bluuebunny/crossref_metadata_2025 huggingface dataset:
Perturbation theory based on the Einstein–Boltzmann system. I. Illustration of the theory for a Robertson–Walker geometry
Authors: Banach Zbigniew , Piekarski Sl/awomir
Published: July 2002

This article is a discussion of how it is possible to do perturbation theory for the Einstein–Boltzmann system about a dust solution. Explicitly expressed, the background Robertson–Walker universe model and one-parameter families of exact solutions are applied to the Einstein–Boltzmann system to obtain a closed-form solution of the equations governing linearized perturbations at late times, when the nonzero pressure of the gas of massive particles may be regarded as being significantly smaller than the energy density. After splitting the distribution function into two structurally different parts, the analysis given here provides a means of deriving the equations of linear hydrodynamics. In fact, due to the specific properties of the background chosen, one can prove that the evolution of suitably defined hydrodynamic variables is exactly decoupled from the evolution of the phase-space function satisfying the linearized Boltzmann equation. For simplicity, the workings of the method are illustrated by assuming that the perturbed metric is also of the Robertson–Walker form. A detailed treatment of the effect of inhomogeneities in an almost-Robertson–Walker universe model will be the subject of the last article in this series.
Solution of three waves interaction type models with nontrivial asymptotic and boundary conditions
Authors: Claude Christophe
Published: July 2002

In the following we introduce a new way to solve the Cauchy problem for non- vanishing potentials at infinity for the spectral problem of the Zakharov and Shabat, Ablowitz, Kaup, Newell, and Segur (ZS-AKNS) hierarchy. Then we apply the results to solve a class of coupled systems, with this nonvanishing condition on the potential and with quite general boundary conditions on the other fields. Finally we present an application to a physical system governed by a three waves interaction type model.
A twistor-inspired Darboux transform for the sine–Gordon equation
Authors: Moorhouse T.
Published: July 2002

The solutions to the sine–Gordon equation which are derived from an ansatz based on the methods of twistor theory are shown to correspond to Darboux transformations for a certain linear equation. The linear problem is shown to arise in several different ways, and a relationship between the Darboux transformation for linear equations of this type and the Bäcklund transformation is examined. A possible extension to well known monopole ansatze is briefly considered.
The conformal anomaly in N-dimensional spaces having a hyperbolic spatial section
Authors: Bytsenko A. A. , Elizalde E. , Odintsov S. D.
Published: July 2002

The conformal anomaly for spinors and scalars on an N-dimensional hyperbolic space is calculated explicitly, by using zeta-function regularization techniques and the Selberg trace formula. In the case of conformally invariant spinors and scalars the results are very much related with those corresponding to an N-dimensional sphere.
Point-group symmetrized boson representation. Algebraic solution for symmetry-adapted bases of O
h
Authors: Chen Jin-Quan , Klein A. , Ping Jia-Lun
Published: July 2002

A point group symmetrized boson representation (SBR) is introduced that is particularly convenient for describing molecular vibrations. In this paper the SBR is elucidated using the example of the molecule SF6 with Oh symmetry. The advantages of the SBR are that its basis vectors have a clear physical picture, their number is very small (equal to one-eighth of the dimension of the reducible representation for Oh), and the irreducible bases for any concrete cases can be obtained trivially from those for the general case without any projection. All the irreducible bases for the group chains Oh⊇D4⊇C4 or Oh⊇D4⊇D2 are tabulated once and for all. As an application, the Hamiltonian in the algebraic model of Iachello and Oss for stretching vibrations of the molecule SF6 is diagonalized in the symmetry adapted bases.
The Lax pair by dimensional reduction of Chern–Simons gauge theory
Authors: Pashaev Oktay K.
Published: July 2002

We show that the Nonlinear Schrödinger Equation and the related Lax pair in 1+1 dimensions can be derived from 2+1-dimensional Chern–Simons Topological Gauge Theory. The spectral parameter, a main object for the Loop algebra structure and the Inverse Spectral Transform, has to appear as a homogeneous part (condensate) of the statistical gauge field, connected with the compactified extra space coordinate. In terms of solitons, a natural interpretation for the one-dimensional analog of Chern–Simons Gauss law is given.
Gauge invariant perturbations of black holes. II. Kerr space–time
Authors: Fernandes Joe F. Q. , Lun Anthony W. C.
Published: July 2002

We cast the perturbed Bianchi identities into a form involving only tetrad and coordinate-gauge invariant field quantities. From the perturbed Bianchi identities we then derive a system of gauge invariant wavelike gravitational perturbation equations. These are the Teukolsky equation, a gauge invariant analog of the Regge–Wheeler equation, and a new gravitational perturbation equation. The Bianchi identities also provide the transformations between the perturbation equations. In particular, the transformation between the Teukolsky equation and the analog of the Regge–Wheeler equation arises in this way. This work extends our previous analysis of the perturbations of the Schwarzschild black hole to the Kerr case.
Topological Casimir energy for a general class of Clifford–Klein space–times
Authors: Williams Floyd L.
Published: July 2002

Using zeta regularization we compute the vacuum energy for free massless scalar fields on ultrastatic space–times R×(Γ\X), where X is an arbitrary noncompact irreducible rank 1 symmetric space and Γ is a cocompact torsion free subgroup of isometries of X. The spaces X include hyperbolic manifolds on which previous authors have focused. Specifically, using a general trace formula, we extend the work of Bytsenko, Goncharov, Zerbini (and others), where X=SO1(m,1)/SO(m), to the other classical rank 1 symmetric spaces X=SU(m,1)/U(m), SP(m,1)/(SP(m)×SP(1)), and the exceptional space X=F4(−20)/Spin(9). We find in general that the trivial unitary character of Γ always induces a negative topological component of the energy.
A generalized formula for integrable classes of surfaces in Lie algebras
Authors: Cieśliński Jan
Published: July 2002

We discuss relations between the approach of Fokas and Gelfand to immersions on Lie algebras and the theory of soliton surfaces of Sym. We show that many results concerning immersions on Lie algebras can be reduced to or interpreted within the soliton surfaces approach. We present also some new results, including a generalization of the Fokas–Gelfand formula for integrable classes of surfaces in Lie algebras [and, in particular, in (pseudo)-Euclidean n-dim. spaces]. The generalized formula is used to formulate a method of constructing integrable classes of surfaces. As an example we discuss the class of linear Weingarten surfaces defined by the linear relationship between Gaussian and mean curvatures. We construct explicitly a one-parameter family of linear Weingarten surfaces parallel (equidistant) to a given pseudospherical surface.
Extension of the Barut–Girardello coherent state and path integral
Authors: Fujii Kazuyuki , Funahashi Kunio
Published: July 2002

We extend the Barut–Girardello coherent state for the representation of SU(1,1) to the coherent state for a representation of U(N,1) and construct the measure. We also construct a path integral formula for some Hamiltonian.
A continued fraction representation for the effective conductivity of a two-dimensional polycrystal
Authors: Clark Karen E.
Published: July 2002

A continued fraction representation for the effective conductivity tensor σ* of a two-dimensional polycrystal is derived. This representation is in terms of a sequence of positive definite symmetric matrices which characterize the underlying geometric structure of the material. The proof is accomplished by considering a particular basis for the Hilbert space of fields in the composite in which the linear operators relevant to determining the effective conductivity take simple forms as infinite matrices. These infinite matrices are then used in the variational definition of the effective conductivity to formulate the continued fraction. This continued fraction is used to derive upper and lower bounds on σ*.
On tracial operator representations of quantum decoherence functionals
Authors: Rudolph Oliver , Maitland Wright J. D.
Published: July 2002

A general quantum history theory can be characterized by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space H. We study operator representations for decoherence functionals on this space of histories. We first give necessary and sufficient conditions for a decoherence functional being representable by a trace class operator on H⊗H, an infinite dimensional analogue of the Isham–Linden–Schreckenberg representation for finite dimensions. Since this excludes many decoherence functionals of physical interest, we then identify the large and physically important class of decoherence functionals which can be represented, canonically, by bounded operators on H⊗H.
A path integral for turbulence in incompressible fluids
Authors: Thacker W. D.
Published: July 2002

In this paper a classical path integral is formulated for incompressible fluids that evolve according to the Navier–Stokes equation. The path integral propagates probability distributions deterministically on the space ℊvol of solenoidal velocity fields. We construct a set of ISp(2) charges associated with the geometry of ℊvol and its Poisson structure, and a pair of supersymmetry charges connected with the Hamiltonian. These charges generate exact symmetries of the classical path integral when the viscosity is set equal to zero. When the effect of dissipation is included, the charges associated with the Poisson structure and the Hamiltonian are no longer conserved. Charges that generate Kolmogorov scaling and Galilean transformations are also constructed. The classical path integral is formulated in terms of vorticity as well.
Geodesic flow on an hyperboloid model and the two-body motion under repulsive Coulomb forces
Authors: Mesón Alejandro M. , Vericat Fernando
Published: July 2002

We show that (in n dimension) the flow defined by the Hamiltonian system for two charged particles of the same sign, is mapped into the geodesic flow over the non-Euclidean space: Hn+⊔∂Hn−−{P̄}, say the hyperboloid with the axis along ê0 which besides having its “boundaries at infinite” identified, it is also punctured at the point P̄≡(ξ0,ξ1,…,ξn)=(−1,0,…,0) (corresponding to the collision states) and whose metric is of negative curvature.
Exact solutions for nonconservative two-velocity discrete Boltzmann models
Authors: Cornille H.
Published: July 2002

Extended discrete kinetic theory (which we call nonconservative), including sources, sinks, creation and annihilation of test particles, inelastic scattering,… added to the elastic collisions, was recently introduced. For instance, the mass conservation law, by adding polynomials of the mass, becomes nonconservative. To the classical two-velocity elastic collision models, we associate two nonconservative models with polynomials of the first and second degree. We obtain exact stationary, similarity, (1+1)-dimensional and periodic solutions. For their stability we study the corresponding nodes and saddles.
Representations of the Poincaré Lie algebra from unitary representations of SO(1,4)
Authors: Buchwalter S. A. , Moylan P.
Published: July 2002

An algebraic isomorphism of an extension of the Lie field of so(1,4) and an extension of the Poincaré Lie field was given in Havlicek and Moylan [J. Math Phys. 34, 5320 (1993)]. Here we use the isomorphism described in that paper in order to obtain matrix elements of the Poincaré Lie algebra generators in a normalizable basis for an arbitrary unitary spherical principal series representation of SO0(1,4).
Spacetime defects: Domain walls and torsion
Authors: Garcia de Andrade L. C.
Published: July 2002

The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature δ-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenböck planar walls are characterized by torsion δ-singularities and zero curvature. It is shown that Weitzenböck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenböck nonstatic torsion walls is investigated.
On pairs of difference operators satisfying [D, X]=Id
Authors: Górski Andrzej Z. , Szmigielski Jacek
Published: July 2002

Dedicated to the memory of Gerda Dorfmeister.   Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider D and X to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The first class, generalizing the central difference scheme, is shown to give unitary equivalent representations. For the second case we construct a large class of examples, generalizing previously known difference operator realizations of [D, X]=Id.
Duals of colored quantum universal enveloping algebras and colored universal 𝒯-matrices
Authors: Quesne C.
Published: July 2002

We extend the notion of dually conjugate Hopf (super)algebras to the colored Hopf (super)algebras Hc that we recently introduced. We show that if the standard Hopf (super)algebras Hq that are the building blocks of Hc have Hopf duals Hq*, then the latter may be used to construct coloured Hopf duals Hc*, endowed with colored algebra and antipode maps, but with a standard coalgebraic structure. Next, we review the case where the Hq’s are quantum universal enveloping algebras of Lie (super)algebras Uq(g), so that the corresponding Hq*’s are quantum (super)groups Gq. We extend the Fronsdal and Galindo universal 𝒯-matrix formalism to the colored pairs (Uc(g),Gc) by defining colored universal 𝒯-matrices. We then show that together with the colored universal ℛ-matrices previously introduced, the latter provide an algebraic formulation of the colored RTT-relations, proposed by Basu-Mallick. This establishes a link between the colored extensions of Drinfeld–Jimbo and Faddeev–Reshetikhin–Takhtajan pictures of quantum groups and quantum algebras. Finally, we illustrate the construction of colored pairs by giving some explicit results for the two-parameter deformations of (U(gl(2)),Gl(2)), and (U(gl(1/1)),Gl(1/1)).
Davey–Stewartson type equations of the second and third order: Derivation and classification
Authors: Folguera Alejandra
Published: July 2002

The inverse spectral method provides an algorithm for generating and solving integrable equations. Here we apply this method to study a family of nonlinear partial differential equation (PDEs) which are two spatial dimensional generalizations of the nonlinear Schrödinger (NLS), the Korteweg–de Vries (KdV) and the modified Korteweg–de Vries (m-KdV) equations. We find simple transformations which reduce this family to a few canonical systems which include the Davey–Stewartson, the Nizkhik–Veselov–Novikov (NVN), and the modified NVN (mod-NVN) equations, and the equations recently derived by Fokas. We also construct Miura maps between the modified NVN and the NVN equations which are valid without any restrictions in the space of solutions. Finally, we present the bi-Hamiltonian formulation of some of the systems presented here.
Constructive inversion of energy trajectories in quantum mechanics
Authors: Hall Richard L.
Published: July 2002

We suppose that the ground-state eigenvalue E=F(v) of the Schrödinger Hamiltonian H=−Δ+vf(x) in one dimension is known for all values of the coupling v>0. The potential shape f(x) is assumed to be symmetric, bounded below, and monotone increasing for x>0. A fast algorithm is devised which allows the potential shape f(x) to be reconstructed from the energy trajectory F(v). Three examples are discussed in detail: a shifted power-potential, the exponential potential, and the sech-squared potential are each reconstructed from their known exact energy trajectories.
An inversion inequality for potentials in quantum mechanics
Authors: Hall Richard L.
Published: July 2002

We suppose: (1) that the ground-state eigenvalue E=F(v) of the Schrödinger Hamiltonian H=−Δ+vf(x) in one dimension is known for all values of the coupling v>0; and (2) that the potential shape can be expressed in the form f(x)=g(x2), where g is monotone increasing and convex. The inversion inequality f(x)⩽f̄(1/4x2) is established, in which the “kinetic potential” f̄(s) is related to the energy function F(v) by the transformation {f̄(s)=F′(v), s=F(v)−vF′(v)}. As an example, f is approximately reconstructed from the energy function F for the potential f(x)=ax2+b/(c+x2).
Differential polynomial expressions related to the Kadomtsev–Petviashvili and Korteweg–de Vries hierarchies
Authors: Schimming Rainer , Strampp Walter
Published: July 2002

An integrable nonlinear partial differential equation typically extends to a hierarchy of integrable equations. There exist several recursive schemes for obtaining these hierarchies. Recently, explicit expressions for the KdV hierarchy have been found. We derive explicit expressions for the hierarchy associated with the KP equation. The main tools are Sato’s theory, Hirota’s formalism, and Bell’s polynomials.
Congruences and canonical forms for a positive matrix: Application to the Schweinler–Wigner extremum principle
Authors: Simon R. , Chaturvedi S. , Srinivasan V.
Published: July 2002

It is shown that a N×N real symmetric [complex Hermitian] positive definite matrix V is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in SO(m,n)[SU(m,n)], for any choice of partition N=m+n. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson’s theorem which states that if N is even then V is congruent also to a diagonal matrix modulo a symplectic matrix in Sp(N,R)[Sp(N,C)]. Applications of these results considered include a generalization of the Schweinler–Wigner method of “orthogonalization based on an extremum principle” to construct pseudo-orthogonal and symplectic bases from a given set of linearly independent vectors.
Scale symmetries of spherical string fluids
Authors: Glass E. N. , Krisch J. P.
Published: July 2002

We consider homothetic maps in a family of spherical relativistic star models. A generalization of Vaidya’s radiating metric provides a fluid atmosphere of radiation and strings. The similarity structure of the string fluid is investigated.
Connection with torsion from Ashtekar–Barbero connection
Authors: Montesinos Merced
Published: July 2002

A natural three-dimensional covariant derivative with torsion emerges from the Ashtekar–Barbero connection in the canonical approach to general relativity. The torsion is related to the extrinsic curvature when the Barbero–Immirzi parameter β does not vanish. Alternatively, torsion can be avoided, but at the price of a nonvanishing covariant derivative of the triad field. The properties of both cases are discussed.
One-instanton prepotentials from WDVV equations in N=2 supersymmetric SU(4) Yang–Mills theory
Authors: Ohta Yűji
Published: July 2002

Prepotentials in N=2 supersymmetric Yang–Mills theories are known to obey nonlinear partial differential equations called Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. In this paper, the prepotentials at the one-instanton level in N=2 supersymmetric SU(4) Yang–Mills theory are studied from the standpoint of WDVV equations. Especially, it is shown that the one-instanton prepotentials are obtained from WDVV equations by assuming the perturbative prepotential and by using the scaling relation as a subsidiary condition but are determined without introducing the Seiberg–Witten curve. In this way, various one-instanton prepotentials which satisfy both WDVV equations and the scaling relation can be derived, but it turns out that among them there exist one-instanton prepotentials which coincide with the instanton calculus.
Null cones from I+ and Legendre submanifolds
Authors: Iriondo Mirta , Kozameh Carlos N. , Rojas Alejandra T.
Published: July 2002

It is shown that the main variable Z of the null surface formulation of GR is the generating family of a constrained Lagrange submanifold that lives on the energy surface H=0 and that its level surfaces Z=const yield Legendre submanifolds on that energy surface. Thus, the singularity structure of past null cones with apex at I+ is obtained by studying the projection map of the Legendre submanifolds to the configuration space. The behavior of the coordinate system defined by the variable Z at the caustic points is analyzed. It is shown that a single function Z(xa,ζ,ζ̄) cannot generate the conformal structure of an asymptotically flat space–time that satisfies the generic and weak energy condition.
Collective dynamics of solitons and inequivalent quantizations
Authors: Garrahan J. P. , Kruczenski M.
Published: July 2002

The collective dynamics of solitons with a coset space G/H as moduli space is studied. It is shown that the collective band for a vibrational state is given by the inequivalent coset space quantization corresponding to the representation of H carried by the vibration. To leading order the collective dynamics is free motion in G/H coupled to background gauge fields determined by the vibrational state.
Field theory in SUq(2)
Authors: Bibikov P. N.
Published: July 2002

We study field theory on the quantum group SUq(2) which is considered as a physical space. We construct deformed equations and Lagrangians for scalar, Dirac, and gauge fields and study their properties. It seems important for us that nontrivial structure of noncommutative differential calculus leads to an appearance of an additional spin 0 gauge field.
Relating Green’s functions in axial and Lorentz gauges using finite field-dependent BRS transformations
Authors: Joglekar Satish D. , Misra A.
Published: July 2002

We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial gauge can be written as a series in terms of those in Lorentz gauges. Our method also applies to operator Green’s functions. We show that this process involves another set of related FFBRS transformations that is derivable from infinitesimal FFBRS. We suggest possible applications.
Off-diagonal terms in symmetric operators
Authors: Jorgensen Palle E. T.
Published: July 2002

In this paper we provide a quantitative comparison of two obstructions for a given symmetric operator S with dense domain in Hilbert space ℋ to be self-adjoint. The first one is the pair of deficiency spaces of von Neumann, and the second one is of more recent vintage; Let P be a projection in ℋ. We say that it is smooth relative to S if its range is contained in the domain of S. We say that smooth projections {Pi}i=1∞ diagonalize S if (a) (I−Pi)SPi=0 for all i, and (b) supi Pi=I. If such projections exist, then S has a self-adjoint closure (i.e., S̄ has a spectral resolution), and so our second obstruction to self-adjointness is defined from smooth projections Pi with (I−Pi)SPi≠0. We prove results both in the case of a single operator S and a system of operators.
Contraction of the Gr,s quantum group to its nonstandard analog and corresponding colored quantum groups
Authors: Parashar Deepak , McDermott Roger J.
Published: July 2002

The quantum group Gr,s provides a realization of the two parameter quantum GLp,q(2), which is known to be related to the two parameter nonstandard GLh,h′(2) group via the contraction method. We apply the contraction procedure to Gr,s and obtain a new Jordanian quantum group Gm,k. Furthermore, we provide a realization of GLh,h′(2) in terms of Gm,k. The contraction procedure is then extended to the colored quantum group GLrλ,μ(2) to yield a new Jordanian quantum group GLmλ,μ(2). Both Gr,s and Gm,k are then generalized to their colored versions, which in turn provide similar realizations of GLrλ,μ(2) and GLmλ,μ(2).
Darboux transformation for the Schrödinger equation with steplike potentials
Authors: Aktosun Tuncay
Published: July 2002

The one-dimensional Schrödinger equation is considered when the potential is asymptotic to a positive constant on the right half line. The corresponding Darboux transformation is established by showing how the scattering solutions, the scattering coefficients, and the potential change when bound states are added or removed. The scattering coefficients are represented as certain integrals, from which their properties can be directly extracted.
Energy in Yang–Mills on a Riemann surface
Authors: Fine Dana
Published: July 2002

Sengupta’s lower bound for the Yang–Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The Yang–Mills critical sets correspond to critical sets of the energy action on a space of paths. This may shed light on a conjecture of Atiyah and Bott concerning Morse theory for 𝒜/𝒢.
The Uq(sln∧) analogue of the XXZ chain with a boundary
Authors: Furutsu H. , Kojima T.
Published: July 2002

We study the Uq(sln∧) analogue of the XXZ spin chain with a boundary magnetic field h. We construct explicit bosonic formulas of the vacuum vector and the dual vacuum vector with a boundary magnetic field. For an application of the explicit formula of the vacuum vector, we derive the integral representation of the boundary spontaneous magnetization.
Phase space tunneling for operators with symbols in a Gevrey class
Authors: Jung Klaus
Published: July 2002

Phase space tunneling and exponential decay of eigenfunctions in phase space are well known for operators with symbols which are analytic in some neighborhood of the real axis. This can be used to prove an adiabatic theorem of exponential order if one assumes the Hamiltonian to depend analytically on time. However to study compactly supported switching processes one has to weaken the analyticity assumptions. Here we examine nonanalytic symbols with Gevrey class regularity and show that we get an exponential decay of the corresponding eigenfunctions with respect to ℏ1/a as ℏ→0, where a>1. The loss of regularity causes a slower decay in ℏ. The analysis is done using the methods of Martinez and its generalization by Nakamura. An upper bound for the rate of decay is given.
Scalar tensor theories and Hadamard state condition
Authors: Salehi H. , Bisabr Y. , Ghafarnejad H.
Published: July 2002

The Hadamard state condition is used to analyze the local constraints on the two-point function of a quantum field conformally coupled to a background geometry. Using these constraints we develop a scalar tensor theory which controls the coupling of the stress-tensor induced by the two-point function of the quantum field to the conformal class of the background metric. It is then argued that the determination of the state-dependent part of the two-point function is connected with the determination of a conformal frame. We comment on a particular way to relate the theory to a specific conformal frame (different from the background frame) in which the large-scale properties are brought into focus.
Classical and quantal Lorentz covariant models of the electromagnetic radiation field
Authors: Aaberge Terje
Published: July 2002

We present Lorentz covariant models of the radiation field, i.e., plane wave solutions of the Maxwell equations satisfying the Coulomb gauge condition. The theory is constructed along traditional lines. We apply the interpretation of the field as a collection of photons and starts by constructing the state space of the photon. The novelty of this formulation is the use of a new action of the Lorentz group on the space of circular helicities of spin 1 which permits the construction of an action on the state space of the photon. Moreover, the generators of the action provide objects that can be used to construct the field observables both in the classical and quantum case. The result is a theory with a tight structure. It is a generalization of the standard theory, a covariant generalization, and it contains this as a special case.
Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)
Authors: Su Yucai , Hughes J. W. B. , King R. C.
Published: July 2002

In a study of finite-dimensional modules of simple Lie superalgebras, Kac introduced certain indecomposable modules, now known as Kac-modules V̄(Λ), which are simple if and only if Λ is typical. For Λ atypical, Hughes et al. presented an algorithm to determine all the composition factors of the Kac-module; they conjectured that there exists a bijection between the composition factors of a Kac-module and so-called permissible codes. The aim in this paper is to contribute to the proof of this conjecture. By constructing explicitly the primitive vector, we prove that for any unlinked code there corresponds a composition factor of the Kac-module. It will be proved in another paper that to any linked code there also corresponds a composition factor of the Kac-module. Thus the proof of the Hughes et al. conjecture will be reduced to the problem whether or not each composition factor corresponds to a linked or unlinked code.
Aperiodic Virasoro algebra
Authors: Twarock R.
Published: July 2002

An aperiodic analog to the Virasoro algebra is introduced and its representation theory is investigated. In particular, highest and lowest weight representations are constructed. An analog to the Kac determinant formula is derived and the implications for unitarity are discussed.
Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points
Authors: Mestel B. D. , Osbaldestin A. H.
Published: July 2002

The universal period-doubling scaling of a unimodal map with an asymmetric critical point is governed by a period-2 point of a renormalization operator. The period-2 point is parametrized by the degree of the critical point and the asymmetry modulus. In this paper we study the asymptotics of period-2 points and their associated scaling parameters in the singular limit of degree tending to 1.
Monte-Carlo simulation of phase transition in the vortex system of high-temperature superconductors (A review)
Authors: Gracheva M. E. , Katargin M. V. , Kashurnikov V. A. , Rudnev I. A.
Published: July 2002

Recent publications on the Monte-Carlo simulation of vortex systems in HTS are reviewed. Dependences of the main parameters of the vortex state (such as energy, heat capacity, thermal motion, and structural order parameter) on extrinsic parameters (temperature and magnetic field) are described. The vortex glass phase, the influence of defects on phase diagrams, as well as the main phase transitions in two- and three-dimensional vortex structures including melting and 2D-3D transition are considered.
On the behavior of a system of double diffusive layers during its evolution
Authors: Tanny (Tanai) Josef , Tsinober A. B.
Published: July 2002

Double diffusive layers, formed by heating a linear stable solute gradient from one vertical side wall, undergo a merging process from their initial to final thickness. This process, excluding the initial and final states, is different in each of several almost identical experiments, and in this sense it is said to be chaotic. The variation of the layer thickness during this process is analyzed and a simple quantitative measure for the level of chaotic behavior is suggested and applied for two different sets of experiments. Each set consists of several almost identical experiments, and the two sets differ in the wall-temperature rise curve. The results for the two rise curves considered, namely, linear and exponential, show a higher level of chaotic behavior for the exponential curve. The influence of the heating rate on the thickness variation is also discussed.
Remark on a result of D. Dritschel
Authors: Pullin D. I. , Moore D. W.
Published: July 2002

A hypothesis put forward by D. Dritschel [J. Fluid Mech. 94, 511 (1988)], namely that an isolated symmetrical disturbance on a uniform vortex patch will filament in time proportional to the inverse square of the disturbance amplitude, is subject to independent testing using a nonintrusive numerical method. The hypothesis that the trend is maintained to substantially smaller amplitudes than were originally considered by Dritschel is both supported and verified. The results may be interpreted as providing limited evidence that contour smoothness is maintained in filamentation and that corner formation does not occur up to the time of wave overturning.
Numerical experiments in supersonic boundary-layer stability
Authors: Erlebacher Gordon , Hussaini M. Y.
Published: July 2002

The three-dimensional (3-D) time-dependent compressible Navier–Stokes equations are numerically solved by a Fourier–Chebyshev collocation method to study the stability of supersonic flows over a flat plate. Several direct simulations carried out in this study suggest the existence of a secondary instability that might provide a route to transition. The interaction of the modes involved in the secondary instability is possibly amenable to a Floquet-type analysis. Pertinent differences between this instability and the analogous incompressible K-type secondary instability are pointed out. Some preliminary results of a 2-D direct simulation of the nonlinear evolution of a second mode perturbation wave are also discussed.
The stability of two-dimensional wakes and shear layers at high Mach numbers
Authors: Papageorgiou Demetrios T.
Published: July 2002

This study is concerned with the stability properties of laminar free-shear-layer flows, and in particular symmetric two-dimensional wakes, for the supersonic through the hypersonic regimes. Emphasis is given to the use of proper wake profiles that satisfy the equations of motion at high Reynolds numbers. In particular the inviscid stability of a developing two-dimensional wake is studied as it accelerates at the trailing edge of a splitter plate. The nonparallelism of the flow is a leading-order effect in the calculation of the basic state, which is obtained numerically. Neutral stability characteristics are computed and the hypersonic stability is obtained by increasing the Mach number. It is found that the stability characteristics are altered significantly as the wake develops. Multiple modes (secondary modes) are found in the near wake that are closely related to the corresponding Blasius ones, but as the wake develops mode multiplicity is delayed to higher and higher Mach numbers. At a distance of about one plate length from the trailing edge, there is only one mode in a Mach number range of 0–20. The dominant mode emerging at all wake stations, and for high enough Mach numbers, is the so-called vorticity mode that is centered around the generalized inflection point layer. The structure of the dominant mode is also obtained analytically for all streamwise wake locations and it is shown how the far-wake limit is approached. Asymptotic results for the hypersonic mixing layer given by a tanh and a Lock distribution are also given.
Numerical simulations of the structure of supersonic shear layers
Authors: Farouk B. , Oran E. S. , Kailasanath K.
Published: July 2002

Time-dependent two-dimensional numerical calculations were performed to study the mixing characteristics of unforced, planar, confined shear layers formed by two parallel streams of air that come into contact after passing over a splitter plate. The evolution of the shear layer was examined by systematically varying the velocities, densities, and the static pressures of the two streams that come into contact at the trailing edge of the plate. At least one of the streams was always supersonic. For the range of the parameters studied, the supersonic shear layers show some organization, albeit less coherent than their subsonic counterparts. The most amplified frequency, obtained by Fourier analysis of the velocity and pressure fluctuations, depends on the effective inlet momentum thickness. Convective Mach numbers of the streams corresponding to each side of the shear layer were found to be quite different. The simulations indicate that the single convective Mach number as derived from an isentropic model is not sufficient to characterize the mixing behavior when the velocity, pressure, and density ratios are changed independently.
Initial laboratory observations of the evolution of a vortex pair in a stratified shear flow
Authors: Delisi Donald P. , Robins Robert E. , Lucas R. David
Published: July 2002

First results are presented for a laboratory experiment and a supporting numerical simulation of the evolution of a vortex pair in a stratified and sheared flow where the Richardson number is 1.0 and the vortex Reynolds number is 14 400. Both the laboratory experiment and the numerical model show that the vortex pair evolves into a single vortex. It is believed that these are the first reported experimental measurements on the evolution of a vortex pair in a stratified shear flow.
Hydrodynamic stability of model shear layer configurations in the presence of a chemical reaction
Authors: Lyell M. J.
Published: July 2002

The stability of model shear layer configurations is investigated in the presence of chemical reactions. The reaction, which is considered to be premixed and laminar, is of an idealized form. The analysis is linear and inviscid. A generalized governing equation for the fluctuation pressure is obtained. Attention is focused on both the zero activation energy case and the quasisteady problem. Specific model problems are investigated. Stability results are compared to known results in the nonreacting flow case.
Eigenfunction expansion of the flow in a spinning and nutating cylinder
Authors: Selmi Mohamed , Li Rihua , Herbert Th.
Published: July 2002

Spin-stabilized projectiles with liquid payloads may experience different types of flight instabilities caused by the fluid motion in the payload cylinder. The first type is known to occur in low viscosity fluids, i.e., at high Reynolds numbers owing to resonance with inertial waves at critical frequencies. The second type originates from a forced secondary flow at arbitrary frequency and is most pronounced for fluids of high viscosity, i.e., relatively low Reynolds numbers. In this paper a method is developed that permits unified analysis of both types of instability since it can be used for flows at high Reynolds numbers inaccessible to other approaches. The method is based on a spatial eigenfunction expansion of the axial velocity component and reduces the three-dimensional problem to one dimension. The eigenfunctions are given in closed form and the eigenvalues are determined numerically by solving a system of nonlinear equations.
Convection in a fluid layer with asymmetric boundary conditions
Authors: Clever R. M. , Busse F. H.
Published: July 2002

Steady convection rolls in a horizontal fluid layer heated from below are described numerically with a Galerkin method. A rigid lower and stress-free upper boundary are assumed, while the temperature is fixed at both boundaries. The stability of the steady solutions with respect to arbitrary three-dimensional infinitesimal disturbances is analyzed and the stability boundaries in the Rayleigh number–wave-number plane are determined for selected Prandtl numbers. It is found that results of the analysis correspond more closely to the case of two rigid boundaries than to the case of two stress-free boundaries. The domains of stability in the case of asymmetric boundaries are larger at high Prandtl numbers than in the case of two rigid boundaries, but smaller for low Prandtl numbers. Some of the asymmetric properties of convection rolls are discussed.
The role of m=0 modal components in the reversed-field-pinch dynamo effect in the single fluid magnetohydrodynamics model
Authors: Nebel R. A. , Caramana E. J. , Schnack D. D.
Published: July 2002

The role of the m=0 modal components on the reversed-field-pinch (RFP) dynamo effect is examined in the single fluid magnetohydrodynamic (MHD) model by comparing results with and without various nonlinear convolutions of the m=0 spectrum. Results indicate that the dynamo effect comes directly from the m=1 instabilities and the effect of other nonlinear convolutions is small. Scaling studies of δB/B with the Lundquist number (S) are also performed. It is found that δB/B is independent of S (diffusionlike scaling), which is consistent with the view that the dynamo effect arises directly from the m=1 modes.
Stability of toroidicity-induced drift waves in divertor tokamaks
Authors: Briguglio S. , Romanelli F. , Bishop C. M. , Connor J. W. , Hastie R. J.
Published: July 2002

The stability of toroidicity-induced drift waves in a tokamak equilibrium with magnetic separatrix is studied both analytically and numerically. In particular, the task of a proper determination of the complex ballooning parameter θ0 is performed by solving the stationarity condition for the eigenvalue. Results show qualitative dependence on the location of the x point in the meridian plane. Specifically, locating the x point in the equatorial plane, both on the outside and on the inside of the plasma, causes a deepening of the well structure in the potential for the eigenmode, thereby enforcing the inhibition of the shear damping and the marginal stability result obtained in the circular magnetic surfaces case. On the other hand, the location of the x point at the top of the plasma produces a flattening of the well and restores the shear damping, yielding stabilization of the mode. A new quasimarginally stable branch, corresponding to modes localized around the x point, is shown to exist at high values of the separatrix parameter k and x-point location close to the equatorial plane.
Numerical simulations of perturbed Vlasov equilibria
Authors: Demeio L. , Zweifel P. F.
Published: July 2002

In this work, the long-time behavior of the solutions of the Vlasov–Poisson system when starting near a spatially homogeneous equilibrium is analyzed numerically. It is found that the asymptotic state toward which the system evolves is not a Bernstein–Green–Kruskal (BGK) equilibrium, but can rather be described by a superposition of BGK modes. Also, it is shown that the small oscillations at the plasma frequency after saturation in the one-sided bump-on-tail instability are due to beating between the unstable mode and the least stable mode.
Nonlinear evolution of the modulational instability
Authors: Goldstein P. P. , Rozmus W.
Published: July 2002

The Ritz variational method has been applied to the nonlinear Schrödinger equation to construct a model for the nonlinear evolution of the modulational instability. The spatially periodic trial function was chosen in the form of a combination of Jacobian elliptic functions, with the dependence of its parameters subject to optimization. The model predicts development of the instability through localization to a quasisoliton state and a periodic recurrence of the initial condition. Theoretical predictions compare well with numerical solutions to the nonlinear Schrödinger equation.
Spark channel stability
Authors: Hill R. D.
Published: July 2002

Analysis of shock underpressure air flowing back into the residual channel of a spark indicates that Rayleigh–Taylor instabilities may grow mainly by affecting flow in the cool air region surrounding the channel.
Radiative properties and line trapping effects in post-explosion inertial fusion plasmas
Authors: MacFarlane J. J. , Wang P.
Published: July 2002

Radiative transfer will play a major role in energy transport within post-explosion inertial confinement fusion (ICF) plasmas. The physical processes affecting radiative energy transport in such moderate-density plasmas are qualitatively different from those of many higher-opacity laboratory plasmas, and reliable analyses of their radiative properties require the use of relatively detailed physical models. In this paper, the radiative processes of plasmas generated by high-gain inertial fusion pellet explosions are investigated. A nonlocal thermal dynamic equilibrium (LTE) radiative transfer/ionization balance code is used in which steady-state ionization and excitation populations are calculated by solving multilevel atomic rate equations self-consistently with the radiation field. It is shown that for much of their hydrodynamic evolution these plasmas are often optically thick to line radiation, but optically thin to the bulk of the continuum radiation. Because of this, line trapping—i.e., the self-attenuation of line radiation in their optically thick cores—plays a critical role in both altering the atomic level populations and in significantly reducing the escaping radiation flux. Results are compared with those obtained using thermal equilibrium, LTE, optically thin, and multigroup radiation diffusion models. Also discussed are the ramifications of the present results for radiation-induced damage in high-gain ICF facilities.
Theory of the m=1 kink mode in toroidal plasma
Authors: de Blank H. J. , Schep T. J.
Published: July 2002

The energy principle of ideal magnetohydrodynamics (MHD) is used to study the ideal MHD stability of the m=1 internal kink mode in a toroidal plasma. The equilibrium configurations that are considered allow for a broad region where the safety factor q is close to unity. This region may extend to the magnetic axis, or may be a singular layer. The minimization of the energy functional yields an implicit equation for the growth rate that can be solved by simple numerical means. The examples that are treated numerically retain the essential features of experimentally expected q profiles. The growth rate depends very sensitively on the q profile close to unity and increases with the width of the q≊1 layer. The highest values are of the order of the inverse aspect ratio ε divided by the poloidal Alfvén time. Nonmonotonic profiles with q>1 on axis are more unstable than monotonic q profiles with q<1. In the latter case, the mode tends to be localized in the q≊1 region instead of in the center.
The drift Hamiltonian in a magnetic field with a separatrix
Authors: Boozer Allen H.
Published: July 2002

In a plasma equilibrium, the simplest coordinates to use for the calculation of particle drift trajectories are magnetic coordinates. Unfortunately, these coordinates are singular on a magnetic separatrix, which makes their use impractical in this region. Here a coordinate system that is nonsingular on a magnetic separatrix while retaining most of the attractive features of magnetic coordinates is developed. In particular, a simple expression for the Hamiltonian for particle drift trajectories is obtained and a simple prescription for making quantities, such as the electric potential, constant on the magnetic surfaces is given.