bluuebunny/crossref_metadata_2025 huggingface dataset:
Inverse wave scattering with discontinuous wave speed
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

The inverse scattering problem on the line is studied for the generalized Schrödinger equation (d2ψ/dx2)+k2H(x)2ψ=Q(x)ψ, where H(x) is a positive, piecewise continuous function with positive limits H± as x → ±∞. This equation, in the frequency domain, describes the wave propagation in a nonhomogeneous medium, where Q(x) is the restoring force and 1/H(x) is the variable wave speed changing abruptly at various interfaces. A related Riemann–Hilbert problem is formulated, and the associated singular integral equation is obtained and proved to be uniquely solvable. The solution of this integral equation leads to the recovery of H(x) in terms of the scattering data consisting of Q(x), a reflection coefficient, either of H±, and the bound state energies and norming constants. Some explicitly solved examples are provided.
Unitary braid group representations
Authors: Constantinescu Florin
Published: July 2002

A large class of braid group representations are proven unitary which means a Hermitian bilinear form left invariant by the representation under consideration exists. This generalizes and improves known results on the Burau and Gassner representations. The elementary methods are naturally suggested by the study of monodromy invariant Hermitian forms. Applications to conformal quantum field theory in two dimensions are mentioned.
On the Lie superalgebra embedding C(n+1)⊃B(0,n) and dimension formulas
Authors: Van der Jeugt J.
Published: July 2002

It is shown that the orthosymplectic Lie superalgebras osp (m/2n) have a nonregular subalgebra osp(1/2n). This implies that paraboson operators can be realized as elements of osp(m/2n). The embedding osp(2/2n)⊇osp(1/2n), or, in a different notation, C(n+1)⊇B(0,n), is studied in more detail. In particular, branching rules are determined for all typical and atypical irreducible representations of osp(2/2n) with respect to the subalgebra osp(1/2n). Finally, dimension and superdimension formulas are given for the Lie superalgebras under consideration.
On the Lie algebras generated by two two-forms in Minkowski space–time
Authors: Coll Bartolomé , San José Martínez Fernando
Published: July 2002

In relativity, planes and two-forms play important roles in the description of physical configurations or objects. When these configurations or objects interact, or are superposed, the corresponding planes or two-forms appear associated by pairs, and the relative position of the pair allows the classification of the particular form of the interaction. Here it is shown that in Minkowski space a pair of planes may adopt 35 relative positions. This result allows the almost complete characterization of the dimension of the Lie (sub)algebras (of the Lorentz group) generated by a pair of two-forms in terms of the relative position of their invariant planes. Furthermore, it is shown that, apart from Patera et al. algebras F2 and F5 (for which the eigenvalues’ ratios have to be computed as well), the position of their invariant planes is also sufficient to determine the algebra itself generated by two two-forms.
Decay of correlations and uniqueness of Gibbs lattice systems with nonquadratic interaction
Authors: Antoniouk Alexander Val. , Antoniouk Alexandra Vict.
Published: July 2002

The aim of this paper is to develop the classical lattice models with unbounded spin to the case of nonquadratic polynomial interaction. We demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the fast decay of correlations for Gibbs measure.
Four dimensional quantum topology changes of space–times
Authors: Ding Shuxue , Maeda Yasushige , Siino Masaru
Published: July 2002

Topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant are investigated. As Riemannian manifolds, which describe quantum tunnelings of space–time, constant negative curvature solutions of the Einstein equation, i.e., hyperbolic geometries are considered. Using four dimensional polytopes, one can explicitly construct hyperbolic manifolds with topologically nontrivial boundaries which describe topology changes. These instantonlike solutions are constructed out of 8-cells, 16-cells, or 24-cells and have several points at infinity called cusps. The hyperbolic manifolds are noncompact because of the cusps but have finite volumes. Topology change amplitudes in the WKB approximation in terms of the volumes of these manifolds are evaluated and it was found that the more complicated the topology changes, the more likely are suppressed.
An ill-posed problem of the continuation of transient data for a hyperbolic equation in a three-dimensional inhomogeneous half-space
Authors: Cao Jiasu , He Sailing , Weston Vaughan H.
Published: July 2002

A time-domain data continuation problem for a second order hyperbolic equation in a three-dimensional inhomogeneous half-space, which is a common problem in time-domain layer-stripping, is considered. Two different approaches, namely the local continuation approach and the wave-splitting approach, are used to propagate the surface data (the Dirichlet and Neumann data) to the data at deeper planes. The local continuation approach requires a regularization in order to obtain a stable numerical result. The wave-splitting approach uses larger transverse spatial domain of dependence, and gives reasonably stable results even without any additional smoothing process.
Separation of variables for the constrained flows
Authors: Zeng Yunbo
Published: July 2002

The separation of variables for some constrained flows of soliton hierarchies are shown. The Lax matrix and r-matrix (either constant or dynamical type) are used to construct the separation variables and separation equation for the constrained flows.
Topological field theories and integrable models
Authors: Martina L. , Pashaev O. K. , Soliani G.
Published: July 2002

We show that the classical non-Abelian pure Chern–Simons action is related to nonrelativistic models in (2+1) dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern–Simons fields, associated with the isotropy subgroup of the considered symmetric space. Thus a relation between the Chern–Simons theory and the Davey–Stewartson hierarchy is established in a natural way. The Bäcklund transformations are interpreted in terms of Chern–Simons constraints. Moreover, certain nonintegrable Heisenberg models can be embedded into the pure Chern–Simons theory. The main classical and quantum properties of these systems are discussed.
On the universal Chamseddine–Connes action. I. Details of the action computation
Authors: Iochum Bruno , Kastler Daniel , Schücker Thomas
Published: July 2002

We give a detailed computation of the bosonic action of the Chamseddine–Connes model which we performed using different techniques.
Adler–Kostant–Symes construction, bi-Hamiltonian manifolds, and KdV equations
Authors: Guha Partha
Published: July 2002

This paper focuses a relation between Adler–Kostant–Symes (AKS) theory applied to Fordy–Kulish scheme and bi-Hamiltonian manifolds. The spirit of this paper is closely related to Casati–Magri–Pedroni work on Hamiltonian formulation of the KP equation. Here the KdV equation is deduced via the superposition of the Fordy–Kulish scheme and AKS construction on the underlying current algebra C∞(S1,g⊗C[[λ]]). This method is different from the Drinfeld–Sokolov reduction method. It is known that AKS construction is endowed with bi-Hamiltonian structure. In this paper we show that if one applies the Fordy–Kulish construction in the Adler–Kostant–Symes scheme to construct an integrable equation associated with symmetric spaces then this superposition method becomes closer to Casati–Magri–Pedroni’s bi-Hamiltonian method of the KP equation. We also add a self-contained Appendix, where we establish a direct relation between AKS scheme and bi-Hamiltonian methods.
Integrability, Stäckel spaces, and rational potentials
Authors: Kalnins E. G. , Benenti S. , Miller, Jr. Willard
Published: July 2002

For a variety of classical mechanical systems embeddable into flat space with Cartesian coordinates {xi} and for which the Hamilton–Jacobi equation can be solved via separation of variables in a particular curvalinear system {uj}, we answer the following question. When is the separable potential function v expressible as a polynomial (or as a rational function) in the defining coordinates {xi}? Many examples are given.
Canonical gauges in the path integral for parametrized systems
Authors: Ferraro Rafael , Simeone Claudio
Published: July 2002

It is well known that—differing from ordinary gauge systems—canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation of the new coordinates is equivalent to the fixation of the original ones; this aim can be achieved only if the Hamiltonian constraint allows for an intrinsic global time. Thus the resulting action, describing an ordinary gauge system and allowing for canonical gauges, can be used in the path integral for the quantum propagator associated with the original variables.
Outer trapped surfaces and their apparent horizon
Authors: Kriele Marcus , Hayward Sean A.
Published: July 2002

We give a new definition of “closed outer trapped surface’’ with respect to a hypersurface and show that the boundary of the trapped region (the apparent horizon) is a marginally trapped surface, i.e., has vanishing outer null expansion. While this is an important and well known result, there does not seem to exist a proof in the literature.
Boundary and initial boundary-value problems for separable backward–forward parabolic problems
Authors: Keller Joseph B. , Weinberger Hans F.
Published: July 2002

A backward–forward parabolic equation is considered in a strip which is infinite in the timelike direction, with boundary conditions on the sides of the strip. The unique bounded solution of the problem is given explicitly by separation of variables. In addition, a similar problem in a semi-infinite strip is treated, with initial data at the end of the strip. It is shown that the solution can be represented arbitrarily closely in the maximum norm by a sum of functions obtain by separation of variables.
Solutions of the modified chiral model in (2+1) dimensions
Authors: Ioannidou T. , Zakrzewski W. J.
Published: July 2002

In this paper we deal with classical solutions of the modified chiral model on R2+1. Such solutions are shown to correspond to products of various factors which we call time-dependent unitons. Then the problem of solving the system of second-order partial differential equations for the chiral field is reduced to solving a sequence of systems of first-order partial differential equations for the unitons.
On infravacua and superselection theory
Authors: Kunhardt Walter
Published: July 2002

In the Doplicher, Haag, and Roberts theory of superselection sectors, one usually considers states which are local excitations of some vacuum state. Here, we extend this analysis to local excitations of a class of “infravacuum” states appearing in models with massless particles. We show that the corresponding superselection structure, the statistics of superselection sectors and the energy-momentum spectrum are the same as with respect to the vacuum state. (The latter result is obtained with a novel method of expressing the shape of the spectrum in terms of properties of local charge transfer cocycles.) These findings provide evidence to the effect that infravacua are a natural starting point for the analysis of the superselection structure in theories with long-range forces.
An increasing entropy for a free quantum particle
Authors: van Winter Clasine
Published: July 2002

For a quantum-mechanical particle without interaction, a linear manifold of states is identified that has a preferred time direction pointing to the future. States with the broken time-reversal symmetry are singled out by their behavior under dilations. At positive times such states can be described in terms of a density operator with the property that the trace of its square decreases as the time increases. This density operator determines an entropy that approaches its least upper bound when the time tends to infinity. The expectation value of the dilation operator was negative in the distant past and will be positive in the remote future. This is the irreversible aspect of the time evolution that causes the entropy to increase, although there is no approach to equilibrium. The density operator with increasing entropy is obtained from the usual density operator by an invertible transformation that is compared with the Λ-transformation in the Prigogine theory of irreversible behavior in K-systems and large Hamiltonian systems with many resonances.
Kodaira-Spencer deformation of complex structures and Lagrangian field theory
Authors: Bandelloni Giuseppe , Lazzarini Serge
Published: July 2002

Similar to the Beltrami parametrization of complex structures on a (compact) Riemann surface, we use in this paper the Kodaira-Spencer deformation theory of complex structures on a (compact) complex manifold of higher dimension. According to the Newlander-Nirenberg theorem, a smooth change of local complex coordinates is implemented with respect to an integrable complex structure parametrize by a Beltrami differential. The question of constructing a local field theory on a complex compact manifold is addressed and the action of smooth diffeomorphisms is studied in the BRS algebraic approach. The BRS cohomology for the diffeomorphisms gives generalized Gel’fand-Fuchs cocycles provided that the Kodaira-Spencer integrability condition is satisfied. The diffeomorphism anomaly is computed and turns out to be holomorphically split as in the bidimensional Lagrangian conformal models. Moreover, its algebraic structure is much more complicated than the one proposed in a recent paper [Losev et al. Nuc. Phys. B 484, 196 (1997)].
A linearizing transformation for the Korteweg–de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations
Authors: Dorren H. J. S.
Published: July 2002

It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of (nonlinear) transformations to the solution of the linear differential equation. It is also shown that similar concepts apply to the nonlinear Schrödinger equation. The role of symmetry is discussed. Finally, the procedure which is followed in the one-dimensional cases is successfully applied to find special solutions of higher-dimensional nonlinear partial differential equations.
Hard chaos in magnetic billiards (on the hyperbolic plane)
Authors: Tasnádi Tamás
Published: July 2002

In this paper some results on the local and global stability analysis of magnetic billiard systems, established on two dimensional Riemannian manifolds of constant curvature are presented, with particular emphasis on the hyperbolic plane. For special billiards, possessing a discrete group of (rotational or translational) symmetry, a geometrical theorem, illustrated by numerical simulations, is given on the stability of trajectories with the same symmetry. We also present sufficient criteria for the global hyperbolicity of the dynamics (hard chaos), and give lower estimations for the Lyapunov exponent in terms of the shape of the billiard.
The identities of the algebraic invariants of the four-dimensional Riemann tensor. II
Authors: Sneddon G. E.
Published: July 2002

This paper makes use of several known results from invariant theory to further investigate the invariants of the Riemann tensor and the identities between them. The work also relies on the idea of expressing the Riemann tensor in terms of two complex matrices in the space of self-dual bivectors. It is shown that all invariants that are of even degree in the trace-free Ricci tensor can be written as polynomial functions of a set of 28 invariants. It is believed that this set is a complete set for this type of invariant. Several identities for matrix polynomials of 3×3 matrices are also obtained. These are used to find a large number of the identities between the 28 invariants. While some of these identities are quite complicated, it is shown how, in the general case, they might be used to obtain all invariants from a knowledge of a smaller set.
On the triple sum formula for Wigner 9j-symbols
Authors: Rosengren Hjalmar
Published: July 2002

We give a new proof of the triple sum formula for Wigner 9j-symbols due to Ališauskas and Jucys. The proof uses explicit expressions for the coupling kernels recently introduced by the author. Parts of our results generalize to general recoupling coefficients.
Lax pairs for integrable lattice systems
Authors: Ward R. S.
Published: July 2002

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes the features that are needed to obtain equations which are local on the spatial lattice.
Second-order mixtures in relativistic Schrödinger theory
Authors: Mattes M. , Sorg M.
Published: July 2002

In relativistic Schrödinger theory the mixtures and pure states can be treated from a unified point of view such that a pure state merely emerges as a special case of a mixture. Here the concept of mixture is of purely local nature and therefore the mixture character (degree of order) can change over space and time. Although the general dynamics does not forbid the transitions from mixtures to pure states (and vice versa), the considered models do admit these transitions only in an asymptotic sense. The general concepts and results are demonstrated by considering the four-component Dirac theory for spinning matter over the Robertson–Walker universes. A detailed study is made for a specific subclass of second-order mixtures sharing many of their properties with the pure states (i.e., wave functions).
The Stäckel systems and algebraic curves
Authors: Tsiganov A. V.
Published: July 2002

We show how the Abel–Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivative of the Abel–Jacobi map is just the Stäckel matrix, which determines n-orthogonal curvilinear coordinate systems in a flat space. The Lax pairs, r-matrix algebras and explicit form of the flat coordinates are constructed. An application of the Weierstrass reduction theory allows us to construct several flat coordinate systems on a common hyperelliptic curve and to connect among themselves different integrable systems on a single phase space.
Tunneling of a massless field through a 3D Gaussian barrier
Authors: Modanese Giovanni
Published: July 2002

We propose a method for the approximate computation of the Green function of a scalar massless field φ subjected to potential barriers of given size and shape in space–time. This technique is applied to the case of a 3D Gaussian ellipsoidlike barrier, placed on the axis between two pointlike sources of the field. Instead of the Green function we compute its temporal integral, that gives the static potential energy of the interaction of the two sources. Such interaction takes place in part by tunneling of the quanta of φ across the barrier. We evaluate numerically the correction to the potential in dependence on the barrier size and on the barrier-sources distance.
Classification of differential calculi on Uq(b+), classical limits, and duality
Authors: Oeckl Robert
Published: July 2002

We give a complete classification of bicovariant first order differential calculi on the quantum enveloping algebra Uq(b+) which we view as the quantum function algebra Cq(B+). Here, b+ is the Borel subalgebra of sl2. We do the same in the classical limit q→1 and obtain a one-to-one correspondence in the finite dimensional case. It turns out that the classification is essentially given by finite subsets of the positive integers. We proceed to investigate the classical limit from the dual point of view, i.e., with “function algebra” U(b+) and “enveloping algebra” C(B+). In this case there are many more differential calculi than coming from the q-deformed setting. As an application, we give the natural intrinsic four-dimensional calculus of κ-Minkowski space and the associated formal integral.
A special irreducible matrix representation of the real Clifford algebra C(3,1)
Authors: Scharnhorst K.
Published: July 2002

4×4 Dirac (gamma) matrices [irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)] are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g., due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4×4 Dirac matrices (Majorana representation) which may prove useful in the future. As a by-product, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras.
Well-posed forms of the 3+1 conformally-decomposed Einstein equations
Authors: Frittelli Simonetta , Reula Oscar A.
Published: July 2002

We show that well-posed, conformally-decomposed formulations of the 3+1 Einstein equations can be obtained by densitizing the lapse and by combining the constraints with the evolution equations. We compute the characteristics structure and verify the constraint propagation of these new well-posed formulations. In these formulations, the trace of the extrinsic curvature and the determinant of the 3-metric are singled out from the rest of the dynamical variables, but are evolved as part of the well-posed evolution system. The only free functions are the lapse density and the shift vector. We find that there is a 3-parameter freedom in formulating these equations in a well-posed manner, and that part of the parameter space found consists of formulations with causal characteristics, namely, characteristics that lie only within the lightcone. In particular there is a 1-parameter family of systems whose characteristics are either normal to the slicing or lie along the lightcone of the evolving metric.
Constraints in Hamiltonian time-dependent mechanics
Authors: Mangiarotti L. , Sardanashvily G.
Published: July 2002

The key point of the study of constraints in Hamiltonian time-dependent mechanics lies in the fact that a Poisson structure does not provide dynamic equations and a Poisson bracket of constraints with a Hamiltonian is ill-defined. We describe Hamiltonian dynamics in terms of Hamiltonian forms and connections on the vertical cotangent bundle V*Q→R seen as a momentum phase space. A Poisson bracket {,}V on V*Q is induced by the canonical Poisson bracket {,}T on the cotangent bundle T*Q. With {,}V, an algebra of first and second class time-dependent constraints is described, but we use the pull-back of the evolution equation onto T*X and the bracket {,}T in order to extend the constraint algorithm to time-dependent constraints. The case of Lagrangian constraints of a degenerate almost regular Lagrangian is studied in detail. One can assign to this Lagrangian L a set of Hamiltonian forms (which are not necessarily degenerate) such that any solution of the corresponding Hamilton equations which lives in the Lagrangian constraint space is a solution of the Lagrange equations for L. In the case of an almost regular quadratic Lagrangian, the complete set of global nondegenerate Hamiltonian forms with the above-mentioned properties is described. We construct the Koszul–Tate resolution of the Lagrangian constraints for this Lagrangian in an explicit form.
Schrödinger’s equation and general relativity
Authors: Vuille Chris
Published: July 2002

Schrödinger’s equation is generalized to a space–time four-manifold, using standard concepts from differential geometry and operator replacement. This fourth-order equation, which reduces and specializes to the Klein–Gordon equation in the flat space limit, can also be obtained from a variational principle, and must be solved in tandem with the Einstein field equations with suitable stress energy. The propagator, for large momenta, varies like 1/p4. A further attractive feature is that no external currents or stress energies need be imposed: these arise naturally. A generalization to fields with arbitrary spin is proposed. Solving the equation would lead to a determination of the mass, just as energies are found in solving Schrödinger’s equation. Flat-space plane wave solutions consist of the superposition of two independent waves, which can be interpreted as propagating strings.
Higher-order mechanical systems with constraints
Authors: Krupková Olga
Published: July 2002

A general mathematical theory covering higher-order mechanical systems subject to constraints of arbitrary order (i.e., depending on time, positions, velocities, accellerations, and higher derivatives) is presented, including higher-order holonomic systems as a particular case. Within differential geometric setting on higher-order jet bundles, the concept of a mechanical system (not necessarily regular, or Lagrangian) is introduced to be a class of 2-forms equivalent with a dynamical form. Dynamics are then represented by means of corresponding exterior differential systems. Higher-order constraint structure on a fibered manifold is defined to be a submanifold endowed with a distribution (canonical distribution, higher-order Chetaev bundle). With help of a constraint structure a constraint force is naturally introduced. Higher-order mechanical systems subject to different kinds of higher-order constraints are then geometrically characterized and their dynamics are studied from a geometrical point of view. Regular and Lagrangian systems appear as important particular cases within the general scheme.
Equivalence of the spinor and tensor methods in the positive energy problem
Authors: Pelykh Volodymyr
Published: July 2002

We prove that nontrivial solutions of the Sen-Witten equation with asymptotically flat data set on maximal hypersurface does not equal zero at any point of this hypersurface. On this basis we ascertain the equivalence of Witten’s spinor method and Nester’s tensor method in the positive energy problem in general relativity.
The statistical analysis of Gaussian and Poisson signals near physical boundaries
Authors: Mandelkern Mark , Schultz Jonas
Published: July 2002

We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the pathologies that affect the likelihood ratio and related constructions. Away from nonphysical regions, the results are exactly the usual central two-sided intervals. The construction is based on including the physical constraint in the derivation of the estimator, leading to an estimator with values that are confined to the physical domain.
On the linear stability theory of Bénard–Marangoni convection
Authors: Benguria Rafael D. , Depassier M. Cristina
Published: July 2002

The linear stability of a fluid bounded above by a free deformable surface is studied numerically. When the heat flux is fixed on the free surface and the lower surface is plane and isothermic, oscillatory instabilities, which may occur at lower values of the Rayleigh number than the critical value for the onset of steady convection, are found.
Shear stabilization of the capillary breakup of a cylindrical interface
Authors: Russo Mathew J. , Steen Paul H.
Published: July 2002

A cylindrical interface containing a viscous liquid set into axial motion is subject to a capillary and to a surface-wave instability. Clues from previous studies suggest that, even though both mechanisms separately are destabilizing, under certain circumstances their mutual interaction can lead to a stable interface; shear can stabilize capillary breakup. These clues lead the authors to consider an axial flow through an annular cross section bounded on the inside by a rigid rod and on the outside by a deformable interface. The competition between the two mechanisms is studied through the temporal growth of infinitesimal axisymmetric and nonaxisymmetric disturbances. This examination of temporal stability shows that, indeed, for geometries corresponding to thin annular layers both instabilities can be completely suppressed—disturbances of all wavelengths decay.
A method for constructing a model form for the Boltzmann equation
Authors: Liu Guangjun
Published: July 2002

The model of the Boltzmann equation is a useful tool for researching the motion of rarefied gases. The Bhatnagar, Gross, and Krook (BGK) model has been widely used. Gross and Jackson suggested a hierarchy of models to improve the BGK model, thus introducing nonlinearities. In the present paper, a different method for constructing a model equation is suggested. The main point of this method is that in the two limiting cases, the viscous flow regime and the molecular flow regime, the solutions of the model equation must be the same as those of the Boltzmann equation. The model equation thus constructed is consistent with that obtained in the Gross and Jackson hierarchy with 13 moments. It satisfied the conservation laws and has an H theorem.
Turbulent stratified interfaces
Authors: Shy S. S. , Breidenthal R. E.
Published: July 2002

In a buoyancy reversing system, a stratified interface between two fluids is known to be unstable to strong perturbations only for relatively large values of a buoyancy reversal parameter. This instability leads to accelerating entrainment, i.e., an entrainment process in which both the size of the entraining eddy and the entrainment rate increase rapidly with time. The relevant parameter is defined as the maximum density increase due to mixing of the two fluids normalized by their density difference before mixing. Stirring grid turbulence with zero mean shear in a water tank has been used to further investigate the interaction phenomena between the buoyancy reversal, the stratification, and the type of disturbance in a two-layer buoyancy reversing system. It is found that, even for relatively large buoyancy reversal parameter, the interface remains stable at large Richardson number. In order to explore independently the role of Reynolds number in stratified flows, a second experiment was carried out in which an aqueous turbulent jet impinged on a stably stratified interface (without buoyancy reversal). Laser-induced fluorescence of a pH indicator revealed the region of mixed fluid. A mixing transition was detected for the stratified interface, analogous to that of nonstratified free-shear flows. This seems to explain why the disturbance (with buoyancy reversal) at the stratified interface must be fully turbulent before it triggers the mixing-induced buoyancy reversal instability. A simple model of the interface has three requirements for buoyancy reversal instability: the mixed fluid must be sufficiently dense, the vortices must complete a rotation, and they must be above the mixing transition condition if the fluids are liquids. This implies certain limits on the buoyancy reversal parameter and the Richardson, Reynolds, and Schmidt numbers.
The influence of intermolecular forces on thin fluid layers
Authors: Hocking L. M.
Published: July 2002

An expression for the disjoining pressure for fluid in the shape of a wedge is obtained in a form that incorporates the contact angle. This expression is used to construct the equation for the shape of the free surface of a thin drop of fluid governed by capillarity, gravity, and van der Waals’ forces. The change in the shape and radius of the drop when intermolecular forces are included is found. The dynamical equation for a fluid layer incorporating all these forces and viscosity is obtained, and solved to determine the draw-down of the edge of a layer of fluid resting on a gently inclined plate when the plate is moving in its own plane.
The kinematics of the four-roll mill
Authors: Higdon J. J. L.
Published: July 2002

Numerical computations are employed to study the flow field produced by a four-roll mill. The radius of the cylinders a, the cylinder spacing 2b, and the size 2l of the square container are varied to assess the effects on the kinematics of the flow field. It is found that a ratio of a/b=0.625 with l/b≥3.0 produces the best approximation to a pure extensional flow. With these parameter values, the extension rate remains constant with an error of less than 1% over an axial region x/b≤0.5. By contrast, the commonly accepted design a/b=0.772 suggested by Fuller and Leal [J. Polym. Sci. Polym. Phys. 19, 557 (1981)] produces a variation in extension rate of 50% over the same region. Streamline patterns and velocity gradient error contours are presented for these two designs.
Experimental evidence of a low-dimensional attractor in the coupling of drift- and ion-sound waves
Authors: Ströhlein G. , Piel A.
Published: July 2002

The nonlinear coupling of drift waves with sound waves is studied in a magnetized plasma. The correlation dimension of the reconstructed phase space is determined by the Grassberger–Procaccia algorithm [Physica D 9, 189 (1983)] from various time series of a single variable. In the case of distinct Fourier modes low-dimensional attractors of D2=(3.9±0.2) and D2=(4.8±0.2) appear, whereas for broadband fluctuations a dimension of D2>10 is found. Time-resolved Fourier spectra demonstrate that a four-wave interaction prevails, involving the drift wave, the sound wave, and the upper and lower sidebands of the drift wave. The number of essential modes is compared to the measured dimensions.
A new Langmuir–Child equation including temperature effects
Authors: Martin Pablo , Donoso Guillermo
Published: July 2002

A generalized Langmuir–Child equation has been obtained wherein the temperature effects appear as a function of the parameter τ=T/q(Vp−VR). The space-charge analysis for planar electrodes is done using kinetic theory and the differential equations are solved using the recently published [J. Math. Phys. 26, 705, 1186 (1985); 28, 330 (1987)] two-point quasifractional approximants.
Nonlinear effects in electron cyclotron plasma heating
Authors: Kotel’nikov I. A. , Stupakov G. V.
Published: July 2002

Nonlinear absorption of an ordinary wave propagating through a plasma perpendicular to a unidirectional magnetic field with a frequency close to the electron gyrofrequency is studied. Electron motion is described using a Hamiltonian averaged over rapid gyromotion. The wave evolution in space and time is governed by two equations for the wave amplitude and phase averaged over the wavelength. A case of strong nonlinearity is considered in which the energy absorbed by an electron from the wave is greater than its thermal energy. For this case, the amount of absorbed power is computed analytically assuming it to be small compared with the power of the microwave beam. An effect of nonlinear refraction of the wave is discussed.
The transport of ions in a turbulent plasma
Authors: McWilliams R. , Okubo M. K. , Wolf N. S.
Published: July 2002

Direct, experimental results show cross-field majority species ion transport which is linearly proportional to electrostatic fluctuation levels. Laser-induced fluorescence was used to tag ions within a plasma. The ion diffusive and convective motion could be observed. In a quiet plasma the ion cross-field diffusion agreed with classical predictions. A controlled level of electrostatic turbulence was then introduced into the plasma. The resulting increase in cross-field diffusion was consistent with D⊥≊4(cTe/eB)(δnini0).
Banana fluxes in the plateau regime for a nonaxisymmetrically confined plasma
Authors: Balescu R. , Fantechi S.
Published: July 2002

The banana (or banana-plateau) fluxes, related to the generalized stresses 〈B⋅∇⋅πα(n)〉, 〈BT⋅∇⋅πα(n)〉 have been determined in the plateau regime, for a plasma confined by a toroidal magnetic field of arbitrary geometry. The complete set of transport coefficients for both the ‘‘parallel’’ (ambipolar) and ‘‘toroidal’’ (nonambipolar) banana fluxes was obtained in the 13-moment (13M) approximation, going beyond the previously known expressions in the nonaxisymmetric case. The main emphasis is laid on the structure of the transport matrix and of its coefficients. It is shown that the Onsager symmetry of this matrix partly breaks down (for the mixed electron–ion coefficients) in a nonaxisymmetrically confined plasma.
Effect of impurity density gradients on low-frequency electrostatic fluctuations
Authors: Mattor Nathan
Published: July 2002

For a plasma with impurities, the density scale lengths for electrons and bulk ions become different. Here it is shown that for drift-wave-type instabilities, the electron density scale length arises in the equations of motion (to lowest order in ion gyroradius), not the density scale length of the bulk ions, as is commonly believed. Thus, when comparing experiments with theoretical predictions, it is appropriate to take the drift frequency as ω*eω*e= −(Ti/Te)ω*i = −(kθcTe/eB)d ln n0e/dr, and the parameter ηi≡d ln Ti/d ln n0e (that is, with ne replacing the more commonly used ni in these terms).
The relationship between q profiles, transport, and sawteeth in tokamaks
Authors: Haas F. A. , Thyagaraja A.
Published: July 2002

The purpose of this paper is to investigate the possible relationships between transport properties such as thermal diffusivity and resistivity on the one hand, and the magnetic properties such as q profile and toroidal flux change on the other, in tokamaks that exist under macroscopically quasistationary conditions. It is experimentally well established that when the sources are held constant over times long compared with energy and particle confinement times, tokamak discharges can exist in a quasistationary state with or without periodic sawteeth superposed on the basic equilibrium.

The principal aim of this study is to provide qualitative physical insight into the nature of such states. For simplicity, single-fluid equations are assumed and the analysis is restricted to a cylinder model. The complete set of conservation equations comprising continuity, pressure balance, Ohm’s law, and energy balance are used along with appropriate sources. The conductive energy loss is assumed to occur due to an anomalous thermal diffusivity. Following earlier time-dependent studies of tokamak transport phenomenology due to the authors [Haas and Thyagaraja, Plasma Phys. Controlled Fusion 28, 1093 (1986)], the friction force in the generalized Ohm’s law is assumed to be described by an effective resistivity tensor with its principal axes in the poloidal and toroidal directions. The toroidal resistivity is taken to be of order Spitzer while the poloidal component ηθ is assumed to be anomalously large compared with ηz. A range of phenomena involving Ohmic discharges, auxiliary heated discharges, and noninductively driven currents is investigated. Attention is drawn to the joint implications of the conservation laws and the general forms of the constitutive relations for the structure of the profiles and conditions for the existence of equilibria. In particular, it is shown that βp>1 is achievable in macroscopically steady conditions, only if a sufficiently strong particle source is present in addition to an energy source. It also follows from the analysis that low βp discharges require an anomalous thermal force type term in Ohm’s law, in addition to the anomalous poloidal resistivity.

Recent experimental results on sawtoothing discharges are used to extend the theoretical considerations from strictly steady discharges to those involving sawteeth. A simple nonlinear dynamical model of sawtoothing is constructed and used to illustrate some of the features of sawtooth oscillations. The paper is intended to complement fuller numerical studies. It may help in understanding transport and large-scale relaxation processes like the sawtooth in tokamaks by providing a set of theoretical relations that can be subjected to a direct experimental test. It is a feature of the results that they are independent of the details of the turbulent dynamics, which are ultimately thought to be responsible both for the form and scaling of the constitutive properties considered.
Adiabatic nonlinear interaction of a localized electron cyclotron wave with a plasma
Authors: Farina Daniela , Pozzoli Roberto , Romé Massimiliano
Published: July 2002

A theoretical model for the adiabatic nonlinear interaction of a localized electron cyclotron wave with a plasma is developed on the basis of the analysis of the electron motion in the wave field, through a relativistic Hamiltonian formalism, for a wave frequency close to a cyclotron harmonic in oblique propagation. The investigation of the electron energy transitions due to a single crossing of the radiation beam provides the computation of the absorbed power density. Its behavior is studied in detail in the case of first and second harmonics, where peculiar features are pointed out and are explained in terms of the basic characteristics of the nonlinear interaction process. For the weakly nonlinear case, completely analytical expressions for the absorbed power density are given.
Plasma heating by a purely growing mode driven by cross-field currents in quasiperpendicular collisionless shock
Authors: Yoon Peter H.
Published: July 2002

A purely growing mode propagating exactly parallel to the ambient magnetic field, driven by a cross-field current was first discussed by Chang et al. [Phys. Rev. Lett. 65, 1104 (1990)]. This paper examines the nonlinear evolution of this instability and the resulting heating of the plasma with particular emphasis on application to the quasiperpendicular collisionless shock wave. It is found that when the cross-field current is due to electrons, the instability saturates to extremely low level and the resulting heating becomes insignificant, whereas if the ions are allowed to drift the saturation level of the unstable wave is very large with substantial heating of both electrons and ions. On the other hand, if the electron drift is determined by equilibrium conditions such as the magnetic field and density inhomogeneities and local electric field at the shock front, it is found that the plasma heating becomes greatly enhanced.
Relativistic theory of radiofrequency current drive
Authors: Balescu R. , Metens T.
Published: July 2002

A fully relativistic kinetic theory of rf current drive in a tokamak is developed for both the lower hybrid and the electron cyclotron mechanisms. The problem is treated as a generalization of the classical transport equations, in which the thermodynamic forces are modified by the addition of a rf-source term. In the limit of weak rf amplitude and neglecting toroidal effects (such as particle trapping), explicit analytical expressions are obtained for the rf-generated current, the dissipated power, and the current drive efficiency. These expressions are fully relativistic and are valid over the whole admissible range of frequencies and for all electron temperatures. The relation between efficiency and parallel relativistic transport coefficients is exhibited. The most important relativistic effect is a dramatic broadening of the frequency range over which the rf-generated current is significantly different from zero.
The structure of ideal magnetohydrodynamics with incompressible steady flow
Authors: Gebhardt Ute , Kiessling Michael
Published: July 2002

The equations of ideal magnetohydrodynamics (MHD) with steady incompressible mass flow are known to be integrable to (1) a scalar elliptic partial differential equation (PDE) for a flux function in the case of helically symmetric systems; and (2) a system of two coupled scalar PDE’s in the case of arbitrary nontoroidal geometries. In the present paper it is shown that these integrated equations do not have the same symmetry properties as the original MHD equations; hence are not general enough. The appropriate generalizations are given, and their structure is analyzed. As a result a classification of stationary states of ideal MHD with flow in terms of isomorphisms to simpler MHD systems is obtained. Under certain mild conditions the involved differential operators can be mapped smoothly to considerably simpler ones; however, the mapping is not necessarily analytic. This transformation technique allows the construction of complicated MHD solutions with flow out of simpler MHD solutions. Some explicit examples are presented.
Selective decay within a one-field model of dissipative drift-wave turbulence
Authors: Naulin V. , Spatschek K. H. , Hasegawa A.
Published: July 2002

It is shown that one-field models can cover the selective decay in density and potential when the density is calculated appropriately.
Distributed absorption model for moderate to high laser powers
Authors: De Groot J. S. , Estabrook K. G. , Kruer W. L. , Drake R. P. , Mizuno K. , Cameron S. M.
Published: July 2002

An analytic model is presented of a planar plasma heated by moderate to high laser powers such as are used to drive fusion pellets. Unlike previous models, this model explicitly includes the temporal evolution of the heat conduction region. It is shown that previous steady-state models apply only to a narrow range of the parameters (laser energy flux and pulse width) used in laser pellet fusion. The new model is shown to agree with flux-limited hydrodynamics simulations. The model and hydrodynamic simulations for classical heat transport show that the mass ablation rate and ablation pressure are essentially independent of laser wavelength for parameters relevant to laser fusion.
Ideal ballooning stability near an equilibrium magnetic island
Authors: Hegna C. C. , Callen J. D.
Published: July 2002

The stability properties of ideal ballooning modes on toroidal flux surfaces near a quasistatic magnetic island are examined. On these surfaces, magnetic field-line trajectories tend to bunch on that part of the magnetic surface closest to the X point of the magnetic island. Because of this preferential bunching, the stabilizing effect of field-line bending due to magnetic shear can be reduced. Eigenfunctions localized in helical angle near the X point and in poloidal angle on the bad curvature side of the tokamak are more susceptible to ballooning instability than are modes in corresponding equilibria without the magnetic island. For a slowly growing island, a growing number of flux surfaces located near the separatrix become ballooning unstable. Secondary ballooning instabilities may play a part in the crash phase of sawteeth or macroscopic island dynamics.