bluuebunny/crossref_metadata_2025 huggingface dataset:
Covariantly constant tensors and holonomy structure in general relativity
Authors: Hall G. S.
Published: July 2002

This paper attempts to give a comprehensive discussion of space-times that admit vector fields or second-order symmetric or skew-symmetric tensor fields which are covariantly constant or recurrent. The relationship between such space-times M and their holonomy group is given.
Quadratic Poisson structures
Authors: Bhaskara K. H. , Rama K.
Published: July 2002

An algebraic characterization of homogeneous quadratic Poisson structures is obtained and some methods to construct examples are given. A sufficient condition for the commutativity of a homogeneous quadratic Poisson structure and the Lie–Poisson structure on the dual of a Lie algebra is given. Quadratic Poisson structures on Lie algebras are discussed. A new Poisson structure is introduced and its application is shown.
Spin projection of Fermion coherent states
Authors: Weiner Brian , Deumens Erik , Öhrn Yngve
Published: July 2002

SU(2) spin-dependent Thouless coherent states are defined by the action of SU(2) on fermionic independent particle states considered as Thouless coherent states. Expressions for the reproducing kernel for this family of spin-dependent coherent states is obtained, which is then used as a generating function for kernels of spin-adapted Thouless coherent states. Using such states it is shown how to obtain spin-projected time-dependent Hartree–Fock equations of motion and spin-projected Hartree–Fock equations both within the Thouless parametrization.
Functions of two-dimensional Bravais lattices
Authors: Folkins Ian
Published: July 2002

The symmetries of a function are considered that takes as its argument an arbitrary two-dimensional Bravais lattice, represented by a 2×2 matrix. Rotating the lattice corresponds to multiplying its matrix on the right by an element of SO(2). Matrices related by left multiplication of an element of SL(2,Z) also refer to the same lattice. Functions of matrices having these two symmetries possess an expansion known as the Roelcke–Selberg decomposition. This decomposition characterizes the function in terms of a set of coefficients (the discrete spectrum) and a function defined on a line in the complex plane (the continuous spectrum). When the function of the lattice refers to its energy, the continuous spectrum can be related to an interatomic potential between the atoms of the lattice. The decomposition can be considered a Landau theory of a strained two-dimensional Bravais lattice, valid for arbitrarily large strains, expanded about any structure. This type of theory may be useful in determining the energies of a material for many different lattice configurations from a knowledge of the energy at only a few of them.
C-integrable nonlinear partial differentiation equations. I
Authors: Calogero F. , Xiaoda Ji
Published: July 2002

A technique to generate C-integrable nonlinear partial differentiation equations (PDEs) (i.e., nonlinear PDEs linearizable by an appropriate Change of variables) is reported, and several examples of such PDEs are exhibited.
Symmetry scattering
Authors: Wehrhahn R. F. , Smirnov Yu. F. , Shirokov A. M.
Published: July 2002

Scattering connected with the symmetry of a system is treated. Symmetries related to Riemannian symmetric spaces of the noncompact type are studied. Several examples are discussed.
D
5 affine toda field theory
Authors: Cho H. S. , Kim J. D. , Koh I. G.
Published: July 2002

The physical channel with a cubic pole in the D5 affine Toda field theory is studied, showing the consistency with the S matrix result up to β4 order. It is found that the interplay between the Landau singularity and renormalization plays a very crucial role in the physical channels.
On pararelativistic quantum oscillators
Authors: Beckers J. , Debergh N. , Nikitin A. G.
Published: July 2002

Different choices of matrices characterizing p=2 parafermions are analyzed in connection with the description of relativistic spin-one particles through the Kemmer formulation. The free and interacting cases are considered and the relations between parasupersymmetry and Kemmer theory are enhanced as it is also the case between supersymmetry and Dirac theory. In that way the oscillatorlike context leads to the characterization of pararelativistic oscillators.
Square-well representations for potentials in quantum mechanics
Authors: Hall Richard L.
Published: July 2002

A single particle moves in one dimension and obeys nonrelativistic quantum mechanics. If the potential shape f(x) is symmetric and vanishes at infinity, then, without loss of generality, it can be represented in the form of a mixture f(x)=∫0∞A(t)w(x/t)dt of square wells w(x). It is shown that A(t)=f′(t) and that the discrete eigenvalues of the Schrödinger operator H=−D2+vf(x) are given approximately by the general formula En≂EAn=mins≳0[s+v∫0∞f′(t)w̄n(st2)dt], where {w̄n(s)}n=0∞ are the known ‘‘kinetic potentials’’ associated with the simple square-well problem. For n=0 or 1, the approximations EnA are lower bounds to the corresponding exact energies En. The general formula is applied to the sech-squared potential and to the truncated quartic oscillator.
N-body quantum scattering theory in two Hilbert spaces. VI. Compactness conditions
Authors: Chandler Colston , Gibson Archie G.
Published: July 2002

It is shown how to implement in a practical way the approximation theory previously developed [J. Funct. Anal. 52, 80 (1983)] for nonrelativistic N-body quantum systems of particles interacting via pair potentials belonging to a certain general class. This is done by constructing the projection operators Π which generate the approximations, and by proving that certain operators Π(J*J−I)Π are Hilbert–Schmidt and that certain other operators VΠE(Δ) are trace class for all finite real intervals Δ. Two types of projections Π are considered. The results for the first type generalize previous results of Combes and Simon for asymptotic channels with only two clusters. The results for the second type provide an alternative approach to N-body scattering and spectral problems which is both practical and theoretically correct. The compactness results are used to prove that the approximate theories are exact theories for approximate Hamiltonians, that the approximate wave operators are asymptotically complete and satisfy the invariance principle, that the kernels of certain N-body equations are compact, and that the Hunziker–van Winter–Zhislin (HVZ) theorem holds for the approximate systems. Furthermore, the approximate Hamiltonians and wave operators converge to the corresponding exact operators in an appropriate limit as the order of the approximation increases.
A contribution to nonstandard superanalysis
Authors: Pestov Vladimir G.
Published: July 2002

The nonstandard (infinitesimal) analysis developed by Robinson is applied to certain foundational aspects of superanalysis. The construction of nonstandard hull due to Luxemburg is used to study ‘‘limit phenomena’’ arising in a Grassmann algebra Λ(q) as the number of generators q tends to infinity. An outcome of such an approach is that under transition t→∞ a superspace of purely odd dimension (0,q) transforms into a superspace of dimension (∞,∞) and not (0,∞) as one would expect. It is suggested that this construction may have something to do with the problem of adequate mathematical description of collective bosonic effects arising within infinite fermionic dimensions.
Separability and Lax pairs for Hénon–Heiles system
Authors: Ravoson V. , Gavrilov L. , Caboz R.
Published: July 2002

The Hamiltonian system corresponding to the (generalized) Hénon–Heiles Hamiltonian H= 1/2(px2+py2)+1/2Ax2+1/2By2+x2y+εy3 is known to be integrable in the following three cases: (A=B, ε=1/3); (ε=2); (B=16A, ε=16/3). In the first two the system has been integrated by making use of genus one and genus two theta functions. We show that in the third case the system can also be integrated by making use of elliptic functions. Finally, using the Fairbanks theorem, we find Lax pairs for each of the three integrable systems under consideration.
Integrability of Toda lattice by generalized variational symmetry approach
Authors: Annamalai A. , Tamizhmani K. M.
Published: July 2002

A systematic method of finding nontrivial generalized variational symmetries are presented herein and the corresponding first integrals for nonlinear dynamical system with two degrees of freedom are derived. Then, a method is applied to a Toda lattice, given by the potential V= ex−y+c1e2y+c2ey+c3e−2x+c4 e−x, where c1, c2, c3, and c4 are parameters. The symmetries and constants of motion are presented explicitly.
Invariant connections on homogeneous spaces
Authors: Kubyshin Yu. A. , Richter O. , Rudolph G.
Published: July 2002

G-invariant metric compatible linear connections on homogeneous spaces G/H are investigated herein. For certain classes of homogeneous spaces the most general form of G-invariant metric and torsion are found.
Nonlinear systems related to an arbitrary space–time dependence of the spectral transform
Authors: Leon Jérôme
Published: July 2002

A general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations is proposed. This allows one to give the general nonlinear evolution corresponding to an arbitrary time and space dependence of the spectral transform (in general nonlinear and with nonanalytic dispersion relations). The main theorem is that the compatibility conditions always give a true nonlinear evolution because it can always be written as an identity between polynomials in the spectral variable k. This general result is then used to obtain first a method to generate a new class of solutions to the nonlinear Schrödinger equation, and second to construct the spectral transform theory for solving initial-boundary value problems for resonant wave-coupling processes (like self-induced transparency in two-level media, or stimulated Brillouin scattering of plasma waves, or else stimulated Raman scattering in nonlinear optics, etc.).
Differential equations for the entropy density, energy density, and number density of statistical mechanics
Authors: Kostin M. D.
Published: July 2002

A partial differential equation is derived for the number density as a function of position, temperature, and chemical potential. In the classical limit where Planck’s constant is zero, it is shown that the expression for the classical number density of statistical mechanics satisfies the resulting equation. Similar partial differential equations are derived for the entropy density and energy density. It is then shown that these partial differential equations can be used to derive easily general expressions for the semiclassical number density, entropy density, and energy density of statistical mechanics.
Special functions from quantum canonical transformations
Authors: Anderson Arlen
Published: July 2002

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the nonperiodic three-body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains the nonperiodic Toda equation as a special case and whose solutions may be obtained by quantum canonical transformation.
A path-integral approach to polynomial invariants of links
Authors: Broda Bogusl/aw
Published: July 2002

A self-contained, genuinely three-dimensional, monodromy-matrix based, nonperturbative, covariant path-integral approach to polynomial invariants of knots and links in the framework of (topological) quantum Chern–Simons field theory is proposed. The idea of ‘‘physical’’ observables represented by an auxiliary topological quantum-mechanical model in an external gauge field is introduced as a replacement for the limited notion of the Wilson loop. The possibility of using various generalizations of the Chern–Simons action (also higher-dimensional ones) as well as a purely functional language thereby arises. The theory is quantized in the framework of the antibracket-antifield formalism of Batalin and Vilkovisky, which is well adapted to this case. Using Stokes’s theorem and formal translational invariance of the path-integral measure we derive a monodromy matrix corresponding to an arbitrary pair of irreducible representations of an arbitrary semisimple Lie group.
The symmetry structure of the anti-self-dual Einstein hierarchy
Authors: Strachan I. A. B.
Published: July 2002

An important example of a multi-dimensional integrable system is the anti-self-dual Einstein equations. By studying the symmetries of these equations, a recursion operator is found and the associated hierarchy constructed. Owing to the properties of the recursion operator one may construct a hierarchy of symmetries and find the algebra generated by them. In addition, the Lax pair for this hierarchy is constructed.
Lax formalism for a family of integrable Toda-related n-particle systems
Authors: Rañada Manuel F.
Published: July 2002

This article can be divided in two parts. First, a Lax representation is obtained for a family of integrable three-particle Toda-related systems. The second part contains the generalization to the case of n particles.
The Affine symmetry of self-dual gravity
Authors: Husain Viqar
Published: July 2002

Self-dual gravity may be reformulated as the two dimensional principal chiral model with the group of area preserving diffeomorphisms as its gauge group. Using this formulation, it is shown that self-dual gravity contains an infinite dimensional hidden symmetry whose generators form the Affine (Kac–Moody) algebra associated with the Lie algebra of area preserving diffeomorphisms. This result provides an observable algebra and a solution generating technique for self-dual gravity.
Heat kernel coefficients for the matrix Schrödinger operator
Authors: Avramidi),),) I. G. , Schimming) R.
Published: July 2002

The heat kernel coefficients Hk to the Schrödinger operator with a matrix potential are investigated. We present algorithms and explicit expressions for the Taylor coefficients of the Hk. Special terms are discussed, and for the one-dimensional case some improved algorithms are derived.
Jaynes–Cummings model governed by the Milburn equation without diffusion approximation
Authors: Chen Xin , Kuang Le-Man , Ge Mo-Lin
Published: July 2002

In this paper, we study the Jaynes–Cummings model governed by the Milburn equation for quantum mechanics. We find the exact solution of the Milburn equation without diffusion approximation and apply this solution to studying nonclassical properties of Jaynes–Cummings model (JCM) in the full range of decoherence parameter γ. The influence of the decoherence on nonclassical properties of JCM for different ranges of γ is investigated in detail.
Two parameter deformation of Grassmann matrix group and supergroup
Authors: Çelïk Salih
Published: July 2002

The two parameter quantum deformations of 2×2 Grassmann matrices, Gr(2), and supermatrices, Gr(1|1), are presented. Gr(2) whose matrix elements are all Grassmannian variables is called the superdual of the general linear group GL(2), and Gr(1|1) whose diagonal matrix elements are Grassmannian variables is called the superdual of the supergroup GL(1|1) whose nondiagonal elements are Grassmannian. Noncentral dual superdeterminant for Grassmann supermatrices belonging to Grp,q(1|1) is constructed. As with the 2×2 quantum matrices, the relations satisfied by the matrix elements of the Grassmann matrices and supermatrices are expressed in terms of an R̂ matrix. The properties of the nth power of a Grassmann supermatrix are given as an Appendix.
The quartic anharmonic oscillator and its associated nonconstant magnetic field
Authors: Allen T. , Anastassiou C. , Klink W. H.
Published: July 2002

Quantum mechanical anharmonic oscillators and Hamiltonians for particles in external magnetic fields are related to representations of nilpotent groups. Using this connection the eigenfunctions of the quartic anharmonic oscillator with potential Vα(x)=(α+(x2/2))2 can be used to determine the eigenfunctions of a charged particle in a nonconstant magnetic field, of the form Bz=β2+β3x. The quartic anharmonic oscillator eigenvalues for low-lying states are obtained numerically and a function which interpolates between α≪0 (a double harmonic oscillator) and α≫0 (a harmonic oscillator) is shown to give a good fit to the numerical data. Approximate expressions for the quartic anharmonic oscillator eigenfunctions are then used to get the eigenfunctions for the magnetic field Hamiltonian.
Casimir free energy of a spherical cavity in a dielectric medium
Authors: Brodsky Anatol M.
Published: July 2002

An expression is derived for the Casimir free energy of a spherical cavity in a polar dielectric medium at finite temperature. In the process of the derivation the general problem of infinities and their renormalization in calculations of Casimir forces is analyzed. It is shown that the renormalized Casimir free energy has a minimum at a finite mesoscopic value of the cavity radius R=RMinCas, with the repulsion for R<RMinCas and the attraction for R⩾RMinCas. The implications of this result for the explanation of cavitation effects are discussed.
Hierarchies of evolution equations associated with certain symmetric spaces
Authors: Kiso Kazuhiro , Kaneda Eiji , Kawai Ei-ichiro
Published: July 2002

Hierarchies of evolution equations associated with certain symmetric spaces are presented. Main examples of such symmetric spaces are Hermitian symmetric spaces and the obtained evolution equations include generalized nonlinear Schrödinger equations. Those results are obtained by extending the Lie algebra in the Ablowitz–Kaup–Newell–Segur scheme from sl(2,C) to more general one.
Stationary rotating matter in general relativity
Authors: Marklund Mattias , Perjés Zoltán
Published: July 2002

Stationary rotating matter configurations in general relativity are considered. A formalism for general stationary space times is developed. Axisymmetric systems are discussed by the use of a nonholonomic and nonrigid frame in the three-space of the time-like Killing trajectories. Two symmetric and trace-free tensors are constructed. They characterize a class of matter states in which both the interior Schwarzschild and the Kerr solution are contained. Consistency relations for this class of perfect fluids are derived. As an example of the application of our procedure, we obtain a solution under the assumption of rigid rotation.
Asymptotic equipartition of energy by nodal points of an eigenfunction
Authors: Chen Goong , Fulling Stephen A. , Zhou Jianxin
Published: July 2002

The time-reduced form of a partial differential equation in vibration or quantum mechanics in one space dimension often satisfies a Sturm-Liouville (S-L) equation. Nodal points of eigenfunctions of the S-L equation form energy barriers. When the S-L equation has constant coefficients, the energy localized in each nodal interval is the same. But when the S-L equation has variable coefficients, strict equipartition of energy by nodal points no longer holds. In this paper, however, we formulate an asymptotic form of the principle of equipartition of energy by nodal points, showing that the energies stored on connected nodal intervals away from the turning points or singularities of the governing equation differ at most by an error of order of magnitude inversely proportion to the frequency. Also, using a numerical example, we demonstrate this asymptotic equipartition principle when a potential barrier is present. In higher dimensions, the formation of nodal lines or nodal (hyper)surfaces is quite unstable. Therefore, equipartition of energy does not hold in an approximate or asymptotic sense.
Gauge transformations in relativistic two-particle constraint theory
Authors: Jallouli H. , Sazdjian H.
Published: July 2002

Using connection with quantum field theory, the infinitesimal covariant Abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding wave equations shown. Because of the three-dimensional projection operation, these transformation laws are interaction dependent. Simplifications occur for local potentials, which result, in each formal order of perturbation theory, from the infra-red leading effects of multiphoton exchange diagrams. In this case, the finite gauge transformation can explicitly be represented, with a suitable approximation and up to a multiplicative factor, by a momentum dependent unitary operator that acts in x-space as a local dilatation operator. The latter is utilized to reconstruct from the Feynman gauge the potentials in other linear covariant gauges. The resulting effective potential of the final Pauli–Schrödinger type eigenvalue equation has the gauge invariant attractive singularity α2/r2, leading to a gauge invariant critical coupling constant αc=1/2.
QED in external field with space–time uniform invariants: Exact solutions
Authors: Gavrilov S. P. , Gitman D. M. , Gonçalves A. E.
Published: July 2002

We study exact solutions of Dirac and Klein–Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are considered separately; they are essentially different. We direct attention to the asymmetry of the quasienergy spectrum, which appears in odd dimensions. The in and out classification of the exact solutions as well as the completeness and orthogonality relations is strictly proven. Different Green functions in the form of sums over the exact solutions are constructed. The Fock–Schwinger proper time integral representations of these Green functions are found. As physical applications, we consider the calculations of different quantum effects related to the vacuum instability in the external field. For example, we present mean values of particles created from the vacuum, the probability of the vacuum remaining a vacuum, the effective action, and the expectation values of the current and energy-momentum tensor.
Iwasawa decomposition of affine Kac–Moody algebras using Satake diagrams
Authors: Pati K. C. , Parashar D.
Published: July 2002

We carry out the Iwasawa decomposition of the affine Kac–Moody algebras within the general framework of involutive automorphisms which are determined with the help of the Satake diagrams corresponding to these algebras. The parabolic subalgebras essential for the construction of induced representations are computed from the Langlands decomposition. In particular, we consider the untwisted versions, viz., A1(1) and A2(1), as representative examples for the purpose of illustration.
Superintegrability in three-dimensional Euclidean space
Authors: Kalnins E. G. , Williams G. C. , Miller W. , Pogosyan G. S.
Published: July 2002

Potentials for which the corresponding Schrödinger equation is maximally superintegrable in three-dimensional Euclidean space are studied. The quadratic algebra which is associated with each of these potentials is constructed and the bound state wave functions are computed in the separable coordinates.
Exact ground state of several N-body problems with an N-body potential
Authors: Khare Avinash
Published: July 2002

The exact (bosonic) ground state and a class of excited states are obtained for several Calogero-type N-body problems in D dimensions when the N bodies are also interacting via an N-body potential of the form −e2/Σri2.
Extended Jordanian twists for Lie algebras
Authors: Kulish P. P. , Lyakhovsky V. D. , Mudrov A. I.
Published: July 2002

Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element ℱ, universal ℛ-matrix and the corresponding canonical element 𝒯. It is shown that the twisted Hopf algebra UF(B∨) is self-dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld–Jimbo quantization to the Jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras.
Absence of confinement in the absence of vortices
Authors: Kovács Tamás G. , Tomboulis E. T.
Published: July 2002

We consider the Wilson loop expectation in SU(2) lattice gauge theory in the presence of constraints. The constraints eliminate gauge field configurations, which, in physical terms, allow the presence of thick center vortices linking with the loop. We prove that, for dimension d⩾3, the so-constrained Wilson loop follows perimeter law, i.e., nonconfining behavior, at weak coupling (low temperature).
Relativistic scattering theory for a δ sphere plus a Coulomb interaction with boundary conditions of second type
Authors: Avossevou G. Y. H. , Hounkonnou M. N.
Published: July 2002

We study stationary relativistic scattering theory for a δ-sphere interaction formally given by the Hamiltonian H=HD+αδ(|x_|−R), x_∈R3, α∈R, R>0 with the boundary conditions of second type. First we give the mathematical definition of the model, self-adjointness of the Hamiltonian, indicial equation, stationary scattering theory and the spectral properties. Next we extend the model by adding a Coulomb potential and provide useful mathematical definitions and corresponding stationary scattering elements.
Induced representations of quantum (1+1) Galilei algebras
Authors: Arratia Oscar , del Olmo Mariano A.
Published: July 2002

We develop a systematic method to construct induced representations of quantum algebras. The procedure makes use of two Hopf algebras with a nondegenerate pairing and a pair of dual bases for them. We apply the method on three different quantum deformations of the Galilei algebra in (1+1) dimensions. We obtain several families of induced representations including some results already known.
Rayleigh–Taylor instability for adiabatically stratified fluids
Authors: Lezzi Adriano M. , Prosperetti Andrea
Published: July 2002

A linear analysis of the effects of compressibility on the stability of two superposed isentropic fluids is presented. The results of the analysis, which differ from those available in the literature for other unperturbed stratifications, are illustrated with several numerical examples. It is found that, in the present conditions, compressibility has a stabilizing effect at small wavelengths and a destabilizing effect at long wavelengths. The magnitude of these effects is, however, small in most circumstances. A physical basis for the interpretation of the results is also described in qualitative terms. This discussion sheds some light on the nature of the differences between the present results and those relative to the case of isothermal stratification.
Stochastic diffusion in two-dimensional periodic flows
Authors: Doxas I. , Horton W. , Berk H. L.
Published: July 2002

The global effective diffusion coefficient D* for a two-dimensional system of convective rolls with a time-dependent perturbation added is calculated. The perturbation produces a background diffusion coefficient D, which is calculated analytically using the Menlikov–Arnold integral. This intrinsic diffusion coefficient is then enhanced by the unperturbed flow to produce the global effective diffusion coefficient D*, which can be calculated theoretically for a certain range of parameters. The theoretical value agrees well with numerical simulations.
Ideal jets falling under gravity
Authors: Dias Frédéric , Christodoulides Paul
Published: July 2002

Steady two-dimensional jets of an inviscid and incompressible fluid emerging from a nozzle and falling under gravity are calculated numerically by series truncation. The nozzle is aimed at an angle β above the horizontal. It is shown that there are flows for all values of β between 0° and 90° and for all values of the Froude number F. Local solutions are constructed to describe the limiting behavior of the flows as F→0 and as F→∞. The problem of a uniform free stream hitting a vertical wall, rising, and forming a jet that falls back upon the oncoming stream is also solved. It is shown that solutions exist only for Froude numbers greater than 2.96.
Homogeneous isotropic turbulence in randomly stirred fluids: Self-consistent mode coupling and perturbation theory
Authors: Bhattacharjee Jayanta K.
Published: July 2002

The randomly stirred model of DeDominices and Martin [Phys. Rev. A 19, 419 (1979)] is considered in the framework of self-consistent mode coupling theories of dynamic critical phenomena. It is found that the theory is finite when the forcing yields the Kolmogorov spectrum. Perturbation theory can now be set up for universal amplitudes and results agree with the renormalization group calculations of Yakhot and Orszag [Phys. Rev. Lett. 57, 1722 (1986); J. Sci. Comput. 1, 1 (1986)].
Behavior of asymmetric unstable modes of a trailing line vortex near the upper neutral curve
Authors: Khorrami Mehdi R.
Published: July 2002

The linear stability of a trailing line vortex subjected to disturbances having azimuthal wave number n=−1 is considered. In the limit of large Reynolds numbers, the corresponding inviscid solution for this wave number is obtained. It is found that near the upper neutral curve, there exists mode crossing and mode switching between the primary and secondary modes. It is also found that viscous forces have both stabilizing and destabilizing effects on inviscid modes, which result in the appearance of a second peak in the growth rate curves.
A simple point vortex model for two-dimensional decaying turbulence
Authors: Benzi R. , Colella M. , Briscolini M. , Santangelo P.
Published: July 2002

The statistical properties of two-dimensional decaying turbulence, for nonsmooth initial conditions, are studied by using a particular model of point vortex dynamics that allows vortex merging. A quantitative agreement with respect to spectral simulations is shown.
Combined effect of sedimentation velocity fluctuation and self-sharpening on interface broadening
Authors: Lee S. , Jang Y. , Choi C. , Lee T.
Published: July 2002

The velocity fluctuation of sedimenting noncolloidal particles leads to the broadening of the interface region. In order to determine the sedimentation velocity fluctuation from the interface broadening quantitatively, the self-sharpening that reduces the broadening has to be considered simultaneously. If the velocity fluctuation effect is described by a diffusion process, the equation of mass conservation of sedimenting particles includes both of these two effects and the functional dependency of the diffusion coefficient on volume fraction is inferred from this equation. The application of the equation of mass conservation requires the volume fraction data as a function of both position and time, which is acquired by NMR-CT. The experimental results show that the interface broadening due to the velocity fluctuation is reduced substantially by the self-sharpening effect in the volume fraction range from 0.01 to 0.15. The dimensionless diffusion coefficient increases as volume fraction increases up to 0.04 where the diffusion coefficient reaches its maximum value, 22, and decreases slowly as volume fraction increases further up to 0.15.
Chemical energy release and dynamics of transitional, reactive shear flows
Authors: Grinstein F. F. , Kailasanath K.
Published: July 2002

Results are reported from numerical studies of a compressible, subsonic reactive mixing layer, on the the effects of chemical-reaction exothermicity on the shear-layer development, and the dependence of these effects on initial conditions. The model solves the unsteady, conservation equations for mass, momentum, energy, and species concentrations. The convective transport equations are solved using the flux-corrected transport (FCT) algorithm and appropriate inflow and outflow boundary conditions. A one-step, irreversible, Arrhenius chemical reaction rate, and realistic (species- and temperature-dependent) modeling of diffusive transport are coupled with the convective transport using time-step splitting. The system studied consists of nonpremixed coflowing streams, where both the fuel (faster stream, hydrogen) and the oxidizer (slower stream, oxygen) are diluted in nitrogen. To facilitate the analysis of the results the flow is organized by low-level, single-frequency velocity perturbation at the inflow. The simulations show that energy release has the effect of reducing the shear layer growth and the amount of chemical product formed−relative to the corresponding cases for which exothermicity is not accounted for, in qualitative agreement with results from previous investigations. The relative mixing-layer growth reduction becomes more pronounced for larger energy release and lower Re, and is significant in terms of both, Reynolds stress, ρu′v′, and the velocity-fluctuation correlation u′v′.

In spite of the relatively fast flows studied, for the regimes considered, the results on the initial mixing-layer growth are significantly sensitive to diffusive transport effects−more so in terms of Reynolds stress, than in terms of product formation. With larger energy release here associated to larger free-stream reactant molar fractions c0, the amount of chemical product in absolute terms is found to increase with energy release−but slower than c0, so that the product formation becomes effectively less efficient. The results of the present work highlight the difficulties involved in making general statements about the effects of exothermicity on the mixing-layer growth, indicating that a careful conceptualization of these properties in terms of initial conditions and other characteristic parameters of the reactive systems under study is required.
Shadowing and the role of small diffusivity in the chaotic advection of scalars
Authors: Klapper I.
Published: July 2002

Using techniques from shadowing theory, the solution of the scalar advection–diffusion equation is studied. It is shown that, under certain circumstances, the effect of small scalar diffusivity is to smooth the zero-diffusivity solution by averaging local fine-scaled structure against a Gaussian. The method of study depends on shadowing and thus fails for nonuniformly stretching systems, its failure suggesting the ways in which the effects of asymptotically small molecular diffusion can become nonlocal in chaotic fluid flows.
Time-dependent instabilities in curved rotating channel flow
Authors: Matsson O. J. E.
Published: July 2002

The principle of exchange of stabilities is not valid for certain regions of the parameter space of curved rotating channel flow and it is shown that for this situation the most unstable mode is inclined traveling roll cells and hence this instability determines the critical Reynolds number.
Visible imaging of edge fluctuations in the TFTR tokamak
Authors: Zweben S. J. , Medley S. S.
Published: July 2002

Images of the visible light emission from the inner wall region of the TFTR tokamak [M. G. Bell et al., in Plasma Physics and Controlled Nuclear Fusion Research 1988, Proceedings of the 12th International Conference, Nice, France (IAEA, Vienna, in press)] have been made using a rapidly gated, intensified TV camera. Strong ‘‘filamentation’’ of the neutral deuterium Dα light is observed when the camera gating time is <100 μsec during neutral-beam-heated discharges. These turbulent filaments vary in position randomly versus time and have a poloidal wavelength of ≊3–5 cm, which is much shorter than their parallel wavelength of ≊100 cm. A second and new type of edge fluctuation phenomenon, which is called a ‘‘merfe,’’ is also described. Merfes are a regular poloidal pattern of toroidally symmetric, small-scale marfes that move away from the inner midplane during the current decay after neutral beam injection. Some tentative interpretations of these two phenomena are presented.
Effect of shear on toroidal ion temperature gradient mode turbulence
Authors: Hong B.-G. , Horton W.
Published: July 2002

The effect of magnetic shear on the toroidal ion temperature gradient-driven drift mode is investigated through two-dimensional fluid simulations. Shear reduces the anomalous thermal transport by localizing the turbulence. Mixing length formulas for anomalous ion thermal transport are derived in various regimes with respect to the strength of the magnetic shear.
Electromagnetic fire-hose instability in a fully relativistic bi-Maxwellian plasma
Authors: Yoon Peter H.
Published: July 2002

Detailed properties of the classical hydromagnetic Alfvén wave and the fire-hose instability, driven by an excess in the parallel energy, are well understood in the nonrelativistic regime. In this Brief Communication, the analysis is extended to the fully relativistic regime. The analysis is carried out for fully relativistic bi-Maxwellian distributions of electrons and ions (or positrons). It is shown that the relativistic effect has a non-negligible effect on the wave and stability properties of the low-frequency modes under certain conditions.
Long-time evolution of the nonlinear thermal instability: What phase survives
Authors: Dimits A. M. , Meerson B.
Published: July 2002

The long-time behavior of thermally unstable one-dimensional disturbances in an optically thin ionized gas, subject to external heating and radiative cooling, is investigated. The intermediate-wavelength limit is considered, corresponding to the most rapidly growing isobaric condensation mode. The ‘‘reaction–diffusion’’ equation, describing the instability dynamics in Lagrangian coordinates, is employed to study the time evolution of small sinusoidal initial perturbations away from the unstable thermal equilibrium. On the relatively short heating–cooling time scale, steep temperature and density fronts develop in the gas, corresponding to spatial coexistence of two locally stable thermal equilibria adjacent to the unstable one on the isobaric heating–cooling curve. It is shown, however, that only one of these states generally survives on the much longer heat conduction time scale. The numerically observed transition to the final ‘‘truly’’ stable state is interpreted in terms of the interaction between traveling temperature fronts which preserve their identity until annihilation.
On the existence of a thermal continuum in nonadiabatic magnetohydrodynamic spectra
Authors: Van der Linden R. A. M. , Goossens M. , Goedbloed J. P.
Published: July 2002

The linear magnetohydrodynamic (MHD) spectrum of an infinite straight cylinder is investigated, taking nonadiabatic terms in the energy equation into account. It is shown that in nonideal MHD, a new continuum arises. Unlike the ‘‘classical’’ Alfvén and slow continua, this thermal continuum consists of modes that are purely exponentially growing or decaying in time. Thus unstable continua can be encountered.
Stabilization of the field-reversed configuration (FRC) tilt instability with energetic ion beams
Authors: Barnes D. C. , Milroy R. D.
Published: July 2002

The stabilization of the internal tilt mode of a field-reversed configuration by injecting a minority energetic ion component has been investigated numerically. Calculations that follow ion orbits in a specified three-dimensional magnetic field configuration, corresponding to a partially tilted field-reversed configuration, demonstrate how a beam can provide a restoring force to the n=1 tilt instability. A fully self-consistent three-dimensional numerical model, which treats the background plasma as a Hall fluid and the energetic ions as a collisionless Vlasov species, has also been developed. Calculations have been made for a variety of beam injection parameters, and indicate that the tilt mode can be stabilized with a beam energy of about 40% of the total, beam plus plasma, energy.
Theory of the relativistic gyrotwistron
Authors: Nusinovich G. S. , Li H.
Published: July 2002

A generalized theory of the relativistic gyrotwistron, the device combining the elements of the gyroklystron and the gyro-traveling wave tube, is presented. A modulation of electrons in the input cavity is considered with the account of modulation in an electron axial momentum that is important for relativistic particles passing through a short cavity. A comprehensive study of large-signal operation of the output waveguide section in the cases of gyroresonance at the fundamental and second cyclotron harmonics has demonstrated a wide variety of electron bunching phenomena and the possibility of achieving high electron efficiency in a wide range of gyrotwistron parameters.
Interaction of regular structures with small-scale fluctuations in drift-wave turbulence
Authors: Muhm A. , Pukhov A. M. , Spatschek K. H. , Tsytovich V.
Published: July 2002

Isolated two-dimensional (2-D) regular vortex structures can coexist with small-scale turbulence in drift-wave turbulence. The aim of the present paper is to develop a mathematical procedure and to derive concrete equations that describe consistently the interaction of a regular strongly nonlinear vortex with small-scale turbulence. The latter is formulated within the weak-turbulence limit. The changes in spatial as well as temporal distributions of the weak drift-wave turbulence due to the interaction with regular structures are calculated. Also, the equations describing the changes of the regular vortices, because of their interaction with the small-scale turbulence, are presented. Within a linear consideration an instability is found which shows that energy can flow to the regular vortices. This instability delivers a microscopic explanation for the self-organization observed in numerical experiments. The analytical calculations are supplemented by numerical evaluations of the relevant transfer processes.
Poloidal viscosity and radial currents
Authors: Kim Y. B. , Hinton F. L.
Published: July 2002

Considerable doubt is cast on the L- to H-mode transition mechanism proposed by Shaing [Phys. Rev. Lett. 63, 2369 (1989)]. Contrary to his assertion, a consistent application of the momentum balance equations shows that ion orbit loss current does not drive large poloidal rotation in tokamaks, in steady state.
Observations of a vacuum spark under different driver conditions of the applied voltage
Authors: Chuaqui H. , Favre M. , Soto L. , Wyndham E.
Published: July 2002

Comparative observations of the Vacuum Spark discharge are presented under differing electrical drive conditions but identical geometrical conditions. A 1.5 Ω 120 nsec, coaxial line is used to provide maximum currents to 90 kA. The line may be operated in the usual switched mode to give a rectangular voltage and current wave form, or in the Hybrid mode, in which case the voltage builds slowly until breakdown occurs. In both modes of operation the value of dI/dt is about 1×1012 A/sec. A Nd:YAG is focused onto either electrode to initiate the discharge. With the laser focused onto the anode a low-density plasma accompanied by intense electron beams is formed. With the laser focused on the cathode a much higher plasma density is observed in the gap, with the formation of a dense tight pinch close to the cathode, in which hot spots form at peak current. The Hybrid mode is favored for its reproducible behavior.
Profile stabilization of tilt mode in a field-reversed configuration
Authors: Cobb John W. , Tajima T. , Barnes Daniel C.
Published: July 2002

The possibility of stabilizing the tilt mode in field-reversed configurations without resorting to explicit kinetic effects such as large ion orbits is investigated. Various pressure profiles, P(Ψ), are chosen, including ‘‘hollow’’ profiles, where current is strongly peaked near the separatrix. Numerical equilibria are used as input for an initial value simulation, which uses an extended magnetohydrodynamic (MHD) model that includes viscous and Hall terms. Tilt stability is found for specific hollow profiles when accompanied by high values of separatrix beta, βsep. The stable profiles also have moderate to large elongation, racetrack separatrix shape, and lower values of s̄, average ratio of Larmor radius to device radius. The stability is unaffected by changes in viscosity, but the neglect of the Hall term does cause stable results to become marginal or unstable. Implications for interpretation of recent experiments are discussed.
Suppression of m=2 islands by electron cyclotron heating in the Texas Experimental Tokamak: Experiment and theory
Authors: Sing D. C. , Austin M. E. , Brower D. L. , Chen J. Y. , Gandy R. F. , Yu C. X. , Wang X.-H. , Bhattacharjee A. , Schnack D. D.
Published: July 2002

Electron cyclotron heating (ECH) is used to suppress m=2 magnetohydrodynamic (MHD) oscillations in the Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. The location of ECH power deposition is controlled by a movable antenna. The MHD activity is suppressed when the ECH beam is directed close to the q=2 surface. The experiment is simulated using a three-dimensional resistive MHD code in cylindrical geometry. For fixed plasma current, the saturated m=2 island width is found to depend on the value of the safety factor at the magnetic axis (q0). The simulation suggests that the observed saturated m=2 island in the pre-ECH plasma, which typically occupies 25% of the minor radius, corresponds to q0∼1.3. The suppression of the island in the presence of ECH is attributed to current profile modification. In some discharges, the m=2 activity does not resume even after the ECH pulse is turned off.
Convective momentum transport, shock viscosity, and the L–H transition in tokamaks
Authors: Shaing K. C. , Hsu C. T.
Published: July 2002

Convective momentum transport associated with V⋅∇V in the momentum equation is calculated for arbitrary values of the poloidal E×B Mach number Mp. Here, V is the plasma flow velocity. The physics origin of the convective momentum transport is associated with the coupling of the poloidal variation of the viscosity-driven flux to that of the flow velocity in the magnetic surface. When the radial gradient scale length of the plasma velocity is of the order of the ion poloidal gyroradius, ρpi, the convective momentum transport becomes comparable to the ion viscosity. At Mp≂1, the ion viscosity associated with shock—the shock viscosity—approximately balances the convective momentum transport to maintain the lowest-order ambipolarity. The implications of the effects of shock and convective momentum transport for the previous L–H transition bifurcation theory [K. C. Shaing and E. C. Crume, Jr., Phys. Rev. Lett. 63, 2369 (1989)] are discussed, and an extended bifurcation theory including these effects is presented. It is shown that the experimentally relevant plasma viscosity, effective plasma viscosity, is very similar to that obtained without including compressibility effects, even if shock exists.
Electron velocity distribution in a weakly ionized plasma with an external electric field
Authors: Rokhlenko A. V. , Lebowitz J. L.
Published: July 2002

The velocity distribution f(v) of the electron component of a weakly ionized plasma is investigated in a spatially homogeneous external electric field E. Both static and time-dependent E are considered. The time evolution of f is described by a Boltzmann equation in which the ions and neutral particles are assumed to have a Maxwellian distribution with a priori specified temperatures while the electron–electron interactions are given by a Landau-type collision integral. The (approximate) solution scheme used to solve this equation for a stationary f (in a constant field) is found to have nonunique solutions for certain ranges of E, in agreement with that found in earlier investigations using a different method of solution. These results are interpreted to correspond to hysteresis effects when the field is changing very slowly: with the true stable solution undergoing a very sharp changeover, possibly a discontinuous transition, at a certain critical E. This can be understood intuitively as a transition in the stationary state of the electrons from a low-energy regime dominated by strong coupling to the ions to a high-energy regime dominated by electron–electron and electron–neutral collisions.