bluuebunny/crossref_metadata_2025 huggingface dataset:
Lie algebraic methods and solutions of linear partial differential equations
Authors: Dattoli G. , Richetta M. , Schettini G. , Torre A.
Published: July 2002

In this paper, an algebraic method to obtain the solution of linear partial differential equations of the evolution type is discussed. The proposed method exploits the Lie differential operators and their matrix realization, to reduce the equation to an easily solvable generalized matrix form. Some applications to problems of specific interest are also discussed.
Bäcklund transformation, conservation laws, and inverse scattering transform of a model integrodifferential equation for water waves
Authors: Matsuno Y.
Published: July 2002

The Bäcklund transformation (BT), an infinite number of conservation laws, and the inverse scattering transform (IST) of a model integrodifferential equation for water waves in fluids of finite depth [Y. Matsuno, J. Math. Phys. 29, 49(1989)] are constructed by employing the bilinear transformation method. The model equation is also shown to pass the Painlevé test. These facts prove the complete integrability of the equation. Both the deep- and shallow-water limits of various results thus obtained are then investigated in detail. In addition, a new method to evaluate conserved quantities for pure N-soliton is developed by utilizing actively the time part of the BT. It is found that the structure of conservation laws exhibits peculiar characteristics in comparison with those of usual water wave equations such as the Benjamin–Ono and the Korteweg–de Vries equations. The most important problem left open in this paper is to solve various IST equations.
How solvable is (2+1)-dimensional Einstein gravity?
Authors: Moncrief Vincent
Published: July 2002

In this paper, the relationship between Witten’s approach to the (2+1)-dimensional, vacuum Einstein equations (for spatially compact space-times) and the conventional Annowitt, Deser, and Misner (ADM) Hamiltonian approach is discussed. It is argued (especially for the space-times with higher genus Cauchy surfaces) that neither approach is complete in itself; Witten’s because it does not provide a technique (even at the classical level) for recovering the space-time metric and the conventional approach because it provides no mechanism for solving a seemingly intractable set of Hamilton equations. It is also argued, however, that the two formulations are instead complementary in the sense that the Wilson loops, which play a key role in Witten’s approach, provide (at least in principle) a mechanism for solving the reduced Hamilton equations and thereby completing the picture at the classical level. An example of this synthesis for the (explicitly computable) case of genus-one hypersurfaces is provided. The more tenuous problem of whether this synthesis can be extended to the quantized Einstein equations will also be discussed. A principal open question is whether the Wilson loops, when expressed in terms of the ADM canonical variables, can be ordered in such a way as to preserve, quantum mechanically, their (classical) Poisson bracket algebra.
Anomalous foliations of Einstein space-times
Authors: Ove Roger
Published: July 2002

T 3×R space-times with a single global spatial Killing vector can be foliated such that the trace of the two-dimensional metric momentum tensor is a constant over the hypersurfaces. This is analogous to constant mean curvature slicing, but is somewhat more algebraically natural in the case with symmetry. Here, the question is addressed of whether Einstein solutions foliated in such a manner exist where the trace of the extrinsic curvature is not of consistent sign over the surface. The relationship between such behavior and the possibility of singularities local in the quotient space of the symmetry is considered.
Explicit construction of nontrivial elements for homotopy groups of classical Lie groups
Authors: Lundell Albert T. , Tosa Yasunari
Published: July 2002

Nontrivial elements of homotopy groups for unitary, orthogonal, and symplectic groups are given explicitly. In particular, (a) representatives of generators of nontrivial homotopy groups of stable special unitary, orthogonal, and symplectic groups are constructed using Clifford algebras; (b) the values for ‘‘winding numbers’’ for stable SU, SO, and Sp are calculated for generators of homotopy groups; and (c) representatives of generators of homotopy groups Πn−2(O(n−1)), Π2n−2(U(n−1)), Π4n−2(Sp(n−1)) are given.
Neutral Einstein metrics in four dimensions
Authors: Law Peter R.
Published: July 2002

In Matsushita [J. Math. Phys. 22, 979–982 (1981), ibid. 24, 36–40 (1983)], for curvature endomorphisms for the pseudo-Euclidean space R2,2, an analog of the Petrov classification as a basis for applications to neutral Einstein metrics on compact, orientable, four-dimensional manifolds is provided. This paper points out flaws in Matsushita’s classification and, moreover, that an error in Chern’s [‘‘Pseudo-Riemannian geometry and the Gauss–Bonnet formula,’’ Acad. Brasileira Ciencias 35, 17–26 (1963) and Shiing-Shen Chern: Selected Papers (Springer-Verlag, New York, 1978)] Gauss–Bonnet formula for pseudo-Riemannian geometry was incorporated in Matsushita’s subsequent analysis. A self-contained account of the subject of the title is presented to correct these errors, including a discussion of the validity of an appropriate analog of the Thorpe–Hitchin inequality of the Riemannian case. When the inequality obtains in the neutral case, the Euler characteristic is nonpositive, in contradistinction to Matsushita’s deductions.
A new 𝒦-matrix approach to N-body scattering
Authors: Gibson A. G. , Waters A. J. , Berthold G. H. , Chandler C.
Published: July 2002

The Chandler–Gibson theory of N-body scattering is used to define a new 𝒦 matrix for N-body quantum scattering systems. The half-on-shell 𝒦 matrix has the proper channel thresholds and may be computed using a 𝒦-matrix form of the CG equations. The on-shell 𝒦 matrix is an Hermitian matrix for all energies and is related to a unitary scattering matrix via a Cayley transform. A B-spline solution method is developed and applied to a two-body and a three-body test problem. The three-body numerical calculations are within 0.5% of the exact solution both below and above the breakup threshold.
Improving the accuracy of WKB eigenvalues
Authors: Lindblom Lee , Robiscoe R. T.
Published: July 2002

A simple method is proposed for improving the accuracy of WKB eigenvalues by using the WKB eigenfunctions as trial functions in a variational-principle expression for the eigenvalues. The first-order eigenvalues obtained from this estimate are shown to differ from the exact values by terms of order ε6 (where ε is an appropriately defined small parameter that specifies the accuracy of the WKB approximation). For comparison, the fifth-order WKB eigenvalues also differ from the exact values by terms of order ε6. Higher-order variational eigenvalues are also defined, and the third-order estimate is shown to differ from the exact by terms of order ε10. The accuracy of these variational and WKB estimates are illustrated with a numerical example.
Sufficient conditions for a curvature tensor to be Riemannian and for determining its metric
Authors: Edgar S. Brian
Published: July 2002

A simple necessary and sufficient condition that a curvature tensor be Riemannian (i.e., that its symmetric connection be metric) is found, in very general conditions, for a four-dimensional space-time manifold. This enables existing uniqueness results for the metric tensor and an associated algebraic procedure for obtaining the metric tensor components from the curvature tensor components (when the curvature tensor is known to be a Riemannian tensor), to be extended to the situation where it is not known a priori whether the curvature tensor has come from a Lorentz metric.
Infinitesimal Bäcklund transformations and Kac–Moody algebras in general relativity
Authors: Mendoza A. , Restuccia A.
Published: July 2002

Infinitesimal Bäcklund transformations are found for the problem of classical general relativity in d dimensions, which by dimensional reduction may be interpreted as gravitation interacting with several Maxwell and scalar fields. The transformations are constructed in terms of the solution of a linear system whose integrability condition yields the original field equations. The Kac–Moody algebra, which generates those transformations, is analyzed.
Exact solutions of nonlinear Schrödinger equation for positive group velocity dispersion
Authors: Mihalache D. , Panoiu N. C.
Published: July 2002

A method is given for obtaining new exact solutions of nonlinear Schrödinger equation describing the propagation of pulses in optical fibers for positive group-velocity dispersion. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system, whose solutions determine the exact solutions of nonlinear Schrödinger equation. The set of exact analytic solutions contains dark solitary waves, dark soliton, periodic, and stationary solutions which are very important from a physical point of view.
Cauchy problem for the linearized version of the Generalized Polynomial KdV equation
Authors: Yordanov Russi G.
Published: July 2002

In the present paper results about the ‘‘Generalized Polynomial Korteweg–de Vries equation’’ (GPKdV) are obtained, extending the ones by Sachs [SIAM J. Math. Anal. 14, 674 (1983)] for the Korteweg–de Vries (KdV) equation. Namely, the evolution of the so-called ‘‘prolonged squared’’ eigenfunctions of the associated spectral problem according to the linearized GPKdV is proven, the Lax pairs associated with the ‘‘prolonged’’ eigenfunctions as well as ‘‘prolonged squared’’ eigenfunctions are derived, and on the basis of some expansion formulas the Cauchy problem for the linearized GPKdV with a decreasing at infinity initial condition is solved.
E. Cartan moment of rotation in Ashtekar’s self-dual representation of gravitation
Authors: Kheyfets Arkady , Miller Warner A.
Published: July 2002

The geometric construction of the E. Cartan moment of rotation associated to the spacetime curvature provides a geometric interpretation of the gravitational field sources and describes geometrically how the sources are ‘‘wired’’ to the field in standard geometrodynamics. The E. Cartan moment of rotation yields an alternate way (as opposed to using variational principles) to obtain Einstein equations. The E. Cartan construction uses, in an essential way, the soldering structure of the frame bundle underlying the geometry of the gravitational field of general relativity. The geometry of Ashtekar’s connection formulation of gravitation is based on a complex-valued self-dual connection that is not defined on the frame bundle of spacetime. It is shown how to transfer the construction of the E. Cartan moment of rotation of Ashtekar’s formulation of the theory of gravity and demonstrate that no spurious equations are produced via this procedure.
Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile
Authors: Fishman Louis
Published: July 2002

The application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one-way Helmholtz equation is briefly reviewed. The role of operator symbols is stressed and their properties briefly discussed. The construction of the operator symbol requires the exact or approximate solution of the (Helmholtz) Weyl composition equation in the Weyl pseudodifferential operator calculus. The exact symbols for several quadratic profiles are presented and briefly analyzed. The symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case. These results are used to illustrate several points pertinent to wide-angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics.
Kantowski–Sachs metrics with source: A massless scalar field
Authors: Xanthopoulos Basilis C. , Zannias Thomas
Published: July 2002

Solutions of the coupled Einstein massless scalar field equation are discussed under the assumption that the metric belongs to the ‘‘Kantowski–Sachs’’ class of metrics. More precisely, the general solution of the coupled Einstein massless scalar field equations is derived under the following assumptions: (a) The scalar field is massless minimally coupled to gravity and obeys the Klein–Gordon equation; and (b) the metric belongs to the spherical Kantowski–Sachs class of metrics. The main feature of the results is a tractable, very simple, compact form of the space-time metric. This is accomplished by expressing the solution in a special coordinate gauge. An analysis of the geometry shows the presence of curvature singularities which consist of a spacelike part and a null part. The spacelike singularity appears to ‘‘squeeze’’ the SO(3) orbits to zero proper area while simultaneously stretching their proper separation to infinity length. The null part appears to squeeze to zero values both SO(3) orbits and their proper separation as well. There also exists a subclass of metrics for which the singularity structure is different. The null singularity is replaced by a spacelike part. Both ‘‘initial’’ and ‘‘final’’ singularities exhibit the same qualitative features and they are of finite proper time away from each other.
Boson–fermion and baryon mapping: Construction of collective subspaces. II. Example: A simple quark shell model
Authors: Meyer Jutta
Published: July 2002

The formalism derived for the boson–fermion and the baryon mapping in Paper I of this series is applied to the single-orbit quark shell model developed by Petry and co-workers for the description of nuclear properties. The multiquark space is reduced to the collective subspace of multinucleon states. A collective representation of states and operators in terms of bosons and ideal fermions or in terms of ideal baryons, respectively, is constructed. The results of the original model in the multinucleon space are exactly reproduced. Finally, the two transformations are compared with a related mapping technique recently published by Pittel, Engel, Dukelsky, and Ring.
Evaluation of Schwinger–de Witt kernels for spin-2̄1 fields through the SO(2,1) Lie algebra
Authors: Rabello S. J. , Vaidya A. N.
Published: July 2002

Using the noncompact SO(2,1)∼SU(1,1) Lie algebra the Schwinger–de Witt kernels for massive spin-1/2 fields are obtained in some classical background gravitational fields. The method makes use of the Schwinger–de Witt proper time representation and Baker–Campbell–Hausdorff formulas.
Gravitational equations in space-time with torsion
Authors: Khodunov A. V. , Zhytnikov V. V.
Published: July 2002

Various representations of equations of gravitational theories in space-time with torsion are considered. Special attention is paid to the case of quadratic Poincaré gauge theory of gravity. Advantages of each representation are discussed. The complete algorithm for calculation of gravitational equations in the framework of the most efficient formalism of spinor-valued exterior forms is presented.
Exact solutions of SL(N,R)-invariant chiral equations one- and two-dimensional subspaces
Authors: Matos Tonatiuh , Rodríguez Guadalupe , Becerril Ricardo
Published: July 2002

A methodology for integrating the chiral equation (ρg,zg−1),z̄+ (ρg,z̄g−1),z=0 is developed, when g is a matrix of the SL(N,R) group. In this work the ansätze g=g(λ) where λ satisfy the Laplace equation and g=g(λ,τ) are made, where λ and τ are geodesic parameters of an arbitrary Riemannian space. This reduces the chiral equation to an algebraic problem and g can be obtained by integrating a homogeneous linear system of differential equations. As an example of the first ansatz, all the matrices for N=3 and one example for N=8, which corresponds to exact solutions of the d=5 and d=10 Kaluza–Klein theory, respectively are given. For the second ansatz the chiral equations are integrated for the subgroups SL(2,R), SO(2,1R), Sp(2,R), and the Abelian subgroups.
Holonomy groups of compact Riemannian manifolds: A classification in dimensions up to ten
Authors: McInnes Brett
Published: July 2002

The possible holonomy groups of compact, locally irreducible Riemannian manifolds are studied. Motivated by applications arising in physics, it is not required that these manifolds be simply connected. In this paper a complete classification up to dimension ten is given, with particular emphasis on the manifolds of dimension six or less. In this latter case, there exist actual examples for every class, so that the possible holonomy groups can be characterized exactly.
Examples of Einstein manifolds with all possible holonomy groups in dimensions less than seven
Authors: McInnes Brett
Published: July 2002

In an earlier work, the possible holonomy groups of all compact locally irreducible Riemannian manifolds of dimensions up to ten were classified, placing particular emphasis on the non-simply-connected case. In this work, the problem of finding examples of manifolds with such holonomy groups is discussed. It is proven, in particular, that it is possible to find (Einsteinian) examples of every one of the 23 holonomy types corresponding to manifolds of dimensions less than 7: Thus, an exact characterization of the groups that can occur as holonomy groups can be given in those dimensions.
Coherent states on the m-sheeted covering group of SU(1,1)
Authors: Vourdas A.
Published: July 2002

Coherent states associated with the m-sheeted covering group of SU(1,1) are considered and such properties as overcompleteness and resolution of the identity are studied. They are used to define analytic representations in which the transformations of the m-sheeted covering group of SU(1,1) are implemented as extended Mobius conformal mappings. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.
Models of q-algebra representations: Matrix elements of the q-oscillator algebra
Authors: Kalnins E. G. , Miller Willard , Mukherjee Sanchita
Published: July 2002

This article continues a study of function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. Here a q analog of the oscillator algebra (not a quantum algebra) is considered. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ‘‘group operators’’ on these representation spaces are computed. This ‘‘local’’ approach applies to more general families of special functions, e.g., with complex arguments and parameters, than does the quantum group approach. It is shown that the matrix elements themselves transform irreducibly under the action of the algebra. q analogs of a formula are found for the product of two hypergeometric functions 1F1 and the product of a 1F1 and a Bessel function. They are interpreted here as expansions of the matrix elements of a ‘‘group operator’’ (via the exponential mapping) in a tensor product basis (for the tensor product of two irreducible oscillator algebra representations) in terms of the matrix elements in a reduced basis. As a by-product of this analysis an interesting new orthonormal basis was found for a q analog of the Bargmann–Segal Hilbert space of entire functions.
Eigenstates of Calogero–Sutherland–Moser model and generalized Schur functions
Authors: Sogo Kiyoshi
Published: July 2002

The eigenvalue problem for the Calogero–Sutherland–Moser model is solved exactly. The complete set of eigenfunctions is given by the homogeneous Laurent polynomials. Its subset consisting of polynomial solutions is expressed by the generalized Schur functions which correspond to the λ-deformed general linear group.
The E
q(2) group via direct quantization of the Lie–Poisson structure and its Lie algebra
Authors: Maślanka Pawel/
Published: July 2002

The quantum group dual to the deformed eq(2) algebra obtained by Celeghini et al. [J. Math. Phys. 31, 2548 (1990)] is constructed.
On diff(S1) covariantization of pseudodifferential operator
Authors: Huang Wen-Jui
Published: July 2002

A study of diff(S1) covariant properties of a pseudodifferential operator of integer degree is presented. First, it is shown that the action of diff(S1) defines a Hamiltonian flow defined by the second Gelfand–Dickey bracket if and only if the pseudodifferential operator transforms covariantly. Second, the covariant form of a pseudodifferential operator of degree n ≠ 0,±1 is constructed by exploiting the inverse of the covariant derivative. This, in particular, implies the existence of a primary basis for WKP(n) (n ≠ 0,±1).
Elastic waves in discontinuous media: Three-dimensional scattering
Authors: Molino F. R. , Sabatier P. C.
Published: July 2002

This report contains an exact study of elastic wave propagation and its scattering in discontinuous media where hard reflectors are onionlike sets of surfaces. In order to reformulate the problem as a finite set of boundary integral equations, the wave motion between reflectors is represented by means of elastic potentials which involve vectorial densities on the surfaces. In the external medium, an outgoing asymptotic condition generalizes the Silver–Müller (and the Sommerfeld) condition to the case of coupled waves (S and P waves) moving with different velocities. The uniqueness of the Green’s function, which guarantees the uniqueness of the direct problem solution, is proven. For any incident wave and arbitrary number of surfaces, the transmission and scattering problems are studied, with and without the simplification obtained by assuming constant Poisson ratios. According to the parameter ranges, the equations which are obtained are well posed, either as second kind Fredholm equations, or because they reduce to the inverse of the sum of the identity operator and a ‘‘small norm’’ bounded operator. The results can be used to describe rigorously the three-dimensional scattering of elastic waves in the frequency domain for any kind of incident wave function (P,S,...) as well as the response to a localized source.
Tuning the properties of matter to any chosen dynamical behavior in cosmological models with elastic media
Authors: Magli Giulio
Published: July 2002

The field equations governing Bianchi type I space–times having elastic media as sources are constructed. Such equations turn out to be a system of three ordinary differential equations for the three independent components of the gravitational field. Plane symmetric and Robertson–Walker space–times are also discussed, and some examples of solutions are given. In the Robertson–Walker case, it turns out that it is possible to ‘‘tune’’ the elastic constitutive equations in such a way that any ‘‘required’’ behavior of the scale factor may be obtained. This feature closely resembles the scalar-field dominated case.
Regularity theorems in the nonsymmetric gravitational theory
Authors: Moffat J. W.
Published: July 2002

Regularity theorems are presented for cosmology and gravitational collapse in non-Riemannian gravitational theories. These theorems establish conditions necessary to allow the existence of timelike and null path complete spacetimes for matter that satisfies the positive energy condition. Non-Riemannian theories of gravity can have solutions that have a nonsingular beginning of the universe, and the gravitational collapse of a star does not lead to a black hole event horizon and a singularity as a final stage of collapse. A perturbatively consistent version of nonsymmetric gravitational theory is studied that, in the long-range approximation, has a static spherically symmetric solution which does not have black hole event horizons and has finite curvature invariants.
Remarks on resolutions of Hilbert–Schmidt operators
Authors: Johnston Carolyn Pfeffer
Published: July 2002

A generalization due to Ali, Antoine, and Gazeau of the notion of square integrability of representations is used to construct operators as integrals over compact homogeneous spaces X=G/H. It is shown that such operators are Hilbert–Schmidt, and a formula for the Hilbert–Schmidt norm is given. Finally, two examples are given demonstrating the dependence of the Hilbert–Schmidt norm on the section σ : X→G used to construct it. One example, involving the three-dimensional Euclidean group, makes interesting use of Bessel coefficients.
Charged particles in a magnetic field on a cone
Authors: Bezerra de Mello E. R. , Bezerra V. B.
Published: July 2002

We analyze the problem of two charged particles moving on a cone in the presence of a static, uniform magnetic field plus a Coulomb interaction. In the specific case where the deficit angle δφ=π, closed expressions for the wave functions and energies are obtained.
The structure of decoherence functionals for von Neumann quantum histories
Authors: Wright J. D. Maitland
Published: July 2002

Gell-Mann and Hartle have proposed a significant generalization of quantum theory in which decoherence functionals perform a key role. Isham–Linden–Schreckenberg have given a penetrating analysis of decoherence functionals for L(H), where H is finite dimensional (dimension greater than 2). In this note their conjecture on the significance of boundedness is verified. In particular, it is shown that when d is a bounded decoherence functional associated with a von Neumann algebra A, then, provided A has no direct summand of type I2, d can be represented as the difference between semi-innerproducts on A.
On the dynamics of the four-dimensional rigid body in a quadratic potential field
Authors: Zhivkov Angel , Stanislavova Milena
Published: July 2002

We study the nondegenerated solutions of the rotation of a four-dimensional rigid body in a quadratic potential field. This problem has 6 degrees of freedom. We obtain 143 topologically different solutions and explicit formulas in Prym theta-functions.
Homothetic motion in radiating and dissipative spheres
Authors: Barreto W. , Castillo L.
Published: July 2002

A method used to study the evolution of radiating dissipative fluid spheres is applied to the case in which the space–time admits a homothetic motion. We obtain a system of equations at the surface of the distribution which is integrated numerically. Considering that the shear viscosity induces anisotropy, we obtain a model derived from the static solution by Herrera, Jiménez, Leal, Esculpi, Ponce de León, and Galina [J. Math. Phys. 25, 3274 (1984)] for homothetic fluids but which includes dynamic variables. Therefore, the profiles of the physical variables at the surface are calculated and discussed in the light of one astrophysical scenario.
Purely magnetic space–times
Authors: Haddow Barry M.
Published: July 2002

Purely magnetic space–times, in which the Riemann tensor satisfies Rabcdubud=0 for some unit timelike vector ua, are studied. The algebraic consequences for the Weyl and Ricci tensors are examined in detail and consideration given to the uniqueness of ua. Some remarks concerning the nature of the congruence associated with ua are made.
Integrability and disorder in mesoscopic systems: Application to orbital magnetism
Authors: Richter Klaus , Ullmo Denis , Jalabert Rodolfo A.
Published: July 2002

We present a semiclassical theory of weak disorder effects in small structures and apply it to the magnetic response of non-interacting electrons confined in integrable geometries. We discuss the various averaging procedures describing different experimental situations in terms of one- and two-particle Green functions. We demonstrate that the anomalously large zero-field susceptibility characteristic of clean integrable structures is only weakly suppressed by disorder. This damping depends on the ratio of the typical size of the structure with the two characteristic length scales describing the disorder (elastic mean-free-path and correlation length of the potential) in a power-law form for the experimentally relevant parameter region. We establish the comparison with the available experimental data and we extend the study of the interplay between disorder and integrability to finite magnetic fields.
A mean field theory for arrays of Josephson junctions
Authors: Parisi Giorgio
Published: July 2002

I present here some results on the mean field theory approach to the statistical mechanics of a D-dimensional array of Josephson junctions in the presence of a magnetic field. The mean field theory equations are obtained by computing the thermodynamical properties. In the high temperature region in the limit D→∞, where the problem is simplified, this limit defines the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e., to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the q-deformed harmonic oscillator. The same arguments can be used to predict the thermodynamical properties in the mean field limit. These results can be extended to the low temperature phase using a conjecture on the equivalence of some system without disorder with appropriate random systems.
Inverse problem in nonstationary multidimensional medium
Authors: Shevtsov Boris M.
Published: July 2002

The problem of a scalar wave propagation from the point impulsive source in the layer of a nonstationary multidimensional medium is considered. The boundary problem for the wave equation is reformulated in the problem with the initial condition using the invariant imbedding method. The integral-differential inverse procedures of the various orders were obtained from the imbedding equations using the singularities method. The order of inverse procedure is defined by the degree of a polynomial in the analytical representation of the medium characteristic near the layer boundary. It was shown that the coefficients of the polynomial are calculated with the help of the differential characteristics of the point impulsive source in the inhomogeneous medium. The cause and character of the multidimensional inverse problem overdefiniteness are considered. The application of the proposed procedure for a statistical problem is discussed.
Dirichlet forms and Dirichlet operators for infinite particle systems: Essential self-adjointness
Authors: Choi Veni , Park Yong Moon , Yoo Hyun Jae
Published: July 2002

We study the Dirichlet forms and the associated Dirichlet operators for Gibbs measures on infinite particle configuration space. The Dirichlet forms are defined to be “gradient-type” forms by introducing a measurable field of rigged Hilbert spaces on the configuration space. Under mild conditions on the interaction including singular potentials, we show that the pre-Dirichlet operator is symmetric and that the closure of the pre-Dirichlet form satisfies the Markovian property. When the interaction is three times differentiable and decreasing sub-exponentially, we show that the Dirichlet operator is essentially self-adjoint on a domain consisting of bounded smooth local functions.
Bäcklund transformation of partial differential equations from the Painlevé-Gambier classification. II. Tzitzéica equation
Authors: Conte Robert , Musette Micheline , Grundland A. Michel
Published: July 2002

From the existing methods of singularity analysis only, we derive the two equations which define the Bäcklund transformation of the Tzitzéica equation. This is achieved by defining a truncation in the spirit of the approach of Weiss et al., so as to preserve the Lorentz invariance of the Tzitzéica equation. If one assumes a third-order scattering problem, this truncation admits a unique solution, thus leading to a matrix Lax pair and a Darboux transformation. In order to obtain the Bäcklund transformation (BT), which is the main new result of this paper, one represents the Lax pair by an equivalent two-component Riccati pseudopotential. This yields two different BTs; the first one is a BT for the Hirota–Satsuma equation, while the second one is a BT for the Tzitzéica equation. One of the two equations defining the BT is the fifth ordinary differential equation of Gambier.
Ground states of a model in nonrelativistic quantum electrodynamics. I
Authors: Hiroshima Fumio
Published: July 2002

The system of a one charged nonrelativistic particle with external potentials minimally coupled to a massless quantized radiation field is considered. An ultraviolet cutoff is imposed on the quantized radiation field and the charged particle has spin 1/2. The class of external potentials considered in this paper contains Coulomb potentials. It is shown that the ground states of the system exist provided that a coupling constant is in a region.
Nonrelativistic quantum Hamiltonian for Lorentz violation
Authors: Kostelecký V. Alan , Lane Charles D.
Published: July 2002

A method is presented for deriving the nonrelativistic quantum Hamiltonian of a free massive fermion from the relativistic Lagrangian of the Lorentz-violating standard-model extension. It permits the extraction of terms at arbitrary order in a Foldy–Wouthuysen expansion in inverse powers of the mass. The quantum particle Hamiltonian is obtained and its nonrelativistic limit is given explicitly to third order.
The dynamics of flow around a cylinder at subcritical Reynolds numbers
Authors: Yokuda S. , Ramaprian B. R.
Published: July 2002

Mean and fluctuating pressure and skin friction around a circular cylinder in cross-flow were studied in the subcritical Reynolds number range, 104–105. Results are presented for two cases, namely, with and without a splitter plate behind the cylinder. The splitter plate was used to suppress vortex shedding. The nonlinear dynamics of the flow around the cylinder was examined to characterize the process of laminar separation in terms of the number of degrees of freedom, and to determine whether the process is chaotic. For this purpose, the Grassberger–Procaccia correlation dimension and the largest Lyapunov exponent were estimated from the time series of the pressure data. The results indicate a correlation dimension of the order of 10–12 both in the presence and absence of the splitter plate. The largest Lyapunov exponent was found to be positive in both cases, suggesting that the process of laminar separation is chaotic. These results are new and are significant from the point of view of modeling and controlling the phenomenon of laminar separation in the future.
Coaxial atomizer liquid intact lengths
Authors: Eroglu Hasan , Chigier Norman , Farago Zoltan
Published: July 2002

Average intact lengths of round liquid jets generated by airblast coaxial atomizers were measured from over 1500 photographs. The intact lengths were studied over a jet Reynolds number range of 18 000 and Weber number range of 260. Results are presented for two different nozzle geometries. The intact lengths were found to be strongly dependent on Re and We numbers. An empirical equation was derived as a function of these parameters. A comparison of the intact lengths for round jets and flat sheets shows that round jets generate shorter intact lengths.
Wave–turbulence interaction in free-surface channel flows
Authors: Rashidi M. , Hetsroni G. , Banerjee Sanjoy
Published: July 2002

Wave–turbulence interaction in turbulent channel flows has been studied using microbubble tracers and visualization. In the experiments, two-dimensional waves of different lengths and amplitudes have been superimposed on a turbulent channel flow via a wavemaker. The conditions were chosen to be such that the frequencies of the interfacial waves were in the range of the ejection frequencies in the undisturbed flow. The results show that the waves cause an increase in the number of wall ejections, giving rise to an increase in the measured values of the turbulence intensities and Reynolds stresses. However, the increases in ejection frequency do not appear to be directly related to wave frequency. They correlate better with wave amplitude. Conditional averaging of the velocity fields shows that while turbulence is increased in the region below the crest of the waves (extending to the wall), it is decreased in the wave troughs. The overall effect of the surface waves, over the range of conditions investigated is, however, to increase turbulence levels.
Eigenvalue problems in three-dimensional Euler flows
Authors: Ohkitani Koji
Published: July 2002

A simple analysis shows that there are two eigenvalue problems associated with vorticity. Dynamically, the vorticity tends to be a simultaneous eigenvector of the rate-of-strain tensor S and the pressure hessian P at the point of maximum enstrophy, as shown in the numerical simulations. This suggests that intense vortex stretching occurs at particular fluid particles. Indeed, high vorticity regions are more localized in Lagrangian marker space than in physical space. It is also shown that the P alignment holds valid even kinematically for random fields.
Experimental study of the formation of field-reversed configurations employing high-order multipole fields
Authors: Slough J. T. , Hoffman A. L.
Published: July 2002

A high-order multipole ‘‘barrier’’ field was applied at the vacuum tube wall in the TRX experiment [Phys. Fluids B 1, 840 (1989)] during both the preionization and field reversal phases of field-reversed configuration (FRC) formation. Use of this field during field reversal resulted in a significant reduction of impurities as well as increased flux trapping. With a large enough Bθ at the wall, sheath detachment from the wall became apparent, and flux loss through the sheath became negligible (<10%). At larger wall Bθ (>1.5 kG), destructive rotational spin-up occurred, driven by Hall current forces. When the multipole barrier field was also applied during either axial discharge or ringing theta current preionization, a very symmetric and uniform breakdown of the fill gas was achieved. In particular, using ringing theta preionization, complete ionization of the fill gas was accomplished with purely inductive fields of remarkably low magnitude, where Ez≤3 V/cm, and Eθ≤20 V/cm. Due to the improved ionization symmetry, about 65% to 75% of the lift-off flux (flux remaining after field reversal) could be retained through the remaining formation processes into an equilibrium FRC. Using the multipole field during both preionization and formation, it was possible to form FRC’s with good confinement with greater than 3 mWb of trapped flux at 15 mTorr D2 or H2 in a 10 cm radius device. Values of s in excess of 4 could be achieved in this manner.
Linear theory of the collective Raman interaction in a free-electron laser with a planar wiggler and an axial guide field
Authors: Freund H. P. , Davidson R. C. , Johnston G. L.
Published: July 2002

A linear stability analysis of the collective Raman interaction in a free-electron laser with combined planar wiggler and axial guide magnetic fields is presented. The analysis involves a perturbation of the cold-fluid model of the interaction about the single-particle trajectories in the combined external fields, and the complete dispersion equation for a monoenergetic beam is obtained. In contrast to the case of a helical wiggler field in which the interaction excites a right-hand circularly polarized wave, the interaction for a planar wiggler and an axial guide field is with an elliptically polarized wave that contains both the left- and right-hand circular components. However, the results indicate that many facets of the interaction are analogous to those found with helical wiggler. In particular, both the transverse velocity and the growth rate of the instability tend to increase near the resonance at which the Larmor and wiggle periods coincide. In addition, a negative-mass regime is found in which the axial electron velocity increases with decreasing beam energy, which drives the beam space-charge modes unstable.
Anomalous fluxes in the plateau regime for a weakly turbulent, magnetically confined plasma
Authors: Balescu R.
Published: July 2002

The anomalous particle and heat fluxes, together with the parallel electric current, are determined for a confined plasma in the plateau regime in the presence of weak electrostatic drift-wave turbulence. Proper account is taken of nonstationarity and of the finite ion Larmor radius (FLR). The quasineutrality of the drift-wave fluctuations imposes a consistency condition, by which the evaluation of the anomalous fluxes is closely related to the drift-wave dispersion equation. On the other hand, these fluxes are related to the thermodynamic forces via the poloidal fluxes. For the weak turbulence approximation considered here, a unified formulation of the anomalous transport problem has been obtained, including all aspects of neoclassical theory. The complete set of transport coefficients is calculated and various relations between them are exhibited. It clearly appears, for instance, that the anomalous ion heat flux is a pure FLR effect that vanishes as the Larmor radius goes to zero. The Onsager symmetry is broken for anomalous transport. The Appendix is devoted to a general discussion of the concept of heat flux in turbulent plasmas.
Experimental investigation of a pseudospark-produced high-brightness electron beam
Authors: Jain K. K. , Boggasch E. , Reiser M. , Rhee M. J.
Published: July 2002

A high-brightness electron beam produced by a six-gap pseudospark chamber operated in 5–25 kV voltage and 30–70 mTorr pressure ranges is experimentally investigated. The electron beam of current 150 A at an average energy of 20 keV and pulse duration of 10 nsec is extracted with a repetitive frequency of ∼10 Hz. The electron-beam current scales linearly with the breakdown voltage and about 20% of the stored energy is converted into the total beam energy. The time-integrated rms emittance of the electron beam is measured, and a typical value is found to be 65 mm mrad, yielding a normalized brightness of the beam Bn≊2×1010 A/(m2 rad2).
Coexistence of stimulated Raman and Brillouin scattering in laser-produced plasmas
Authors: Baldis H. A. , Villeneuve D. M. , Labaune C. , Pesme D. , Rozmus W. , Kruer W. L. , Young P. E.
Published: July 2002

Many different plasma instabilities and plasma modes can coexist in laser plasmas. These instabilities are usually treated as if they occur in isolation, however, more attention has recently been paid to how they interact with each other. This paper reviews three examples of experiments that have demonstrated an interaction between stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS). In each case, the presence of SBS is seen to modify the behavior of the SRS process. In one case, SRS was totally suppressed by seeding SBS. The same mechanism might also be responsible for the gap in the Raman spectrum. Some theoretical and numerical studies of the interaction between SRS and SBS are also discussed, showing how increasingly detailed models can give improved agreement with experimental observations.
Theory of mean poloidal flow generation by turbulence
Authors: Diamond P. H. , Kim Y.-B.
Published: July 2002

The mechanism for generation of mean poloidal flow by turbulence is identified and elucidated. Two methods of calculating poloidal flow acceleration are given and shown to yield predictions which agree. These methods link flow generation to the quasilinear radial current or the Reynolds stress 〈ṼrṼθ〉. It is shown that poloidal acceleration will occur if the turbulence supports radially propagating waves and if radial gradients in the turbulent Reynolds stress and wave energy density flux are present. In practice, these conditions are met in the tokamak edge region when waves propagate through the outermost closed flux surface or when convection cells with large radial correlation length are situated in steep gradient regions. The possible impact of these results on the theory of the L→H transition is discussed.
Brillouin limit for non-neutral plasma in inhomogeneous magnetic fields
Authors: Turner Leaf
Published: July 2002

The effect of magnetic field inhomogeneity upon the maximum density of non-neutral plasma that can be confined in hydrostatic equilibrium under the combined influence of electrostatic and magnetostatic fields is explored in two cases of azimuthally symmetric geometries: first, a plasma in an arbitrary vacuum poloidal magnetic field, B=Br(r,z)r̂+Bz(r,z)ẑ, and second, a toroidal plasma in a toroidal vacuum magnetic field. For the poloidal field case, it is demonstrated that the Brillouin limit on number density can be achieved only with a homogeneous axial magnetic field. For the toroidal field case, it is demonstrated that although the Brillouin limit does not provide a limitation on the local number density confined, it nevertheless does provide an upper limit on the total amount of non-neutral plasma confined in equilibrium. It is also demonstrated that when viscosity is present in the toroidal field case, its effect to first order in the inverse aspect ratio can be opposed by a readjustment of only the external electrostatic potential.
Lower-hybrid-drift instability and radiative collapse of a dense Z pinch
Authors: Robson A. E.
Published: July 2002

The increased resistivity resulting from the lower-hybrid-drift (LHD) instability is shown to increase the Pease–Braginskii current IPB in a Z pinch and to make radiative collapse harder to achieve; IPB becomes a function of both the line density and the pinch radius and a minimum dI/dt is necessary to induce collapse. The effect of the LHD instability is greatest in a hydrogen pinch, and decreases with increasing atomic number.
Scattered light near the laser wavelength from Nova two-color experiments
Authors: Young P. E. , Baldis H. A. , Estabrook K. G.
Published: July 2002

A laser-produced plasma has been studied in which there is a peak plasma density between critical and quarter-critical for a substantial amount of time (∼400 psec). The behavior of temporally and spectrally resolved light near the wavelength of the interaction laser λ0, is compared to the decay with time of the peak plasma density inferred from three-halves harmonic emission and Raman scattered light. Evidence for seeding of stimulated Brillouin scattering by the two-plasmon decay instability is presented.
Instabilities associated with a negative rf resistance in current-carrying ion sheaths
Authors: Ohno N. , Komori A. , Tanaka M. , Kawai Y.
Published: July 2002

Coherent instabilities on the order of the ion plasma frequency are generated by applying a dc voltage between a meshed grid and a disk target in an unmagnetized plasma. The instability occurs in the ion-rich current-carrying sheath on the negatively charged grid when some ions are reflected from the grid to the sheath edge by the potential difference between two plasmas divided by the grid. The exciting mechanism of the instability has been identified as a negative rf resistance associated with the ion inertia in the ion-rich sheath, coupled to an ion resonance caused by a positive feedback due to the reflection of ions in the sheath region. The frequency of the instability, which is proportional to the plasma density, is basically determined by the ion transit time through the sheath, and thus, is proportional to the product of inverse sheath thickness and average ion velocity related to the applied voltage.