bluuebunny/crossref_metadata_2025 huggingface dataset:
IR spectra of tropolone(OH) and tropolone(OD)
Authors: Redington Richard L. , Redington Theresa E. , Montgomery Jason M.
Published: July 2002

Infrared spectra of tropolone(OH) and tropolone(OD) obtained from vapor phase, solvated, and rare gas matrix-isolated samples, and from fluorescence dip infrared spectroscopy experiments by Frost et al. on jet-cooled samples, are analyzed with the guidance of high level ab initio molecular orbital (MO) computations. It is found that the anharmonicity of the double minimum global potential energy surface of S0 tropolone is manifested by multistate local resonance networks coupling fundamental vibrations to nearby overtone and combination states. These resonance networks pervade the IR spectrum of tropolone above 500 cm−1, and the absorbances are much more strongly perturbed from harmonic level predictions than the frequencies. Some of the IR absorbances are also sensitive to intermolecular interactions. At maximum spectral resolutions reaching ∼0.2 cm−1 only the v1 and v22 (OH stretching and nascent skeletal tunneling) vibrations show resolved vibrational state-specific tunneling doublets. The tunneling behavior of tropolone is analyzed in the accompanying article.
Time decay and spectral kernel asymptotics
Authors: Osborn T. A. , Wong R.
Published: July 2002

For quantum systems in R3 defined by a Hamiltonian H given as the sum of the negative Laplacian perturbed by a real-valued potential v(x), the large time behavior of the fundamental solution of the time-dependent Schrödinger equation is investigated. For a suitably restricted class of potentials that have algebraic decay as ‖x‖→∞, the continuous spectrum portion of the fundamental solution is characterized by an asymptotic expansion as t→±∞, which is uniform in compact subsets of R3×R3. These results are then applied to derive the large energy asymptotic expansions of the spectral kernel associated with H.
Transient thermodynamics of electromagnetic media in general relativity
Authors: Barrabès Claude
Published: July 2002

This paper is devoted to a study of the constitutive equations of relativistic electromagnetic media, when submitted to transitory processes, following the causal thermodynamics of Müller–Israel. The formalism of differential geometry is used to describe the kinematical and dynamical evolution of the medium and the thermodynamical description is given in terms of local functional relations. According to the hypothesis of Müller–Israel, the second-order terms in the deviation from thermodynamical equilibrium are taken into account in the expression of the entropy current. The relaxation terms which then appear in the transport equations restore the causality. Several cases corresponding to various kinds of media are investigated.
Scattering by a parabolic cylinder—A uniform asymptotic expansion
Authors: Ott R. H.
Published: July 2002

A uniform asymptotic expansion in the variable, determining the location of the observer for the fields scattered by a perfectly conducting parabolic cylinder, is derived. This expansion can be applied to scattering by arbitrary smooth convex surfaces of variable curvature. The accuracy of numerical results is examined.
Minimization of the energy functional of a one-dimensional fermionic system in the large-N limit
Authors: Andrić I. , Mikelić A.
Published: July 2002

A one-dimensional system of N nonrelativistic fermions in the confining potential is studied in the large-N limit where a classical limit appears.
Structural invariance of the Schrödinger equation and chronoprojective geometry
Authors: Burdet G. , Perrin M.
Published: July 2002

We describe an extension of the chronoprojective geometry and show how its automorphisms are related to the invariance properties of the Schrödinger equation describing a quantum test particle in any Newton–Cartan structure.
On the relation between gauge theories, moving frames, fiber bundles, and parastatistics
Authors: Macrae Kenneth I.
Published: July 2002

We write down standard gauge field theory in a basis-independent manner using the ideas of moving frames (fiber bundles). Then we describe the construction of frames for gauging parafields. To do this (frames) bases for fields are replaced by Clifford matrices. These matrices are in one-to-one correspondence with the number of spinor components. We briefly examine the objects upon which they can act (through matrix multiplication on the left). These objects bear the same relations to spinors that spinors do to vectors. Finally, we show how to construct a set of inner products for the parabases that yield the same action and n-point functions as in the standard field theory.
A new representation for planar Feynman graphs in terms of strings
Authors: Hong Tuan R.
Published: July 2002

We study the planar graphs of a massless scalar φ3 field theory in d Euclidean dimensions. We show, using a lattice cutoff, that any graph G can be expressed as a function of strings defined on the dual of G (in the sense of graph theory). We furthermore obtain a series expansion of the Feynman graph in powers of (1/d). The powers are proportional to the total length of the strings drawn on d copies of the dual of G for a given subset of these strings which never cross either themselves or each other on the same copy.
Topological closure as the necessary condition for frustration or phase transitions
Authors: Nencka-Ficek H.
Published: July 2002

It is shown that the same conditions are necessary for both frustration in Ising models with negative multispin interactions present and phase transition in analogous ferromagnetically coupled models.
Quantization of systems with many degrees of freedom by the method of collective coordinates: Quantum mechanics around a classical periodic orbit
Authors: Müller-Kirsten H. J. W. , Wiedemann A.
Published: July 2002

A fairly complete perturbation theoretical solution of the Schrödinger equation around a classical periodic orbit is given as an example demonstrating the quantization of a system with many degrees of freedom by the method of collective coordinates. In particular, explicit expressions are derived for the creation and annihilation operators of quantum fluctuations orthogonal to the classical path, as well as the corresponding eigenfunctions, in both the adiabatic and nonadiabatic domains. It is also shown that corresponding expressions become proportional (and thus can be linked) in domains where they overlap. Finally the splitting of asymptotically degenerate states, and hence the band structure of the resulting spectrum, is calculated.
On the stability of the telegraph equation
Authors: Swart J. H.
Published: July 2002

The linear first-order boundary conditions that will lead to a stable (well-posed) problem for the telegraph equation in quarter space are established.
Multidimensional inverse scattering: An orthogonalization formulation
Authors: Yagle Andrew E.
Published: July 2002

The three-dimensional Schrödinger equation inverse scattering problem is solved using an orthogonalization approach. The plane waves propagating in free space are orthogonalized with respect to an inner product defined in terms of a Jost operator. The resulting integral equation is identical to the generalized Gel’fand–Levitan equation of Newton, although the present derivation is simpler and more physical than that of Newton. Newton’s generalized Marchenko equation is derived from the defining integral equation for the Jost operator. These integral equations are shown to be solved by fast algorithms derived directly from the properties of their solutions. This paper thus presents a simple interpretation of Newton’s two integral equations, two fast algorithms for solving these integral equations, and relations between the various approaches. This is a generalization of previously obtained results, which are also reviewed here, for the one-dimensional inverse scattering problem.
On the solution of the Tolman–Oppenheimer–Volkov equation with the ultrarelativistic equation of state
Authors: Toimela Tuomo
Published: July 2002

The Tolman–Oppenheimer–Volkov equation is studied in the case of the ultrarelativistic equation of state. The original system of two first-order differential equations is turned into one first-order equation that is independent of the central density, plus an integral. It is shown how the physical solutions are related to the analytically known infinite central density solution. The results are further generalized into the arbitrary γ-law equation of state, p(γ−1)ρ. Finally, the case of a nonzero bag constant is briefly discussed.
A limit theorem for basic states of disordered structures
Authors: Korzeniowski Andrzej
Published: July 2002

Let a(t,ω) be a stationary process such that 0<E[1/a(t,ω)]<∞. It is shown that the random boundary-value problem Hy=−(d/dt)a(t,ω)(dy/dt)=λy, y(0)=y′(L)=0, has a unique solution (λi(ω,L), yi(t,ω,L)) for i≥0 and λi(ω,L)/λoi(L)→1 almost surely as L→∞, where λoi(L) is the ith eigenvalue of the averaged Hamiltonian Hoy=−[1/E(1/a(t,ω))] (d2y/dt2) =λy, y(0)=y′(L)=0 .
Confinement and redistribution of charges and currents on a surface by external fields
Authors: Arnoldus Henk F. , Jelski Daniel , George Thomas F.
Published: July 2002

The old problem of light scattering from a perfectly conducting surface is addressed. An electromagnetic field is incident upon the boundary, where it induces a charge and current distribution. These charges and currents emit the reflected fields. A set of equations for the charges and currents on the surface is derived by eliminating the E and B fields from Maxwell’s equations with the aid of the appropriate boundary conditions. An explicit and general solution is achieved, which reveals the confinement and redistribution of the charge and the current on the surface by the external field. Expressions are obtained for the surface resolvents, or the redistribution matrices, which represent the surface geometry. Action of a surface resolvent on the incident field, evaluated at the surface, then yields the charge and current distributions. The Faraday induction appears as an additional contribution to the charge density. Subsequently, the reflected fields are expanded in spherical waves, which have the surface-multipole moments as a source. Explicit expressions are presented for the surface-multipole moments, and it is pointed out that charge conservation on the surface sets constraints on these moments. The results apply to arbitrarily shaped surfaces and to any incident field. For a specific choice of the surface structure and the external field, the solutions for the charge, the current, and the reflected fields are amenable to numerical evaluation.
Existence and analyticity of many-body scattering amplitudes at low energies
Authors: Dereziński Jan
Published: July 2002

Two-cluster–two-cluster scattering amplitudes for N-body quantum systems are studied. Our attention is restricted to energies below the lowest three-cluster threshold. For potentials falling off like r−1−δ it is proved that in this energy range these amplitudes exist, are continuous, and that the asymptotic completeness holds. Moreover, if the potentials fall off exponentially it is proved that these amplitudes can be meromorphically continued in the energy, with square root or logarithmic branch points at the two-cluster thresholds.
A new class of lattice identities
Authors: Low F. E.
Published: July 2002

Some identities involving two-dimensional lattice sums of a class of integrals are derived. A simple application to theta functions is given.
Second-order equation fields and the inverse problem of Lagrangian dynamics
Authors: Thompson G.
Published: July 2002

The transformation properties of determined, autonomous systems of second-order ordinary differential equations, identified as vector fields on the tangent bundle of the space of dependent variables, are derived and studied. The inverse problem of Lagrangian dynamics is studied from this transformation viewpoint as well as the problem of alternative Lagrangians. In particular, regular Lagrangians which are analytic as functions of the first derivatives are considered. Finally, the inverse problem for second-order systems corresponding to the geodesic flow of a symmetric linear connection is investigated.
Absolutely continuous spectra of quasiperiodic Schrödinger operators
Authors: Chierchia Luigi
Published: July 2002

Several aspects of the general and constructive spectral theory of quasiperiodic Schrödinger operators in one dimension are discussed. An explicit formula for the absolutely continuous (a.c.) spectral densities that yields an immediate proof of the fact that the Kolmogorov–Arnold–Moser (KAM) spectrum constructed by Dinaburg, Sinai, and Rüssmann [Funkt. Anal. Prilozen. 9, 8 (1975); Ann. Acad. Sci. 357, 90 (1980)] is a subset of the a.c. spectrum is provided. Some quasiperiodicity properties of the Deift–Simon a.c. eigenfunctions are proved, namely, that the normalized phase of such eigenfunctions is a quasiperiodic distribution. In the constructive part the Dinaburg–Sinai–Rüssmann theory is extended to quasiperiodic perturbations of periodic Schrödinger operators using a KAM Hamiltonian formalism based on a new treatment of perturbations of harmonic oscillators. Particular attention is devoted to the dependence upon the eigenvalue parameter and a complete control of KAM objects is achieved using the notion of Whitney smoothness.
There is no isolated p-p wave
Authors: Yip P. F.
Published: July 2002

A theorem is presented that basically states that there are no nontrivial well-behaved, spatially asymptotically flat space-times which are p-p waves at infinity.
Substitutional symmetries and extra degeneracies of real symmetric matrices
Authors: Siddall T. H. , Sullivan J. J.
Published: July 2002

The relation between substitutional symmetry operations that leave a real symmetric matrix invariant and the degeneracies exhibited by the matrix in diagonal form are examined. The usual application of group theory to this problem is formulated. Substitutional (and other) symmetries can exist, which do not form part of the invariance group. These symmetries can cause extra degeneracy of the root system and are frequently encountered in some physical applications such as the Hückel model of molecular bonds. Some general features that lead to extra degeneracy are noted and illustrative examples are given for systems of six equivalent centers.
Threshold singularities of two-cluster–two-cluster scattering amplitudes for dilation analytic potentials
Authors: Dereziński Jan
Published: July 2002

Two-cluster–two-cluster scattering amplitudes are studied for N-body quantum systems with potentials that are both dilation analytic and exponentially decaying. It is proved that under quite broad assumptions these amplitudes can be meromorphically continued in the energy, with square root or logarithmic branch points at the two-cluster thresholds.
Limit theorems for spin systems with an Abelian discrete symmetry
Authors: Caticha Nestor
Published: July 2002

Exponential convergence in the number of states is proved for the pressure of a class of discrete Abelian spin systems, to the O(2) invariant model’s pressure in d dimensions. Analogous results are obtained for the convergence of the expectation values of a class of functions under more stringent conditions.
Factorization of zero curvature representations
Authors: Dodd R. K. , Paul S. K.
Published: July 2002

The factorization of the L operator in a Lax pair {L,A} has been extremely useful in the theory of integrable systems. For instance, the Miura transformation is obtained by factorizing the Schrödinger operator; −∂2x +u−k2=(−∂x+a)(∂x+b) requires that u=k2−ax+a2 and a=b. In a recent paper an analogous procedure for the factorization of zero curvature representations was presented. In this paper the theory of this method is developed and applied to the third-order scalar Lax equation.
Correlated states and collective transition operators for multilevel atomic systems. II. Symmetry properties
Authors: Rai Jagdish , Mehta C. L. , Mukunda N.
Published: July 2002

The symmetry properties of the N-particle multilevel system are studied. For indistinguishable particles, the total wave function must be either symmetric or antisymmetric in the exchange of any two particles. The internal states of the multilevel system are combined with suitable spatial wave functions to produce a totally symmetric or antisymmetric wave function. The problem of degeneracy and the method of combining a given permutational symmetry of the internal wave function with the same or the conjugate symmetry for the spatial part are described. It is found that Young’s diagram corresponding to the given irreducible representation of the permutation group plays an important role.
The Virasoro algebra and group in four dimensions
Authors: Zhang Yao-Zhong
Published: July 2002

The Virasoro algebra and group are examined in (3+1)-dimensional theory with an Abelian gauge field coupled with the gravitational field. The two-cocycle for the group is constructed by using the so-called descent equation. Its infinitesimal version gives the Schwinger–Jackiw–Johnson term in the Virasoro algebra in 3+1 dimensions. It appears that in the case of an external monopole field the Virasoro algebra and group in 3+1 dimensions are the direct generalization of the standard ones in 1+1 dimensions, respectively.
Algebraic construction of one-dimensional quasiperiodic tilings
Authors: Litvin Daniel B.
Published: July 2002

For an arbitrary one-dimensional quasiperiodic tiling constructed via the grid method with periodically spaced grids, an algebraic equation is derived for the positions of the vertices dependent on a single variable, the cardinal position of the vertices.
Ring characterization of scalar product spaces and Gel’fand triples
Authors: Kruszyński Pawel/
Published: July 2002

It has been proved that if an involution + exists in a subring of continuous linear maps in a locally convex topological vector space 𝒮 with the property (ξA)+=ξ* A+, and A+ A=0 iff A=0, then there exists in 𝒮 a Hermitian scalar product 〈 , 〉 such that + is the adjoint operation with respect to 〈 , 〉. The existence of a corresponding Gel’fand triple 𝒮⊆H⊆𝒮′ has been shown.
Localized bound states of fermions interacting via massive vector bosons
Authors: Ionescu D. C. , Reinhardt J. , Müller B. , Greiner W. , Soff G.
Published: July 2002

A model for composite systems consisting of fermions with internal degrees of freedom interacting via intermediate vector bosons (IVB) is constructed. Highly localized, low-mass bound states are found in the Hartree–Fock approximation. The dependence of these states as function of the coupling constant and vector boson mass is investigated. In the limit of infinite vector boson mass the interaction is described by Fermi-type contact forces.
Infinitesimally deformed field and string theories
Authors: Ahmed E. , Hegazi A. S.
Published: July 2002

The infinitesimally deformed oscillator algebra is used to derive the infinitesimally deformed Heisenberg algebra. Hence, the infinitesimally deformed field theories and string theories are constructed. The physical meaning of these theories is discussed.
Inverse scattering problem for anisotropic media
Authors: Boutet de Monvel A. , Shepelsky D.
Published: July 2002

An inverse scattering problem for a second order matrix differential equation on the line related to the wave propagation in anisotropic media is studied herein. A reconstruction procedure is given based on the Riemann–Hilbert problem of analytic factorization of matrix functions and a uniqueness theorem is proven.
Kicked dynamics on Hilbert spaces: A nonstandard approach
Authors: Bertoglio Néstor , Fernández Claudio
Published: July 2002

The main purpose of this work is to provide a rigorous interpretation of kicked models, with the aid of nonstandard analysis. These modes are represented by evolution equations involving Dirac’s delta functions of time and the method used consists of approximating them by smooth functions on the *R.
Evolution of Kaluza–Klein inhomogeneous model with a cosmological constant
Authors: Banerjee A. , Panigrahi D. , Chatterjee S.
Published: July 2002

A scenario is discussed in a Kaluza–Klein type of space–time with a cosmological constant for an inhomogeneous matter field obeying an equation of state p=kρ≠p5, where k is a constant, p is the isotropic pressure in the three-space, and p5 is that for the extra fifth dimension. It is found that the usual three-dimensional space expands exponentially while, depending on the signature of the arbitrary constants of integration, the extra scale either expands indefinitely or exhibits the desirable feature of dimensional reduction. It is interesting to point out that in the former case both the scales do not show any big bang type of singularity. Moreover, p5 automatically vanishes in this model. The present work is very general in nature because in special cases it reduces to some well-known solutions in the relevant field.
Hamiltonian structure of Dubrovin’s equation of associativity in 2-d topological field theory
Authors: Galvão C. A. P. , Nutku Y.
Published: July 2002

A third order Monge-Ampère type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac’s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra.
An algebra arising from 2-state chiral Potts model and Sklyanin algebra
Authors: Fukushima Nobuhisa
Published: July 2002

We construct a C-algebra 𝒞 associated with an R-matrix of the 2-state chiral Potts model. This algebra will be shown to coincide with the Sklyanin algebra at an 8-torsion point and, in the self-dual case, with Uq(sl2) at the fourth root of unity.
Quasi-exactly solvable spin 1/2 Schrödinger operators
Authors: Finkel Federico , González-López Artemio , Rodrı́guez Miguel A.
Published: July 2002

The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave functions with polynomial components to be equivalent to a Schrödinger operator are found. Systematic simplifications of these conditions are analyzed, and are then applied to the construction of new examples of multi-parameter QES spin 1/2 Hamiltonians in one dimension.
Summational invariants
Authors: Mackrodt Christof , Reeh Helmut
Published: July 2002

General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering.
Uncertain dynamical systems defined by pseudomeasures
Authors: Hamm Andreas
Published: July 2002

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so-called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the conventional probability measure, and fuzzy dynamical systems in which the pseudomeasure is a so-called possibility measure. New results about possibilistic systems and their relation to deterministic and to stochastic systems are derived by using idempotent pseudolinear algebra. By expressing large deviation estimates for stochastic perturbations in terms of possibility measures, we obtain a new interpretation of the Freidlin–Wentzell quasipotentials for stochastic perturbations of dynamical systems as invariant possibility densities.
Higher-dimensional models in gravitational theories of quartic Lagrangians
Authors: Kleidis K. , Kuiroukidis A. , Papadopoulos D. B. , Varvoglis H.
Published: July 2002

Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The space–time consists of one time direction and two maximally symmetric subspaces, filled with matter in the form of an anisotropic fluid. Numerical integration of the cosmological field equations indicates that exponential, as well as power law, solutions are possible. We carry out a dynamical study of the results in the Hext−Hint plane and confirm the existence of attractors in the evolution of the Universe. Those attracting points correspond to “extended” De Sitter space–times in which the external space exhibits inflationary expansion, while the internal one contracts.
Dirichlet operators on loop spaces: Essential self-adjointness and log-Sobolev inequality
Authors: Park Yong Moon , Yoo Hyun Jae
Published: July 2002

For each γ∈[0,1] and potential function V:Rd→R, we consider the Dirichlet form Eμ(γ) and the associated Dirichlet operator Hμ(γ) for the Gibbs measure μ on the loop space E={ω∈C([0,1];Rd):ω(0)=ω(1)}. The Gibbs measure μ is related to the Gibbs state of the quantum anharmonic oscillator with the potential V via the Feynman–Kac formula. We formulate Dirichlet forms in the framework of rigged Hilbert spaces which are related to the loop space E. We then give an approximate criterion for the essential self-adjointness of Dirichlet operators associated with Dirichlet forms given by probability measures on Hilbert spaces. Under appropriate conditions on the potential, we apply the approximate criterion to show that the Dirichlet operator Hμ(γ) is essentially self-adjoint on the domain of smooth cylinder functions. In addition, if the potential satisfies a uniform convexity condition, we prove that the Dirichlet operator Hμ(γ) has a gap at the lower end of spectrum. We also show that the Gibbs measure μ satisfies the log-Sobolev inequality. We use the approximation method developed by Albeverio, Kondratiev, and Röckner with necessary modifications.
“Clock rate synchronizable” reference frames in curved space–times
Authors: Gao Sijie , Kuang Zhiquan , Liang Canbin
Published: July 2002

It is well known that all reference frames that are clock synchronizable are hypersurface orthogonal. A weaker requirement for clock synchronization was first suggested by Zhao [Z. Zhao, Sci. China 34(7), 835 (1991)] using coordinate language. Reference frames satisfying this requirement are hence referred to as class Z in the present paper. We give a geometrical definition of class Z reference frames and investigate their physical meaning as well as geometrical properties in detail. Finally, another kind of reference frame referred to as class z̃ is introduced and its possible relation to another of Zhao’s claims is pointed out.
Two-form gauge fields in the Becchi–Rouet–Stora–Tyutin superspace
Authors: Barcelos-Neto J. , Thibes R.
Published: July 2002

We consider a geometrical description for tensor gauge fields. Based on this geometrical treatment, we develop the theory involving one- and two-form gauge fields by means of the Becchi–Rouet–Stora–Tyutin (BRST) superfield formalism. This permits us to directly obtain invariant Lagrangians for both BRST and anti-BRST transformations and we shall see that all the ingredients of the formalism (ghosts, ghost-for-ghosts and all the auxiliary fields) naturally occur. We introduce collective fields to construct the field–antifield quantum action in a generic gauge. We deal with both Abelian and non-Abelian cases. In this last case, the BRST superspace formulation sheds more light on this still open problem.
Symmetries of history quantum theories and decoherence functionals
Authors: Rudolph Oliver
Published: July 2002

Recently, Schreckenberg investigated symmetries in the context of history quantum theories. In the case that the space of histories is given by the set of projectors on some finite dimensional Hilbert space he obtained, first, a complete characterization of all physical symmetries of history quantum theories — an analog of Wigner’s theorem — and, second, a complete mathematical characterization of symmetries of single decoherence functionals. In this paper we extend Schreckenberg’s results to the case where the underlying space of histories is given by the set of projectors on some infinite dimensional Hilbert space.
A version of Thirring’s approach to the Kolmogorov–Arnold–Moser theorem for quadratic Hamiltonians with degenerate twist
Authors: Chandre C. , Jauslin H. R.
Published: July 2002

We give a proof of the Kolmogorov–Arnold–Moser (KAM) theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring’s approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is that the iteration of canonical transformations on which the proof is based stays within the space of quadratic Hamiltonians. We show that Thirring’s proof for nondegenerate Hamiltonians can be adapted to Hamiltonians with degenerate twist. This case, in fact, drastically simplifies Thirring’s proof.
Maxwell fields in anisotropic space–times
Authors: Wollensak Matthias
Published: July 2002

Maxwell’s equations are rewritten with respect to anholonomic orthonormal frames and applied to the case when the background is described by a diagonal Bianchi-type I universe. It is shown that solutions analogous to plane wave solutions in flat space–time must obey two transversality conditions when the space–time is anisotropic. Analytic solutions are presented for propagation along the respective coordinate axes and a special stiff fluid model. Furthermore, by use of a generally applicable ansatz the long- and short-time behavior of waves traveling in the axisymmetric Kasner universe have been investigated.
Modified real structures for quantum groups and applications
Authors: Grensing G.
Published: July 2002

A modification of the standard  * -structure on a quasitriangular Hopf algebra is introduced by means of which, in particular, the quantum deformation Uq(su2) can be endowed with a real structure for q a pure phase. As opposed to the standard definition, its modified version not only works for the quantum group regarded as an algebra, but as a quasitriangular Hopf algebra if q is of modulus one. Applications to two relevant examples are given, which are known to require quantum symmetries: the anisotropic Heisenberg chain and the Landau theory on the torus, thus solving some unitarity problems that have always resisted a satisfactory solution.
Algebraic expressions for some SO(N) Racah coefficients
Authors: Ruan Dong , Sun Hong-zhou
Published: July 2002

In this paper the algebraic expressions for SO(N) Racah coefficients involving the coupling of three irreducible representations (1 0̇), (m1 m2 m3 0̇) and (1 0̇) are given by using the building-up process. Their properties are discussed in detail.
On the limiting power of the set of knots generated by 1+1- and 2+1-braids
Authors: Bikbov R. , Nechaev S.
Published: July 2002

We estimate from above the set of knots, Ω(n,μ), generated by closure of the n-string 1+1- and 2+1-dimensional braids of irreducible length μ(μ≫1) in the limit n≫1.
Even moments of a polymer chain distribution
Authors: Hoffman Gary G.
Published: July 2002

An algorithm is presented for the evaluation of the even moments of the end-to-end separation of a polymer chain. The only assumption made in the distribution function is that the energy of the chain depends only on the individual bond lengths of the chain. This assumption covers many of the commonly used distribution functions.
Evaporation and condensation on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules
Authors: Sone Yoshio , Ohwada Taku , Aoki Kazuo
Published: July 2002

The behavior of a semi-infinite expanse of a gas bounded by its plane condensed phase, where evaporation or condensation is taking place, is considered on the basis of the linearized Boltzmann equation for hard-sphere molecules. The half-space boundary-value problem of the linearized Boltzmann equation for hard-sphere molecules is solved numerically by the finite difference method introduced in the temperature jump problem by the authors. The local behavior of the gas (the velocity distribution function of gas molecules, the density and temperature of the gas, etc.) as well as the relations among the macroscopic variables on the condensed phase and at infinity is obtained.
Aerosol particle deposition in numerically simulated channel flow
Authors: McLaughlin John B.
Published: July 2002

The trajectories of rigid spherical particles in a turbulent channel flow are computed using a pseudospectral computer program to simulate the three-dimensional, time-dependent flow field. It is assumed that the channel is vertical so that gravity cannot directly cause the deposition of particles on the walls. The particles are assumed to be sufficiently small and widely separated so that their influence on the fluid velocity field can be ignored. It is found that when the particles are assigned random initial locations with initial velocities that are equal to the local fluid velocity, the particles tend to accumulate in the viscous sublayer. At the edge of the viscous sublayer, the particles that deposit on the wall typically possess normal components of velocity that are comparable in magnitude to the intensity of the normal component of the velocity in the core of the channel (i.e., of the order of magnitude of the friction velocity). A shear-induced lift force having the form derived by Saffman for laminar flow is found to have virtually no effect on particle trajectories, except within the viscous sublayer where it plays a significant role both in the inertial deposition of particles and in the accumulation of trapped particles. The Reynolds number of the particles that deposit does not remain small compared with unity.
Modeling two-dimensional detonations with detonation shock dynamics
Authors: Bdzil J. B. , Stewart D. S.
Published: July 2002

One of the principal shortcomings of the computer models that are presently used for two-dimensional explosive engineering design is their inadequate treatment of the explosive’s detonation reaction zone. Current methods lack the resolution to both calculate the broad gas expansion region and model the thin reaction zone with reasonable detail. Recently an alternative method for modeling the reaction zone has been developed. This method applies when the radius of curvature of the shock is large compared to the reaction-zone length. In this limit, the dynamics of the interaction between the chemical heat release and the two-dimensional flow in the reaction zone is quasisteady. It is summarized by a relation Dn(κ), between the local normal shock velocity Dn and shock curvature κ. When this relation is combined with the kinematic surface condition (an equation that describes how disturbances move along the shock), the two-dimensional reaction-zone calculation is reduced to a one-dimensional calculation.
A large-eddy simulation scheme for turbulent reacting flows
Authors: Gao Feng , O’Brien Edward E.
Published: July 2002

A general methodology is developed for simulating complicated reacting flow problems. This method combines the large-eddy simulation (LES) technique with the existing probability density function (PDF) approach for turbulent reacting flows and provides a closed form representation for all terms that are involved in the simulations. Some other issues related to this problem are also discussed.
Toward a hydrodynamic theory of sonoluminescence
Authors: Löfstedt Ritva , Barber Bradley P. , Putterman Seth J.
Published: July 2002

For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.
Quasilinear diffusion modeling of the alpha-loss-cone instability in a tandem-mirror reactor
Authors: Ho S. K. , Smith Gary R. , Miley G. H.
Published: July 2002

The anisotropic loss-cone distribution of fusion-born alpha particles in a mirror system is capable of destabilizing low-frequency plasma waves. A one-and-one-half-dimensional quasilinear diffusion model is developed to study the nonlinear evolution of the alpha distribution function resulting from enhanced diffusion in velocity space and radial position driven by the unstable Alfvén wave. It is found that pitch-angle scattering of the resonant alphas into the loss cone causes significant losses while radial losses are negligible for a reactor-size plasma. For a typical tandem-mirror reactor, the alpha plasma heating is greatly reduced and ignition in the central cell cannot be achieved.
Are Einstein’s transition probabilities for spontaneous emission constant in plasmas?
Authors: Griem H. R. , Huang Y. W. , Wang J.-S. , Moreno J. C.
Published: July 2002

The quenching of spontaneous emission coefficients, presumably by electron collisions, which was recently inferred at Princeton from measured intensity ratios of visible and extreme-ultraviolet lines from a common upper level in laser blow-off plasmas, was investigated using a ruby laser. The line intensity ratios of the Civ 3s-3p and 2s-3p transitions, for similar laser targets, show a similar dependence on separation from the target as the previous experiments. Both of these results can, however, be interpreted in terms of density gradients and Stark broadening without invalidating Einstein A values. This interpretation also applies to Ciii and Nv line intensity ratios, which are further compromised by blends with other lines. The quenching of Arii lines by photon collisions, which had been reported by the same Princeton group, can finally be shown to have been mimicked by other effects, in this case by the Rabi oscillations and associated power broadening in the argon ion laser cavity.
Nonlinear dynamics of one-dimensional supersonic Langmuir waves
Authors: Jungwirth K. , Breizman B. N.
Published: July 2002

In this review specific features of dynamics of Langmuir waves in the supersonic regime are illustrated with several examples. It is shown that the limit of an adiabatic approximation considerably extends the range of analytically solvable problems. It permits one to formulate and rigorously analyze the modulational instability, as well as to explain many empirical laws deduced from numerical simulations. The formulation describes not only collapsing cavities in two and three dimensions, but predicts also the existence of ‘‘compound’’ solitons in a one-dimensional model. In the same model the transition from weak turbulence to the adiabatic approximation is analyzed, including phenomena of ion-sound emission by autolocalized and self-trapped plasmons. Further, the individual and collective processes of soliton formation, their mutual collisions, and their destruction by ion-sound pulses are discussed.
Magnetic and electric current morphology in the plasma ejected by a laser-irradiated foil
Authors: Sanmartín Juan R. , Reinicke Peter
Published: July 2002

A quasisteady model for the plasma ablated from a thick foil by a laser pulse, at low φaλ2L and R/λ2L within a low, narrow range, is given (φa is absorbed intensity, λL wavelength, R focal-spot radius). An approximate analytical solution is given for the two-dimensional plasma dynamics. At large magnetic Reynolds number RM, the morphology of the magnetic field shows features in agreement with recent results for high intensities. Current lines are open: electric current flows toward the spot near its axis, then turns and flows away. The efficiency of converting light energy into electric energy peaks at RM∼1. Both the validity of the model and accuracy of the solution are discussed. The neighborhood of the spot boundary is analyzed in detail by extending classical Prandtl–Meyer results.
Neutral particle energy analysis and charge exchange power loss in edge-dominated spheromaks
Authors: Mayo R. M. , Kirschenbaum L. S.
Published: July 2002

Neutral particle density profiles have previously been calculated for spheromak plasmas [Phys. Fluids B 2 (1990) 115]. Here, the formalism is extended to calculate the one-dimensional (1-D) profile of the egressing neutral energy flux to correctly treat profile and attenuation effects. If is found that the energy flux profile is strongly dependent on Ti,Te,ne profiles and magnitudes, and regions of the plasma have been identified as localized ‘‘hot spots’’ for charge-exchange power loss in some cases. In addition, the total charge exchange power loss is found to be in order-of-magnitude agreement with predictions from a zero-dimensional (0-D) model and can account for the bulk of the edge-dominated spheromak power loss.
Parametric decay of an electromagnetic wave into high- and intermediate-frequency electrostatic waves in a magnetized plasma
Authors: Mjo/lhus Einar
Published: July 2002

Parametric decay of an electromagnetic wave into electrostatic waves of high or intermediate frequencies in a magnetized plasma is studied theoretically. Three processes are included: (ia) decay into two high-frequency waves, max(ωpe,Ωe)<Ω1,2<ωUH (ωpe is electron plasma frequency, Ωe is electron gyrofrequency, ωUH is upper-hybrid frequency, and Ω1,2 are frequencies of the daughter waves); (ib) decay into two intermediate-frequency waves, min(ωp,Ωe)>Ω1,2>ωLH (ωLH is the lower-hybrid frequency); and (ii) decay into one of each of these wave modes. The ion motion is neglected; consequently, the coupling coefficient vanishes in the infinite pump-wavelength approximation. The calculation is then carried to the next order in k/K where k,K are the wave numbers of the pump wave and the daughter waves. This approximation is appropriate when the daughter waves are described in the electrostatic approximation. Explicit expressions for the growth rates of the three processes are obtained.
Theory of the self-induced electric field at a cathodic arc spot
Authors: Daybelge U.
Published: July 2002

Effects of the metal plasma jet emitted from the cathode spot of a vacuum arc (or a unipolar arc) on the surrounding electric field variation are investigated. It is shown, using a 2-D magnetogasdynamical model, that the cooling of the expanding metal plasma over the cathode surface leads to a strong variation of the electrical conductivity across the thermal boundary layer. This effect, which was ignored in previous theories of the cathode spot, coupled with the induced electric field caused by the plasma motion across magnetic fields which are caused by the arc current and the external currents, gives rise to a strong electric field at the cathode surface. Solving a mixed-boundary-value problem for the electric potential, it is shown that the induced electric field is consistent with the random and the directed retrograde motions of the cathodic arc spot.
Anomalous losses from relativistic electron rings in decreasing toroidal fields
Authors: Meger R. A. , Parker M. R. , Fleischmann H. H.
Published: July 2002

Anomalously enhanced fast-electron losses are observed on relativistic E layers in the RECE-Christa device when the applied toroidal magnetic field decreases to zero in times shorter than ring lifetime. These losses consistently occur in a certain region of the field-reversal parameter and the ratio of applied toroidal to axial magnetic fields at the ring position. The critical parameter range is independent of the radial gradient of the applied mirror field, the background gas pressure, and the rate-of-decay of Bθ; however, it depends on the axial length of the rings, and there may be a threshold in dBθ/dt. The observed parameter dependence as well as the absence of any kink or tilt motions point to new orbital resonances as the cause of these losses.
Inverse resonance absorption in an inhomogeneous magnetized plasma
Authors: Barr H. C. , Boyd T. J. M. , Gardner G. A. , Rankin R.
Published: July 2002

The linear mode conversion of a plasma wave to a light wave in a magnetized plasma has been examined theoretically and by computer simulation. This conversion is the inverse of resonance absorption exhibiting an identical dependence on magnetic field and density scale length with an optimum conversion efficiency of approximately 60%. Radiation from this source may contribute to the harmonic spectra observed from laser-irradiated plasmas.
A nonlocal expression for the ponderomotive potential
Authors: Hatori Tadatsugu
Published: July 2002

An expression for the ponderomotive potential, which is applicable to the case where the scale length of rf amplitude variation is comparable to the excursion length and the Larmor radius, is presented. This expression is used to explain the empirical scaling law for the potential.
Lie group invariance properties of radiation hydrodynamics equations and their associated similarity solutions
Authors: Coggeshall Stephen V. , Axford Roy A.
Published: July 2002

The Lie group invariance properties of the one-dimensional radiation hydrodynamic equations with the equilibrium diffusion approximation, a local thermodynamical equilibrium assumption, and an arbitrary material equation of state are derived. These properties are used systematically to generate similarity solutions of these equations for a given form of the equation of state. A comprehensive list of allowed similarity solutions for a perfect gas is presented. Several special cases that have been found previously by other authors appear in the list. Many other cases not reported previously are also presented. An example numerical solution is given for a piston-driven shock with a thermal precursor.
Dissociation–association equilibrium of magnetic particle chains in homogeneous magnetic fields
Authors: Wilhelm H. E.
Published: July 2002

An idealized statistical theory of chaining in a dilute suspension of macroscopic magnetic particles in a rarefied gas is presented when an external homogeneous magnetic field is present. The primary colloidal particles are assumed to be spherical, of the same size, and to have saturated magnetic moments. The magnetochemical potentials and the association–dissociation equations are derived for chains consisting of v≥1 magnetic grains, in dependence of the temperature T, the density Nv of chains, and the homogeneous magnetic field B0. High field intensities B0 are shown to shift the chain length distribution F=F(v) in favor of long chains, v≫1, whereas increasing temperatures T move the maximum of this statistical distribution to smaller chain lengths, v→1. The theory appears to be in qualitative agreement with oven experiments using an external magnetic field for the alignment and stabilization of the chains.
Alternatives to the Euler and Navier–Stokes equations for monatomic gases
Authors: Butler D. S.
Published: July 2002

The Chapman–Enskog approximation scheme is not uniformly convergent because it does not approximate sufficiently the behavior of molecules in the high-speed tail of a distribution. Asymptotic analysis of the binary collision term in the Boltzmann equation is used to show that collisions involving high-speed molecules can redistribute molecules within an energy level more easily than between levels. Chapman–Enskog theory is reformulated by assuming near equilibrium, only within each energy level, instead of over all energy levels.