bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum entropies of nonprobabilistic matrices
Authors: Jumarie Guy
Published: July 2002

Von Neumann defined the informational entropy of a density matrix ρ by the expression S(ρ)=−tr(ρ ln ρ). [J. Von Neumann, Die Mathematischen Grundlagen der Quantummechanik (Springer-Verlag, Berlin, 1932)]. Here, starting from the definitions of Shannon entropy and of Renyi entropy of random variables, and using some (reasonable) rules of inference, two expressions are obtained for the quantum entropy of a given square (deterministic) matrix, irrespective of any probabilistic framework and/or any randomization technique. These definitions apply directly to linear operators on Hilbert spaces even when they are not of positive trace class, and they contain Von Neumann entropy as a special case. These new measures of uncertainty could provide new approaches to some problems related to structure complexity.
Bounded perturbations of the generalized random fields
Authors: Gielerak Roman
Published: July 2002

Functional DLR equations corresponding to the bounded perturbations of sufficiently regular generalized Gaussian random fields are studied. Certain uniqueness theorems are proved. Some qualitative properties of the set of the corresponding Gibbs states are described.
Conformal and critical embeddings, infinite magic square, and a new Clifford product
Authors: Arcuri Regina C.
Published: July 2002

It is known how the conformal subalgebras of classical algebras are related to the quark model representation. The relationship between conformal and critical embeddings of exceptional algebras and conformal field theories should be better understood. Through the analysis of conformal and critical embeddings of N=2 magic square, an infinite magic square was constructed in which the only Lie algebras appearing are the orthogonal ones. Exploiting the mathematical structure of the Hermitian symmetric spaces contained in the infinite magic square, a new Clifford product through a Jordan algebra defined via a triple bracket is obtained. A more formal structure is studied and given to this new Clifford product; starting from a Clifford algebra C(n,m), with its generators γi special elements γ and Γi of C(n,m) are constructed satisfying certain axioms. Defining then a new Clifford product, it will be shown that indeed Γi ’s are generators of another Clifford algebra 𝒞.
Green’s functions in WKB approximation
Authors: Pfirsch D. , Sudan R. N.
Published: July 2002

A systematic technique based on a variational principle is developed for obtaining WKB Green’s functions for a non-Hermitian set of inhomogeneous, nonstationary differential equations in a space of arbitrary dimensions. A key element in this technique involves the use of the Van Vleck determinant for the amplitudes of WKB functions.
Lie structures in parasupersymmetric quantum mechanics: I. The standard supersymmetrization procedure
Authors: Beckers J. , Debergh N.
Published: July 2002

Parasupersymmetric quantum mechanics leads to the construction of new Lie structures that are called Lie parasuperalgebras. They are characterized by double commutation relations between even and odd generators and include as particular substructures the usual Lie superalgebras. Oscillatorlike systems in one spatial dimension are especially exploited in order to put such structures in evidence but n-dimensional extensions are easily determined. These developments in the standard supersymmetrization procedure will be considered first and the spin orbit coupling one will be considered in a subsequent article [J. Beckers and N. Debergh, J. Math. Phys. ▪▪, ▪▪▪ (1991)].
Noninvertible Bogoliubov transformations and instability of embedded eigenvalues
Authors: Arai Asao
Published: July 2002

A class of noninvertible Bogoliubov transformations in an abstract Boson Fock space is used to construct in the Fock space a family of self-adjoint operators H which are quadratic in the annihilation and the creation operators and are of the form H=H0+HI with the property that the unperturbed part H0 may have embedded-eigenvalues unstable under the perturbation HI. Scattering theory associated with the pair (H0,H) is also discussed. In application to quantum field theory, the family of the operators H gives a unified description for the Hamiltonians of models of a quantum harmonic oscillator coupled to a quantized scalar or radiation field.
Linear perturbations of plane polarized plane waves. II. The Einstein–Maxwell perturbations
Authors: Xanthopoulos Basilis C.
Published: July 2002

The general solution of the linearized Einstein–Maxwell equations off the general plane polarized plane gravitational and electromagnetic waves space-time is determined. The solution is obtained using the Newman–Penrose formalism. The dependences of all the Newman–Penrose variables on the two spatial directions spanning the planar wave fronts and on advanced time are analyzed in normal modes. The problem is reduced into solving one second-order ordinary differential equation, called the master equation, depending on the two unspecified functions (of retarded time) of the background solution and the three parameters characterizing the normal modes. Then, the general solution of the linearized Einstein–Maxwell equations is expressed in terms of solutions of the master equation.
Product representation for the harmonic series of a unit vector
Authors: Brown R. W. , Convery M. E. , DeLaney D. B.
Published: July 2002

A representation is found for the finite Fourier series of a vector whereby any constant constraint on its magnitude is completely solved and automatically satisfied. The representation is a product of rotations, one set for each harmonic, such that the independent degrees of freedom are identified as rotational angles. Examples for the first few harmonics are presented. A recursive procedure is found whereby one can relate the standard Fourier coefficients to the angles.
The q-analog of the boson algebra, its representation on the Fock space, and applications to the quantum group
Authors: Sun Chang-Pu , Ge Mo-Lin
Published: July 2002

In this paper, a realization of the q-deformed boson operators on the Fock space from a generally algebraic point of view is given. The representations of the quantum group (Cn)q are thereby constructed in terms of this realization. Some infinite- and finite-dimensional representations of the q-analog of the Heisenberg–Weyl algebra are obtained on certain quotient spaces. Finally, the q-deformed differential realization of quantum group given by Alvarez-Gaume, Gomez, and Sierra (Preprint CERN-Th 5369/89) is derived from the boson realization.
Path integral treatment for a screened potential
Authors: Boudjedaa T. , Chétouani L. , Guéchi L. , Hammann T. F.
Published: July 2002

The propagator relative to an effective screened potential, which generalizes the Hulthén potential and the Kepler problem, is calculated via the path integration over the noncompact group SU(1,1). The energy spectrum and the wave functions of bound and scattering states, are deduced.
Kink number in general relativity
Authors: Dunn K. A. , Harriott T. A. , Williams J. G.
Published: July 2002

A comparison of general relativity with the theory of skyrmions is used to develop a method for counting the number of Finkelstein–Misner kinks in any given general relativistic metric. Some examples of kink number computations are presented.
Duality and Yang–Mills fields on quaternionic Kähler manifolds
Authors: Galicki Krzysztof , Poon Yat Sun
Published: July 2002

The concept of a self-dual connection on a four-dimensional Riemannian manifold is generalized to the 4n-dimensional case of any quaternionic Kähler manifold. The generalized self-dual connections are minima of a modified Yang–Mills functional. It is shown that our definitions give a correct framework for a mapping theory of quaternionic Kähler manifolds. The mapping theory is closely related to the construction of Yang–Mills fields on such manifolds. Some monopole-like equations are discussed.
Integrability of seventh-order KdV-like evolution equations using formal symmetries and perturbations of conserved densities
Authors: Bilge Ayşe Hümeyra
Published: July 2002

Seventh-order evolution equations of the form ut=d/dx where G is a differential polynomial with certain scaling properties are classified using the integrability test of Mikhailov–Shabat–Sokolov based on the existence of formal symmetries. The integrability of these equations is checked using Kodama’s method based on the perturbation of the conserved densities of the KdV equation. According to these tests, the only integrable KdV-like seventh-order equations are the KdV, Sawada–Kotera, and Kaup equations. It is also shown that these equations are characterized by the existence of two conserved densities.
Regulated propagator on the flat torus and its Weyl properties
Authors: Cohen E. , Kluberg-Stern H. , Navelet H.
Published: July 2002

The regulated propagator G′ε(ξ,ξ′) is considered for points ξ and ξ′ on the two-dimensional flat torus and with a regularization analogous to the proper-time method with cut-off ε. The inequivalent tori are labeled by a modular parameter τ. In this regularization, the propagator has an expansion in eigenmodes which is a particular Jacobi–Riemann function with beautiful properties and which can be transformed to an integral representation by a Sommerfeld–Watson method. This latter method allows one to derive exact analytic expressions in several domains of the parameters ‖ξ−ξ′‖, ε, and of the parameter τ. For generic value of τI≡Im(τ) and small value of the cut-off ε we recover the known results relative to short-distance phenomena. At large value of τI≂O(cst/4πε), the propagator diverges as τI and the coefficient is computed. A general formula for the Weyl variation of the propagator is derived; again the behavior of the Weyl variation at fixed τI is reproduced, while the behavior at large τI is novel. As a result we find that to O(√1/τI) the Weyl variation of the propagator at large τI is local in the Weyl variation δφ(ξ).
Asymptotic solution to the QCD–parton branching equation
Authors: Chan A. H. , Chew C. K.
Published: July 2002

High-energy multiparticle production events have been heavily studied using varies models, particularly the QCD-based parton branching model first proposed by A. Giovannini [Nucl. Phys. B 161, 429 (1979)]. Presented here is an asymptotic solution that is the probability distribution by using a simple saddle point approach. Its mechanism and properties will also be elucidated.
On the geometry of spontaneous symmetry breaking
Authors: Sardanashvily Gennadi
Published: July 2002

Given a principal bundle P→X with a structure group G and an associated Higgs bundle Σ with a standard fiber G/H, the case of a matter bundle E whose standard fiber admits action only of an exact symmetry subgroup H of G is examined. In the presence of a fixed Higgs field σ: X→Σ, matter fields are represented by sections of a matter bundle Eh associated with the corresponding reduced subbundle Ph of P. The totality of matter fields and Higgs fields is described by sections of the bundle Ẽ which is the composite bundle EH→Σ→X where EH→Σ is the bundle associated with the principal H-bundle P→Σ. The bundle Ẽ fails to be associated with a principal bundle. To construct a connection Γ: Ẽ→J1Ẽ on Ẽ, the canonical jet bundle morphism J1EH×J1Σ→J1Ẽ is used.
Jet methods in nonholonomic mechanics
Authors: Giachetta Giovanni
Published: July 2002

Classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle τ: M→R. The framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly. For systems with linear constraints a new interpretation is given of Appell’s equations as first-order differential equations associated with a suitable vector field. The d’Alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints. The equivalence between the equations of motion arising from this generalization, the ones set up on Gauss’ principle of least constraint and Hertz’s principle of least curvature is established.
On equations of motion on compact Hermitian symmetric spaces
Authors: Berceanu S. , Gheorghe A.
Published: July 2002

The classical equations of motion on compact coherent state manifolds that have Hermitian symmetric space structure are considered. In the case of Hamiltonians linear in the generators of the group that determines the structure of the manifold of coherent states, the classical motion and the quantum evolution are both described by the same first-order second degree differential equation. The explicit forms of the classical equations of motion as Matrix Riccati equations on the Grassmann manifold GA(Cn) and the coset manifold SO (2n)/U(n), attached to the Hartree–Fock and, respectively, Hartree–Fock–Bogoliubov problem are obtained.
The metaplectic representation of suq(1,1) and the q-Gegenbauer polynomials
Authors: Floreanini Roberto , Vinet Luc
Published: July 2002

The metaplectic representation of the quantum algebra suq(1,1) is shown to provide a group-theoretic setting for certain basic orthogonal polynomials generalizing the usual Gegenbauer polynomials.
Toy model for gravitational kinks
Authors: Dunn K. A. , Harriott T. A. , Williams J. G.
Published: July 2002

The homotopy properties of gravity in 1+1 dimensions are shown to imply the existence of structures analogous to the Finkelstein–Misner kinks of general relativity. A formalism is developed for the construction of kink metrics and a number of simple kink solutions for the (1+1)-dimensional equations are presented−including an n-kink solution that is locally transformable to the usual de Sitter solution and a one-kink solution that is locally transformable to one of the standard FLRW solutions. The relationship between the kink count and the hypersurface decomposition of the space-time manifold is explained in detail.
A supersymmetric Dirac oscillator with scalar coupling
Authors: Dixit V. V. , Santhanam T. S. , Thacker W. D.
Published: July 2002

It is shown that a relativistic wave equation with a scalar coupling correctly describes the Dirac oscillator in the sense that in the nonrelativistic limit this results in the Schrödinger equation for the harmonic oscillator with an extra σ⋅r̂ term. It is demonstrated that this equation has built-in supersymmetry, and that it guarantees the stability of the Dirac vacuum.
A closed form solution of the one-dimensional Born–Green–Yvon equation for a hard-rod fluid
Authors: Kaup D. J. , Paine Gregory H.
Published: July 2002

Using the method of the inverse scattering transform, we can generate an infinite number of closed form solutions for the one-dimensional, nonlinear Born–Green–Yvon differential-difference equation that governs an approximate expression for the equilibrium pair correlation function of a homogeneous system of hard rods.
On a two-parameter generalization of Hecke algebras and the XY chain in a magnetic field
Authors: Martin Paul
Published: July 2002

The structure and representation theory of a two-parameter generalization of Hecke algebras, denoted HL(q,η), which plays an important role in the construction of the L-site XY chain in a magnetic field is investigated. In particular, the structure of the XY chain representation of the algebra, on C2⊗L, and hence the structure of the centralizer algebra EndHL(q,η)(C2⊗L) for the XY chain representation, is analyzed. It is proved that the full algebra never reduces to the ordinary (one-parameter) Hecke algebra HL(q) in any specialization of the parameters, but contains the Hecke algebra as a quotient in a certain specialization of one of the parameters. This corrects an earlier claim of Hinrichsen and Rittenberg [Phys. Lett. B 275, 350 (1992)]. Bounds are established on the generic dimension of the centralizer algebra 4 ≤ dim(EndHL(q,η)(C⊗L2)) ≤ 8 (the upper bound is realized in every known case). Hence, it is argued that the structure of the centralizer algebra is independent of L, which is consistent with a result of Hinrichsen and Rittenberg, but that it is isomorphic to two commuting copies (rather than one copy) of the Pauli matrices. This contrasts sharply with the dimension of EndHL(q)(C⊗L2), which grows without bound as L increases.
Line soliton interactions of a nonisospectral and variable-coefficient Kadomtsev–Petviashvili equation
Authors: Chan W. L. , Li Kam-Shun , Li Yi-Shen
Published: July 2002

An extension of the dressing method is developed to solve a nonisospectral and variable coefficient generalization of the Kadomtsev–Petviashvili equation. Nonstandard dynamics of the one-soliton solutions are presented. Decomposition of the two-solitons and their interactions are studied in detail.
Possible solution of strong CP problem in generalized unimodular gravity
Authors: Frampton Paul H. , Ng Y. Jack , Van Dam Hendrik
Published: July 2002

It was recently pointed out how constrained gravitational dynamics offers a possible solution of the cosmological constant problem at the quantum level. Here we point out that the same theory may be used to solve the strong CP problem without recourse to wormholes or to the introduction of any new particle.
Octonionic particles and the S7 symmetry
Authors: Cederwall Martin
Published: July 2002

A manifestly Lorentz covariant quantization scheme for (super) particles in ten dimensions is given, using octonionic twistor variables, also applying to D=3, 4, and 6. The field-dependent gauge algebra for the twistor variables is (a superextension of) the seven-sphere. A BRS treatment of this symmetry is performed. Comments are made on conformal invariance and the topology of twistor space.
On the group aspects of Riemann–Hilbert transformations
Authors: Lu Jing-fa , Ge Mo-lin , Liu Chao
Published: July 2002

The more general algebraic structures of two-dimensional integrable systems are derived in a model independent manner by using the infinitesimal Riemann–Hilbert transformation. It is found that the resulting algebra decomposes into many families and, for each family, there is a Lie multialgebra structure. Examples of the chiral sigma models, four-dimensional self-dual Yang–Mills field, sine–Gordon, and Liouville equations and the BZ gravity are given with two special Lie products equipped therein.
Lattice Virasoro algebras, unitarity, and the eight-vertex model
Authors: Johannesson Henrik
Published: July 2002

An infinite set of lattice Virasoro algebras is constructed for the eight-vertex model, with the logarithm of the corner transfer matrix as the central element. By imposing unitarity, the c=1 algebra is uniquely singled out.
Limiting Gibbs states and dynamics for thermal photons
Authors: Hertle Jochen , Honegger Reinhard
Published: July 2002

For thermal photons, the limiting Gibbs state is investigated in the framework of algebraic quantum theory. For the one-particle Hamiltonian, the square root of the local Laplacians with Dirichlet boundary conditions is used. The local regions are only demanded to have the segment property and the thermodynamic limit is performed along a nearly arbitrary family of such local regions. Also, the limiting dynamics as a noncontinuous group of Bogoliubov transformations on an extension of the quasilocal Weyl algebra and as a W* dynamics on the GNS–von Neumann algebra is derived. After having performed the limits, the photon algebra is restricted to the physical (transversal) photons. The crucial mathematical method in verifying these results are comparisons of the semigroups of the square root of the Laplacians in different regions of the ν-dimensional Euclidean space by means of the ordering of positivity preserving operators.
A generating technique for Einstein gravity conformally coupled to a scalar field with Higgs potential
Authors: Gal’tsov Dmitry V. , Xanthopoulos Basilis C.
Published: July 2002

Starting from any solution of the Einstein equations, with cosmological term, coupled to a minimally coupled massless scalar field, a solution of the Einstein equations is constructed, conformally coupled to a massless self-interacting scalar field with the usual Higgs potential. When the cosmological constant vanishes, the Higgs term disappears and the transformation procedure reduces to that obtained by Bekenstein in 1974. As an example, a nonsingular cosmological solution is constructed that describes the restoration of spontaneously broken symmetry.
Surface integrals for electromagnetic energy
Authors: Benn I. M. , Wood W. P.
Published: July 2002

The definition of electromagnetic field energy for systems with singular sources is considered. It is shown that whereas for an electrostatic system of point charges one can identify an interaction energy density that is integrable, no sensible improper integral can be defined for dipole, or higher-order multipole, sources. It is shown how force and torque density forms can be obtained by examining the field dependence of certain ‘‘potential forms.’’ In the static case closed two-forms can be introduced that act as potentials for the force and torque two-forms. As these forms are constructed out of the fields in source-free regions singularities are avoided.
Integrable systems based on SU(p,q) homogeneous manifolds
Authors: del Olmo M. A. , Rodríguez M. A. , Winternitz P.
Published: July 2002

The general theory of the separation of variables in Hamilton–Jacobi and Laplace–Beltrami equations on the SU(p,q) hyperboloid is used to introduce completely integrable Hamiltonian systems on O(p,q) hyperboloids. Each of the q+1 different Cartan subalgebras of su(p,q) leads to a different integrable O(p,q) potential. Different complete sets of integrals of motion are obtained for each of the integrable systems.
On the dimensionality of space–time
Authors: Lämmerzahl Claus , Macias Alfredo
Published: July 2002

Within constructive axiomatics of space–time geometry based on elements of quantum mechanics it can be shown that by means of the study of the dynamical behavior of general matter fields in a geometry-free way one can give reasons for the dimension of space–time to be four.
Tomimatsu–Sato electrovacuum cosmic string solutions for δ=2 interacting with gravitational waves
Authors: Papadopoulos Demetrios B. , Xanthopoulos Basilis C.
Published: July 2002

We present cylindrically symmetric solutions of the Einstein–Maxwell electrovacuum equations, considering a δ=2 Tomimatsu–Sato solution, describing a cylindrical symmetric space–time. The solutions exhibit an angle deficit, are asymptotically flat, smooth everywhere without curvature singularities and for various values of the parameters may be interpreted as open cosmic strings with gravity and electromagnetism coupled in a relativistic manner.
Variable coefficient third order Korteweg–de Vries type of equations
Authors: Gürses Metin , Karasu Atalay
Published: July 2002

It is shown that the integrable subclasses of the equations q,t=f(x,t)q,3 +H(x,t,q,q,1) are the same as the integrable subclasses of the equations q,t=q,3 +F(q,q,1).
Chaos and geometrical resonance in the damped pendulum subjected to periodic pulses
Authors: Chacón Ricardo
Published: July 2002

The chaotic behavior of a damped pendulum driven by a periodic string of pulses is studied by means of Melnikov’s analysis. The reduction of homoclinic chaos, in the asymptotic case of infinite period driving, is explained in terms of geometrical resonance.
Separation of variables in (1+2)-dimensional Schrödinger equations
Authors: Zhdanov R. Z.
Published: July 2002

Using our classification of separable Schrödinger equations with two space dimensions published in J. Math. Phys. 36, 5506 (1995) we give an exhaustive description of the coordinate systems providing their separability. Furthermore, we apply these results to separate variables in the heat, Hamilton–Jacobi, and Fokker–Planck equations.
The algebraic structure of the gl(n|m) color Calogero–Sutherland models
Authors: Ju Guo-xing , Wang Shi-kun , Wu Ke
Published: July 2002

We extend the study on the algebraic structure of the su(n) color Calogero–Sutherland (CS) models to the case of gl(n|m) color CS model and show that the generators of the super-Yangian Y(gl(n|m)) can be obtained from two gl(n|m) loop algebras. Also, a super W∞ algebra for the SUSY CS model is constructed.
Invariant tensors and Casimir operators for simple compact Lie groups
Authors: Mountain Arthur J.
Published: July 2002

The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing nonprimitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.
The Eikonal equation in flat space: Null surfaces and their singularities. I
Authors: Frittelli Simonetta , Newman Ezra T. , Silva-Ortigoza Gilberto
Published: July 2002

The level surfaces of solutions to the eikonal equation define null or characteristic surfaces. In this paper we study, in Minkowski space, properties of these surfaces. In particular, we are interested both in the singularities of these “surfaces” (which can, in general, self-intersect and be only piecewise smooth) and in the decomposition of the null surfaces into a one-parameter family of two-dimensional wavefronts which can also have self-intersections and singularities. We first review a beautiful method for constructing the general solution to the flat-space eikonal equation; it allows for solutions either from arbitrary Cauchy data or for time-independent (stationary) solutions of the form S=t−S0(x,y,z). We then apply this method to obtain global, asymptotically spherical, null surfaces that are associated with shearing (“bad”) two-dimensional cuts of null infinity; the surfaces are defined from the normal rays to the cut. This is followed by a study of the caustics and singularities of these surfaces and those of their associated wavefronts. We then treat the same set of issues from an alternative point of view, namely from Arnold’s theory of generating families. This treatment allows one to deal (parametrically) with the regions of self-intersection and nonsmoothness of the null surfaces, regions which are difficult to treat otherwise. Finally, we generalize the analysis of the singularities to the case of families of characteristic surfaces.
Picard–Fuchs equations and Whitham hierarchy in N=2 supersymmetric SU(r+1) Yang–Mills theory
Authors: Ohta Yűji
Published: July 2002

In general, Whitham dynamics involves infinitely many parameters called Whitham times, but in the context of N=2 supersymmetric Yang–Mills theory it can be regarded as a finite system by restricting the number of Whitham times appropriately. For example, in the case of SU(r+1) gauge theory without hypermultiplets, there are r Whitham times and they play an essential role in the theory. In this situation, the generating meromorphic one-form of the Whitham hierarchy on the Seiberg–Witten curve is represented by a finite linear combination of meromorphic one-forms associated with these Whitham times, but it turns out that there are various differential relations among these differentials. Since these relations can be written only in terms of the Seiberg–Witten one-form, their consistency conditions are found to give the Picard–Fuchs equations for the Seiberg–Witten periods.
The averaged null energy condition for general quantum field theories in two dimensions
Authors: Verch Rainer
Published: July 2002

It is shown that in any local quantum field theory in two-dimensional Minkowski space–time possessing a mass gap and an energy-momentum tensor, the averaged null energy condition is fulfilled for the set of those vector states which correspond to energetically strongly damped, local excitations of the vacuum. This set of physical vector states is translation invariant and dense. The energy-momentum tensor of the theory is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat space–time.
Generalized Chern–Simons form and descent equation
Authors: Okumura Yoshitaka
Published: July 2002

We present the general method to introduce the generalized Chern–Simons form and the descent equation which contain the scalar field in addition to the gauge fields. It is based on the technique in a noncommutative differential geometry (NCG) which extends the four-dimensional Minkowski space M4 to the discrete space such as M4×Z2 with two point space Z2. However, the resultant equations are not only dependent on NCG, but also are justified by the algebraic rules in the ordinary differential geometry.
Reconstruction of the joint time-delay Doppler-scale reflectivity density in the wide-band regime. A frame theory based approach
Authors: Rebollo-Neira L. , Plastino A. , Fernandez-Rubio J.
Published: July 2002

The inverse scattering problem concerning the determination of the joint time-delay Doppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula, involving the echoes of a frame of outgoing signals and its corresponding reciprocal frame, is developed. A “realistic” situation with respect to the transmission of a finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.
Lie superalgebras and the multiplet structure of the genetic code. II. Branching schemes
Authors: Forger Michael , Sachse Sebastian
Published: July 2002

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra 𝔬𝔰𝔭(5|2) and differing only in details of the symmetry breaking pattern during the last step.
Level-one highest weight representation of Uq[sl(N̂|1)] and Bosonization of the multicomponent Super t−J model
Authors: Yang Wen-Li , Zhang Yao-Zhong
Published: July 2002

We study the level-one irreducible highest weight representations of the quantum affine superalgebra Uq[sl(N̂|1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible Uq[sl(N̂|1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t−J model by using the bosonized vertex operators.
Inertia effects of a localized force distribution near a wall in a slow shear flow
Authors: Shibata M. , Mei C. C.
Published: July 2002

From recorded observations in oscillatory flows over a bed sparsely covered with sand, it has been suggested that the initial stage of ripple formation involves hydrodynamic interaction at a distance among particles which are far apart. This mechanism appears to be common to both a thick layer of sand bed and a monolayer of beads on a smooth plane. In view of these facts it is helpful to study first a simpler problem that is of relevance in laminar flows. Specifically, the case where the typical particle radius is much smaller than the spacing, which is in turn much smaller than the thickness of Stokes boundary layer, is considered. With a view to examining the far field, a quasisteady Oseen approximation is invoked, and the boundary-layer flow is replaced by a linear shear and the particle by a localized force distribution. The results are used to infer the tendency of interaction between two particles.
Dissipative hydrodynamic interactions via lattice-gas cellular automata
Authors: Ladd Anthony J. C. , Frenkel Daan
Published: July 2002

A three-dimensional lattice-gas model has been used to determine the dissipative hydrodynamic interactions between spherical particles. When the particles are close together the accuracy of the lattice-gas simulations is superior to typical integral-equation solutions of the creeping-flow equations. Moreover, the computational requirements scale linearly with system size, instead of quadratically or cubically. A new set of microrules have been implemented, which simulate a constant-velocity, no-slip boundary condition at the solid–fluid surfaces. Numerical results for various drag coefficients are reported.
Transition to irreversibility for the dispersion of a tracer in porous media
Authors: Rigord P. , Calvo A. , Hulin J. P.
Published: July 2002

The transition from reversibility to irreversibility for tracer dispersion in an unconsolidated porous medium made of 2 and 4 mm diam glass beads has been studied; a low dead volume electrochemical technique has been used to produce and detect the tracer. It is shown that the transition occurs over a small number of layers (ten) at the inlet of the sample; this distance depends only on the ratio of the penetration distance and the bead diameter and varies very little with the Peclet number. For large penetration distances, the dispersion length values obtained in classical transmission dispersion measurements are recovered (dispersion has become fully irreversible). At very small distances, dispersion is largely reversible and dispersion coefficient values 20 or 80 times smaller than the asymptotic value have been measured.
Large eddy simulation of magnetohydrodynamic turbulent channel flows under a uniform magnetic field
Authors: Shimomura Yutaka
Published: July 2002

Magnetohydrodynamic turbulent channel flows under a uniform magnetic field are studied by using a large eddy simulation technique. The effect of a uniform magnetic field is incorporated into the subgrid-scale model in the form of a local damping factor. Compared with the experiment, this model is shown to work better than the usual Smagorinsky model in both turbulent and laminar states. This model predicts the detailed structures of the present flows, for which, one-point global turbulence models of ensemble mean type are helpless.
Visualization of the spanwise cellular structure of the laminar wake of wall-bounded circular cylinders
Authors: König Michael , Eisenlohr Holger , Eckelmann Helmut
Published: July 2002

End effects give rise to cells of different frequencies appearing simultaneously across the span of a circular cylinder in the laminar Reynolds number range. Each cell is associated with a different angle between the vortex axis and the cylinder. König et al. [Phys. Fluids A 2, 1607 (1990)] suggested that the discontinuities in the Reynolds–Strouhal number relationship are due to the movement of the cell boundaries across the span with the Reynolds number. In this Letter, flow visualization of the parallel, intermediate, extreme and end-cell modes of vortex shedding supports these results.
On the statistical properties of truncated Gram–Charlier series expansions in turbulent wall-bounded flows
Authors: Durst F. , Jovanović J. , Johansson T. G.
Published: July 2002

Higher-order correlations were measured in a turbulent boundary layer using the LDA measuring technique. In the paper, comparisons are made between the measured and predicted correlations obtained by utilizing the properties of truncated Gram–Charlier series expansions. Several theoretically derived relationships between correlations of different orders were confirmed by the experimental data. The experimental and theoretical results support the applicability of truncated Gram–Charlier series expansions for a refined statistical analysis of the conservation equations for higher-order moments of turbulent property fluctuations.
Rotating free-shear flows. I. Linear stability analysis
Authors: Yanase Shinichiro , Flores Carlos , Métais Olivier , Riley James J.
Published: July 2002

Using linear stability analysis, the instability characteristics are examined of both planar wakes and mixing layers subjected to rigid-body rotation with axis of rotation perpendicular to the plane of the ambient flow. In particular, the tendency of rotation to stabilize or destabilize three-dimensional motions is addressed. In the inviscid limit the results are consistent with the criterion established by Pedley [J. Fluid Mech. 35, 97 (1969)] and Bradshaw [J. Fluid Mech. 36, 177 (1969)]. Cyclonic rotation and strong anticyclonic rotation tend to stabilize three-dimensional motions, whereas weaker anticyclonic rotation (Ro≳1) acts to destabilize these motions. This latter instability is in the form of streamwise rolls, similar to previous results obtained for boundary layer and channel flows. It is found that this instability is stronger than the coexisting Kelvin–Helmholtz instability for roughly the range 1.5<Ro<8, and its effect is maximum for Ro≂2. For the case of constant ambient shear, exact solutions are obtained which give further insight into the nature of the instability.
Bubbly flows through a converging–diverging nozzle
Authors: Ishii Ryuji , Umeda Yoshikuni , Murata Shigeaki , Shishido Norihiko
Published: July 2002

Characteristics of bubbly flow through a vertical, two-dimensional, converging–diverging nozzle are investigated theoretically and experimentally. First, a new model equation of motion governing a dispersed bubble phase is proposed. This is compared in detail with those proposed previously by several researchers. Next, hyperbolicity of the resultant systems of governing equations for the bubbly flow is investigated in detail. Numerical simulations of bubbly flows through a converging–diverging nozzle are carried out by using the proposed system of model equations. In order to check the validity of the numerical results and then the proposed system, they are compared with the experiments which were performed previously in the authors’ laboratory in a water–nitrogen blow-down facility. It will be shown that the numerical results obtained by using the proposed system of model equations agree well with the experiments.
A numerical study of Richtmyer–Meshkov instability in continuously stratified fluids
Authors: Pham T. , Meiron D. I.
Published: July 2002

Theory and calculations are presented for the evolution of Richtmyer–Meshkov instability in two-dimensional continuously stratified fluid layers. The initial acceleration and subsequent instability of the fluid layer are induced by means of an impulsive pressure distribution. The subsequent dynamics of the fluid layer are then calculated numerically using the incompressible equations of motion. Initial conditions representing single-scale perturbations and multiple-scale random perturbations are considered. It is found that the growth rates for Richtmyer–Meshkov instability of stratified fluid layers are substantially lower than those predicted by Richtmyer for a sharp fluid interface with an equivalent jump in density. A frozen field approximation for the early-time dynamics of the instability is proposed, and shown to approximate the initial behavior of the layer over a time equivalent to the traversal of several layer thicknesses. It is observed that the nonlinear development of the instability results in the formation of plumes of penetrating fluid. Late in the process, the initial momentum deposited by the impulse is primarily used in the internal mixing of the layer rather than in the overall growth of the stratified layer. At intermediate times, some evidence for the existence of scaling behavior in the width of the mixing layer of the instability is observed for the multiple-scale random perturbations, but not for the single-scale perturbations. The time variation of the layer thickness differs from the scaling derived using ideas of self-similarity due to Barenblatt [Non-Linear Dynamics and Turbulence, edited by G. I. Barenblatt, G. Ioos, and D. D. Joseph (Pitman, Boston, 1983), p. 48] even at low Atwood ratio, presumably because of the inhomogeneity and anisotropy due to the excitation of vortical plumes.
Anomalous transport arising from nonlinear resistive pressure-driven modes in a plasma
Authors: Hamaguchi Satoshi
Published: July 2002

Anomalous transport caused by fluctuations of resistive pressure-driven modes is discussed within the framework of magnetohydrodynamics (MHD). The nonlinear-reduced equations describing fluctuations localized near a particular magnetic field line are derived for tokamak and reversed-field-pinch (RFP) plasmas, taking into account nonzero viscosity and heat conductivity. For an ideally stable but resistively slightly unstable plasma, the anomalous transport is caused particularly by convective motions. The convection is studied as bifurcation from the linearly unstable equilibrium and the expression of the anomalous transport in a tokamak plasma is obtained as a function of the mean pressure gradient near the critical point. In order to evaluate the effects of the convection on the anomalous transport under various conditions, the reduced equations are also solved numerically. It is found that Nusselt number, that is, the ratio of the total heat conductivity including the anomalous heat transport to the classical collisional heat conductivity, is significantly large under some conditions. This partially accounts for the large heat losses in controlled thermonuclear fusion devices.
Amplification of a high-frequency electromagnetic wave by a relativistic plasma
Authors: Yoon Peter H.
Published: July 2002

The amplification of a high-frequency transverse electromagnetic wave by a relativistic plasma component, via the synchrotron maser process, is studied. The background plasma that supports the trasnverse wave is considered to be cold, and the energetic component whose density is much smaller than that of the background component has a loss-cone feature in the perpendicular momentum space and a finite field-aligned drift speed. The ratio of the background plasma frequency squared to the electron gyrofrequency squared is taken to be sufficiently larger than unity, ω2ρ/ω2c >1. Such a parameter regime is relevant to many space and astrophysical situations. A detailed study of the amplification process is carried out over a wide range of physical parameters including the loss-cone index l, the ratio of the electron mass energy to the temperature of the energetic component α=mc2/T, field-aligned drift speed βd, the normalized density ω2ρ/ω2c, and the wave propagation angle θ.
Fluctuation spectrum and transport from ion temperature gradient driven modes in sheared magnetic fields
Authors: Hamaguchi Satoshi , Horton Wendell
Published: July 2002

The ion temperature gradient driven mode or ηi-mode turbulence is reinvestigated based on two-component compressible fluid equations with the polarization drift velocity and adiabatic electrons. The scaling of the anomalous ion heat conductivity with magnetic shear s=Ln/Ls and the excess of ηi over the critical value ηi,c for marginal stability is found to vary as χi=g(ρs/Ln)(cTi/eB) (ηi−ηi,c)exp(−αs), where g≂1 and α≂5.
Experimental study of filamentation in laser–plasma interactions
Authors: Young P. E.
Published: July 2002

The filamentation instability can lead to regions of increased laser intensity when a spatially nonuniform laser beam interacts with a plasma. An experimental technique will be described that identifies the density perturbation produced by filaments. The growth of filaments has been investigated and, when the laser intensity is large enough, the transverse density profile of the filament can be measured. Evidence of filament growth influenced by plasma flow and density gradients is presented.
Effects of plasma flow on error field islands
Authors: Jensen T. H. , Leonard A. W. , La Haye R. J. , Chu M. S.
Published: July 2002

The subject of magnetic islands, due to error fields in devices such as tokamaks, is of importance for understanding energy and angular momentum confinement observed in existing devices and for a rational determination of the accuracy required for the coils of future large devices. Simple arguments show that, for parameter values of interest, the viscous drag on plasma inside an island, caused by a toroidal flow of plasma outside the island, can affect the islands significantly. This subject is studied using a numerical implementation of a simple, almost ideal magnetohydrodynamical, two-dimensional model. A simplified version of the model is also studied analytically. The study suggests that the islands shrink somewhat as the drag force is applied and that there is an upper limit to the total drag force that a surface of islands can sustain; when this maximum drag force is approached, large gradients in the current density are formed, which may give rise to instabilities that make invalid the two-dimensional assumption.
Kinetic simulations of laser filamentation in plasmas
Authors: Epperlein E. M.
Published: July 2002

The effects of nonlocal electron heat transport on the nonlinear evolution of both thermal and ponderomotive laser filamentation in plasmas have been modeled using the Fokker–Planck (FP) code spark. The code solves the FP equation for electrons, the full hydrodynamic equations for cold ions, and the paraxial wave equation for laser light, in Cartesian geometry. Filamentation simulations, under the experimental conditions reported by Young et al. [Phys. Rev. Lett. 61, 2336 (1988)], confirm recent theoretical predictions [E. M. Epperlein, Phys. Rev. Lett. 65, 2145 (1990)] that the kinetic thermal mechanism should dominate over the ponderomotive one. It is further demonstrated that it is important to include the ion hydrodynamics.
Migma early-time density profiles
Authors: Godfrey Brendan B.
Published: July 2002

Equations describing the evolution of the Migma plasma equilibrium before the onset of diamagnetism are derived. As an illustrative case, the equations are solved for the early-time Migma density and current profiles in an approximately uniform magnetic field. The density is found to vary as r−1/2 near the axis, rather than the r−1 usually assumed. (The improved profiles should prove useful in stability analyses or for initializing computer simulations.) Evolution of the equilibrium near the axis at later times is evaluated as a second illustrative case, showing that the density there eventually does approach an r−1 profile. Suggestions for computing equilibria in more general, possibly diamagnetic, fields also are presented.