Abstract:
A flexible ribbon speaker is disclosed. A flexible conductive membrane is placed within an appropriately shaped magnetic field formed by a flexible magnet assembly in such a way that current passing through the membrane interacts with the magnetic field, causing the membrane to vibrate and produce sound. The design of the membrane and of the magnet assembly, along with additional structural elements allows the speaker to be bent. Due to its flexibility, the ribbon speaker of the invention can be located in places that were hitherto inconvenient.

Description:
FIELD AND BACKGROUND OF THE INVENTION  
         [0001]    The present invention relates to acoustic transducer systems, and more specifically, to flexible ribbon speakers.  
           [0002]    There exist many types of speakers, devices that convert electrical signals to sound. One type of speaker that is exceptionally popular amongst music connoisseurs is the ribbon speaker. Ribbon speakers operate by passing the output current I of an amplifier through conductors placed in a magnetic field B. As a result of the force F=I×B generated, the conductors vibrate, transducing the electrical signal to an acoustic signal.  
           [0003]    The operation of a ribbon speaker can best be understood with reference to FIG. 1. The ribbon speaker  10  comprises a substantially planar membrane  12  supported within a rigid frame  14  and disposed within magnetic field  16  produced by two magnets  18   a  and  18   b.  In FIG. 1, the north pole of magnet  18   a  faces the thin edge of membrane  12  and is indicated by the notation “N”. The south pole of magnet  18   b  is hidden from view in FIG. 1, but also faces the thin edge of membrane  12  and opposes the north pole of magnet  18   a.  Since the opposite poles of the magnets face each other, magnetic field  16  is horizontal and parallel to the surface of membrane  12 . Membrane  12  is conductive. When current  20 , corresponding to an audio signal, passes through membrane  12 , force  22  is produced, causing membrane  12  to vibrate, producing acoustic energy.  
           [0004]    When designing a membrane, a number of factors must be considered. To reduce the amount of heat generated and to generate the maximal force at a given potential, electrical resistance should be low. The mass of the membrane should be low for maximal conversion efficiency and greatest response. Typical membranes, such as in U.S. Pat. No. 4,550,228, are aluminum or beryllium foils. There are membranes made of lightweight nonconductive sheets with conductors cemented to their surfaces, as described in U.S. Pat. No. 3,919,499 or coated with a conductive material. Multilayer membranes have been described in U.S. Pat. No. 5,212,736 and in U.S. Pat. No. 5,953,438.  
           [0005]    The greatest disadvantage of the ribbon speakers known to the art is that they are heavy constructions, having massive rigid frames. Ribbon speakers are thus generally inappropriate for use in motor vehicles where they may be considered a safety hazard. Similarly, ribbon speakers are not unobtrusive. When placed in a home, an interior designer must plan the arrangement of the home around the ribbon speakers. Ribbon speakers are expensive and thus not readily available to the general public.  
           [0006]    It would be highly advantageous to have a ribbon speaker that is cheaper to produce than existing ribbon speakers. It would be advantageous that such a ribbon speaker would have a structure that gives more freedom to designers to place the ribbon speaker as desired.  
         SUMMARY OF THE INVENTION  
         [0007]    The above and other objectives are achieved by the flexible ribbon speaker provided by the present invention.  
           [0008]    In general a flexible ribbon speaker  24  of the present invention, depicted in FIG. 2 a,  is made up of two parts: a flexible magnet assembly  26  and a flexible planar membrane  28  of which at least part is electrically conductive. The two parts of speaker  24  must be so associated that a) magnetic field  30  produced by flexible magnet assembly  26  is substantially parallel to the electrically conductive parts of membrane  28 ; b) conducting elements  32  of membrane  28  are situated in areas where magnetic field  30  is relatively strong; and that c) when speaker  24  is bent, FIG. 2 b,  conducting elements  32  of membrane  32  remain in the proper position relative to magnetic field  30 .  
           [0009]    Further, current flowing through the membrane at any point is preferably perpendicular to the magnetic field produced by the flexible magnet assembly.  
           [0010]    In some instances the third requirement leads to the necessity of adding structural elements to hold the membrane in the proper position. In other instances, the requirement that the magnetic field be substantially parallel to the membrane leads to the necessity of adding structural elements to limit the flexibility of the speaker in the direction parallel to the magnetic field.  
           [0011]    Although many possibilities exist, the flexible magnet assembly is most preferably selected from one of two main types of assemblies.  
           [0012]    The first preferable magnet assembly is an arrangement of flexible magnets. Flexible magnets are well known to one skilled in the art, and are usually made of magnetic materials such as ferrites or Nd—Fe—B mixtures (e.g. Magnequench made by Delco Remy a division of General Motors (Anderson, Ind.)) dispersed in a flexible matrix such as rubber or polyvinylchloride. Flexible magnets are commercially available in many shapes and sizes, for instance, from The Electrodyne Company (Batavia, Ohio) or Group Arnold (Marengo, Ill.).  
           [0013]    The second preferred type of magnet assembly is an arrangement of non-flexible magnets on a non-magnetic holder. In the arrangement depicted in FIG. 3, the holder is a linear chain  34  made of links  36  to which a plurality of magnets  38  is attached in a row along the length of chain  34 . Chain  34  is most preferably a chain that is inflexible in one direction, such as a motorcycle drive chain. In contrast, in the arrangement depicted in FIG. 4, the holder is a flexible two-dimensional construction  40 , for instance a wire mesh web such as a chain-link fence, on which a plurality of magnets  42  is attached in the form of a two-dimensional array of magnets. Another possibility is that  40  is a flexible sheet or a woven fabric such as cloth to which magnets  42  are attached.  
           [0014]    The membrane used for a speaker of the present invention can be any one of the membranes with which one skilled in the art is acquainted. In general the membranes are very thin and have a low mass.  
           [0015]    A first preferred type of membrane is a conductive sheet, most preferably made of aluminum or beryllium foil (see, for example, U.S. Pat. No. 5,212,736). It is also possible to use a foil or sheet of substantially non-conductive material that is coated or laminated with a conductive material. To lend strength and rigidity along the axis of the membrane that is parallel to the magnetic field and flexibility in the axis that is perpendicular to the magnetic field, it is often advantageous to use a corrugated sheet, film or foil.  
           [0016]    A second preferred type of membrane is a non-conductive substrate in the form of a sheet held within the magnetic field. Such a sheet can be a polymer film, for example a polyamide film, as described in U.S. Pat. No. 4,303,711, a polyimide film such as Kapton (E. I. DuPont de Nemours &amp; Co., Inc., Wilmington, Del.)) or a polyester film such as Mylar (E. I. DuPont de Nemours &amp; Co., Inc., Wilmington, Del.). Onto the non-conductive sheet discrete conductive paths, such as aluminum or copper wires are attached, for example, by adhesive. If wires are attached to the membrane, it is most preferable to use flat wires that can dissipate heat efficiently and, due to the I greater contact surface area, are bound more robustly to the membrane.  
           [0017]    Further, there are in general two preferred arrangements of the magnet assembly relative to the membrane. The first preferred arrangement is one where the magnet assembly is substantially within the plane defined by the membrane, coplanar and to the sides of the membrane, as depicted in FIG. 2 a.  The second preferred arrangement is one where the magnet assembly is substantially contained within a plane in front or behind the membrane and parallel to the plane defined by the membrane. In the second preferred arrangement it is often necessary to interpose some structure between the membrane and the magnet assembly to prevent incidental contact between the membrane which may damage the membrane or cause a rustling sound. Such a structure is preferably a soft material such as woven cloth or felt. This structure can be a single sheet or discrete pieces. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0018]    The invention is herein described, by way of example only, with reference to the accompanying drawings, where:  
         [0019]    [0019]FIG. 1 (prior art) is a cut-away schematic depiction of a typical ribbon speaker;  
         [0020]    [0020]FIG. 2 a  is a general schematic depiction of a speaker of present invention in a flat configuration;  
         [0021]    [0021]FIG. 2 b  is a general schematic depiction of the speaker of FIG. 2 a  in a bent configuration;  
         [0022]    [0022]FIG. 3 is a schematic depiction of one type of magnet assembly of the present invention, made up of a chain with attached magnets;  
         [0023]    [0023]FIG. 4 is a schematic depiction of one type of magnet assembly of the present invention, made up of a wire mesh web with an attached two-dimensional array of magnets;  
         [0024]    [0024]FIG. 5 is a schematic depiction of a speaker of the present invention having a corrugated aluminum membrane flanked by two flexible bar magnets;  
         [0025]    [0025]FIG. 6 is a partial schematic depiction of a speaker of the present invention having a non-conductive polyamide membrane to which aluminum conductors have been cemented;  
         [0026]    [0026]FIG. 7 a  is a partial schematic depiction of a speaker of the present invention having a chain of non-flexible magnets as the magnet assembly;  
         [0027]    [0027]FIG. 7 b  is an enlarged view of the U-shaped bracket holding apart the links of the magnetic assembly of FIG. 7 a;    
         [0028]    [0028]FIG. 8 is a partial schematic depiction of a speaker of the present invention having an arrangement of four flexible bar magnets and a Mylar membrane to which a serpentine aluminum conductor has been cemented;  
         [0029]    [0029]FIG. 9 is a schematic depiction of a speaker of the present invention having a planar magnet with strips of alternating magnetic polarity and a Kapton membrane;  
         [0030]    [0030]FIG. 10 a  is a schematic depiction of a speaker of the present invention having a wire mesh web with an attached two-dimensional array of magnets as the magnet assembly, hanging from a ceiling;  
         [0031]    [0031]FIG. 10 b  is an enlarged view of the two-dimensional array of magnets of FIG. 10 a;    
         [0032]    [0032]FIG. 11 is a schematic depiction of a speaker of the present invention made up of a perforated flexible sheet to which a plurality of flexible bar magnets is attached, overlain with a Kapton membrane with a serpentine conductive path; and  
         [0033]    [0033]FIG. 12 is a schematic depiction of a speaker of the present invention made up of a soft material sandwiched between a planar magnet with strips of alternating magnetic polarity and a Kapton membrane with a serpentine conductive path. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0034]    The principles and operation of a system according to the present invention may be better understood with reference to the drawings and the accompanying description of the embodiments below, in which like reference numerals refer to like parts throughout all of the figures. It is to be understood that the descriptions below are illustrative, and are not intended to restrict the present invention to the specific details set forth below.  
         [0035]    In FIG. 5, a first embodiment of the present invention, speaker  44 , is depicted. Membrane  46  is made of corrugated aluminum foil. Along the two vertical edges of membrane  46  are two flexible bar magnets,  48   a  and  48   b.  The north pole of magnet  48   a  and the south pole of magnet  48   b  are placed to oppose each other, generating a horizontal magnetic field  50 . In order to ensure that membrane  46  remains within magnetic field  50 , membrane  46  is attached to magnets  48   a  and  48   b  with clasps  52 . Rigid crosspieces  54   a  and  54   b  connect magnet  48   a  to magnet  48   b.  This construction leads to speaker  44  being rigid in the vertical dimension but flexible in the horizontal dimension.  
         [0036]    An amplifier  56  produces a current  58  that enters speaker  44  through an input plug  60  to membrane  46 . Current  58  travels through membrane  46  vertically, interacting with magnetic field  50  to produce a force  62 , vibrating membrane  46  to produce sound. The circuit is completed through an output plug  64  back to amplifier  56 .  
         [0037]    When a force is applied to bend speaker  44  horizontally, the flexibility of membrane  46  and of magnets  48   a  and  48   b  allows speaker  44  to bend. Clasps  52  keep membrane  46  within magnetic field  50  and maintain the structural integrity of speaker  44 . The rigidity of cross pieces  54   a  and  54   b  resists vertical bending of speaker  44 .  
         [0038]    In FIG. 6, a second embodiment of the present invention, a speaker  66  is depicted. Speaker  66  is of the same general construction as speaker  44  excepting that membrane  68  is a non-conductive film of polyamide. For clarity, not shown are bar magnets, clasps and rigid crosspieces resembling magnets  48   a  and  48   b,  clasps  52  and rigid crosspieces  54   a  and  54   b  respectively. Flat aluminum strips  70  on the surface of membrane  68  conduct current  58  through magnetic field  50  to produce force  62 , causing membrane  68  to vibrate.  
         [0039]    In FIG. 6, membrane  68  is illustrated as being transparent so as to allow viewing of a plurality of non-conductive rigid secondary cross-members  72 . Secondary cross members  72  are connected between the bar magnets of speaker  66  and lend further rigidity to the speaker in the direction perpendicular to magnetic field  50 . To ensure that membrane  68  remains properly positioned when speaker  66  is bent, secondary cross-members  72  are fashioned with protrusions  74 . Attached to the tips of protrusions  74  is a layer of soft material such as felt to allow non-damaging incidental contact between membrane  68  and protrusions  74 .  
         [0040]    In FIG. 7 a,  a third embodiment of the present invention, a speaker  76  is depicted. Speaker  76  is of the same general construction as speaker  66 , excepting that magnetic field  50  is produced by two chains  78   a  and  78   b.  Chains  78   a  and  78   b  are fashioned as described above and in FIG. 3. To each of chains  78   a  and  78   b  are attached a multiplicity of small non-flexible magnets  80  attached in a row, so that like poles of all magnets  80  of one chain face in the same direction. Chains  78   a  and  78   b  are complementary in that the north pole of all magnets  80  attached to chain  78   a  face towards membrane  68  and the south pole of all magnets  80  attached to chain  78   b  face towards membrane  78 . In this way magnetic field  50  produced by chains  78   a  and  78   b  is parallel to membrane  68 . Along each of chain  78   a  and  78   b  are clasps  52 , configured to hold membrane  68 .  
         [0041]    U-shaped brackets  82  are configured to hold chains  78   a  and  78   b  apart despite the attractive force of magnetic field  50 . FIG. 7 b  is a detailed view of chains  78   a  and  78   b  Connected by U-shaped bracket  82  are links  84  attached to magnet holder  86  to which a magnet  80  is attached. To ensure that membrane  68  remains within magnetic field  50  when speaker  76  is bent, a plurality of pairs of woolen threads  84  are tied to opposing links  84  and pass on either side of membrane  68 .  
         [0042]    In FIG. 8, a fourth embodiment of the present invention, speaker  86  is depicted. The magnet assembly is made of a plurality of vertically placed flexible bar magnets  88   a,    88   b,    88   c,  and  88   d  flanked by flexible side bars  90   a  and  90   b.  A rigid upper crosspiece  92  connects magnets  88   a,    88   b,    88   c,    88   d  and side-bars  90   a  and  90   b.  Not shown are a lower crosspiece and secondary cross-members resembling upper crosspiece  92  and secondary cross-members  72  respectively. Magnets  88   a,    88   b,    88   c  and  88   d  are arranged so that like poles of adjacent magnets face each other. Magnetic field  94  has four important components  94   a,    94   b,    94   c,  and  94   d.  Each component produced starts from one pole of one magnet and ends at the opposite pole of the same magnet. A flat aluminum serpentine conductor  96  is attached to the surface of a non-conducting Mylar membrane  98 . Serpentine conductor  96  is fashioned with a plurality of long segments  100   a,    100   b,    100   c  and  100   d  in the vertical dimension, that is perpendicular to magnetic field components  94   a,    94   b,    94   c  and  94   d  and parallel to magnets  88   a,    88   b,    88   c  and  88   d.  Long segments  100   a,    100   b,    100   c  and  100   d  are connected to each other by short segments of serpentine conductor  96 . Long segment  100   a  passes over magnet  88   a,  long segment  100   b  passes over magnet  88   b,  long segment  100   c  passes over magnet  88   c,  and long segment  100   d  passes over magnet  88   d.  Due to the serpentine shape of conductor  96 , current passing through long segments  100   a  and  100   c  travels in one direction whereas current passing through long segments  100   b  and  100   d  travels in the opposite direction. Due to the orientation of magnets  88   a,    88   b,    88   c  and  88   d,  magnetic field components  94   a  and  94   c  produced by magnets  88   a  and  88   c  respectively are in one direction whereas magnetic field components  94   b  and  94   d  produced by magnets  88   b  and  88   d  respectively are in the opposite direction. The forces produced by the product of currents in segments  100   a,    100   b,    100   c  and  100   d  passing through magnetic field components  94   a,    94   b,    94   c  and  94   d  respectively are all in the same direction, leading to effective vibration of membrane  98 .  
         [0043]    Clasps  52  are connected to sidebars  90   a  and  90   b  and are configured to hold membrane  98  in proximity to magnets  88   a,    88   b,    88   c  and  88   d.    
         [0044]    As in speaker  44  depicted in FIG. 5, upper crosspiece  92  and a lower crosspiece (not shown) are configured to connect the top and bottom ends of magnets  88   a,    88   b,    88   c,    88   d  and sidebars  90   a  and  90   b.  Rigid secondary cross-members (not shown) resembling secondary cross-members  72  are attached to sidebars  90   a  and  90   b  and are interposed between magnets  88   a,    88   b,    88   c,    88   d  and membrane  98 . This interposition prevents incidental contact between membrane  98  and any one of magnets  88   a,    88   b,    88   c  or  88   d.  As described for speaker  66  and in FIG. 6, on the secondary cross-members are protrusions to which a layer of soft material such as felt is attached to allow non-damaging incidental contact between membrane  98  and the protrusions. The rigidity of upper crosspiece  92 , of the lower cross-piece, and of the secondary cross-members prevents speaker  86  from bending in the vertical direction.  
         [0045]    In FIG. 9, a fifth embodiment of the present invention, a speaker  102  is depicted. A one-piece planar magnet  104  is made in accordance with the teachings of U.S. Pat. No. 5,424,703 so that planar magnet  104  is magnetized to have a plurality of parallel strips, where adjacent strips have opposite magnetic polarity. Membrane  98  is a sheet of non-conductive Kapton film with a serpentine conductor  96  passing in a manner analogous to that described for speaker  86  of FIG. 8 through the magnetic fields produced by magnet  104 . Flexible holders  106   a  and  106   b  are formed each with two parallel grooves, back groove  108  and front groove  110 . Magnet  104  is inserted into and held in place by back grooves  108  of holders  106   a  and  106   b  whereas membrane  98  is inserted into and held in place by front grooves  110  of holders  106   a  and  106   b.  Rigid crosspieces  112   a  and  112   b  hold flexible holders  106   a  and  106   b  together and prevent bending of speaker  102  along the vertical axis. Disposed on the surface of magnet  104  is a plurality of non-conducting protrusions  114  to prevent incidental contact between magnet  104  and membrane  98  when speaker  102  is bent. The interaction of a current passing through serpentine conductor  96  and the magnetic field of magnet  104  is analogous to that of speaker  86  that has been described hereinbefore and is therefore not discussed in further detail.  
         [0046]    In a variation of speaker  102 , incidental contact between membrane  98  and magnet  104  is prevented by the interposition of a sheet of a soft material such as felt or fabric instead of non-conducting protrusions  114 .  
         [0047]    In FIG. 10 a,  a sixth embodiment of the present invention, a speaker  116  is depicted suspended from a ceiling  118  by hooks  120 . A DVD player  122  transmits a music signal  124  through an infrared transmitter  126 . An amplifier  128  receives the signal from infrared transmitter  126 . Amplifier  128  receives power from an electrical outlet  130  and feeds signal current to speaker  116  through a plug  132 , producing music. The shape and the hanging position of speaker  116  from ceiling  118  are esthetically pleasing.  
         [0048]    Magnet assembly  134  and membrane  98  are attached to a support rod  136  so that the attachment points of membrane  98  and magnet assembly  134  are close together. In proximity to support rod  136 , membrane  98  and magnet assembly  134  are separated by a non-conducting spacer bar  138  and hang downwards as a result of gravitational forces. A non-conducting spacer ridge  140  is attached to the bottom edge of magnet assembly  134  to prevent contact between membrane  98  and magnet assembly  134 .  
         [0049]    Membrane  98  is made of polyamide and has an attached serpentine conductor  96 . Due to the low intrinsic weight of a polyamide film, a weight  142  is added to ensure that membrane  98  hangs downwards and does not crinkle or warp and that membrane  98  is held in contact with spacer bar  138  and spacer ridge  140 .  
         [0050]    Magnet assembly  134  is a flexible wire mesh web similar to that described in FIG. 4. In FIG. 10 b,  details of magnet assembly  134  are depicted. Magnets  144  of each vertical column are oriented so that the poles thereof are all oriented in one direction and in opposition to the poles of magnets  144  of an adjacent vertical column. A magnetic field  94  with a component parallel to the plane of magnet assembly  134  is produced over the spaces between two adjacent vertical columns of magnets  144 , similar in form to magnetic field  94  of speaker  86  described in FIG. 8.  
         [0051]    Serpentine conductor  96  of membrane  98  is made so that long segments  100  pass through magnetic field  94  produced over the spaces between two adjacent vertical columns of magnets  144  indicated in FIG. 10 b  by arrows. The interaction of a current passing through serpentine conductor  96  and magnetic field  94  is analogous to that of speaker  86  that has been described hereinbefore and is therefore not discussed in further detail.  
         [0052]    Attached to each magnet  144  is a non-conducting protrusion  146  made of a soft material. Protrusions  146  prevent membrane  98  from making incidental contact with magnets  144 .  
         [0053]    Exclusively for illustrative purposes, magnet assembly  134  is a 70 centimeter square, with 729 magnets  144  arranged in a 27 by 27 magnet matrix. Each magnet  144  is a 2 centimeter square. Each magnet  144  is separated from adjacent magnets  144  by 0.5 cm so that each of the 26 vertical spaces between two adjacent vertical columns of magnets  144  is 0.5 cm wide. Serpentine conductor  96  has 26 long vertical segments  100 , each long segment  100  located on membrane  98  so that when membrane  98  hangs in position parallel to magnet assembly  134  as illustrated in FIG. 10 a,  the long segments are within the components of magnetic field  94  that are present above spaces between two adjacent vertical columns of magnets  144 .  
         [0054]    In FIG. 11 a seventh embodiment of the present invention, a speaker  148  is depicted. On a flexible sheet  150  with a plurality of perforations  152  are attached a plurality of flexible bar magnets  154 . Magnets  154  are attached in parallel to each other with one pole facing sheet  150  and the opposite pole facing upwards. Magnets  154  are arranged so that opposite poles of adjacent magnets face upwards so as to produce magnetic field  94  similar to the magnetic fields produced by magnet  104  of speaker  102  as described above and in FIG. 9. To the upper surface of each of magnets  154  is attached a layer of soft material  156 . Attached to two opposing ends of sheet  150 , parallel to and flanking magnets  154 , are two flexible side-bars  158 . Attached to side-bars  158 , for example by adhesive, is a Kapton membrane  98  (illustrated in FIG. 11 as being transparent). Membrane  98  lies over magnets  154  and makes contact with soft material  156 . On membrane  98  is attached a serpentine conductor  96 . Membrane  98  is attached to side-bars  158  and lain over magnets  154  in such a way so that long segments  100  of serpentine conductor  96  are located above an area between two magnets  154 , a region where magnetic field  94  is substantially parallel to membrane  98 . The interaction of a current passing through serpentine conductor  96  and magnetic field of magnet  94  is analogous to that of speaker  86  that has been described hereinbefore and is therefore not discussed in further detail.  
         [0055]    To lend rigidity to speaker  148  in the dimension perpendicular to magnets  154 , a plurality of rigid plastic bars  160  is attached to the underside of sheet  150 .  
         [0056]    In FIG. 12 an eighth embodiment of the present invention, a speaker  162  is depicted. A one-piece planar magnet  104  having parallel strips of alternating magnetic polarity, similar to magnet  104  of speaker  102  as described above and in FIG. 9. On top of magnet  104  is a sheet of a soft material  164  such as felt or fabric. On top of sheet of soft material  164  is a membrane  98  made of Kapton. The edges  166 , parallel to the parallel strips of magnet  104 , of magnet  104 , soft material  164  and membrane  98  are joined together, for example, by adhesive. Attached to membrane  98  is a serpentine conductor  96 . As described for speaker  148 , membrane  98  is placed in such a way that long segments  100  of serpentine conductor  96  are located above the area where strips of opposing magnetic polarity of magnet  104  abut. The interaction of a current passing through serpentine conductor  96  and the magnetic field of magnet  104  is analogous to that of speaker  86  that has been described hereinbefore and is therefore not discussed in further detail.  
         [0057]    The thickness and compressibility of soft material  164  is chosen so that soft material  164  ensures that there is no incidental contact between magnet  104  and membrane  98 .  
         [0058]    It is clear to one skilled in the art that speakers  148  and  162  are exceptionally simple and cheap to produce in many sizes and shapes.  
         [0059]    While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made.