bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalized Abelian sandpile model
Authors: Chau H. F. , Cheng K. S.
Published: July 2002

A sufficient condition is presented herein for which the particle addition operations commute in the eventual phase space of a general cellular automata-type of sandpile model. The commutative nature of the particle addition operations results from the reduction of the eventual phase space. It suggests that a large number of self-organized critical models can be reduced to the Abelian sandpile if only the long term behavior of these systems is considered.
Asymptotic scattering operators and drift velocity in charged particle transport problems
Authors: Busoni Giorgio , Frosali Giovanni
Published: July 2002

In this article the long-time behavior of the evolution of one species of charged particles in a neutral gas under the influence of an acceleration field is studied. After a short review of the literature on runaway phenomenon, the mathematical definitions of drift velocity and runaway phenomenon based on the distribution function are given. The linear Boltzmann equation in a three-dimensional spatially homogeneous system is considered. Under suitable conditions on the acceleration field and on the collision frequency, the existence of asymptotic operators is proven in a three-dimensional setting. Then wave operators are introduced and are used to characterize the long-time behavior of the solutions. Finally, using such operators the long-time behavior of the drift velocity is estimated.
An exact solution for a dielectric atmosphere in general relativity
Authors: Junevicus G. J. G.
Published: July 2002

The Einstein–Maxwell equations are solved for a dielectric perfect fluid atmosphere surrounding a static charged spherically symmetric body. Energy conditions are applied to ensure that the solution is physically reasonable.
Recursion relation in SU(N) integral in quantum chromodynamics
Authors: Tanimura N. , Tanimura O.
Published: July 2002

On the basis of the Schwinger–Dyson variational method the recursion relations of the character expansion coefficients of the SU(N) gauge action are derived. Three recursion relations that are associated with the Casimir invariants of the second, third, and fourth orders are shown to be enough to determine the character expansion coefficient of every representation recursively in SU(N).
Topological symmetry breaking in self-interacting theories on toroidal space–time
Authors: Elizalde Emilio , Kirsten Klaus
Published: July 2002

The possibility of topological mass generation through symmetry breaking in a simple model consisting of a self-interacting (massive or massless) λφ4 scalar field on the space–time TN×Rn, n, N∈N0−TN being a general torus—is investigated. The nonrenormalized effective potential is calculated and the specific dependences of the generated mass on the compactification lengths and on the initial mass of the field are determined. Later, in order to obtain the renormalized topologically generated mass, the analysis is restricted to n+N=4 dimensions. It is shown that if the field is massive no symmetry breaking can occur. On the contrary, when it is massless, for n=1 and n=0 and for values of the vector of compactification lengths belonging to some specific domain of RN, symmetry breaking does actually take place. Explicit values of the mass topologically generated in this way are obtained.
The absence of the absolutely continuous spectrum for δ ′ Wannier–Stark ladders
Authors: Exner P.
Published: July 2002

A modification of the Kronig–Penney model consisting of equidistantly spaced δ ′ interactions is considered. We prove that an absolutely continuous spectrum of such a system disappears under the influence of an external electric field. The result extends to periodic lattices of nonidentical δ ′ interactions and potentials which are lower unbounded and, up to a bounded term, asymptotically decreasing with bounded first two derivatives.
Nontrivial path integrals for nonrenormalizable fields—Multicomponent ultralocal models
Authors: Zhu Chengjun , Klauder John R.
Published: July 2002

A nontrivial lattice-space path integral formulation of nonrenormalizable multicomponent ultralocal models is constructed from the nonperturbative operator solutions presented in a recent paper. The indefinite, nonclassical, singular potential required for the nontriviality has different effects on distributions compared to the single-component case, however, the essential property of reweighting the distribution at the origin is similar. The appearance of additional nonclassical, singular potentials suggests that we cannot always place the classical Lagrangian or classical Hamiltonian directly into the path-integral formulation, or in other words, a straightforward canonical quantization of fields with infinite degrees of freedom does not always apply.
An optimization approach to a three-dimensional acoustic inverse problem in the time domain
Authors: He Sailing , Kabanikhin Sergei I.
Published: July 2002

An optimization approach to a three-dimensional acoustic inverse problem is considered in the time-domain. The velocity and the density are reconstructed by minimizing an objective functional. By introducing a dual function, the gradient of the objective functional is found with an explicit expression. The parameters are then reconstructed by an iterative algorithm (the conjugate gradient method). The uniqueness of the solution is also proved.
Path integration, anticommuting variables, and supersymmetry
Authors: Rogers Alice
Published: July 2002

A geometric theory of path integration on supermanifolds is developed, and used to establish a path-integral formula for the super heat kernel exp(−D/2t−D/τ) of the Dirac operator D/ on a Riemannian manifold. The earlier part of the paper describes an extension of Wiener measure, Brownian motion, and stochastic calculus to include paths in spaces parametrized by anticommuting variables; these constructions are then combined with the geometrical data of a Riemannian manifold to construct stochastic differential equations whose solutions provide appropriate superpaths for the study of the Dirac operator.
Phase-space formalism: Generalized Hermite polynomials, orthogonal functions and creation–annihilation operators
Authors: Dattoli G. , Torre A.
Published: July 2002

Hermite polynomials with many variables and many indices play a crucial role within the framework of phase-space formulation of classical or quantum mechanics. A generalized operational formalism useful to handle these polynomials is discussed and also a new set of creation–annihilation operators associated to the phase-space harmonic oscillator orthogonal functions is introduced. The Fourier transform of these orthogonal functions is studied by discussing the analogies with the ordinary case. Finally, the integral representation of the generalized Hermite polynomials and a simple technique to deal with the generalized heat equation are discussed.
Partial order of quantum effects
Authors: Lahti Pekka J. , Ma̧czynski Maciej J.
Published: July 2002

The set of effects is not a lattice with respect to its natural order. Projection operators do have the greatest lower bounds (and the least upper bounds) in that set, but there are also other (incomparable) effects which share this property. However, the coexistence, the commutativity, and the regularity of a pair of effects are not sufficient for the existence of their infima and suprema. The structure of the range of an observable (as a normalized POV measure) can vary from that of a commutative Boolean to a noncommutative non-Boolean subset of effects.
Perturbation method for the energy-momentum tensor of an optical soliton
Authors: Arthur K. , Burzlaff J.
Published: July 2002

Electromagnetic fields of solitons, which are expansions in a small parameter measuring the bandwidth of the radiation over the carrier frequency are studied herein. Conservation laws for energy and momentum are derived from Maxwell’s equations using perturbation expansions in this small parameter. In this derivation, densities are averaged over half a period of the carrier wave, and certain symmetries of the susceptibility are exploited. The general procedure is outlined and the leading terms are explicitly calculated.
The high-temperature expansion of the hierarchical Ising model: From Poincaré symmetry to an algebraic algorithm
Authors: Meurice Y.
Published: July 2002

It is shown that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincaré groups. Using these symmetries, it is shown that the intricate sums appearing in the calculation of the high-temperature expansion of the magnetic susceptibility can be performed, at least up to the fourth order, using elementary algebraic manipulations which can be implemented with a computer. These symmetries appear more clearly if we use the two-adic fractions to label the sites. Then the new algebraic methods are applied to the calculation of quantities having a random walk interpretation. In particular, it is shown that the probability of returning to the starting point after m steps has poles at D=−2,−4,...,−2m, where D is a free parameter playing a role similar to the dimensionality in nearest neighbor models.
Dirac and reduced quantization: A Lagrangian approach and application to coset spaces
Authors: Ordóñez C. R. , Pons J. M.
Published: July 2002

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The ‘‘first reduce and then quantize’’ and the ‘‘first quantize and then reduce’’ (Dirac’s) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the ‘‘first reduce’’ method is emphasized. One of the main results is the relation between the propagator obtained à la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out.
Difference Calogero–Moser systems and finite Toda chains
Authors: van Diejen J. F.
Published: July 2002

Limits of a recently introduced n-particle difference Calogero–Moser system with elliptic potentials are studied. We obtain hyperbolic and rational difference Calogero–Moser systems with an eight-parameter external field and (finite) difference Toda chains with four-parameter potentials acting on the boundary particles. Hamiltonians for a number of known integrable n-particle systems, such as Ruijsenaars’ relativistic Calogero–Moser and Toda models and their generalizations associated with classical root systems, can be seen as special cases of the Hamiltonians considered in this paper.
Overcomplete basis for one-dimensional Hamiltonians
Authors: Bergeron H. , Valance A.
Published: July 2002

It is demonstrated for one-dimensional Hamiltonians, and under a special hypothesis on the ground state wave function, that it is possible to build an analytical overcomplete basis that generalizes the coherent state basis of the harmonic oscillator, without any reference to group theory. The semi-classical consequences of this formalism are developed and the usual ideas of normal and antinormal expansions for operators are extended.
On curved vortex solutions in the Abelian Higgs model
Authors: Dobrowolski T.
Published: July 2002

It is proven that curved Abrikosov–Nielsen–Olesen vortex solutions of the Abelian Higgs model exist around world sheets given by solutions of Nambu–Goto equations with additional constraints. The explicit form of these constraints is also found.
Outline of a generally covariant quantum field theory and a quantum theory of gravity
Authors: Rovelli Carlo
Published: July 2002

We study a tentative generally covariant quantum field theory, denoted the T theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field; it is based on the loop representation, and on a certain number of quantization choices. Four-dimensional diffeomorphism-invariant quantum transition probabilities can be computed from the theory. We discuss the choices on which the T theory relies, and the possibilities of modifying them.
Classification of the local extensions of the SU(3) chiral current algebra
Authors: Stanev Yassen S.
Published: July 2002

All local extensions of the chiral algebra of observables are classified for SU3 level k conformal current algebra models. This method is based on analyzing the polynomial solutions of the corresponding Knizhnik–Zamolodchikov equations.
Applications of quantum and classical Fisher information to two-level complex and quaternionic and three-level complex systems
Authors: Slater Paul B.
Published: July 2002

In the Bayesian theory of statistical inference, as first suggested by Harold Jeffreys in highly influential work, one can employ the square root of the determinant of an n×n Fisher information matrix as a reparametrization-invariant prior (generally unnormalized) measure over an n-dimensional family (Riemannian manifold) of probability distributions. Jeffreys’ ansatz is adopted here to the quantum context, that is, with regard to density matrices rather than probability distributions, by computing the quantum Fisher information matrices (associated with Helstrom and Holevo) for the three-, five-, and eight-dimensional convex sets of two-level complex, two-level quaternionic, and three-level complex systems, respectively. In both the two-level cases, the priors have been normalized to probability distributions over the 2×2 density matrices, while, in the much more computationally demanding three-level situation, no such normalization has been accomplished. An argument is made for the general form, in terms of eigenvalues, that the (unnormalized) prior should assume over the (n2−1)-dimensional convex set of n×n density matrices.
The successive reflection method in three dimensional particle transport
Authors: Belleni-Morante Aldo , Totaro Silvia
Published: July 2002

The free streaming operator T is considered in a convex three dimensional region V, with diffusive multiplying boundary conditions. Some mathematical properties of T are examined by writing the particle density as an infinite series which takes into account successive reflections on ∂V, and by introducing an operator which in some sense annihilates the multiplying effect of ∂V.
Two relativistic boson models in the Schrödinger picture in three space–time dimensions
Authors: Frochaux E.
Published: July 2002

A family of unitary representations of the Poincaré group is constructed, which describes two relativistic quantum bosons with weak interaction in three space–time dimensions. The mathematical formalism is the Schrödinger picture of quantum mechanics in the momentum space. The eigenvalue equation for the bound states is given and compared with the Schrödinger equation.
Symplectic completion of symplectic jets
Authors: Rangarajan Govindan
Published: July 2002

In this paper, we outline a method for symplectic integration of three degree-of-freedom Hamiltonian systems. We start by representing the Hamiltonian system as a symplectic map. This map (in general) has an infinite Taylor series. In practice, we can compute only a finite number of terms in this series. This gives rise to a truncated map approximation of the original map. This truncated map is however not symplectic and can lead to wrong stability results when iterated. In this paper, following a generalization of the approach pioneered by Irwin (SSC Report No. 228, 1989), we factorize the map as a product of special maps called ‘‘jolt maps’’ in such a manner that symplecticity is maintained.
Instantons and splitting
Authors: Sordoni V.
Published: July 2002

In this paper we compare various formulas for the leading term of the amplitude of the splitting of the eigenvalues of semiclassical Schrödinger operators with multiple wells.
Topological equivalence of tilings
Authors: Kellendonk Johannes
Published: July 2002

We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are topologically equivalent whenever their associated groupoids are isomorphic.
On the causal structure of Minkowski spacetime
Authors: Thomas Launey J. , Wichmann Eyvind H.
Published: July 2002

The causal structure of Minkowski spacetime M is discussed, in terms of the notions of causal complementation and causal completion. These geometric notions are relevant for quantum field theory and the theory of the Klein-Gordon equation. Particular attention is given to closed, convex, causally complete subsets of M, and the properties of such sets are discussed. The study of such sets is motivated by potential applications to the theory of local nets of von Neumann algebras. The notion of the envelope of uniqueness of a subset of M, familiar from the theory of the wave equation, is discussed, and some results about the relation of this envelope to the causal completion of the set are presented.
The q-isotropic oscillator
Authors: Chan Gordon , Finkelstein Robert , Oganesyan Vadim
Published: July 2002

We have obtained in configuration space the state functions of the q-isotropic oscillator by laddering the state functions of the q-linear oscillator. Starting from the q-Hermite functions of the linear oscillator one obtains the q-associated Laguerre functions of the isotropic oscillator. The energy spectrum is obtained from the curvature of the wave function at a point where the potential energy vanishes.
Form invariance of differential equations in general relativity
Authors: Chimento Luis P.
Published: July 2002

Einstein equations for several matter sources in Robertson–Walker and Bianchi I type metrics, are shown to reduce to a kind of second-order nonlinear ordinary differential equation ÿ+αf(y)ẏ+βf(y)∫f(y)dy+γf(y)=0. Also, it appears in the generalized statistical mechanics for the most interesting value q=−1. The invariant form of this equation is imposed and the corresponding nonlocal transformation is obtained. The linearization of that equation for any α, β, and γ is presented and for the important case f=byn+k with β=α2(n+1)/(n+2)2 its explicit general solution is found. Moreover, the form invariance is applied to yield exact solutions of some other differential equations.
Affine realizations of sphere algebras
Authors: Bruce S. , Salgado P.
Published: July 2002

The group Map(M,G) of smooth mappings from a compact manifold M to a simple Lie group G is an infinite-dimensional Lie group. The simplest case is when M=S1. The central extension of the corresponding Lie algebra Map(S1,g) (with g the Lie algebra of G) is an affine Kac–Moody algebra. The representations of Map(S1,g) and of its central extension have been thoroughly investigated. Less work has been done for higher-dimensional M. We discuss the particular cases when M is the two- and three-spheres Sn, n=2,3. In this work we construct particular realizations of the centrally extended Map(Sn,g) from a given realization of an affine Kac–Moody algebra.
The potential constraints of the complex (1+2)-dimensional soliton systems and related Hamiltonian equations
Authors: Chen Deng-yuan
Published: July 2002

Potential complete constraints (symmetric and nonsymmetric) of the complex KP and MKP systems are derived by using the general theory for a nonlinear equation to be a Hamiltonian system. All the complex Hamiltonian equations corresponding to this kind of constraint are obtained, which contain the famous nonlinear Schrödinger equations and several new Hamiltonian equations. In addition, the classical Kaup–Newell system and the Heisenberg system are also led by a new reduction approach from the MKP system.
Continuous time and consistent histories
Authors: Isham C. J. , Linden N. , Savvidou K. , Schreckenberg S.
Published: July 2002

We discuss the use of histories labelled by a continuous time in the approach to consistent-histories quantum theory in which propositions about the history of the system are represented by projection operators on a Hilbert space. This extends earlier work by two of us [C. J. Isham and N. Linden, J. Math. Phys. 36, 5392–5408 (1995)] where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about the time average of the energy. We also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.
The role of a form of vector potential — normalization of the antisymmetric gauge
Authors: Florek Wojciech , Wałcerz Stanisław
Published: July 2002

Results obtained for the antisymmetric gauge A=[Hy,−Hx]/2 by Brown and Zak are compared with those based on pure group-theoretical considerations and corresponding to the Landau gauge A=[0, Hx]. Imposing the periodic boundary conditions one has to be very careful since the first gauge leads to a factor system which is not normalized. A period N introduced in Brown’s and Zak’s papers should be considered as a magnetic one, whereas the crystal period is in fact 2N. The “normalization” procedure proposed here shows the equivalence of Brown’s, Zak’s, and other approaches. It also indicates the importance of the concept of magnetic cells. Moreover, it is shown that factor systems (of projective representations and central extensions) are gauge-dependent, whereas a commutator of two magnetic translations is gauge-independent. This result indicates that a form of the vector potential (a gauge) is also important in physical investigations.
Vacuum polarization and the geometric phase: Gauge invariance
Authors: Mickelsson Jouko
Published: July 2002

A nonperturbative approach to the vacuum polarization for quantized fermions in external vector potentials is discussed. It is shown that by a suitable choice of counterterms the vacuum polarization phase is both gauge and renormalization independent, within a large class of nonperturbative renormalizations.
Stationary generalized Kerr–Schild spacetimes
Authors: Sopuerta Carlos F.
Published: July 2002

In this paper we have applied the generalized Kerr–Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike vector fields, from which some properties of the solutions are studied in a coordinate-free way. These spacetimes are algebraically special being their Petrov types II and D. This family includes all the classical vacuum Kerr–Schild spacetimes, excepting the plane-fronted gravitational waves, and some other interesting solutions as, for instance, the Kerr metric in the background of the Einstein Universe. However, the family is much more general and depends on an arbitrary function of one variable.
Three-dimensional metrics with a spherical homogeneous model
Authors: Patrangenaru Victor
Published: July 2002

One finds the moduli spaces of isocurved homogeneous metrics on S3. Then, one determines the germs of three-dimensional analytic metrics with a spherical homogeneous model.
Radon–Nikodym derivatives of quantum instruments
Authors: Holevo A. S.
Published: July 2002

A convenient representation for Radon–Nikodym derivatives of completely positive (c.p.) instruments on B(H) with respect to a scalar measure is suggested, similar to the Stinespring–Kraus representation for c.p. maps, but involving possibly nonclosable unbounded operators. The structure of covariant c.p. instruments is studied in detail. In particular, an exhaustive description is given to instruments covariant with respect to shifts or rotations, corresponding to “position” or “angle” measurements.
On the electrodynamic group: The relativistic radiation reaction force
Authors: Prieto Angel
Published: July 2002

The relativistic force exerted by a classical electromagnetic field on an electron is examined from the point of view that associates the differential geometry of the space–time trajectory with a continuous group of transformations. The group relevant to this particular case is the group generated by the electromagnetic field tensor (electrodynamic group). This group is studied in some detail by treating separately the two parts of the Liénard–Wiechert expression for the tensor. The intrinsic differential equations of the space–time trajectories associated with the electrodynamic group are obtained by the Cartan method of the moving frame. These equations show that the curvature of the trajectory is associated only with the generalized Coulomb field and the hypertorsion with the radiation field. According to these equations, the relativistic force may have two components along orthogonal spacelike directions: The first, an apparent force, reduces to the Coulomb force in the nonrelativistic limit. The other is orthogonal to the four-momentum and to the apparent force; this is the radiation reaction force. In the nonrelativistic limit it manifests itself as a frictional force reducing the momentum. The approach also offers a point of view of the conventional treatment of radiation reaction in which the nonlocality in time emerges from the geometry of the problem. The implications pertaining to other areas of physics of the causal connection found between the hypertorsion and the radiation field are briefly considered.
Demazure modules and vertex models: The sl̂(2) case
Authors: Foda Omar , Misra Kailash C. , Okado Masato
Published: July 2002

We characterize, in the case of sl∧(2),the crystal base of the Demazure module Ew(Λ) in terms of extended Young diagrams or paths for any dominant integral weight Λ and Weyl group element w. Its character is evaluated via two expressions, “bosonic” and “fermionic.”
Symmetry classification and exact solutions of the Kramers equation
Authors: Spichak Stanislav , Stognii Valerii
Published: July 2002

The complete classification of Lie symmetries for the Kramers equation is described. Group invariance under infinitesimal transformations is used to generate a wide class of exact solutions. Some of the known solutions are obtained as particular cases. The general results can also be used to solve some types of moving-boundary problems. We researched some Q-conditional symmetry properties of this equation.
On the number of bound states for the one-dimensional Schrödinger equation
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

The number of bound states of the one-dimensional Schrödinger equation is analyzed in terms of the number of bound states corresponding to “fragments” of the potential. When the potential is integrable and has a finite first moment, the sharp inequalities 1−p+∑j=1p Nj⩽N⩽∑j=1p Nj are proved, where p is the number of fragments, N is the total number of bound states, and Nj is the number of bound states for the jth fragment. When p=2 the question of whether N=N1+N2 or N=N1+N2−1 is investigated in detail. An illustrative example is also provided.
A constructive index theorem, phase operators, and phase-difference operators
Authors: Yu Sixia , Zhang Yongde
Published: July 2002

A constructive reversed index theorem concerning the polar decomposition of an operator into a product of a unitary exponential phase operator and a Hermitian amplitude operator is investigated. Its applications to the construction of Hermitian phase operators of fermions and phase-difference operators between bosons or fermions are presented. Specifically, a Hermitian operator is constructed for the phase difference between a single-mode fermion and boson, which is justified by the fact that it is exactly the interaction part of the Hamiltonian of the Jaynes-Cummings Model. Furthermore, a Hermitian phase operator of a single-mode boson can also be defined referring to a single-mode fermion. All those quantized phases and phase-differences are found to obey a quantum addition rule instead of the ordinary commutative addition rule.
Implementation of an iterative map in the construction of (quasi)periodic instantons: Chaotic aspects and discontinuous rotation numbers
Authors: Chakrabarti A.
Published: July 2002

An iterative map of the unit disk in the complex plane is used to explore certain aspects of self-dual, four-dimensional gauge fields (quasi)periodic in the Euclidean time. These fields are characterized by two topological numbers and contain standard instantons and monopoles as different limits. The iterations do not correspond directly to a discretized time evolution of the gauge fields. They are implemented in an indirect fashion. First, (t,r,θ,φ) being the standard coordinates, the (r,t) half-plane is mapped on the unit disk in an appropriate way. This provides an (r,t) parametrization of Z0, the starting point of the iterations and makes the iterates increasingly complex functions of r and t. These are then incorporated as building blocks in the generating function of the fields. We explain in what sense and to what extent some remarkable features of our map (indicated in the title) are thus carried over into the continuous time development of the fields. Special features for quasiperiodicity are studied. Spinor solutions and propagators are discussed from the point of view of the mapping. Several possible generalizations are indicated. Some broader topics are also discussed.
Characteristic surface data for the eikonal equation
Authors: Newman Ezra T. , Perez Alejandro
Published: July 2002

A method of solving the eikonal equation, in either flat or curved space–times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front singularities that are associated with their level surfaces (the characteristic surfaces or “big wave fronts”).
Dissipative canonical flows in classical and quantum mechanics
Authors: Gough John
Published: July 2002

A theory of stochastic flows over the algebra of observables of a dynamical system is presented in which the main objective is to ensure that the overall canonical/symplectic structure on the algebra is preserved. We study both classical and quantum systems and the importance of physical interpretation in the Stratonovich interpretation is stressed. We find the natural formulation of quantum dissipative systems to be given in terms of quantum stochastic calculus. This treatment allows for a physically meaningful treatment of both constant and nonlinear dissipation. As an application, we quantize a mechanical system with the same nonlinear damping mechanism as the van der Pol oscillator.
On the explicit solutions of the elliptic Calogero system
Authors: Gavrilov L. , Perelomov A. M.
Published: July 2002

Let q1,q2,…,qN be the coordinates of N particles on the circle, interacting with the integrable potential ∑j<kN℘(qj−qk), where ℘ is the Weierstrass elliptic function. We show that every symmetric elliptic function in q1,q2,…,qN is a meromorphic function in time. We give explicit formulas for these functions in terms of genus N−1 theta functions.
Power-law low-temperature asymptotics for spatially nonhomogeneous s-wave superconductors
Authors: Gabovich A. M. , Voitenko A. I.
Published: July 2002

It is shown that low temperature asymptotics of various thermodynamic and transport properties of s-wave superconductors can become power-law ones if wide distributions of gap values exist, originating from structure domains, charge stripes, charge-density waves or other mesoscopic nonhomogeneities. The relevant experimental data for high-Tc oxides are analyzed on the basis of the developed theory.
Turbulent flow in a conical diffuser: Overview and implications
Authors: Azad R. S. , Kassab S. Z.
Published: July 2002

Turbulent flow in a conical diffuser has been examined through determination of the mean pressures, mean strain rates, energy, shear stress, triple products, length scale, and balances of energy and shear stress. Some quantities are more revealing than others in pointing out the complexity of a flow subjected to an adverse pressure gradient. Sudden application of extra strain rate to the flow seems to affect conditions so drastically that a final picture of the flow in terms of mean and turbulent fields becomes unrecognizable in relation to the initial condition. Initially all the measured parameters show rapid changes in their values and thus characterize a region of importance. Dynamics of the flow reflected by some parameters such as kinetic energy attain asymptotic values in the outlet region of the diffuser and, in turn, show a type of equilibrium of the flow. Additionally, the expanding wall region toward the exit has a low mean velocity and very high turbulence intensity. Finally, there is a growth of core region in the last one-third of the diffuser; this layer shows exceptionally high values of the higher moments.
Planform selection in rotating convection
Authors: Goldstein H. F. , Knobloch E. , Silber M.
Published: July 2002

Three-dimensional convection in a rotating fluid layer is studied near the onset of the steady-state instability using symmetric bifurcation theory. The problem is formulated as a bifurcation problem on a doubly periodic square lattice. Symmetry considerations determine the form of the ordinary differential equations governing the evolution of the marginally stable modes. From the symmetry analysis the relative stability of rolls and squares can be determined. Stable solutions exist only if both patterns bifurcate supercritically, and the one with the largest Nusselt number is the stable one. The theory is illustrated by explicit calculations for idealized boundary conditions, and the bifurcation diagrams given for all values of the Taylor and Prandtl numbers.
Enhancement of stability in uniformly elongating plastic jets with electromagnetic fields
Authors: Littlefield David L.
Published: July 2002

The stability of rapidly stretching, perfectly plastic jets when subjected to axial magnetic fields is studied in this analysis. The jet is assumed to be uniformly elongating, infinitely long, and isothermal. An axial magnetic field, assumed to be provided by a solenoid in the surrounding vacuum, is initiated at time t=0. Linear perturbation theory is employed to calculate the time evolution of small disturbances in the jet. Results of the calculations indicate that imposed axial magnetic fields inhibit the growth rates of instabilities in the jet. Entrained magnetic fields, however, are present after the jet leaves the solenoid, and increase the growth rates of disturbances. As a consequence, the overall growth rates are strongly dependent on the magnetic Reynolds number. This result is explained in terms of the applicable magnetohydrodynamic (MHD) stability mechanisms in the jet.
Inverse cascades in three-dimensional anisotropic flows lacking parity invariance
Authors: Galanti B. , Sulem P.-L.
Published: July 2002

A three-dimensional flow stirred by an anisotropic body force lacking parity invariance, may be unstable to large-scale perturbations. This is the anisotropic kinetic alpha (AKA) effect. When an extended range of scales is linearly unstable, an inverse cascade develops. Eventually, the flow is dominated by modes corresponding to the largest available scales.
A mapping closure for multispecies Fickian diffusion
Authors: Gao Feng , O’Brien Edward E.
Published: July 2002

It is shown how to construct amplitude mapping closures for molecular diffusion in a multispecies turbulent flow. The mappings are an extension of an earlier single-species mapping and they retain the property of an asymptotic approach to Gaussian states. The closure, in conjunction with a suitable closure for turbulent advection, is expected to be useful in treating multispecies diffusion as part of a single-point pdf modeling of chemically reactive flows.
Quantification of chaotic dynamics for heavy particle dispersion in ABC flow
Authors: Wang Lian-Ping , Burton Thomas D. , Stock David E.
Published: July 2002

A six-dimensional nonlinear dynamic system describing the Lagrangian motion of a heavy particle in the Arnold–Beltrami–Childress (ABC) flow was numerically studied. Lyapunov exponents and fractal dimension were used to quantify the chaotic motion. A single set of ABC flow parameters and a limited set of initial conditions were used. Given these restrictions, the following were found. (1) Attractor fractal dimension varies significantly with Stokes number, and, depending on inertia, periodic, quasiperiodic, and chaotic attractors may exist. (2) Particle drift reduces the fractal dimension when the drift is small. It can also cause irregular jumps when the drift parameter is close to one. (3) Quasiperiodic orbits on smooth two-dimensional manifolds were shown to be the most common ultimate solutions of the system when either the inertia or the drift is relatively large. (4) Different initial conditions can lead to different attracting sets; however, most of them have the same dimension. (5) A direct measure of dispersion based on mean square displacement was defined, but no relation between this dispersion measure and fractal dimension was found.
Convection velocity in supersonic turbulent boundary layers
Authors: Spina Eric F. , Donovan John F. , Smits Alexander J.
Published: July 2002

The convection velocity of large-scale organized motions was measured in a Mach 3 boundary layer using streamwise-separated hot wires. The broadband convection velocity, determined from space-time correlations, is 0.9U∞ across the entire outer region of the boundary layer. The convection velocity of individual structures was deduced using a pattern recognition technique, and this revealed that the majority of the large-scale structures convect at nearly the same velocity. A comparison of the present results to previous measurements indicates negligible Reynolds number and Mach number effects on convection velocity.
Mapping closure and non-Gaussianity of the scalar probability density functions in isotropic turbulence
Authors: Gao Feng
Published: July 2002

An attempt is made to assess the amplitude mapping closure for turbulent scalar fields. The closure assumption is shown to be in very good agreement with the results obtained from direct numerical simulations (DNS) of passive scalars in isotropic turbulence. The amplitude mapping closure is then employed to investigate the non-Gaussian properties of one-point scalar probability density functions (pdf) in isotropic flows. It is shown that the general relaxation of a scalar pdf to a Gaussian distribution can only be expected when the scalar variance is very small. Some non-Gaussian characteristics imposed by initial and boundary conditions persist throughout the course of scalar evolution.
Absolute and convective instability of a compressible jet
Authors: Zhou Z. W. , Lin S. P.
Published: July 2002

The absolute and convective instability of a jet of an inviscid compressible fluid emanating into another inviscid compressible fluid is investigated. It is shown that the compressibility of the ambient fluid, as well as the surface tension, tends to promote absolute instability. The absolute instability can be reduced to the convective one by reducing the surface tension and/or increasing the compressibility of the jet fluid, depending on the flow parameters.
Self-organizing particle dispersion mechanism in a plane wake
Authors: Tang L. , Wen F. , Yang Y. , Crowe C. T. , Chung J. N. , Troutt T. R.
Published: July 2002

Experimental and numerical results concerning solid particle motion in a plane wake are presented that demonstrate the importance of large-scale vortex structures in self-organizing dispersion processes. Previous studies have demonstrated that a time scale ratio involving the aerodynamic response time of the particles and a characteristic time of the vortex structures is an important parameter for indicating the qualitative and quantitative nature of the dispersion process. A stretching and folding mechanism associated with vortex development and merging interactions has been suggested as a description for characterizing particle dispersion in plane mixing layers at intermediate time scale ratios. For plane wakes where large-scale vortex mergers rarely occur, a highly organized particle dispersion process focuses intermediate time scale ratio particles along the boundaries of the large-scale vortices. The fractal correlation dimension associated with chaotic systems is found to be a useful parameter for quantifying the relative organization of the dispersion patterns as a function of the particle time scale ratio.
Asymptotic equations for the stretching of vortex filaments in a background flow field
Authors: Klein Rupert , Majda Andrew J. , McLaughlin Richard M.
Published: July 2002

Recently, two of the authors have derived [Physica D 49, 323 (1991)] and analyzed [Physica D 53, 267 (1991)] a new asymptotic equation for the evolution of small-amplitude short-wavelength perturbations of slender vortex filaments in high Reynolds number flows. This asymptotic equation differs significantly from the familiar local self-induction equation in that it includes some of the nonlocal effects of self-stretching of the filament in a simple fashion. Here, through systematic asymptotic expansions, the authors derive a modification of this asymptotic equation that incorporates the important additional effects of strain and rotation from a general background flow field. The main requirement on the background flow is that it does not displace the unperturbed background filament. The new asymptotic equations exhibit in a simple fashion the direct competition in filament dynamics between internal effects such as self-induction and self-stretching and external effects of background flows involving strain and rotation. Solutions of these asymptotic equations revealing various aspects of this competition are analyzed in detail through both theory and numerical simulation. An application is also presented for the nonlinear stability of a columnar vortex to suitable perturbations in a straining, rotating, background environment.
Approximate and exact renormalization theories for a model for turbulent transport
Authors: Avellaneda Marco , Majda Andrew J.
Published: July 2002

The capability of renormalization group methods (RNG) and Lagrangian renormalized perturbation theories (RPT) to reproduce a renormalized theory of eddy diffusivity for turbulent transport diffusion is discussed in the context of a simplified model with an exact renormalization theory that has recently been developed by the authors. The model problem involves transport diffusion by simple shear flows with turbulent velocity statistics, infrared divergences, and no separation of scales; the exact renormalization theory exhibits a remarkable range of different phenomena as parameters defining the velocity statistics are varied with four distinct regions requiring renormalization so that the model is a stringent test for approximate theories of eddy diffusivity via either RNG or RPT methods. Despite the different philosophy in RNG and RPT methods, all of these different approximations collapse to give the exact theory of eddy diffusivity for one region in the model with infrared divergence that is adjacent to the Kolmogorov value. The RNG methods are very flexible but do not give the exact anomalous scaling exponents for the other three regions with infrared divergence as expected with an ε-expansion procedure. The Lagrangian RPT methods always yield the correct scaling exponents but a much more elaborate analysis of the explicit structure of the model problem is needed to achieve this. In other regions of renormalization, including the Kolmogorov value, the RPT methods predict nonlocal equations for eddy diffusivity while the exact renormalization theory involves local diffusion equations with time-dependent diffusivity; these nonlocal equations are a poor approximation for the actual renormalized dynamics and the Lagrangian direct interaction approximation (DIA) only slightly improves the behavior over the Lagrangian first-order smoothing approximation. On the other hand, RNG methods alway predict a simple local diffusivity in the model and there are regions of renormalization where the rigorous theory for eddy diffusivity is nonlocal.
Solitary waves on a shelf
Authors: Shen Samuel Shanpu , Gong Lianger
Published: July 2002

By asymptotic analysis, it has been demonstrated that there exists a stationary solitary wave on the downstream side of a flat shelf when the upstream velocity U* is greater than or equal to U*C ≳ U(0)*, where U(0)* is the propagation speed of shallow-water waves and UC* is determined by Eq. (12). The solitary wave is found by solving a forced Korteweg–de Vries equation. The amplitude of the solitary wave is proportional to the upstream velocity and the downstream elevation is inversely proportional to the upstream velocity. A second branch of solutions of the forced Korteweg–de Vries equation are also found, which are uniform flows both far upstream and far downstream.
Kelvin–Helmholtz instabilities in radiating flows
Authors: Bodo G. , Massaglia S. , Rossi P. , Trussoni E. , Ferrari A.
Published: July 2002

The linear Kelvin–Helmholtz stability regime of two radiating fluids in relative motion is discussed. The study is carried out in plane geometry and in the vortex-sheet approximation. Attention is focused on the effects of radiation losses on the instability pattern: it is found that the principal effect is the suppression of the cutoff at Mach number M=2√2, typical of the adiabatic Kelvin–Helmholtz mode; in particular radiation effects are small on the instability below the cutoff, while they become dominant above. Radiating fluids are also typically affected by thermal instability. In fact thermal modes are found also in the present case: they may have growth rates comparable to the Kelvin–Helmholtz instability above the cutoff.
The stability analysis of magnetohydrodynamic equilibria: Comparing the thermodynamic approach with the energy principle
Authors: Brinkmann R. P.
Published: July 2002

This paper is a contribution to the stability analysis of current-carrying plasmas, i.e., plasma systems that are forced by external mechanisms to carry a nonrelaxing electrical current. Under restriction to translationally invariant configurations, the thermodynamic stability criterion for a multicomponent plasma [Phys. Rev. Lett. 56, 143 (1986); Phys. Fluids 30, 3713 (1987)] is rederived within the framework of nonideal magnetohydrodynamics (MHD). The chosen dynamics neglects scalar resistivity, but allows for other types of dissipation effects both in Ohm’s law and in the equation of motion. In the second section of the paper the thermodynamic stability criterion is compared with the ideal MHD based energy principle of Bernstein et al. [Proc. R. Soc. London Ser. A 244, 17 (1958)]. With the help of Schwarz’s inequality it is shown that the former criterion is always more ‘‘pessimistic’’ than the latter, i.e., that thermodynamic stability implies stability according to the MHD principle, but not vice versa. This result confirms the physical plausible idea that dissipational effects tend to weaken the stability properties of current-carrying plasma equilibria by breaking the constraints of ideal MHD and allowing for possibly destabilizing effects such as magnetic field line reconfiguration.