: In the Claims 1. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid, the vessel having a cavity formed in at least one side thereof; a magnetic pumping or mixing element positioned in the vessel concentric with the cavity; at least one superconducting element positioned in or adjacent to the cavity for levitating the pumping or mixing element; a wall defining a chamber around the superconducting element, the chamber thermally isolating and/or separating the superconducting element from the vessel; a cooling source thermally linked to the superconducting element; a motive device for rotating the pumping or mixing element or the superconducting element and the pumping or mixing element together relative to the cavity. 2. The system according to claim 1, wherein a first wall of the vessel defines a portion of the cavity, said wall being formed of a material having a first thickness that is less than the thickness of the material forming a remainder of the vessel. 3. The system according to claim 2, wherein the first wall of the vessel is circular in cross-section. 4. The system according to claim 1, wherein said wall defining a chamber around the superconducting element is the outer wall of a cryostat adapted for insertion into the cavity. 5. The system according to claim 4, wherein the pumping or mixing element includes a levitation magnet concentric with the superconducting element in the cryostat. 6. The system according to claim 5, wherein said superconducting element is annular and a portion of the chamber defined by said wall is annular for receiving the annular superconducting element. 7. The system according to claim 6, wherein said motive device includes a shaft carrying a plurality of alternating polarity driving magnets at one end, said driving magnets being inserted in a thermally separated or isolated bore in said cryostat, said bore being concentric with the annular chamber for housing said superconducting element. 8. The system according to claim 7, wherein said levitation magnet corresponds in at least one dimension to the superconducting element and further includes a plurality of driven magnets having alternating polarities, said driven magnets being aligned with said driving magnets rotated by said motive device, whereby said levitation magnet levitates said pumping or mixing element while said driven magnets transmit driving torque to said pumping or mixing element from said driving magnets. 9. The system according to claim 7, further including a platform in said chamber for supporting the superconducting element, wherein the platform is thermally linked to the cooling source. 10. The system according to claim 9, wherein the thermal linking is provided by either a rod extending from the cooling source to the platform for supporting the superconducting element or a cryocooler serving as the cooling source in thermal engagement with the platform. 11. The. system for according to claim 1, wherein the chamber surrounding the superconducting element is evacuated or insulated. 12. The system according to claim 1, wherein: the pumping or mixing element includes a levitation magnet having a magnetization vector, the at least one superconducting element is comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis, and the A-B planes are parallel to the magnetization vector; and the C-axis is peφendicular to the magnetization vector. 13. The system according to claim 1, further including: at least twø superconducting elements, each comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis, and wherein: the A-B planes of each segment are parallel to the magnetization vector; and the C-axis of each segment is peφendicular to the magnetization vector. 14. The system according to claim 1, further including: first and second superconducting elements, each comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis, and wherein the A-B planes of each segment comprising the first superconducting element are parallel to the magnetization vector; the C-axis of each segment comprising the first superconducting element is peφendicular to the magnetization vector; the A-B planes of each segment comprising the second superconducting element are peφendicular to the magnetization vector; the C-axis of each segment comprising the second superconducting element is parallel to the magnetization vector. 15. The system according to claim 1, further including: first, second, and third superconducting elements, each comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis, and wherein; the A-B planes of the segments of the first and third superconducting elements are parallel to the magnetization vector; the C-axes of the segments of the first and third superconducting elements are peφendicular to the magnetization vector; the A-B planes of the segments of the se.cond superconducting element are peφendicular to the magnetization vector; the C-axis of the segments of the second superconducting element are parallel to the magnetization vector. 16. The system according to claim 1, further including at least three superconducting elements, each arranged in an annular or polygonal configuration, and wherein the pumping or mixing element includes an annular levitation magnet that is positioned in the vessel such that each of three of the four sides of the levitation magnet are juxtaposed to one of said three superconducting elements. 17. The system according to claim 16, wherein each superconducting element is comprised of a plurality of contiguous or non-contiguous segments. 18. The system according to claim 1, wherein: the pumping or mixing element includes a disc-shaped body for overlying an upper wall of the cavity, said body carrying an annular levitation magnet surrounding a cylindrical sidewall defining the cavity in the vessel; and the superconducting element is annular and positioned in or adjacent to the cavity for interacting with the annular levitation magnet. 19. A system for levitating a permanent magnet having a magnetization vector, comprising: at least two superconducting elements, each positioned on a different side of the magnet and comprised of a plurality of segments of a superconducting material in a superconducting state, each having a crystallographic structure comprising A-B planes and a C-axis, and wherein the A-B planes of each segment are substantially parallel to the magnetization vector; and the C-axes of each segment are substantially peφendicular to the magnetization vector. 20. The system according to claim 19, wherein the levitation magnet forms a part of a rotor, impeller, or other type of pumping or mixing element. 21. The system according to claim 19, wherein the levitation magnet is annular, a first superconducting element is positioned adjacent to the inner surface of the opening in the annular levitation magnet, and a second superconducting element is positioned opposite the first superconducting element. 22. The system according to claim 20, further including a third superconducting element comprised of a plurality of segments of a superconducting material, each having a crystallographic structure comprising A-B planes and a C- axis, and wherein the A-B planes of each segment comprising the third superconducting element are substantially peφendicular to the magnetization vector; and the C-axis of each segment comprising the third superconducting element is substantially parallel to the magnetization vector. 23. The system according to claim 22, wherein the third superconducting element is positioned adjacent to an upper or lower surface of said annular levitation magnet. 24. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid; a magnetic pumping or mixing element positioned in the vessel; at least one superconducting element positioned adjacent to the vessel for levitating the pumping or mixing element; a cryostat including a chamber thermally isolating and/or separating the superconducting element from the vessel and a cooling source thermally linked to said superconducting element; a motive device for rotating said cryostat, including said cooling source and superconducting element. 25. The system according to claim 24, wherein the cooling source in the rotating cryostat is a Stirling-cycle cryocooler and the system further includes a power source for supplying power to the rotating cryocooler by way of a dynamic electrical connection. 26. The system according to claim 25, wherein the dynamic electrical connection is a slip ring. 27. The system according to claim 24, further including at least one bearing supporting the cryostat and permitting low-friction rotational motion, wherein the motive device includes a motor for rotating a pulley that is coupled to the cryostat by an endless belt. 28. The system according to claim 24, further including at least one bearing supporting the cryostat and permitting low-friction rotational motion, wherein the motive device includes a motor having a driven shaft that is coupled to the cryostat. 29. A system for levitating a magnet having a magnetization vector; comprising: first and second superconducting elements, each positioned on a different side of the levitation magnet and comprising a plurality of segments of a superconducting material in a superconducting state, with each segment having a crystallographic structure comprising A-B planes and a C-axis, and wherein: the A-B planes of the segments comprising the first superconducting element are substantially parallel to the magnetization vector; the C-axes of the segments comprising the first superconducting element are substantially peφendicular to the magnetization vector; the A-B planes of the segments comprising the second superconducting elements are substantially peφendicular to the magnetization vector; the C-axes of the segments comprising the second superconducting element are substantially parallel to the magnetization vector. 30. The system according to claim 29, wherein the levitation magnet forms a part of a rotor, impeller, or other type of pumping or mixing element. 31. The system according to claim 29, wherein the levitation magnet is annular, the first superconducting element is positioned adjacent to the inside surface of the opening in the annular levitation magnet or an opposite outside surface thereof, and the second superconducting element is positioned adjacent to the upper or lower outer surface of the levitation magnet. 32. The system according to claim 30, further including a third superconducting element comprised of a plurality of segments of a superconducting material, each segment having a crystallographic structure comprising A-B planes and a C-axis, and wherein: the A-B planes of the segments comprising the third superconducting element are substantially parallel to the magnetization vector; the C-axes of the segments comprising the third superconducting element are substantially peφendicular to the magnetization vector; and the third superconducting element is positioned opposite the first superconducting element. 33. A system for levitating a magnet having a magnetization vector, comprising: first, second, and third superconducting elements, each positioned on a different side of the levitation magnet and comprised of a plurality of segments of a superconducting material in a superconducting state, with each segment having a crystallographic structure comprising A-B planes and a C-axis, and wherein the A-B planes of the segments comprising the first and third superconducting elements are substantially parallel to the magnetization vector; the C-axes of the segments comprising the first and third superconducting elements are substantially peφendicular to the magnetization vector; the A-B planes of the segments comprising second superconducting element are substantially peφendicular to the magnetization vector; the C-axes of the segments comprising the second superconducting element are substantially parallel to the magnetization vector, whereby the levitation of the magnet is both stabilized and enhanced by the orientation of the planes and axes of the superconducting element relative to the magnetization vector. 34. The system according to claim 33, wherein each superconducting element is positioned such that the C-axis passes substantially through the center of the levitation magnet. 35. The system according to claim 34, wherein the levitation magnet is annular. 36. A method of levitating and rotating a magnetic element in a vessel having a cavity, such as for pumping or mixing a fluid, comprising: placing the magnetic element in a vessel concentric with the cavity; levitating the magnetic element above a superconducting element maintained in a superconducting state in accordance with a field cooling protocol and held in an evacuated or insulated chamber positioned adj acent to the cavity in the vessel; and rotating the magnetic element. 37. A method of levitating a magnet having a magnetization vector, comprising: providing first and second elements in a superconducting state in accordance with a field cooling protocol for levitating the magnet, each said superconducting element being positioned on a different side of the magnet and comprising a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C-axis; orienting the A-B planes of the segments comprising the first superconducting element to be substantially parallel to the magnetization vector; orienting the C-axes of the segments comprising the first superconducting element to be substantially peφendicular to the magnetization vector; orienting the A-B planes of the segments comprising the second superconducting elements to be substantially peφendicular to the magnetization vector; and orienting the C-axes of the segments comprising the second superconducting element to be substantially parallel to the magnetization vector. 38. A method of levitating a magnet having a magnetization vector, comprising: providing first and second superconducting elements in a superconducting state in accordance with a field cooling protocol for levitating the levitation magnet, each said superconducting element being positioned on a different side of the levitation magnet and comprising a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C-axis; orienting the A-B planes of the segments comprising the first superconducting element to be substantially parallel to the magnetization vector; orienting the C-axes of the segments comprising the first superconducting element to be substantially peφendicular to the magnetization vector; orienting the A-B planes of the segments comprising the second superconducting elements to be substantially parallel to the magnetization vector; and orienting the C-axes of the segments comprising the second superconducting element to be substantially peφendicular to the magnetization vector. 39. A method for levitating a magnet having a magnetization vector, comprising: providing first, second, and third superconducting elements in a superconducting state in accordance with a field cooling protocol for levitating the magnet, each positioned on a different side of the magnet and comprised of a plurality of segments of a superconducting material, with each segment having a crystallographic structure comprising A-B planes and a C-axis; orienting the A-B planes of the segments comprising the first and third superconducting elements to be substantially parallel to the magnetization vector; orienting the C-axes of the segments comprising the first and third superconducting elements to be substantially peφendicular to the magnetization vector; orienting the A-B planes of the segments comprising second superconducting element to be substantially peφendicular to the magnetization vector; and orienting the C-axes of the segments comprising the second superconducting element to be substantially parallel to the magnetization vector, whereby the levitation of the magnet is both stabilized and enhanced by the orientation of the planes and axes of the superconducting elements relative to the magnetization vector. 40. A pumping or mixing element for a system including a superconducting element for levitating the pumping or mixing element and a plurality of alternating polarity driving magnets for rotating the pumping or mixing element, comprising: a body carrying an annular levitation magnet and a plurality of alternating polarity driven magnets corresponding to the alternating polarity driving magnets. 41. The element according to claim 40, wherein the body is disc-shaped and the annular levitation magnet depends from said body. 42. The element according to claim 41, wherein the driven magnets are embedded in the body in a circular configuration inside of the periphery of the opening in the annular levitation magnet. 43. A cryostat for keeping one or more annular superconducting elements in a superconducting state thermally isolated from a vessel having a cavity formed in a sidewall thereof defining an annular outer portion for receiving a portion of a pumping or mixing element including a levitation magnet, comprising: an outer wall defining an annular chamber for housing the one or more annular superconducting elements, said annular chamber being evacuated or insulated to thermally isolate the superconducting element from the wall, said outer wall including an annular channel for receiving the annular outer portion of the vessel with the portion of the pumping or mixing element. 44. The cryostat according to claim 43, further including a bore or opening concentric with the annular chamber and exposed to the ambient environment for receiving a portion of a motive device for rotating the pumping or mixing element. 45. A system for pumping or mixing a fluid in a vessel positioned on a stable support structure, comprising: a magnetic pumping or mixing element for placement in the vessel; at least one superconducting element for levitating said pumping or mixing element; a cooling source thermally linked to said superconducting element; a motive device for rotating said superconducting element and said cooling source together. 46. The system for pumping or mixing a fluid according to claim 45, further including a cryostat having a wall defining a chamber for thermally isolating the superconducting element, wherein said cryostat is rotated with the superconducting element and the cooling source. 47. The system for pumping or mixing a fluid according to claim 46, wherein said cryostat is supported by a bearing permitting rotational motion, said motive device is a motor, and an endless belt is provided for transmitting the rotary motion produced by said motor to said cryostat to rotate the superconducting element. 48. The system for pumping or mixing a fluid according to claim 45, wherein the cooling source is an electric cryocooler that is coupled to a power source by a dynamic electrical connection. 49. The system for pumping or mixing a fluid according to claim 48, wherein the dynamic electrical connection comprises either a pair of electrical contacts on the rotating cryocooler for engaging a corresponding pair of stationary electrical contacts in communication with the power source or a slip ring. 50. The system for pumping or mixing a fluid according to claim 45, wherein the vessel is supported by a stable support structure positioned between said superconducting element and said magnetic pumping or mixing element. 51. The system for pumping or mixing a fluid according to claim 45, wherein the magnetic pumping or mixing element includes a levitation magnet comprised of plurality of alternating polarity segments and the superconducting element is comprised of a plurality of segments, each having a crystallographic C- axis oriented in the radial direction. 52. The system for pumping or mixing a fluid according to claim 45, wherein: the vessel includes a cavity and the pumping or mixing element is concentric with the cavity; the superconducting element is housed in a vacuum jacket of a cryostat, and the cryostat is at least partially introduced into the cavity such that the superconducting element induces levitation in the pumping or mixing element. 53. The system for pumping or mixing a fluid according to claim 52, wherein the cavity acts as a centering or support post for the concentric pumping or mixing element when in a non-levitated position. 54. The system for pumping or mixing a fluid according to claim 45, wherein the vessel is a flexible bag. 55. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid; a magnetic pumping or mixing element positioned in the vessel; at least one superconducting element positioned adj acent to the vessel for levitating the pumping or mixing element; a cryostat having a wall defining a chamber around the superconducting element, said chamber thermally isolating and/or separating the superconducting element from the vessel, and a cooling source thermally linked to said superconducting element; a motive device for rotating said cryostat. 56. The system according to claim 55, wherein a first wall of the vessel defines a cavity, said wall being formed of a material having a first thickness that is less than the thickness of the material forming a remainder of the vessel. 57. The system according to claim 56, wherein the first wall of the vessel is cylindrical. 58. The system according to claim 56, wherein said cryostat is adapted for insertion into the cavity. 59. The system according to claim 55, wherein the pumping or mixing element includes a combined levitation and driven magnet that is concentric with the superconducting element in the cryostat. 60. The system according to claim 59, wherein said superconducting element is annular. 61. The system according to claim 59, wherein the cryostat is rotatably supported and the motive device is a motor and an endless belt that transfers the rotary motion produced by said motor to said cryostat to cause said superconducting element to rotate. 62. The system according to claim 61, wherein the cryostat is rotatably supported by one or more bearings or bearing assemblies, each of which is in turn supported by a stable support structure. 63. The system according to claim 55 , further including a platform in said chamber for supporting the superconducting element, wherein the platform is thermally linked to the cooling source. 64. The system for according to claim 55, wherein the chamber around the superconducting element is evacuated or insulated. 65. The system according to claim 55, wherein: the pumping or mixing element includes a levitation magnet comprised of a plurality of segments having alternating polarities and a magnetization vector, the superconducting element is comprised of a plurality of segments of a superconducting material having a crystallographic structure comprising A-B planes and a C-axis, and the C-axis of each segment is oriented in the radial direction. 66. The system according to claim 55, wherein the C-axis of each segment of the superconducting element is parallel to the magnetization vector of each said levitation magnet. 67. A container for use in a pumping or mixing system using a levitating pumping or mixing element having an opening, said pumping or mixing element being driven by way of magnetic coupling, comprising: a flexible body for holding a fluid a cavity defined by a cylindrical wall adjacent to said body, wherein the wall passes through the opening to loosely hold the pumping or mixing element in place, such as when transporting the container or in the event of accidental decoupling of the pumping or mixing element. 68. The container according to claim 67, wherein the wall has an oversized portion for preventing the pumping or mixing element from inadvertently lifting from the post. 69. A method of levitating and rotating a magnetic element, such as for pumping or mixing a fluid, comprising: placing the magnetic element in a vessel having a cavity; levitating the magnetic element using a superconducting element; rotating the magnetic element in the vessel about the cavity in a non- contact fashion. 70. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid, said vessel having a cavity formed therein; a magnetic pumping or mixing element positioned in the vessel at a position concentric with the cavity; at least one superconducting element positioned in or adjacent to the cavity for levitating the pumping or mixing element relative to the vessel; a wall defining a chamber around the superconducting element, said chamber thermally isolating and/or separating the superconducting element from the vessel; a cooling source thermally linked to said superconducting element, a motive device for rotating said pumping or mixing element or said superconducting element and said pumping or mixing element, and means for assisting in maintaining a proper position of the levitating pumping or mixing element relative to the cavity. 71. The system according to claim 70, wherein the assisting means includes a first magnetic structure positioned on the pumping or mixing element and a second magnetic structure positioned in or on one of the wall defining the chamber around the superconducting element or the vessel in juxtaposition to the first magnetic structure, wherein the adjacent surfaces of the first and second magnetic structures have like polarities and thus repel each other. 72. The system according to claim 70, wherein the assisting means includes a first magnetic structure positioned on the pumping or mixing element and a second magnetic structure positioned in or on one of the wall defining the chamber around the superconducting element or the vessel in juxtaposition to the first magnetic structure, wherein the adjacent surfaces of the first and second magnetic structures have like polarities. 73. The system of claim 72, wherein the first and second magnetic structures are each ring magnets. 74. The system of claim 72, wherein the first and second magnetic structures are each comprised of arrays of magnets. 75. The system according to claim 70, wherein the pumping or mixing structure includes an opening and defines an annulus with the cavity, whereby upon rotating about the cavity, fluid is drawn through the annulus and out the opening to enhance the pumping or mixing action provided. 76. The system according to claim 70, wherein the superconducting element is comprised of a pair of spaced arrays of superconducting elements and the pumping or mixing element includes spaced arrays of alternating polarity levitation magnets. 77. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid, said vessel having a cavity formed in at least one side thereof; a magnetic pumping or mixing element positioned in the vessel at a position concentric with the cavity and including at least one levitation magnet structure; at least one superconducting element positioned in or adjacent to the cavity for levitating the pumping or mixing element; a wall defining a chamber around the superconducting element, said chamber thermally isolating and/or separating the superconducting element from the vessel; a cooling source thermally linked to said superconducting element, a motive device for rotating either said pumping or mixing element alone or said superconducting element and said pumping or mixing element; a first magnetic levitation-assist structure positioned on the pumping or mixing element; and a second magnetic structure positioned in, inside or on one of the wall defining the chamber around the superconducting element or in, inside, or on the vessel in juxtaposition to the first magnetic levitation-assist structure, wherein the adjacent ends of the first and second magnetic structures have like polarities. 78. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid, said vessel having a cavity formed in at least one side thereof; a magnetic pumping or mixing element positioned in the vessel at a position concentric with the cavity and including first and second arrays of alternating polarity levitation magnets; at least two spaced arrays of superconducting elements positioned in or adjacent to the cavity in juxtaposition to the first and second arrays of alternating polarity levitation magnets; a wall defining a chamber around the superconducting element, said chamber being evacuated or insulated to thermally isolate and/or separate the superconducting element from the vessel; a cooling source thermally linked to said superconducting element, and a motive device for rotating said pumping or mixing element or said superconducting element. 79. The system according to claim 78, further including: means for assisting in maintaining the proper positioning of the levitating pumping or mixing element relative to the cavity. 80. A method of pumping or mixing a fluid, comprising: positioning a pumping or mixing element in a vessel; levitating the pumping or mixing element using a superconducting element positioned in an evacuated or insulated chamber adjacent to the vessel; rotating the pumping or mixing element; using one or more pairs of assist magnets to separately or simultaneously attract or repel the pumping or mixing element to maintain a proper position relative to the vessel. 81. The method according to claim 80, wherein the vessel includes a cavity, the pumping or mixing element is adjacent to and concentric with the cavity, and the step of levitating includes inserting the chamber in which the superconducting element is positioned into the cavity in juxtaposition with the adjacent pumping or mixing element. 82. The method according to claim 80, further including simultaneously attracting and repelling the pumping or mixing element to maintain a proper position relative to the vessel. 83. A system for pumping or mixing a fluid in a vessel capable of holding the fluid, said vessel having a cavity, using a magnetic pumping or mixing element positioned in the vessel concentric with the cavity, comprising: a cryostat including a cooling source thermally linked to a superconducting element and capable of selectively holding the superconducting element below a transition temperature and a chamber that is evacuated or insulated to thermally isolate and/or separate the superconducting element from the vessel, wherein said cryostat is positioned in said cavity but external to the vessel; a first motive device for rotating said cryostat, including said cooling source and superconducting element; and a second motive device for moving the cryostat and hence the superconducting element therein relative to the cavity. 84. The system of claim 83, wherein the vessel includes an engagement structure having a surface that corresponds to a matching surface on the pumping or mixing element and these surfaces are in engagement when the pumping or mixing element is in a non-levitated or resting position. 85. The system of claim 84, wherein the cryostat is moved to a first position adjacent to the magnetic pumping or mixing element in the non-levitated position, the superconducting element is cooled to below the transition temperature to form a magnetic coupling with the magnetic pumping or mixing element, and the cryostat is moved to a second position to separate the matching surfaces and levitate the pumping or mixing element. 86. The system of claim 85, wherein the cryostat is rotated once in the second position such that the levitating pumping or mixing element is rotated as a result of the magnetic coupling formed. 87. The system of claim 86, wherein the superconducting element is warmed or allowed to warm to above the transition temperature to allow the matching surface of the pumping or mixing element to rest on or engage the support surface. 88. A system for pumping or mixing a fluid, comprising: a vessel for holding the fluid having a cavity, said vessel including a tapered or frusto-conical engagement surface; a magnetic pumping or mixing element positioned in the vessel concentric with the cavity and having a surface matching the engagement surface; a device for levitating the pumping or mixing element in the vessel such that the matching surface is separated from the engagement surface; a device for rotating the pumping or mixing element once levitated. 89. The system according to claim 88, wherein the device for levitating the pumping or mixing element comprises a cryostat including a cooling source thermally linked to a superconducting element and capable of selectively holding the superconducting element below a transition temperature and a chamber that is evacuated or insulated to thermally isolate and/or separate the superconducting element from the vessel. 90. The system according to claim 89, wherein said cryostat is positioned in said cavity but external to the vessel and the device for rotating the pumping or mixing element further includes a first motive device for rotating said cryostat, including said cooling source and superconducting element. 91. The system according to claim 89, further including a second motive device for moving the cryostat and hence the superconducting element therein relative to the cavity. 92. As assembly for use in pumping or mixing a fluid using a pumping or mixing element that is selectively levitated, comprising: a vessel for holding the fluid having a cavity, said vessel including a tapered or frusto-conical engagement surface; said magnetic pumping or mixing element positioned in the vessel concentric with the cavity and having a surface matching the tapered or frusto- conical engagement surface, wherein in a non-levitated position, the pumping or mixing elements rests on and is centered relative to the cavity by the engagement established between the matching surfaces, but in a levitated position, the surfaces are separated. 93. A method for levitating a magnetic pumping or mixing element in a vessel for holding a fluid having at least one cavity formed therein, with the pumping or mixing element being generally concentric with the cavity and initially in a non- levitated or resting position, comprising: positioning a superconducting element at a first position in the cavity, but external to the vessel, in alignment with the magnetic pumping or mixing element in the vessel; cooling the superconducting element to below a transition temperature to form a magnetic coupling with the magnetic pumping or mixing element; and moving the superconducting element to a second position in the cavity to induce levitation in the pumping or mixing element. 94. The method of claim 93, further including the step of thermally isolating or separating the superconducting element from the vessel. 95. The method of claim 93, further including the step of centering the pumping or mixing element in the non-levitated position. 96. The method of claim 94, wherein the step of centering comprises: providing a first alignment structure on or adjacent to the vessel; providing a second matching alignment structure on the pumping or mixing element; wherein the first and second alignment structures are in contact when the pumping or mixing element is at a non-levitated position and are separated when the pumping or mixing element is levitated. 97. A system for pumping or mixing a fluid by levitating and rotating a magnetic impeller or rotor in a vessel, comprising: at least one superconducting element for levitating the pumping or mixing element; a cryostat thermally isolating the superconducting element from the ambient environment, said cryostat including a portable Stirling-cycle cryocooler for cooling the superconducting element to below a transition temperature. 98. The system according to claim 97, further including a motive device for rotating the cryostat, including the cryocooler and the superconducting element to induced rotation in the magnetic impeller or rotor.

Inventors: TERENTIEV ALEXANDRE N, TERENTIEV, ALEXANDRE, N.
Applicants: LEVTECH INC, TERENTIEV ALEXANDRE N, LEVTECH, INC., TERENTIEV, ALEXANDRE, N.
Application year: 2001
Main classification: H02N15
IPC codes: A61M1, B01F13, B01F15, F04D13, F04D29, F16C39, H01L39, H02N15