bluuebunny/crossref_metadata_2025 huggingface dataset:
Exact solutions of plane symmetric cosmological models
Authors: Hojman Roberto , Santamarina Jorge
Published: March 2003

The exact solutions for perfect fluid plane symmetric cosmological models with cosmological constant are derived. It is also shown that under an appropriate transformation the Λ=0 and Λ≠0 cases are mathematically equivalent.
Cosmological solutions of the Einstein equation with heat flow
Authors: Sanyal Abhik Kumar , Ray Dipankar
Published: March 2003

Solutions of Einstein equation for fluids with heat flow are obtained, generalizing the results of Bergmann.
Coupled electromagnetic and gravitational linearized perturbations of the Kerr–Newman metric
Authors: Bellezza V. , Ferrari V.
Published: March 2003

A new gauge and tetrad invariant equation governing the coupled electromagnetic-gravitational perturbations for the Kerr–Newman metric and involving a closed 2-form is obtained. Operating on this equation with the complex vectorial formalism as developed by Crossman, we have found three equations for the gauge and tetrad invariant quantities χ1B(≡3ψ2Aφ0B−2φ1Aψ1B), χ−1B(≡3ψ2Aφ2B−2φ1Aψ3B), and χ0B(≡3ψ2Aφ1B−2φ1Aψ2B +2φ5/21Aφ̄−1/21Aφ̄1B).
An explicit formula for the Casimir energy of an arbitrary compact smooth surface without boundary
Authors: Sen Siddhartha
Published: March 2003

An explicit formula for the finite part of the Casimir energy of a scalar field φ(x,t) defined on a smooth, compact two-dimensional Riemannian manifold X without boundary is derived. The formula involves the metric tensor on X and its derivatives.
Hamiltonian formulation of the KdV equation
Authors: Nutku Y.
Published: March 2003

We consider the canonical formulation of Whitham’s variational principle for the KdV equation. This Lagrangian is degenerate and we have found it necessary to use Dirac’s theory of constrained systems in constructing the Hamiltonian. Earlier discussions of the Hamiltonian structure of the KdV equation were based on various different decompositions of the field which is avoided by this new approach.
Indefinite metric and other-than-Feynman propagators as tools in a relativistic two-body problem
Authors: Günther Marian
Published: March 2003

By embedding the usual physical Fock space P of a simple field theory in a larger non-Hilbert representation space R, a formalism is obtained permitting the use of Δ̄ propagators instead of the Feynman propagators ΔF to represent the internal particle lines in Feynman graphs. The new formalism is subsequently applied to a Bethe–Salpeter equation in the g2 approximation of its kernel and an exact solution of the latter is obtained exhibiting much simpler analytical features compared to its standard counterpart—the so-called Wick equation.
Integration conditions for first-order differential linear equations in higher-dimensional gauge theories
Authors: Fairlie D. B. , Nuyts J.
Published: March 2003

Generalized self-duality type relations for gauge fields in higher-dimensional spaces are discussed from the point of view of orbits, strata, and stability groups. It is explained how to obtain them as integrability conditions for first-order gauge-invariant linear differential equations.
Some series of infinitely many symmetry generators in symmetric space chiral models
Authors: Hou Bo-yu
Published: March 2003

This paper shows that, starting from any conserved current generated by some given infinitesimal symmetry generator, one may use finite dual transformations to induce infinitely many infinitesimal symmetry generators. Thus, besides starting from ordinary isotopic and space-time translation, this paper also discovers the infinitesimal generators for Bäcklund transformation, for dual symmetry itself and other general cases, and then uses them to generate infinitely many local or nonlocal currents, respectively.
On the integrability of nonlinear Dirac equations
Authors: Steeb W.-H. , Oevel W. , Strampp W.
Published: March 2003

The integrability of nonlinear Dirac equations is discussed applying recent results in soliton theory. Using the Lie point transformation groups of the nonlinear Dirac equations we reduce these partial differential equations to systems of ordinary differential equations and study whether these systems are integrable. We also discuss whether Lie–Bäcklund vector fields exist. We conclude that the nonlinear Dirac equations are not integrable.
Critical properties of pseudospin Hamiltonians
Authors: Gilmore R.
Published: March 2003

The thermodynamic critical properties of a simple class of pseudospin model Hamiltonians are discussed. This class of models includes the spin van der Waals model and the Meshkov–Glick–Lipkin model as particular cases. Second-order thermodynamic phase transitions occur when the spin–spin interaction contributes negatively in a particular direction and the linear interaction term is orthogonal to the direction(s) of greatest energy gain through the spin–spin interaction.
Kaluza–Klein theory derived from a Riemannian submersion
Authors: Hogan P. A.
Published: March 2003

Taking a Riemannian submersion as our starting point, we obtain some formulas derived from O’Neill’s fundamental equations of a submersion and compare them with the basic equations of Bergmann’s approach to Kaluza–Klein theory in five dimensions. Having imposed Hermann’s sufficient conditons for the submersion to be a principal fiber bundle, we study the conclusions that can be drawn from the derived formulas.
Orthogonal polynomials with exponential weight in a finite interval and application to the optical model
Authors: Mach R.
Published: March 2003

A quadrature procedure is developed which makes the construction of momentum-space meson-nucleus optical potentials more accurate. We deal with numerical evaluation of integrals with finite t-integration range which contain exp(Dt) explicitly, where D is a parameter. The Gaussian rule is used with abscissas determined as roots of orthogonal polynomials with exponential weight function in the interval [−1,1]. Recurrence relations and inequalities for these polynomials are obtained. A nonlinear recursion is derived, which permits the evaluation of abscissas and weights without accumulation of roundoff error. The nonlinear recursion is solved by means of an iterative procedure, the convergence properties of which are established. The quadrature procedure is summarized as an easily implementable algorithm. The rate of convergence is demonstrated for several test integrals.
Two-dimensional time-dependent Hamiltonian systems with an exact invariant
Authors: Grammaticos B. , Dorizzi B.
Published: March 2003

We present a direct approach to investigate the existence of an exact invariant for two-dimensional Hamiltonians, in which the potential depends explicitly on time. The method is based on an expansion of the invariant in the velocities. The problem is solved completely for invariants linear and quadratic in the momenta. Our results contain as a particular case the results of Lewis and Leach on one-dimensional systems.
The Liouville–Bäcklund transformation for the two-dimensional SU(N) Toda lattice
Authors: Popowicz Ziemowit
Published: March 2003

We describe the Liouville–Bäcklund transformation for the two-dimensional SU(N) Toda lattice with free end points. Integration of this transformation gives us the general solution of this equation, which depends on the N arbitrary solutions of the two-dimensional Laplace equation.
General prolongations and (x, t)-depending pseudopotentials for the KdV equation
Authors: Molino Pierre
Published: March 2003

Given an exterior differential system on a manifold M, we study general prolongations of the system on a locally trivial fiber bundle (M̃, π̃, M) by a Cartan–Ehresmann connection. We characterize such prolongations for the system associated with the KdV equation without any assumption of ‘‘(x, t) independence.’’ The partial Lie algebra discovered by Wahlquist–Estabrook [J. Math. Phys. 16, 1 (1975)] appears by this way as an intrinsic tool. Simple analytic pseudopotentials are classified up to diffeomorphism.
Proof of an algorithm for the evaluation of the branching multiplicity SO(2n)→SO(2n−2)⊗U(1)
Authors: Amar V. , Dozzio U. , Oleari C.
Published: March 2003

The proof of an algorithm, previously proposed by us, for the evaluation of the branching multiplicity SO(2n)→SO(2n−2)⊗U(1) is given. This proof is based on explicit construction of lowering shift operators for the class Dn of Cartan.
Estimation of inverse temperature and other Lagrange multipliers: The dual distribution
Authors: Tikochinsky Y. , Levine R. D.
Published: March 2003

It is shown that the problem of parameter estimation for distributions of the exponential type, has a unique consistent Bayesian solution: The requirement that Bayes’ rule and maximum entropy lead to the same inverse distribution determines the loss function. Similarly, the demand that the best estimate for a random variable, given an observed value of that variable, coincides with the observed value, determines the prior distribution for the corresponding conjugate parameter. Properties of the dual distribution thus determined are investigated. In particular, the symmetrical role of parameter and constraint as a pair of conjugate variables is shown to imply an inherent uncertainty principle. Possible applications to temperature fluctuations and to an imbedding of classical mechanics in a statistical background are indicated.
Decoupling of a system of partial difference equations with constant coefficients and application
Authors: Phares Alain J.
Published: March 2003

Consider D multi-variable functions, Aj(n), j=1 to D, where n stands for the evaluation point in the associated multi-dimensional space of coordinates (n1,n2,...). Let us assume that the Aj’s satisfy a system of D linearly coupled finite difference equations: the value of each function Ai at the evaluation point n is given as a linear combination of the values of this function and others at shifted evaluation points. By introducing D suitable generating functions, Gj, j=1 to D, one is able to replace the D coupled difference equations by a system of D linear equations where the Gj’s play the role of the D unknowns. After solving this new system of equations, it is then possible to construct a difference equation for each of the Aj’s relating the value of Ai at the evaluation point n to the values of Ai itself at shifted arguments. The solution of such a decoupled equation can then be handled using the multi-dimensional combinatorics function technique.
Propensities and the state-property structure of classical and quantum systems
Authors: Gisin N.
Published: March 2003

In quantum physics the tests of most properties do not have predetermined outcomes. The latter have nevertheless well-defined probabilities of being realized during a test. Following Popper we interpret these probabilities as physical propensities. A first purpose of the present article is to formalize the propensity interpretation in the framework of state-property structures. Next, Gleason’s theorem asserts that in the Hilbert space there exists a unique propensity function (i.e., one probability measure for each state vector); the propensities are thus uniquely determined by the state vector. Conversely, we prove that if the state-property structure admits one and only one propensity function, then the set ℒ of all properties is a complete atomic orthomodular lattice. We point out that according to our assumption the probabilistic aspect of the system is entirely determined by its deterministic aspect. Assuming furthermore that each property can be ideally tested, it follows that ℒ is isomorphic to the direct union of Hilbertian space lattices. We recover thus the purely classical and purely quantum frameworks as the two extreme cases. The intermediate cases correspond to quantum mechanics with—possibly continuous—superselection variables. Finally, we prove that a system is classical, i.e., all properties are mutually compatible, if and only if the propensity function is dispersion free. In our approach the quantum probabilities appear thus as a generalization of classical determinism rather than a generalization of classical probabilities.
Electromagnetic fields invariant up to a duality rotation under a group of isometries
Authors: Henneaux Marc
Published: March 2003

Electromagnetic fields invariant up to a duality rotation under a group H of space–time isometries are analyzed. The symmetry equations h*F=cos α(h)F+sin α(h)F* are integrated by noticing that α defines a homomorphism of H to SO(2). Applications of that concept to Einstein–Maxwell equations are studied. Cosmological models are considered. Special attention is paid to Bianchi universes which are shown to admit nontrivial, spatially homogeneous-up-to-a-duality-rotation, electromagnetic fields of all algebraic types. All L.R.S. type-V solutions to Einstein–Maxwell equations in which the electromagnetic field shares the symmetry of the gravitational field up to a duality transformation are derived. Discrete isometries are also analyzed.
Exactly solvable irreversible processes on one-dimensional lattices
Authors: Wolf N. O. , Evans J. W. , Hoffman D. K.
Published: March 2003

We consider the kinetics of a process where the sites of an infinite 1-D lattice are filled irreversibly and, in general, cooperatively by N-mers (taking N consecutive sites at a time). We extend the previously available exact solution for nearest neighbor cooperative effects to range N cooperative effects. Connection with the continuous ‘‘cooperative car parking problem’’ is indicated. Both uniform and periodic lattices, and empty and certain partially filled lattice initial conditions are considered. We also treat monomer ‘‘filling in stages’’ for certain highly autoinhibitory cooperative effects of arbitrary range.
Exactly solvable irreversible processes on Bethe lattices
Authors: Evans J. W.
Published: March 2003

We consider the kinetics of processes where the sites of a Bethe lattice are filled irreversibly and, in general, cooperatively by monomers, dimers, or polyatomics. For nearest neighbor and sometimes more general cooperative effects (including random filling as a special case), we show that the infinite hierarchy of rate equations for probabilities of empty subconfigurations can be exacty truncated and solved using a shielding property of empty sites. We indicate, in certain cases, a connection between these Bethe lattice solutions and certain approximate truncation solutions for corresponding processes on ‘‘physical’’ 2-D and 3-D lattices with the same coordination number.
Dirac equation for a linear potential
Authors: Glasser M. L. , Shawagfeh N.
Published: March 2003

The Dirac equation is solved for a linear potential. The complete asymptotic behavior of the solution in the nonrelativistic regime is developed by means of the comparison differential equation technique.
On superfield formulation of Euclidean supersymmetry
Authors: Lukierski J. , Nowicki A.
Published: March 2003

The superfield formulation of D=4 super-Euclidean QFT is given. The correspondence with Poincaré supersymmetry is explained. The description of supersymmetric Euclidean Yang–Mills theory is presented and the off-shell extension of the topogical charge by fermionic terms is obtained.
Some exact solutions of nonlinear chiral field equations
Authors: Chanda Pranab Krishna , Ray Dipankar , De Utpal Kumar
Published: March 2003

Some new exact solutions of the nonlinear field equations for the chiral invariant model of pion dynamics are presented here. These solutions are a further generalization of some previous works presented by one of the authors (Ray). It is interesting to note that equations in (3.2) obtained by Ray (1978) are conformally invariant. Hence from any solution of these equations one can immediately generate infinitely many other solutions of these equations simply by replacing (x 1, x 2) by ( y, z), where y and z are any two mutually conjugate solutions of Laplace’s equations. Further, a striking similarity in form of these equations with one of the two generalized Lund–Regge equations makes the study of the solutions of these equations more worthwhile with the view that the study of the solutions of these equations will eventually lead to the study of the solution of a larger class of equations that will include these equations and generalized Lund–Regge equations as special cases.
Maximum entropy in the problem of moments
Authors: Mead Lawrence R. , Papanicolaou N.
Published: March 2003

The maximum-entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem. In important special cases, such as the Hausdorff moment problem, we establish necessary and sufficient conditions for the existence of a maximum-entropy solution and examine the convergence of the resulting sequence of approximations. A number of explicit illustrations are presented. In addition to some elementary examples, we analyze the maximum-entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems. We also briefly indicate possible applications to the Lee–Yang theory of Ising models, to the summation of divergent series, and so on. The general conclusion is that maximum entropy provides a valuable approximation scheme, a serious competitor of traditional Padé-like procedures.
The connection between variational principles in Eulerian and Lagrangian descriptions
Authors: Bampi F. , Morro A.
Published: March 2003

The question of whether there exists a connection between variational principles in Eulerian and Lagrangian descriptions is investigated. By having recourse to a proper view of the Eulerian description it is shown that a variational principle in one description holds whenever a corresponding variational principle in the other description is given. This theoretical conclusion is operative in that a precise rule for writing the new Lagrangian is exhibited. As an application, a new Lagrangian for fluid dynamics in the Eulerian description is determined.
Blow-up regularization of singular Lagrangians
Authors: Cariñena José F. , Rañada Manuel F.
Published: March 2003

We propose a method for regularizing singular Lagrangians by adding new degrees of freedom. We illustrate this regularization method with some particular examples. This procedure is shown to be very useful when the Lagrangian is homogeneous of degree one in the velocities giving rise to an identically vanishing Hamiltonian.
The equivalence problem for nonconservative mechanics
Authors: Werth J.-E.
Published: March 2003

A geometric study of the equivalence problem for nonconservative mechanical systems is presented. Three equivalence relations for mechanical systems arise naturally in this framework: ℒ-, 𝒢-, and ℋ-equivalence. Necessary and sufficient conditions for the ℋ-equivalence of two systems are derived. The connection between 𝒢-transformations, 𝒢-equivalence, and canonical transformations is investigated. Furthermore, the relationship to (geometric) quantization is discussed.
The exponential mapping in Clifford algebras
Authors: Froelich John , Salingaros Nikos
Published: March 2003

The exponential mapping takes the Lie algebra of the Lorentz group into the Lorentz group. Each element of the group is defined as a formal power series, while the product of two exponential elements usually involves an infinite sum of commutator terms, such as in the Baker–Campbell–Hausdorff formula. Because of the special arithmetic in Clifford algebras, many Baker–Campbell–Hausdorff-like formulas and identities can be calculated or summed exactly when they involve only elements from the algebra. We calculate exact identities for the Baker–Campbell–Hausdorff formula and related formulas in the quaternion and dihedral algebras. These are useful in treatments of the Lorentz group, and make possible a truly finite (as opposed to infinitesimal) description of a transformation group in physics.
The Kostant partition function for simple Lie algebras
Authors: Schmidt Jeffrey R. , Bincer Adam M.
Published: March 2003

A simple algorithm is developed for evaluating the Kostant partition function for any simple Lie algebra. The algorithm may also be used to express the partition function for one Lie algebra in terms of the partition function for another, with the latter algebra not necessarily a subalgebra of the former. A special role in the algorithm is played by the sum of the simple roots. Explicit, closed-form expressions are given for the partition function for a variety of special cases.
Probability manifolds
Authors: Gudder Stanley P.
Published: March 2003

The concept of a probability manifold M is introduced. The global properties of M inherited from its local structure are then considered. It is shown that a deterministic spin model due to Pitowski falls within this general framework. Finally, we construct a phase-space model for nonrelativistic quantum mechanics. These two models give the same global description as conventional quantum mechanics. However, they also give a local description which is not possible in conventional quantum mechanics.
On the adiabatic stability of solitons and the matching of conservation laws
Authors: Lochak Pierre
Published: March 2003

We derive a series of identities which generalize and simplify the results obtained for adiabatically modulated solitons in the case of perturbed specific integrable equations. It stresses the importance of the variational properties of the solitons, which make an adiabatic theorem plausible. A precise conjecture is made and its validity discussed from different points of view.
Statistical interpretation of the Klein–Gordon equation in terms of the space-time Weyl curvature
Authors: Santamato E.
Published: March 2003

It is shown that a simple statistical interpretation of the Klein–Gordon equation can be obtained, provided a nontrivial vector transplantation law in space-time is assumed. The whole theory is constructed by using only classical probabilistic and dynamical concepts and applies equally well to both charged and neutral particles.
On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
Authors: Fokas A. S. , Ablowitz M. J.
Published: March 2003

The inverse problem associated with a rather general system of n first-order equations in the plane is linearized. When the system is hyperbolic, this is achieved by utilizing a Riemann–Hilbert problem; similarly, a ‘‘∂̄’’ (DBAR) problem is used when the system is elliptic. The above result can be employed to linearize the initial value problem associated with a variety of physically significant equations in 2+1, i.e., two spatial and one temporal dimensions. Concrete results are given for the n-wave interaction in 2+1 and for various forms of the Davey–Stewartson equations. Lump solutions (solitons in 2+1) of the latter equation are given a definitive spectral characterization and are obtained through a linear system of algebraic equations.
Resonance fluorescence spectra of a strong bichromatic field interacting with a three-level atom in the ‘‘V’’ configuration
Authors: Mavroyannis Constantine
Published: March 2003

We have considered the fluorescence spectra arising from the interaction of a three-level atom in the ‘‘V’’ configuration with two strong electromagnetic fields whose initially populated modes ωa and ωb are equal to the two atomic transition frequencies, respectively. The excitation spectra are calculated by making use of the Green function formalism where the hierarchy of the Green functions is truncated by a decoupling scheme which takes into account photon–photon correlations from each laser field in the limit of high photon densities. The excitation spectra consist of the central peak of the excitation frequency ωa and four pairs of sidebands, which are peaked at the frequencies ωa±η1(2)1/2, ωa±η2/(2)1/2, ωa±(η21+η22)1/2/(2)1/2, and ωa±2(η21+η22)1/2/(2)1/2, where η1 and η2 are the Rabi frequencies of the two laser fields, respectively. Similar spectra are exhibited near the excitation frequency ωb. Numerical calculations for selected values of the Rabi frequencies are graphically presented and compared with those known in the literature. In the Appendix expressions for the excitation spectra are derived first when the two laser fields are treated classically, and second, when the fields are quantized but photon–photon correlations are neglected. It is shown that when the two laser fields are treated classically, the derived results are identical to those obtained when the fields are quantized only when photon–photon correlations arising from each laser field are discarded. The derived results when the fields are quantized but without photon–photon correlations taken into account are also identical to those obtained by the use of the dressed-atom approach. The appearance of the new sidebands reveals the boson character of the photon fields in question. The merit of the method is that it yields results describing both the classical as well as the quantum nature of the photon fields involved.
Extension of Ruelle’s stability criteria to continuous systems
Authors: Abi-Ghanem Georges , Nguyen V. V.
Published: March 2003

For a compatible description of state transition in discrete and continuous representations of a one material system, an extension of Ruelle’s stability criteria is now given.
Perfect fluid models of Bianchi type-I in modified Brans–Dicke cosmology
Authors: Singh T. , Singh Tarkeshwar
Published: March 2003

The spatially homogeneous and anisotropic Bianchi type-I cosmological solutions of modified Brans–Dicke theory containing barotropic fluid have been obtained by imposing a condition on the cosmological parameter Λ(φ). The particular case when p=ρ has been discussed in detail.
Sensitivity analysis of stochastic kinetic models
Authors: Dacol D. K. , Rabitz H.
Published: March 2003

A formalism for sensitivity analysis of stochastic models describing fluctuation phenomena in chemically reacting systems is developed. The method is not restricted to chemical kinetics and can be used to analyze any model of a physical system whose state variables obey stochastic differential equations with white noise. Expressions for the sensitivity coefficients and densities are obtained. These expressions are suitable for direct evaluation by means of a stochastic simulation in a computer. The relationship between these quantities and the response functions studied in statistical mechanics is discussed.
The Gauss and the Weingarten equations for extended objects and their spinorization
Authors: Takahashi Y.
Published: March 2003

Gürsey’s program of geometrization and spinorization of motion of the classical point particle is generalized to the objects with spatial extension. For this purpose, the Gauss and the Weingarten equations in differential geometry were adopted. Since the spinorized version of the Gauss and the Weingarten equations is much less stringent than the original equations, it is expected that it serves to provide us with a way in which solutions are easily obtained.
Twisted boundary conditions for gauge theories on a torus
Authors: Actor Alfred
Published: March 2003

Gauge theories on the torus T2 and higher-dimensional tori are considered. The compactness of these manifolds induces boundary conditions on path integrals, one for each compactified dimension. Gauge fixing affects these boundary conditions, causing them to be nonperiodic in certain gauges, the nonperiodicity being expressed in terms of a gauge transformation or ‘‘twist.’’ The eigenvalues of the twist functions can be interpreted as spin variables in an effective spin theory, as is done in temperature field theory. The spin theory action, the effective potential, center symmetry, and the high-temperature limit are discussed. We clarify the connection between this spin theory and t’Hooft’s formalism for gauge theories on a torus.
Analyticity properties and a convergent expansion for the glueball mass and dispersion curve of strongly coupled Euclidean 2+1 lattice gauge theories
Authors: O’Carroll Michael , de Almeida Braga Gastão
Published: March 2003

For certain strongly coupled (2/g2≡β>0 and small) Euclidean Z3 lattice gauge theories we show that the glueball mass m(β) associated with the truncated plaquette–plaquette correlation function admits the representation m(β)=−4 ln β+r(β). r(β)=∑∞n=0bnβn is a gauge group representation dependent function, analytic at β=0. A finite algorithm is given for determining bn. bn depends on a finite number of the β=0 Taylor series coefficients of the finite lattice correlation function at a finite number of points, increasing with n, of Z3.
Tensor operator realizations of E6 and structural zeros of the 6j-symbol
Authors: Vanden Berghe G. , De Meyer H. , Van der Jeugt J.
Published: March 2003

For the exceptional Lie algebra E6 minimal SO(3) tensor operator realizations are constructed which correspond to the maximal decomposition of E6 in the respective chains E6⊃F4⊃SO(3), E6⊃SU(3)⊗G2⊃SO(3)⊗SO(3), E6⊃F4⊃SO(3)⊗G2⊃SO(3)⊗SO(3), E6⊃Sp(8)⊃SO(3), and E6⊃G2⊃SO(3). Two particular realizations are shown to provide a basis in which certain structural zeros of Racah’s 6j-symbol can be explained.
Group theoretic treatment of the Dirac–Coulomb equation and matrix elements of its tensor operators
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

The solution of the Dirac–Coulomb equation obtained by Wong and Yeh is interpreted in terms of the SU(2)×SO(2,1) group. All electromagnetic transition probabilities can be considered as matrix elements of the tensor operators of this group, and evaluated exactly. The cases considered include transitions from bound-to-bound, bound-to-continuum, and continuum-to-continuum states.
On the old–new method of solving nonlinear equations
Authors: Kalinowski M. W.
Published: March 2003

A method for solving a quasilinear nonelliptical equation of the second order is developed. We give classification and parametrization of simple elements of the equation. An equation of potential stationary flow of compressible gas in a supersonic region is considered as an example. A new exact solution is obtained which may be treated as a nonlinear analog of stationary wave.A gauge structure for the equation and an analog of Bäcklund transformation are introduced.
Transmission through cutoffs and resonances in the double phase-integral approximation
Authors: Skorupski Andrzej A.
Published: March 2003

Using the double phase-integral approximation technique developed earlier for the wave equation d2ψ/dz2+Q2(z) ψ=0, we derive analytical formulas for the reflection (R), transmission (T), and absorption (A) coefficients. They are valid to arbitrary order in the expansion parameter, for functions Q2(z) having either two cutoffs or one cutoff and one resonance. For two examples of this type the formulas for R, T, and A are checked against numerical results, using approximations up to fifth order.
Coherent state theory of the noncompact symplectic group
Authors: Rowe D. J.
Published: March 2003

An extended coherent state theory is presented for the noncompact Sp(3,R) group which reveals a simple relationship between the Sp(3,R) algebra and its contracted u(3)-boson limit. The relationship is used to derive a remarkably accurate analytic expression for Sp(3,R) matrix elements for the generic lowest-weight representations. The expression is shown to be exact whenever the states involved are multiplicity free with respect to the u(3) subalgebra. It is further shown how exact matrix elements are easily calculated in general. Dyson and Holstein–Primakoff type u(3)-boson expansions are given.
Remarks about inverse diffraction problem
Authors: Ramm A. G.
Published: March 2003

From the scattering data one finds the support function or the principal curvatures of the surface of a reflecting obstacle. From either of these data the surface is effectively reconstructed.
Massless fermions and Kaluza–Klein theory with torsion
Authors: Wu Yong-Shi , Zee A.
Published: March 2003

A pure Kaluza–Klein theory contains no massless fermion in four-dimensional theory. We investigate the effect of introducing torsion on the internal manifold and find that there are massless fermions. The hope is that given an isometry group the representation to which these fermions belong is fixed, in contrast to the situation in Yang–Mills theory. We show that this is indeed the case, but the representations do not appear to be the ones favored by current theoretical prejudice. The cases with parallelizable torsions on a group manifold as the internal manifold are analyzed in detail.
Relativistic effects in magnetohydrodynamic wave propagation
Authors: Murphy George L.
Published: March 2003

Relativistic modifications of Alfv́en waves are discussed for cases in which magnetic and relativistic terms are comparable. For atmospheric waves there are corrections to velocities, amplitudes, and polarizations. The mass current of the wave itself causes dispersion.
Enhancement of damping of a large amplitude wave
Authors: Sugihara Ryo , Yamanaka Kaoru
Published: March 2003

By evaluating the exact population difference between resonant electrons with velocities smaller and larger than the phase velocity, a correction to Landau damping proportional to the square of the wave amplitude is obtained theoretically.
Motion of a rising thermal
Authors: Shui Ven H. , Weyl Guy M.
Published: March 2003

The simple model used by Wang [C. P. Wang, Phys. Fluids 16, 744 (1973)] to describe the motion of a turbulent thermal in a uniform or a stably stratified atmosphere is modified and extended. A simple expression is derived which enables one to determine the entrainment coefficient from data on the rise and the size of a thermal. Analytical solutions are obtained for the maximum rise and the corresponding size of a thermal in a stable atmosphere. The model is applicable to thermals of all sizes, but comparisons with large thermals formed by strong explosions have been stressed. The results show good agreement between theory and observation and indicate that the entrainment coefficient for these thermals is of the same order of magnitude as those for other thermals (α ≃ 0.25) reported in the literature. The numerical result reported by Wang is shown to be a special case of the more general analytical solution derived in the present work.
Stimulated Compton backscatter from free electrons in laser−induced fusion plasmas
Authors: Albritton James R.
Published: March 2003

Stimulated Compton backscatter of incident Nd:glass laser photons (h/ω≃ 1 eV) from free electrons (n<1019/cm3 at κT ≃ 103 eV) in laser−induced fusion plasmas is investigated. The threshold for stimulated amplification of reflected radiation against spontaneous loss is 109 W/cm2 incident intensity while the low gain of the system determines the threshold effectively at 1015 W/cm2. For 5×1018 free electrons/cm2 in the plasma, steady state reflectivities of 10−4 are calculated for 1016 W/cm2 incident intensity. This results from the gain being driven to small values when stimulated photon scatter dominates particle collisions and thereby tends to level the resonant scattering interval of the electron momentum distribution. At lower incident intensities or on the time scales of the transients, interesting experiments might be designed to examine this phenomenon.
Resonances in light scattered from a plasma in a magnetic field
Authors: Peratt A. L.
Published: March 2003

Expressions are developed for the electron density fluctuation spectrum for monochromatic radiation incident upon a magnetized plasma in thermal equilibrium. The method is based upon the full−wave derivation of a formal relation between the autocorrelations of particle density and dielectric tensor. Collisions are introduced into the formulation via a BGK and a Fokker−Planck collision term in the Boltzmann equation. An enhancement of the scattered spectra due to the excitation of longitudinal slow−wave resonances is predicted when the differential scattering vector is aligned primarily perpendicular to the magnetic field, provided that the collision−to−cyclotron frequency ratio satisfies the relation ν/Ω ≪ 1 in the BGK model or ν/Ω ≪ Ω2m/k2KT in the Fokker−Planck model.
Condition for slow wave propagation in plasmas
Authors: Gagliardi L. John
Published: March 2003

A new general condition for the propagation of slow waves in plasma waveguide systems is derived from the full boundary value problem. Unlike previous calculations, a nonzero collision frequency is retained throughout. The plasmas are assumed to constitute the center conductor of a coaxial waveguide system.
Damping and saturation of electron plasma wave echoes
Authors: Moeller Charles
Published: March 2003

A description is given of theoretical and experimental work on the damping of a second−order electron plasma wave echo due to velocity space diffusion in a low temperature magnetoplasma. Sufficient precision was obtained to verify the theoretically predicted cubic rather than quadratic or quartic dependence of the damping on exciter separation. Compared with the damping predicted for Coulomb collisions in a thermal plasma in an infinite magnetic field, the magnitude of the damping was approximately as predicted, while the velocity dependence of the damping was weaker than predicted. The discrepancy is consistent with the actual non−Maxwellian electron distribution of the plasma. In conjunction with the damping work, echo amplitude saturation was measured as a function of the velocity of the electrons contributing to the echo. Good agreement was obtained with the predicted J1 Bessel function amplitude dependence, as well as a demonstration that saturation did not influence the damping results.
Three wave backscatter interactions in a finite region
Authors: Harvey R. W. , Schmidt George
Published: March 2003

The space-time, three wave, coupled mode equations are numerically integrated for a backscatter process in a finite region, with zero-reflection boundary conditions. It is found that only spatially aperiodic steady states are stable. Effects of damping on the scattered waves are investigated.
Model for the production and transport of energetic particles in a laser produced plasma
Authors: Manheimer Wallace M. , Klein H. H.
Published: March 2003

A model is presented for the production and transport of energetic electrons in a laser produced plasma. The basic assumption is that the laser deposits its energy in the form of a large amplitude plasma wave. The energy is given to particles as the electrostatic wave propagates outward and damps. Theory and simulations show that the maximum energetic particle velocity is between about five and seven thermal velocities, and that the heat flux is limited to about (1/4) nmV3e.
Numerical simulation of isotropic turbulence
Authors: Betchov R.
Published: March 2003

The equations of Euler are integrated numerically for isotropic homogeneous box turbulence. The triple correlations build up, and the correlations of order five and seven show some evidence of strong phase relations near the end of the spectral range. The stretching of vorticity occurs mostly in directions perpendicular to local collision axis, and at points showing strong velocity gradients. These properties agree with experimental or analytical results. Some stability tests are described.
Knudsen layer for tracer gas diffusion
Authors: Ytrehus T. , Smolderen J. J. , Wendt J. F.
Published: March 2003

The diffusion of a tracer gas from a plane, porous boundary into a steady, rarefied background is investigated using the BGK model to account for collisions between the tracer and the background molecules. In a limited region close to the central part of the wall the diffusion process is nearly one-dimensional, and the resulting kinetic diffusion equation is shown to be identical to the shear flow equation in the Kramers problem of flow along an infinite wall. This observation suggests that density measurements, rather than measurements of velocity, can be used to assess the validity of the linearized BGK model in describing flows in kinetic boundary layers. Estimates of the required sensitivity of the experimental technique are given.
Spectrum of ideal magnetohydrodynamics of axisymmetric toroidal systems
Authors: Goedbloed J. P.
Published: March 2003

The spectrum of ideal magnetohydrodynamics in toroidal systems is shown to concentrate around three continua where the singular fast, the Alfvén, and the slow modes become polarized purely normal and purely tangential to the magnetic surfaces. A new toroidal effect is encountered, viz., coupling of the Alfvén and slow continuum modes by the presence of geodesic curvature. Due to this effect the slow and Alfvén modes are no longer polarized purely parallel and purely perpendicular to the field lines as they are in the case of the diffuse linear pinch. The pure polarizations of these continuum modes are only found asymptotically when ω2→∞, which point turns out to be a clusterpoint of all three kinds of magnetohydrodynamic modes characterizing each of them uniquely.
Numerical simulation of neoclassical diffusion
Authors: Tsang K. T. , Matsuda Y. , Okuda H.
Published: March 2003

Cross-field diffusion of a plasma in a model toroidal magnetic field has been studied numerically. The result in a system with toroidal symmetry shows three distinct regimes of diffusion with respect to the collision frequency as predicted by theory. When a weak nonsymmetry is introduced in the model adding a small ripple on the toroidal field, the enhanced diffusion due to superbanana flux is observed in the region of low collision frequencies in agreement with theoretical prediction.
Computational study of nonlinear plasma waves: I. Simulation model and monochromatic wave propagation
Authors: Matsuda Y. , Crawford F. W.
Published: March 2003

An economical low-noise plasma simulation model originated by Denavit is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation. These tests serve to establish the low-noise features of the model, and to verify the theoretical linear dispersion relation at wave energy levels as low as 10−6 of the plasma thermal energy: Better quantitative results are obtained, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories.
Computational study of nonlinear plasma waves: II. Sideband instability and satellite growth
Authors: Matsuda Y. , Crawford F. W.
Published: March 2003

The low-noise plasma simulation model is applied to study two phenomena associated with large amplitude wave propagation and the resulting particle trapping: sideband instability and satellite wave growth. Simulations are carried out to observe amplification of test waves and growth from noise. They are performed in parameter ranges for which detailed quantitative comparison with available theories is possible, and which are readily accessible experimentally. The study of sideband instability confirms the applicability of quasi−linear theory at short times, and parametric coupling theory in the time-asymptotic limit, and reproduces features analogous to those observed in laboratory experiments. The growth of a satellite wave in the presence of a large amplitude wave and a test wave is shown to be explicable by a simple theory involving slow modulation of the large amplitude wave.
Experimental observation of the ion-ion beam instability in a cylindrical geometry
Authors: Romesser Thomas , Hershkowitz Noah
Published: March 2003

The ion-ion beam instability is investigated in a cylindrical geometry. In the presence of a cylindrically symmetric ion beam a coherent ion-ion beam instability is observed for a well-defined range of beam velocity. This instability gives rise to cylindrical standing waves whose frequency depends upon beam velocity. The beam distribution function is measured to be a ring in velocity space. The dispersion relation appropriate for the cylindrical standing waves is solved numerically and is shown to be in good agreement with the experimentally observed instability.
Radial plasma structure during a theta-pinch implosion: Flute instabilities
Authors: McKenna K. F. , Kristal R. , Zimmermann E.L.
Published: March 2003

Flute instabilities have been observed during the implosion of an ≈1×1014 cm−3 initial electron density theta pinch. The flutes occupy only a fraction of the plasma self-luminosity pattern and disappear after formation of the plasma column. The total structure of the luminosity patterns has been correlated with the imploding plasma density and magnetic field distribution.
Diffusion of a passive scalar at large Prandtl number according to the abridged Lagrangian interaction theory
Authors: Mjolsness R. C.
Published: March 2003

An explicit solution is obtained for the viscous-convective range of the abridged Lagrangian interaction theory valid when Pr≫1. The spectrum function differs markedly from that of a previous explicit theory of Batchelor. This difference may be of use in interpreting experimental data.
Negative ion plasmas
Authors: Wong A. Y. , Mamas D. L. , Arnush D.
Published: March 2003

In a plasma composed of negative (SF−6) ions, positive (Ar+) ions, and electrons (with ne/n+ reducible to less than 10−3) a fast ion mode (vph≈9Cs), due to the out-of-phase motion between positive and negative ions, is observed with reduced spatial attenuation. This fast ion mode exhibits spatial growth in the presence of a fast ion beam. Diffusion properties of the negative ion plasma are also presented.
Probability distributions in a round heated jet
Authors: Venkataramani K. S. , Tutu N. K. , Chevray R.
Published: March 2003

Measurements of the marginal and joint probability density functions of the longitudinal and radial components of the velocity, and temperature at three different radial positions of an axisymmetric heated turbulent air jet are presented. The results are compared with normal distributions.
Derivation of the free-jet Mach-disk location using the entropy-balance principle
Authors: Young Wen S.
Published: March 2003

The molar-entropy change of a gas expansion in a free jet is analyzed. Relating the entropy change along the expansion process to the entropy change evaluated using the thermodynamic properties of the initial and final states, one finds that the Mach-disk location is proportional to the square root of the pressure ratio p0/p∞ in agreement with the empirical expression given by Ashkenas and Sherman. The analysis shows further that the Mach-disk location is independent of the temperature ratio T0/T∞, and is only a weak function of the specific heat ratio γ.
Relaxation of an isotropic plasma with two different energy populations
Authors: Peyraud Nelly
Published: March 2003

The relaxation of isotropic plasma toward thermodynamic equilibrium is studied. Such plasmas are linearly stable and the relaxation is mainly governed by electron-electron interactions. It is shown that if there is a bump-on-tail of the distribution function, due, for example, to efficient superelastic collisions in a plasma with metastable atoms, the relaxation frequency becomes larger than the classical electron-electron relaxation frequency.