bluuebunny/crossref_metadata_2025 huggingface dataset:
Gravitational perturbations of algebraically special space-times via the ℋℋ equation
Authors: Torres del Castillo G. F.
Published: July 2002

By using the approach to the Einstein field equations based on the existence of a congruence of null two-dimensional surfaces, it is shown that a scalar potential that satisfies a second-order linear partial differential equation generates gravitational perturbations of a given algebraically special solution of the Einstein vacuum field equations with cosmological constant. Generalizations of this result to the case of simultaneous perturbations of the gravitational and the matter fields are also indicated.
Lobachevskian quantum field theory in 2ν dimensions
Authors: Kerimov G. A.
Published: July 2002

In this, the first of a series of papers on quantum field theory in a Lobachevskian space (a space-time, topologically Euclidean, of constant negative curvature), the scalar fields are considered. These Lobachevskian fields, which are related in the flat-space limit to the Euclidean fields, act in a space ℋ, which again has Fock space structure. A formalism is presented that is valid in an arbitrary number of dimensions and therefore allows the use of dimensional regularization.
Analysis of the Moyal product in a flat space
Authors: Kammerer J-B.
Published: July 2002

This paper studies the mathematical properties of Moyal product defined in the space R2n. They correspond to the properties of quantum mechanics and permit us to consider classical mechanics as a limit of quantum mechanics when Planck’s constant vanishes. A table of formulas and two algebras give in particular the necessary results for the approximation of the Moyal product and for the spectral resolution.
Deformation and contraction in Clifford algebras
Authors: Ablamowicz R.
Published: July 2002

Spin ideals of Clifford algebras over quadratic spaces of any rank are constructed through contractive limits of suitably deformed classical spin ideals of nondegenerate Clifford algebras. The deformation of the algebraic structures, including the standard Witt basis for the quadratic space, results only from a deformation of the underlying quadratic form. It is shown that a contractive limit of deformed twistor spaces, considered as spin ideals of the Dirac–Clifford algebra, provides a decomposable representation space for the Galilei–Clifford algebra. The limit spin ideals of degenerate Clifford algebras are then decomposed into indecomposable Clifford modules.
Classical particles with internal structure. II. Second-order internal spaces
Authors: Atre M. V. , Mukunda N.
Published: July 2002

A systematic study of classical relativistic particles with internal structure, initiated in a previous paper, is continued and a study of second-order internal spaces (SOS) is presented within the framework of the Lagrangian form of constrained dynamics. Such internal spaces Q are those for which a phase-space treatment must necessarily use the cotangent bundle T*Q. The large variety of possible SOS’s—ten discrete cases and two one-parameter families—is separated into those capable of a manifestly covariant description, and those for which special methods based on the transitive action of SL(2,C) on a coset space are needed. The concept of the isotopy representation plays an important role in this context. Seven of the possible discrete SOS’s are shown to be describable in a manifestly covariant way; two discrete and one one-parameter family of SOS’s are shown to be unphysical in the sense that no Lagrangians can be written in which the internal and the space-time position variables are nontrivially coupled; and the remaining single discrete and one one-parameter family are shown to be physical though not describable in a manifestly covariant way. General phase-space methods uniformly applicable to all SOS’s are developed; and as an illustrative example a Lagrangian model for an SOS in which the internal space is spanned by two orthonormal spacelike unit vectors is presented.
Yang–Mills theory and the Batalin–Fradkin–Vilkovisky formalism
Authors: McMullan David
Published: July 2002

In this paper a generalized dynamical description of classical Yang–Mills theory will be presented. As a consequence of this work, a firm dynamical underpinning to the Batalin–Fradkin–Vilkovisky (BFV) formalism will emerge. This in turn will supply a precise geometric characterization of the ghost and conjugate ghost fields.
Jauch–Piron states in W*-algebraic quantum mechanics
Authors: Amann Anton
Published: July 2002

A state φ on a W*-algebra ℳ is said to fulfill the Jauch–Piron condition if φ(p)=φ(q)=1 for projections p,q∈ℳ implies φ(p∧q)=1. Here p∧q denotes the infimum of p and q in the projection lattice of ℳ. The Jauch–Piron condition is a compatibility condition between the algebraic and the lattice-theoretic approach for the description of physical systems. Normal (i.e., σ-weakly continuous) states always fulfill the Jauch–Piron condition. It is argued that states not fulfilling this condition should be regarded as unphysical. It is shown that a state φ on a σ-finite factor ℳ is singular if and only if projections e, f∈ ℳ exist such that φ(e)=φ( f )=1 and e∧f=0. In particular, any pure state φ on ℳ fulfilling the Jauch–Piron condition is normal, which implies that the underlying factor ℳ is of type I. Furthermore, the following result is proved: Let φ be a pure Jauch–Piron state on W*-algebra ℳ with separable predual and without any commutative summand. Then φ is normal and a central projection z0∈ ℳ exists such that φ(z0)=1 and z0 ℳz0 is a factor of type I. Thus, cum grano salis, pure Jauch–Piron states exist only on commutative W*-algebras and type I factors. The former case corresponds to classical theories, the latter to Hilbert-space quantum mechanics. The implications of these results on the interpretation of quantum mechanics are discussed.
Exact solutions of the multidimensional classical φ6-field equations obtained by symmetry reduction
Authors: Winternitz P. , Grundland A. M. , Tuszyński J. A.
Published: July 2002

The often used φ6 model of classical critical phenomena is studied in (3+1)-dimensional Minkowski and Euclidean spaces. The Euler–Lagrange equations describing the kinetics of the scalar order parameter are in this case nonlinear Klein–Gordon equations. The method of symmetry reduction is systematically applied to derive all the solutions invariant under subgroups with generic orbits of codimension 1. Whenever the obtained ordinary differential equations have the Painlevé property, they can be transformed to one of two standard forms. These are then solved in terms of elliptic functions or elementary ones. This results in a large number of new exact solutions. Particularly interesting solutions are found in the immediate vicinity of the tricritical point. Our treatment of the φ6 theory is complete only for the four-dimensional spaces M(3,1) and E(4), but many of the results are given for the more general cases of M(n,1) and E(n+1).
An application of filtering theory to parameter identification using stochastic mechanics
Authors: Beumee J. G. B. , Rabitz H.
Published: July 2002

An estimation method for unknown parameters in the initial conditions and the potential of a quantal system using the stochastic interpretation of quantum mechanics and some results in system theory are presented. According to this interpretation the possible trajectories of a particle through coordinate space may be represented by the realization of a stochastic process that satisfies a stochastic differential equation. The drift term in this equation is derived from the wave function and consequently contains all unknown parameters in the initial conditions and the potential. The main assumption of the paper is that a continuous sequence of position measurements on the trajectory of the particle can be identified with a realization of this stochastic process over the corresponding period of time. An application of the stochastic filtering theorems subsequently provides a minimum variance estimate of the unknown parameters in the drift conditional on this continuous sequence of measurements. As simple illustrations, this method is used to obtain estimates for the initial momentum of a free particle given measurements on its trajectory and to construct an estimator for the unknown parameters in a harmonic potential. It is shown that an optimal estimator exists if the stochastic processes are associated with a wave function from a potential of the Rellich type. In addition the a posteriori probability density of the parameters in the quantal system is calculated, assuming that all parameters involved prescribe a Rellich potential.
Heisenberg inequality and the complex field in quantum mechanics
Authors: Lahti Pekka J. , Maczynski Maciej J.
Published: July 2002

Observables A and B satisfy the Heisenberg inequality if the product of their variances has a positive lower bound independent of the state of the system. In the Hilbert space formulation of quantum mechanics it is a consequence of the Schwarz inequality that the Heisenberg-type inequality Var(A,φ)⋅Var(B,φ)≥ (1)/(4) ‖〈Aφ‖Bφ〉−〈Bφ‖Aφ〉‖2 holds for any pair of observables A and B (represented as self-adjoint operators) and for any (vector) state (represented as a unit vector). If inf{‖〈Aφ‖Bφ〉−〈Bφ‖Aφ〉‖ ‖φ∈dom(A) ∩dom(B)}≠0 then A and B satisfy the Heisenberg inequality. In the present paper the derivability of the Heisenberg-type inequality is analyzed within the general theoretical frame of a sum logic. It is shown that any real-valued non-negative function (A,α)→f(A,α) of observables A and of states α, which has a symmetry property f(A+B,α)+f(A−B,α)=2f(A,α)+2f(B,α) with respect to observables, satisfies the Heisenberg-type inequality f(A,α)⋅f(B,α)≥ (1)/(4) ‖ f(A+B,α)−f(A,α)−f(B,α)‖2 for all observables A and B and for all states α. The natural probabilistic realizations f1(A,α)=Exp(A2,α) and f2(A,α)=Var(A,α) of such functions are then analyzed. It turns out that only with the complex extension of the theory can the Heisenberg inequality be attained in the Hilbert space realization of the theory. This is used as an argument in favor of the complex field as the scalar field of quantum mechanics.
Massive fields at null infinity
Authors: Winicour J.
Published: July 2002

The question of whether massive fields are consistent with the asymptotics of massless fields at null infinity is addressed. As a first step, it is shown at the level of linearized theory that massive fields have O(1/R∞) asymptotic behavior.
On the Heisenberg and orthosymplectic superalgebras of the harmonic oscillator
Authors: Beckers J. , Dehin D. , Hussin V.
Published: July 2002

The new invariance superalgebra osp(2,2n)(+sh(2,2n) for an n-dimensional quantum harmonic oscillator is proposed, and the corresponding supersymmetric Hamiltonian is constructed. This superalgebra is related to the structure osp(3,2n) recently studied by Englefield [J. Phys. A 21, 1309 (1988)]. By interchanging the even and odd characters of the fundamental generators belonging to the Heisenberg superalgebra sh(2,2n), the connection between both structures is established and its consequences exploited. The specific cases n=1,2,3 are discussed and compared with recent contributions. Some general conclusions are also summarized.
Characteristic functions and higher order Lagrangians
Authors: Buchdahl H. A.
Published: July 2002

In the context of the extension of the Hamilton–Jacobi theory to include Lagrangians involving higher derivatives the characteristic function seems not to have been considered. This omission is here rectified.
The propagator in the generalized Aharonov–Bohm effect
Authors: Oh C. H. , Soo C. P. , Lai C. H.
Published: July 2002

The nonrelativistic propagator is derived by formulating the generalized Aharonov–Bohm effect, valid for any gauge group in a general multiply connected manifold, as a gauge artifact in the universal covering space. The loop phase factors and the free homotopy propagators arise naturally. An explicit expression for the propagator when there are two solenoids present is given.
Exact path integral solution of the Coulomb plus Aharonov–Bohm potential
Authors: Chetouani L. , Guechi L. , Hammann T. F.
Published: July 2002

The Green’s function for the sum of the Coulomb and Aharonov–Bohm potentials is calculated exactly in the path integral formalism. The energy spectrum is deduced.
An algorithm for calculating the roots of a general quintic equation from its coefficients
Authors: King R. B. , Canfield E. R.
Published: July 2002

Classical mathematics is used to derive an algorithm for expressing the roots of a general quintic equation in terms of its coefficients. This algorithm requires the solution of two quadratic equations and one cubic equation as well as the evaluation of two infinite series, namely, one Jacobi nome and one theta series. This algorithm has been implemented on a microcomputer.
(1+1)-Dimensional hierarchies of multispeed discrete Boltzmann model equations
Authors: Cornille Henri
Published: July 2002

Multispeed discrete Boltzmann models in Rd, satisfying all conservation laws and leading to well-defined temperatures, are studied. The (1+1)-dimensional restriction of the system of partial differential equations (PDE) satisfied by the densities of these models can be classified. One class is characterized, along a chosen coordinate, by the number and location of the independent densities and by the number and physical meaning of the independent collision terms. Each class defines a hierarchy of PDE that depends on the dimension d of a particular model in Rd. Different classes associated either with two velocity speeds 1, and 1, (d)1/2 and 2, and 2, (d)1/2 or three velocity speeds 0, 1, and 0, 2, are obtained. Each class represents a d-hierarchy of a well-known discrete model. The simplest exact solutions which are the similarity shock wave solutions are discussed and compared with the Rankine–Hugoniot solutions.
Eigenfunction expansions associated with the curl derivatives in cylindrical geometries: Completeness of Chandrasekhar–Kendall eigenfunctions
Authors: Yoshida Zensho
Published: July 2002

Eigenfunctions of the curl derivatives are used in many different fields of theoretical physics. For example, in plasma physics, an eigenfunction of curl represents a certain eigenstate of a plasma that has the force-free property. The present theory proves that the spectral resolution of the curl operator gives a complete eigenfunction expansion of a solenoidal vector field with homogeneous boundary and flux conditions. Useful decomposition theories and a previous abstract result [Math. Z. 204, 235 (1990)] are concisely summarized. Explicit eigenfunctions have been studied in cylindrical geometries. Chandrasekhar–Kendall functions [Astrophys. J. 126, 457 (1957)], which are eigenfunctions of the curl derivatives in a cylindrical domain, give an orthogonal complete basis of the Hilbert space that is the orthogonal complement of the space of irrotational vector fields.
Models with Hopf terms
Authors: de Azcárraga J. A. , Izquierdo J. M. , Zakrzewski W. J.
Published: July 2002

The geometrical structure of the Hopf term and its relation to the spin of a skyrmion is studied. An ansatz describing the most general one-skyrmion field configuration in three dimensions is introduced and various properties of the physical Hopf term for it are exhibited. The extension to seven dimensions is also made. Some comments are also made about the quantization of the coefficient of the Hopf term in the action.
Prolongation structure of the Landau–Lifshitz equation
Authors: Roelofs G. H. M. , Martini R.
Published: July 2002

The prolongation method of Wahlquist and Estabrook is applied to the Landau–Lifshitz equation. The resulting prolongation algebra is shown to be isomorphic to a subalgebra of the tensor product of the Lie algebra so(3) with the elliptic curve vα2−vβ2=jβ−jα (α,β=1,2,3), which is essentially a subalgebra of the Lie algebra applied by Date et al. in a different context. Taking a matrix representation of so(3) gives rise to a Lax pair of the Landau–Lifshitz equation in agreement with the results found by Sklyanin. A system of related equations is deduced which can be used for the computation of auto-Bäcklund transformations of the Landau–Lifshitz equation.
The Wick-ordered exponential of the dipole field as a field of type 𝒮
Authors: Moschella U.
Published: July 2002

We construct the Wick-ordered exponential of the dipole field, an infrared singular field. We show that the field operator is an object much more singular than its own vacuum expectation values. The actual construction involves the spaces of type 𝒮 by Gelfand and Shilov and seems to provide the most general distributional scheme for the choice of test function in (gauge) quantum field theories.
Rigorous calculation of the collective excitation spectrum in a mean field model
Authors: Momont B.
Published: July 2002

The dynamics of macroscopic density fluctuations is studied in the Overhauser model. The spectral decomposition of the time derivative on the Hilbert space of macroscopic density fluctuations is completely determined. The spectrum of the collective excitations is rigorously calculated.
Quantized braided groups
Authors: Hlavatý Ladislav
Published: July 2002

Algebras that represent a generalization of both quantum groups, quantum supergroups, and braided groups are defined. They are given by a pair of solutions of the Yang–Baxter equation that satisfy some additional conditions. Several examples are presented.
Multiparameter link invariants from quantum supergroups
Authors: Links J. R. , Zhang R. B.
Published: July 2002

A method is developed for constructing multiparameter link invariants for a class of representations of the quantum supergroups Uq(gl(m‖n)). The cases Uq(gl(1‖1)) and Uq(gl(2‖1)) are studied in detail. In the former we obtain a multiparameter generalization of the Alexander–Conway invariants.
Resolution of missing label problems; a new perspective on K-matrix theory
Authors: Rowe D. J.
Published: July 2002

K-matrix theory is an effective algebraic way of determining inner products and constructing orthonormal bases vectors for the carrier spaces of induced representations of Lie groups and Lie algebras. The theory is applied in this paper to give canonical resolutions of missing label problems.
Some extensions of semiclassical limit ℏ → 0 for Wigner functions on phase space
Authors: Arai Takahiro
Published: July 2002

The semiclassical asymptotics of the unitary quantum propagator applied to the Wigner functions, which are associated with the initial quantum state belonging to Schwartz class, are considered herein. The limit ℏ → 0 of the semiclassical asymptotics of these Wigner functions is investigated. As a consequence of this result, there exists a simple semiclassical asymptotic, which obeys the unitary conservation law over any finite time interval [0,T].
Mass spectra from field equations. II. The electromagnetic contribution
Authors: Good R. H.
Published: July 2002

In the first article a method for finding a mass spectrum from a given field equation was developed. The method is extended here to provide for the self-electromagnetic effect on the rest mass. The process is described by example: the method is applied here for the equations of a complex scalar field interacting with the electromagnetic field. A spectrum of charged-particle masses is obtained. A quantum number for the charges of the mass levels appears. After some special assumptions about the dependence on the vector potential are made, there are finite electromagnetic contributions to the rest masses of the particle states.
Number density, entropy density, and energy density of statistical mechanics for D-dimensional grand canonical ensembles
Authors: Kostin M. D.
Published: July 2002

A partial differential equation for the number density of a D-dimensional grand canonical ensemble is used to derive an explicit expression for the semiclassical number density. This is accomplished by first using the Bloch equation and its solutions to derive the classical number density and then combining the classical result with a Planck’s constant expansion of the partial differential equation to obtain the semiclassical formula. Similar results are also derived for the entropy density, energy density, and grand potential density of a D-dimensional grand canonical ensemble.
Knotted periodic orbits in Rössler’s equations
Authors: El-Rifai E. A. , Ahmed E.
Published: July 2002

Knots corresponding to the Rössler chaotic model are defined. A systematic method to determine the knots for any order of the chaotic trajectory is given. For the m chaotic path Rm, a minimal (2m−1)-braid representative is given. Hence the order of the chaotic trajectory is knot invariant. An algorithm for constructing any Rössler knot, using a figure eight knot, is given.
Racah coefficients and 6−j symbols for the quantum superalgebra Uq
(osp(1‖2))
Authors: Minnaert Pierre , Mozrzymas Marek
Published: July 2002

The tensor product of three irreducible representations of the quantum superalgebra Uq(osp(1‖2)) is studied and the super-q analogs of Racah coefficients and 6−j symbols for the quantum superalgebra Uq(osp(1‖2)) are defined. Racah coefficients and 6−j symbols depend on the superspin l and the parity λ which characterize the irreducible representations of Uq(osp(1‖2)) but the dependence on parities can be factored out so that one can define parity independent 6−j symbols. It is shown that the 6−j symbols for the quantum superalgebra Uq(osp(1‖2)) satisfy symmetry properties and orthogonality relations similar to those of the 6−j symbols for quantum algebra Uq(su(2)).
Quantum-classical correspondence using projection operators
Authors: Omnès Roland
Published: July 2002

Classical properties, associated with a large phase space domain with a smooth boundary as compared to the Planck constant, are shown to be expressed quantum-mechanically by a family of quantum projection operators with the help of known theorems in microlocal analysis. Under the conditions of Egorov’s theorem, the conservation of this correspondence under classical/quantum dynamics is asserted.
Wigner distribution function for finite systems
Authors: Atakishiyev Natig M. , Chumakov Sergey M. , Wolf Kurt Bernardo
Published: July 2002

We construct a Wigner distribution function for finite data sets. It is based on a finite optical system; a linear wave guide where the finite number of discrete sensors is equal to the number of modes which the guide can carry. The dynamical group for this model is SU(2) and the wave functions are sets of N=2l+1 data points. The Wigner distribution function assigns classical c-numbers to the operators of position, momentum, and wave guide mode.
Strict quantization of coadjoint orbits
Authors: Landsman N. P.
Published: July 2002

A strict quantization of a compact symplectic manifold S on a subset I⊆R, containing 0 as an accumulation point, is defined as a continuous field of C*-algebras {Aℏ}ℏ∈I, with A0=C0(S), and a set of continuous cross sections {Q(f)}f∈C∞(S) for which Q0(f)=f. Here Qℏ(f*)=Qℏ(f)* for all ℏ∈I, whereas for ℏ→0 one requires that i[Qℏ(f),Qℏ(g)]/ℏ→Qℏ({f,g}) in norm. We discuss general conditions which guarantee that a (deformation) quantization in a more physical sense leads to one in the above sense. Using ideas of Berezin, Lieb, Simon, and others, we construct a strict quantization of an arbitrary integral coadjoint orbit Oλ of a compact connected Lie group G, associated to a highest weight λ. Here I=0∪1/N, so that ℏ=1/k, k∈N, and A1/k is defined as the C*-algebra of all matrices on the finite-dimensional Hilbert space Vkλ carrying the irreducible representation Ukλ(G) with highest weight kλ. The quantization maps Q1/k(f) are constructed from coherent states in Vkλ, and have the special feature of being positive maps.
Chaos in the Gyldén problem
Authors: Diacu Florin , Şelaru Dan
Published: July 2002

We consider the Gyldén problem—a perturbation of the Kepler problem via an explicit function of time. For certain general classes of planar periodic perturbations, after proving a Poincaré–Melnikov-type criterion, we find a manifold of orbits in which the dynamics is given by the shift automorphism on the set of bi-infinite sequences with infinitely many symbols. We achieve the main result by computing the Melnikov integral explicitly.
Functional versus canonical quantization of a nonlocal massive vector-gauge theory
Authors: Amorim R. , Barcelos-Neto J.
Published: July 2002

It has been shown in literature that a possible mechanism of mass generation for gauge fields is through a topological coupling of vector and tensor fields. After integrating over the tensor degrees of freedom, one arrives at an effective massive theory that, although gauge invariant, is nonlocal. Here we quantize this nonlocal resulting theory both by path integral and canonical procedures. This system can be considered as equivalent to one with an infinite number of time derivatives and consequently an infinite number of momenta. This means that the use of the canonical formalism deserves some care. We show the consistency of the formalism we use in the canonical procedure by showing that the obtained propagators are the same as those of the (Lagrangian) path integral approach. The problem of nonlocality appears in the obtainment of the spectrum of the theory. This fact becomes very transparent when we list the infinite number of commutators involving the fields and their velocities.
Lattice electromagnetic theory from a topological viewpoint
Authors: Teixeira F. L. , Chew W. C.
Published: July 2002

The language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice. It is shown that differential forms and their discrete counterparts (cochains) provide a natural bridge between the continuum and the lattice versions of the theory, allowing for a natural factorization of the field equations into topological field equations (i.e., invariant under homeomorphisms) and metric field equations. The various potential sources of inconsistency in the discretization process are identified, distinguished, and discussed. A rationale for a consistent extension of the lattice theory to more general situations, such as to irregular lattices, is considered.
Group invariant solutions for the N=2 super Korteweg–de Vries equation
Authors: Ayari M. A. , Hussin V. , Winternitz P.
Published: July 2002

The method of symmetry reduction is used to solve Grassmann-valued differential equations. The (N=2) supersymmetric Korteweg–de Vries equation is considered. It admits a Lie superalgebra of symmetries of dimension 5. A two-dimensional subsuperalgebra is chosen to reduce the number of independent variables in this equation. We are then able to give different types of exact solutions, in particular soliton solutions.
Method of handling the divergences in the radiation theory of sources that move faster than their waves
Authors: Ardavan H.
Published: July 2002

The nonintegrable singularities that arise when the retarded potentials associated with supersonically or superluminally moving sources are differentiated are closely related to those encountered in the context of the Cauchy problem for hyperbolic equations over odd-dimensional space-times. The purpose of this paper is to point out that the field components are given in these cases by Hadamard’s finite parts of the resulting divergent integrals, as in the case of the Cauchy problem, and to show that the procedure familiar from the subluminal regime—which is used by Hannay—is not applicable when there are source elements that approach the observer with the wave speed and zero acceleration at the retarded time.
Irreversible weak limits of classical dynamical systems
Authors: Gentili F. , Morchio G.
Published: July 2002

A general discussion is given of weak limits of classical dynamical systems depending on a parameter. The resulting maps are shown to be invertible if and only if they define a group of measure preserving point transformations. The irreversible case automatically leads to positive bistochastic maps and is characterized in terms of convergence properties of the corresponding automorphisms of the observable algebra. Necessary and sufficient conditions are given for the limit to define a time-independent Markov process. Two models are discussed, for a particle in a periodic potential, and for a particle interacting with fixed configurations of external obstacles.
Instability and chaos in spatially homogeneous field theories
Authors: Salasnich Luca
Published: July 2002

Spatially homogeneous field theories are studied in the framework of dynamical system theory. In particular, we consider a model of inflationary cosmology and a Yang–Mills–Higgs system. We discuss also the role of quantum chaos and its application to field theories.
Dimension of the global attractor for damped semilinear wave equations with critical exponent
Authors: Shengfan Zhou
Published: July 2002

We obtain an estimate of the upper bound of the Hausdorff dimension of the global attractor for damped semilinear wave equations with a critical exponent. The obtained Hausdorff dimension decreases as the damping grows for large damping.
Gauge fixation and global phase time for minisuperspaces
Authors: Simeone Claudio
Published: July 2002

Homogeneous and isotropic cosmological models whose Hamilton–Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system are used to define a global phase time in terms of the canonical coordinates and momenta of the minisuperspaces. The procedure clearly shows how the geometry of the constraint surface restricts the choice of time; the consequences that this has on the path integral quantization are discussed.
A new perturbative technique for solving integro-partial differential equations
Authors: Becker Peter A.
Published: July 2002

Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown distribution function. The standard approach to solving the resulting nonlinear partial differential equation involves the use of predictor–corrector algorithms, which often require many iterations to achieve an acceptable level of convergence. In this paper we present an alternative procedure that allows us to separate a family of integro-partial differential equations into two related problems, namely (i) a perturbation equation for the temperature, and (ii) a linear partial differential equation for the distribution function. We demonstrate that the variation of the temperature can be determined by solving the perturbation equation before solving for the distribution function. Convergent results for the temperature are obtained by recasting the divergent perturbation expansion as a continued fraction. Once the temperature variation is determined, the self-consistent solution for the distribution function is obtained by solving the remaining, linear partial differential equation using standard techniques. The validity of the approach is confirmed by comparing the (input) continued-fraction temperature profile with the (output) temperature computed by integrating the resulting distribution function.
Symmetries of boundary value problems in mathematical physics
Authors: Makai M. , Orechwa Y.
Published: July 2002

The problem considered here is to find a function satisfying a linear elliptic differential or integral equation inside a finite simply region V and another linear first-order differential or integral equation on the ∂V boundary. The symmetries of the above problem form a point group. We show that if the homogeneous problem has only the trivial solution, then the symmetry of the solution inside V inherits the symmetry of the boundary value, given on ∂V. The boundary value is decomposed into irreducible components and the physical meaning of the irreducible components is highlighted. We then apply the results to investigate a widely utilized numerical solution technique that is based on a variational principle and utilizes two approximations. The first one approximates, the solution inside V by a polynomial, the second approximation assumes the solution on the boundary to be a low-order polynomial. By means of group representation theory, we show that the mentioned approximations may fail for certain combinations. The predicted problems have been observed in the VARIANT code, which is routinely used to solve the multigroup neutron diffusion equation. Our method is also applicable to the Schrödinger, and to heat conductance and wave equations.
Isospectral deformation of some shape invariant potentials
Authors: Jafarizadeh M. A. , Esfandyari A. R. , Panahi-Talemi H.
Published: July 2002

Here we generalize the isospectral deformation of the discrete eigenspectrum of Eleonsky and Korolev [Phys. Rev. A 55, 2580 (1997)] to continuous eigenspectrum of some well-known shape-invariant potentials. We show that the isospectral deformations preserve their shape invariance properties. Hence, using the preserved shape invariance property of the deformed potentials, we obtain both discrete and continuous eigenspectrum of the deformed Rosen–Morse, Natanzon, Rosen–Morse with added Dirac delta term, and Natanzon with added Dirac delta term potentials, respectively. It is shown that deformation does not change their other pecurialities, such as the reflectionless property of the Rosen–Morse potential and the penetrationless property of the Natanzon one.
Construction of quasi-two- and higher-dimensional quantum integrable models
Authors: Kundu Anjan
Published: July 2002

A class of quantum integrable quasi-two- and higher-dimensional quantum spin as well as strongly correlated electron systems with localized interactions are proposed. The basic idea of construction is to introduce interchain interactions in an array of spin chains or one-dimensional Hubbard models through twisting transformation. The models allow explicit quantum R-matrix, Lax operator, and exact eigenvalue solution.
A new procedure for specifying nonradiating current distributions and the fields they produce
Authors: Marengo Edwin A. , Ziolkowski Richard W.
Published: July 2002

This paper reports a new procedure for specifying monochromatic nonradiating (NR) current distributions (NR sources) and the electric and magnetic fields they produce (NR fields). Vector spherical harmonics and a Fourier–Bessel series are used to derive a new vector spherical-wave expansion for continuous NR fields confined within a spherical volume. The analysis yields complete orthogonal sets in terms of which all such NR fields can be expanded. By making use of a Maxwell operator representation for NR current distributions, we obtain a new series expansion for NR current distributions confined within a spherical volume. The analysis also yields complete sets for such NR current distributions. The developed theory is illustrated with special cases.
Cluster expansion for P(φ)2: explicit estimates
Authors: Prodan E.
Published: July 2002

We apply the tree expansion to the polynomial self-interacting quantum fields in two dimension. In the range of small coupling constants, we show that the expansion is also convergent when the full propagator is considered and the theory is regularized by normal ordering. Explicit estimates of the convergency ranges are given.
On thermodynamics of supercooled liquids and glasses
Authors: Bakai A. S.
Published: July 2002

Thermodynamics of glass-forming liquids and glasses is considered taking into account the contribution of heterophase fluctuations to the free energy. The role of heterophase fluctuations in liquids and glasses is played by nuclei of noncrystalline solids and nuclei of the liquid phase respectively. Crystalline solid state is not considered. Free energy is described on the bases of the droplet model and the model of mixed state. It is shown that three regions of stability of different structural states of the system exist on the (P,T) plane. Two of them are stability regions for droplet structural states, while the mixed state is stable in the third region in which heterophase fluctuations have the form of isolated drops. In this state, two infinite percolating clusters (liquid and noncrystalline solid) coexist. The width of the temperature interval [Tt1,Tt2] in which the mixed state is stable increases with configuration entropy (complexity) of the noncrystalline solid fraction. In the approach used, weak first-order phase transitions are observed at T=Tt1 and T=Tt2. It is shown that first- and second-order phase transitions are possible in the mixed state. The criteria for the existence of these phase transitions are obtained. Equations of state and expressions for thermodynamic parameters (entropy, heat capacity, compressibility, and thermal expansion coefficient) are derived for the droplet and mixed states.
On the secondary instability in plane Poiseuille flow
Authors: Kim John , Moser Robert D.
Published: July 2002

Numerical experiments were performed to clarify apparent differences between experimental observations and a theoretical prediction of the secondary instability in plane Poiseuille flow. It is shown that subharmonic breakdown is unlikely in natural transition as a result of the initial growth of what we call the ‘‘minus’’ modes and consequent forcing of Orr–Sommerfeld modes present in the background noise. Subharmonic breakdown was achieved only when these minus modes were continuously suppressed.
Prediction of large-scale transition features in the wake of a circular cylinder
Authors: Braza M. , Chassaing P. , Minh H. Ha
Published: July 2002

A direct numerical simulation of the viscous incompressible flow around a circular cylinder is carried out in the Reynolds number range 2000–10 000 by solving the two-dimensional time-dependent Navier–Stokes equations, using a pressure–velocity finite-volume method. Apart from the vortex shedding phenomenon, it is shown that transition waves develop in the separated shear layers and lead to mixing layer eddies. The ratio of the computed transition wave frequency over Strouhal number is in good agreement with experimental results. This allows the supposition that the instability leading to mixing layer eddies has a predominant two-dimensional origin and is predicted by the Navier–Stokes equations.
Surface-tension- and coupled buoyancy-driven instability in a horizontal liquid layer. Overstability and exchange of stability
Authors: Gouesbet G. , Maquet J. , Rozé C. , Darrigo R.
Published: July 2002

Overstability for simultaneous surface-tension- and buoyancy-driven instability in a horizontal infinite liquid layer is theoretically investigated by means of a small disturbance analysis. Formulation and results are given in dimensionless forms. Critical wavenumbers, time constants, and Marangoni numbers are computed. Besides the influence of Prandtl, Bond, and crispation numbers, the modifications induced by interfacial viscosities, heat transfer at the free surface, buoyancy with respect to a pure Marangoni mechanism, and different thermal conditions at the rigid wall, are included in the analysis. The case of exchange of stability is considered as a special case of overstability. This work provides a generalization of Takashima’s work [J. Phys. Soc. Jpn. 50, 2745, 2751 (1981)] concerning a pure Marangoni mechanism (with less general conditions).
Time correlations and random sweeping in isotropic turbulence
Authors: Nelkin Mark , Tabor M.
Published: July 2002

The Lagrangian and Eulerian frequency spectrum in isotropic turbulence is considered without a mean flow, concentrating on its second moment, the mean-square acceleration. The pressure and viscous contributions are reviewed and the scaling properties of the advective term 〈[(v⋅∇)v]2〉 are examined. Random sweeping from this term is shown to be dominant at large Reynolds numbers if the fluctuation spectrum of the kinetic energy v2(x) scales as k−5/3. If on the other hand it satisfies the same Kolmogorov scaling as the pressure going as k−7/3, then the recent renormalization group prediction of no sweeping is recovered. This question is subject to direct experimental resolution. The experiments of Van Atta and Wyngaard [J. Fluid Mech. 72, 673 (1975)] strongly indicate that the spectrum of v2 goes as k−5/3 at high Reynolds numbers, thereby supporting the sweeping hypothesis.
On the three-dimensional motion of an infinitely thin vortex sheet in an ideal fluid
Authors: Kaneda Yukio
Published: July 2002

The three-dimensional motion of an infinitely thin vortex sheet in an ideal fluid is studied on the basis of a Lagrangian representation of the motion. Some conservation properties associated with the motion are derived from the representation. The motion of an axisymmetric vortex sheet of a small area located far from the symmetry axis is analyzed in some detail.
Lagrangian velocity autocorrelation in isotropic turbulence
Authors: Kaneda Yukio , Gotoh Toshiyuki
Published: July 2002

An analysis is made of the Lagrangian and the Eulerian velocity autocorrelations RL(s,t) and RE(s,t) at times s and t for small time lag τ=s−t in isotropic decaying turbulence, and it is shown that under appropriate conditions RE≤RL for small τ in three dimensions, irrespective of the form of the energy spectrum. The behaviors of RE and RL not limited to small τ are studied by direct numerical simulations in two dimensions. The values of RL obtained by the Lagrangian renormalized approximation are found to be in good agreement with the simulations and with the existing data of three-dimensional simulations and experiments.
Simulation of scalar mixing by stationary isotropic turbulence
Authors: Jiang Tai-Lun , O’Brien Edward E.
Published: July 2002

A closure model at the two-point probability density function level is proposed, and numerically solved, for the case of passive scalar mixing in stationary isotropic turbulence. It is found that the ratio of the initial scalar microscale to the velocity microscale, λφ)0/λ, in the range 0.56–2.97, has little effect on the scalar decay rate when the initial scalar-to-velocity integral length scale ratio, Lφ)0/L, is roughly fixed at 2.0. On the other hand, when λφ)0/λ is fixed at 1.97 the ratio Lφ)0/L is found to have a significant effect on the scalar decay rate. These results mimic those from earlier direct numerical simulation (DNS) calculations, but at an accelerated time scale. The mechanical-to-scalar time scale ratio, which in stationary turbulence is inversely proportional to λ2φ, has the same asymptotic value as was reached in DNS and has the same dependence on initial conditions.
Conditions for absolute instability in the cyclotron resonance maser
Authors: Davies John A.
Published: July 2002

In this paper exact analytic conditions for absolute instability in the cyclotron resonance maser are presented for the case of a cold-beam, lossless circular waveguide and infinite interaction length in the axial direction. The conditions are expressed in terms of the parallel beam velocity, the applied magnetic field strength, and the strength of the coupling between the beam and waveguide modes. The results are applicable to both the gyrotron and cyclotron autoresonance maser operating regimes.
A self-consistent theory of radial transport of field-aligned current by microturbulence
Authors: Terry P. W. , Diamond P. H.
Published: July 2002

The radial transport of field-aligned current resulting from collisionless microturbulence is examined self-consistently. The self-consistent treatment of mode coupling is shown to constrain the transport in such a way that the relaxation of current gradients is regulated solely by electrostatic fluctuations that couple to ion dissipation, even in the presence of temperature gradients and temperature anisotropy. As a consequence, the radial flux of parallel current induced by collisionless microinstabilities is insufficient to account for the dynamo in reversed field pinch plasmas.
Physics of the L to H transition in the DIII-D tokamak
Authors: Burrell K. H. , Carlstrom T. N. , Doyle E. J. , Gohil P. , Groebner R. J. , Lehecka T. , Luhmann N. C. , Matsumoto H. , Osborne T. H. , Peebles W. A. , Philipona R.
Published: July 2002

The L to H transition in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. I, p. 159] is associated with a decrease in the edge density and magnetic fluctuations. In addition, in single-null divertor plasmas, a reduction in the heat flux asymmetry between the inner and outer divertor hit spots occurs. These observations indicate that the L to H transition is associated with the reduction in anomalous, fluctuation-connected transport across the outer midplane of the plasma. Magnetic fluctuations are measured with a poloidally distributed set of Mirnov loops while density fluctuations are detected with multiple fixed-frequency microwave reflectometers. Spectroscopic observations of edge poloidal and toroidal rotation have allowed the inference that the radial electric field just inside the separatrix is negative in the L mode and becomes more negative at the L to H transition. These changes in fluctuations and in the edge electric field occur in plasmas where the H mode is created by neutral beam heating, electron cyclotron heating, and even by Ohmic heating alone. Accordingly, these changes are characteristic of the H mode and are not artifacts of the heating method. Several published theories of the L to H transition involve the effects of the electric field and edge plasma rotation. The observations in this paper have been critically compared with these theories.
Optimum theory for the energy dissipation in a turbulent pinch
Authors: Wang Cai Yi , Bhattacharjee A.
Published: July 2002

Rigorous lower bounds are computed for the total energy dissipation in a steady driven reversed-field pinch. A variational principle is given in which energy and helicity balance, conservation of toroidal magnetic flux, and the ensemble-averaged Ohm’s law are imposed as constraints. The lowest bounds are found with the natural boundary condition derived from the variational principle. The effect of the space variation of the resistivity is also included. It is shown that the theoretical results are consistent with observations from the Los Alamos ZT-40M experiment [Phys. Fluids 27, 1671 (1984)].
Helicon waves and efficient plasma production
Authors: Komori A. , Shoji T. , Miyamoto K. , Kawai J. , Kawai Y.
Published: July 2002

Helicon waves generated by radio-frequency (rf) waves are experimentally demonstrated to have the characteristics of Landau damping, as predicted theoretically, and fully ionized plasmas are realized by this efficient coupling of rf powers to plasmas. Excited waves are identified as a helicon wave by measuring wavelengths in the plasma along the magnetic field and comparing with the dispersion relation. Good agreement is found between experimental and theoretical results.
Structure of the electrostatic wave of linear mode conversion in a magnetized plasma
Authors: Mjo/lhus E.
Published: July 2002

When an electromagnetic wave is linearly converted into an electrostatic wave, large enhancement of the wave amplitude occurs, due to the large ratio between the group velocities. The objective of this paper is to study the structure of the electrostatic wave field when such a mode conversion takes place in a magnetized plasma, and compare the amplitude enhancement with that of an unmagnetized plasma. In a magnetized plasma, the electric field of an electrostatic wave in the plasma resonance region is in the generic case governed by a third-order differential equation first discussed by Piliya and Fedorov [Zh. Eksp. Teor. Fiz. 57, 1198 (1969)]. The validity and interpretation of this equation is discussed. Full wave solutions obtained numerically are exhibited, and compared with the unmagnetized case. In particular, scaling laws describing how the maximum electric field amplitude for given energy flux depends on the magnetic field parameters are obtained.