bluuebunny/crossref_metadata_2025 huggingface dataset:
Open string diagrams I: Topological type
Authors: Nag Subhashis , Sankaran Parameswaran
Published: July 2002

An arbitrary Feynman graph for string field theory interactions is analyzed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the nonorientable cases. Algorithms are found to mechanically compute the topological characteristics of the resulting surface from the structure of the signed oriented graph. Whitney’s permutation-theoretic coding of graphs is utilized.
Twistor phase space dynamics and the Lorentz force equation
Authors: Bette Andreas
Published: July 2002

Using the Lorentz force equation as an input a Hamiltonian mechanics on the nonprojective two twistor phase space T×T is formulated. Such a construction automatically reproduces dynamics of the intrinsic classical relativistic spin. The charge appears as a dynamical variable. It is also shown that if the classical relativistic spin function on T×T vanishes, the natural conformally invariant symplectic structure on T×T reduces to the natural symplectic structure on the cotangent bundle of the Kal/uża–Klein space.
Variations of the parallel propagator and holonomy operator and the Gauss law constraint
Authors: Lewandowski Jerzy , Newman Ezra T. , Rovelli Carlo
Published: July 2002

A simple derivation is presented of the equations for the variation of the parallel propagator and the holonomy operators of Yang–Mills (YM) connections caused by variations of both the connection and the path. The derivation does not make any direct use of functional derivatives and is based on the solution of the varied parallel transport equation. In particular, the different forms that these equations take for a two parameter family of curves in E3 are discussed. As an example of this formalism, it is shown how any congruence defines a solution of the Hamilton–Jacobi version of the Gauss law constraint of YM theories, or equivalently, of the Dirac quantum-Gauss law constraint.
Collective nuclear potential within the microscopic Sp(6,R) model
Authors: Blokhin A. L.
Published: July 2002

An algorithm for projecting a microscopic nuclear Hamiltonian with a central interaction onto the enveloping algebra of the Sp(6,R) group is presented in parallel with the development of a practical procedure for constructing the corresponding part of the Sp(6,R)⊇SO(3) integrity basis. The latter is shown to consist of the invariants of the monopole–quadrupole tensor and its polynomial analogs, coupling the collective and vortex spin degrees of freedom. The algorithm uses vector coherent-state techniques and is displayed on the basis of a generic Sp(6,R) irreducible representation. The collective Hamiltonian is also shown to be expandable in terms of the enveloping algebra of the (A−1)-dimensional rotational group, where A is the total number of nucleons.
Wave propagation in complex systems of cutoffs and resonances
Authors: Skorupski Andrzej A.
Published: July 2002

Propagation of an electromagnetic wave in a nonhomogeneous medium in the presence of cutoffs and resonances is examined. Approximate formulas are derived for the reflection, transmission, and absorption coefficients, given in terms of the phase-integrals associated with all pairs of the neighboring cutoffs and/or resonances. The total (even) number of cutoffs and resonances is arbitrary, and phase-integral approximations up to the ninth order are admitted.
Interaction of kink-type solutions of the harmonic map equations
Authors: Grundland A. M. , Kovalyov M. , Sussman M.
Published: July 2002

In this article the interaction of kink-type solutions [as defined below in Eqs. (1.5), (1.6)] of the harmonic map equations is studied. It is shown that if two kinks enter an interaction, two kinks emerge from it as a result. The shape of the emerging kinks is related to the shape of the original ones via a certain Goursat problem.
Numerical twistor procedure for solving a nonlinear field equation
Authors: Moorhouse T. , Ward R. S.
Published: July 2002

This paper concentrates on an integrable SU(2) chiral equation in two space and one time dimensions, admitting soliton solutions. It is, in effect, a reduction of the self-dual Yang–Mills equations in 2+2 dimensions, and can therefore be solved by twistor methods. However, only some solutions can be constructed explicitly, and to solve a general initial-value problem requires some kind of numerical computation. The paper describes a way of implementing the twistor solution procedure numerically in order to do this.
Symplectic reduction of higher order Lagrangian systems with symmetry
Authors: de León M. , Pitanga Paulo , Rodrigues P. R.
Published: July 2002

One can develop a symplectic reduction procedure for higher order Lagrangian systems with symmetry. The reconstruction procedure of the dynamics is also studied and an application (spinning particle) is given at the end of the work.
On certain states on free *-algebras and their GNS representations
Authors: Lenczewski Romuald
Published: July 2002

States on free *-algebras expressed in terms of ordered partitions are studied. To this class belong twisted limit states that are derived from a convolution type q- analog of the quantum central limit theorem (qclt) for twisted free *-bialgebras 𝒞q, studied previously in the case of quantum groups. A special form of the GNS representation in terms of generalized creation and annihilation operators, A(v) and A(v*), respectively, living in the infinite tensor product of Hilbert spaces is given leading to a generalization of the Fock space. It is also shown that another family of states of similar combinatorics can be obtained from the convolution series.
Abelian Chern–Simons theory and linking numbers via oscillatory integrals
Authors: Albeverio Sergio , Schäfer Jörg
Published: July 2002

A rigorous mathematical model of Abelian Chern–Simons theory based on the theory of infinite-dimensional oscillatory integrals developed by Albeverio and Ho/egh-Krohn is introduced. A gauge-fixed Chern–Simons path integral is constructed as a Fresnel integral in a certain Hilbert space. Wilson loop variables are defined as Fresnel integrable functions and it is shown in this context that the expectation value of products of Wilson loops with respect to the Chern–Simons path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops, as conjectured by Witten. Furthermore, a lattice Chern–Simons action is proposed which converges to the continuum limit.
Integral equations versus internal variables in the search for an effectively hyperbolic thermal transport equation
Authors: Nettleton R. E.
Published: July 2002

To obtain a thermal wave equation predicting finite phase velocity in the infinite-frequency limit Grad’s 13-moment method and extended thermodynamics have added a term linear in the time derivative of the heat flux to Fourier’s law. When nonlocal effects are added via a term linear in the heat flux Laplacian, the problem of nonhyperbolicity and infinite phase velocity recurs. One approach postulates an infinite hierarchy of coupled equations, each of which describes time evolution of a flux appearing in the preceding hierarchy equation. This is shown to disagree in the high-frequency limit with an evolution equation derived by projection operators from the Liouville equation, in which memory and nonlocal effects are represented by integrals over time and space. Nonlocal effects disappear in the infinite-frequency limit of the latter, but not of the former.
On some colliding plane wave solutions
Authors: Bretón Nora
Published: July 2002

A one-to-one correspondence is presented which enables one to pass from colliding plane waves with parallel polarizations and electromagnetic field to nonparallel polarized colliding plane waves in vacuum and conversely. This correspondence is used to derive new solutions to Einstein’s equations in the context of colliding plane waves. This generating technique has its antecedent in the Bonnor trans- formation for stationary axisymmetric solutions.
Isotropic geometry and twistors in higher dimensions. II. Odd dimensions, reality conditions, and twistor superspaces
Authors: Harnad J. , Shnider S.
Published: July 2002

This work is a continuation of the study of higher-dimensional generalizations of the twistor correspondence in conformally compactified Minkowski space begun in Part I [J. Harnad and S. Shnider, J. Math. Phys. 33, 3197–3209 (1992)]. The case of odd-dimensional spaces is treated, with an equivariant diffeomorphism (Cartan map) defined between Grassmannians (or flag manifolds) of totally isotropic subspaces of a complex vector space with respect to a nondegenerate quadratic form, and minimal orbits in the Grassmannians (or flag manifolds) based upon spinor modules. Then the Cartan maps for the real forms of signature (p,q) are considered. The extensions to super-Grassmannians are also discussed, with emphasis upon the cases of dimensions 4, 6, and 10. It is found that in dimensions greater than 4, the natural choice for the superdouble flag space correspondence does not result in the expected supernull line foliation arising in the application to the supersymmetric Yang–Mills equations although in dimension 6 the model constructed is relevant to chiral supergravity.
SU3 coherent state operators and invariant correlation functions and their quantum group counterparts
Authors: Sazdjian Hagop , Stanev Yassen S. , Todorov Ivan T.
Published: July 2002

Coherent state operators (CSOs) are defined as operator valued functions on G=SL(n,C) being homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional representations of G with multiplicity 1. CSOs provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of SU3. The quantum group deformation of the construction gives rise to a noncommutative coset space. A ‘‘standard’’ polynomial basis is introduced in this space (related to but not identical with the Lusztig canonical basis) that is appropriate for writing down Uq(sl3) invariant 2-point functions for representations of the type (λ,0) and (0,λ). General invariant 2-point functions are written down in a mixed Poincaré–Birkhoff–Witt type basis.
Asymptotic expansions of Witten–Reshetikhin–Turaev invariants for some simple 3-manifolds
Authors: Lawrence R. J.
Published: July 2002

For any Lie algebra 𝔤 and integral level k, there is defined an invariant Zk*(M, L) of embeddings of links L in 3-manifolds M, known as the Witten–Reshetikhin–Turaev invariant. It is known that for links in S3, Zk*(S3, L) is a polynomial in q=exp (2πi/(k+c𝔤v), namely, the generalized Jones polynomial of the link L. This paper investigates the invariant Zr−2*(M,○/) when 𝔤 =𝔰𝔩2 for a simple family of rational homology 3-spheres, obtained by integer surgery around (2, n)-type torus knots. In particular, we find a closed formula for a formal power series Z∞(M)∈Q[[h]] in h=q−1 from which Zr−2*(M,○/) may be derived for all sufficiently large primes r. We show that this formal power series may be viewed as the asymptotic expansion, around q=1, of a multivalued holomorphic function of q with 1 contained on the boundary of its domain of definition. For these particular manifolds, most of which are not Z-homology spheres, this extends work of Ohtsuki and Murakami in which the existence of power series with rational coefficients related to Zk*(M, ○/) was demonstrated for rational homology spheres. The coefficients in the formal power series Z∞(M) are expected to be identical to those obtained from a perturbative expansion of the Witten–Chern–Simons path integral formula for Z*(M, ○/). © 1995 American Institute of Physics.
A definition of the Ponzano–Regge quantum gravity model in terms of surfacesa)
Authors: Iwasaki Junichi
Published: July 2002

We show that the partition function of the Ponzano–Regge quantum gravity model can be written as a sum over surfaces in a (2+1)-dimensional space–time. We suggest a geometrical meaning, in terms of surfaces, for the (regulated) divergences that appear in the partition function.
Holonomy and entropy estimates for dynamically triangulated manifolds
Authors: Carfora M. , Marzuoli A.
Published: July 2002

We provide an elementary proof of the exponential bound to the number of distinct dynamical triangulations of an n-dimensional manifold M (n≥2), of given volume and fixed topology. The resulting entropy estimates emphasize the basic role, in simplicial quantum gravity, of the moduli spaces Hom(π1(M),G)/G associated with the representations of the fundamental group of the manifold, π1(M), into a Lie group G.
Quantum Riemann surfaces for arbitrary Planck’s constant
Authors: Klimek Slawomir , Lesniewski Andrzej
Published: July 2002

We continue our study of quantum Riemann surfaces initiated in Refs. [S. Klimek and A. Lesniewski, Commun. Math. Phys. 146, 103–122 (1992); Lett. Math. Phys. 24, 125–139 (1992); 32, 45–61 (1994)]. We construct a one parameter family of deformations of compact Riemann surfaces of genus g≥2. Our construction does not require any discreteness condition on the value of Planck’s constant. It coincides with the construction of Ref. [Lett. Math. Phys. 24, 125–139 (1992)] in the case when Planck’s constant assumes the discrete set of values dictated by geometric quantization.
An ongoing big bang model in the special relativistic Maxwell–Dirac equations
Authors: Das A.
Published: July 2002

An exact, analytical solution of the combined Maxwell–Dirac equation is presented. The solution is regular inside a wedgelike domain of the flat space–time. On the boundary of that domain, the solution exhibits singular behavior.
Geometric interpretation of fractal symmetries of a finite linear chain
Authors: Lulek T. , Olchawa R.
Published: July 2002

The recipe of Weyl has been applied to two crystallographically distinct realizations of a regular orbit of the cyclic group of order N: the linear chain and the n-dimensional toroidal crystal, with n being the number of different prime integers dividing N, and Sylow factors of N being the Born–von Kármán periods. It follows that some fractallike symmetries of the linear chain are isomorphic images of multidimensional inversions, which are purely geometric operators.
SU3 isoscalar factors
Authors: Williams H. T.
Published: July 2002

A summary of the properties of the Wigner–Clebsch–Gordan coefficients and iso- scalar factors for the group SU3 in the SU2⊗U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture (Braunschweig’s) which has been the basis of previous work on the SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar factors are produced, along with an algorithm which allows numerical determination of the factors from the recursion relations. The algorithm produces isoscalar factors which share all the symmetry properties under permutation of states and conjugation which are familiar from the SU2 case. The full set of symmetry properties for the SU3 Wigner–Clebsch–Gordan coefficients and isoscalar factors are displayed.
Lax–Nijenhuis operators for integrable systems
Authors: Kosmann-Schwarzbach Y. , Magri F.
Published: July 2002

The relationship between Lax and bi-Hamiltonian formulations of dynamical systems on finite- or infinite-dimensional phase spaces is investigated. The Lax–Nijenhuis equation is introduced and it is shown that every operator that satisfies that equation satisfies the Lenard recursion relations, while the converse holds for an operator with a simple spectrum. Explicit higher-order Hamiltonian structures for the Toda system, a second Hamiltonian structure of the Euler equation for a rigid body in n-dimensional space, and the quadratic Adler–Gelfand–Dickey structure for the KdV hierarchy are derived using the Lax–Nijenhuis equation.
Tau-functions and dressing transformations for zero-curvature affine integrable equations
Authors: Ferreira Luiz A. , Miramontes J. Luis , Guillén Joaquı́n Sánchez
Published: July 2002

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac–Moody algebras 𝔤. Their common feature is that they have some special “vacuum solutions” corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of 𝔤; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of 𝔤. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail.
Information gains expected from separate and joint measurements of N identical spin-1/2 systems: Noninformative Bayesian analyses
Authors: Slater Paul B.
Published: July 2002

An investigator is assumed to have N replicas of a spin-1/2 system, but lacks any specific knowledge pertinent to constructing a 2×2 density matrix for it. We compute—within a noninformative Bayesian framework—the expected information gains for various measurement schemes, first, separate and, then, joint in nature. In particular, we obtain a result which fully accords with a certain plausibility argument of Peres, while the parallel result in a recent analysis of Massar and Popescu does not.
Asymptotic completeness for Rayleigh scattering
Authors: Spohn Herbert
Published: July 2002

We consider an electron bound by some anharmonic external potential and coupled to the quantized radiation field in the dipole approximation. We prove asymptotic completeness for the photon scattering. This means that an arbitrary initial state has a long time asymptotic, which consists of electron plus radiation field in their coupled ground state and finitely many outgoing photons.
Wave equations and kinematical integrals for complexified Maxwell–Klein–Gordon fields
Authors: Cardoso J. G.
Published: July 2002

The dynamics of Maxwell–Klein–Gordon fields in the framework of complex Minkowski space is considered. It is particularly shown that the procedures involved in the actual derivation of the wave equations which control the propagation of photons lead naturally to new structures describing the corresponding sources. The relevant kinematical integrals are readily built up by utilizing a suitable defining two-spinor expression for the energy-momentum tensor of the complete theory.
Uniform high frequency approximation to scattering from infinite strip
Authors: Goldberg J. , Berger Thomas , Dashen Roger
Published: July 2002

A new technique for approximating the high frequency scattering amplitude from flat obstacles is used to solve the problem of acoustic plane wave scattering from an infinite soft strip. This method yields the leading order terms in a uniform high frequency asymptotic expansion for the scattering amplitude which reduce to the results found with the geometrical theory of diffraction in the regions in which that theory is valid. The asymptotic expressions derived here are compared with exact numerical solutions and are found to be accurate for all angles of incidence and reflection.
Multiple-time constants of the motion for manifestly Poincaré-invariant Newtonian-like equations of motion for point particles
Authors: Woodcock Harry W.
Published: July 2002

While it is known that manifest Poincaré invariance of equations of motion for an isolated system of N interacting point particles is not a guarantee of conserved quantities, here it is shown that if such equations of motion have a Newtonian-like form (e.g., the formalism of Havas and Plebański), then ten multiple-time constants of the motion can be constructed by direct integration of the equations of motion. That these directly integrated quantities may be regarded as the ten standard relativistic multiple-time conserved quantities is verified by showing that a known subset, the Lagrangian-based multiple-time conserved quantities that are usually derived from symmetries of manifestly Poincaré-invariant variational principles, here can be obtained by substitution of the Lagrangian forces (which are read from the Newtonian-like Lagrangian equations of motion) into the directly integrated multiple-time forms. This method of obtaining relativistic multiple-time conserved quantities shows that, contrary to some previous statements in the literature, a manifestly Poincaré-invariant “Newton’s third law of motion” is not necessary to guarantee the existence of a conserved four-momentum. Furthermore, an analogous calculation in Newtonian mechanics (using a Galilei-invariant integration parameter instead of a Poincaré-invariant one) yields Newtonian multiple-time constants of the motion. The standard one-time forms of Newtonian conserved quantities do follow from these Newtonian multiple-time constants of the motion when all N times are chosen to be equal and the two-body forces follow from a sum of particle-symmetric two-body potential energies depending only on the mutual interparticle separations. A main result of this direct integration method of obtaining classical relativistic conserved quantities (which involve integrals over the whole motion) is that such quantities are far more analogous to the Newtonian multiple-time constants of the motion (which are just integrals of the equations of motion, independent of any symmetries of these equations) than to the standard Newtonian conservation laws (which apply only under restricted conditions).
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
Authors: de León Manuel , de Diego David Martı́n
Published: July 2002

We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems.
Nonperturbative formulation of relativistic two-particle states in the scalar Yukawa model
Authors: Darewych J. W. , Shapoval D. V. , Simenog I. V. , Sitenko A. G.
Published: July 2002

We investigate a variational approach to the study of two-particle bound states in quantum field theory. The scalar Yukawa model, in which scalar “nucleons” interact via “meson” exchange, is considered. A variational trial state that contains one or two scalar nucleons with any number of mediating scalar mesons is used to derive integral equations for the one- and two-nucleon systems. Numerical solutions of these equations are obtained in 1+1 dimensions. Comparison is made with perturbative and nonrelativistic approximations that have been used in earlier calculations.
A solvable model for excitonic complexes in one dimension
Authors: Markvardsen Anders J. , Johnson Neil F.
Published: July 2002

It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body “charged excitons” (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.
SU(N) monopoles and Platonic symmetry
Authors: Houghton Conor J. , Sutcliffe Paul M.
Published: July 2002

We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N−1 monopoles with minimal symmetry breaking. Using this we construct families of tetrahedrally symmetric SU(4) and SU(5) monopoles. In the moduli space approximation, the SU(4) one-parameter family describes a novel dynamics where the monopoles never separate, but rather, a tetrahedron deforms to its dual. We find a two-parameter family of SU(5) tetrahedral monopoles and compute some geodesics in this submanifold numerically. The dynamics is rich, with the monopoles scattering either once or twice through octahedrally symmetric configurations.
A combinatorial approach to diffeomorphism invariant quantum gauge theories
Authors: Zapata José A.
Published: July 2002

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in separable Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory.
Shear-free null quasi-spherical space–times
Authors: Bartnik Robert
Published: July 2002

We study the residual gauge freedom within the null quasi-spherical (NQS) gauge for space–times admitting an expanding shear-free null foliation. By constructing the most general NQS coordinates subordinate to such a foliation, we obtain both a clear picture of the geometric nature of the residual coordinate freedom, and an explicit construction of nontrivial NQS metrics representing some well-known space–times, such as Schwarzschild, accelerated Minkowski, and Robinson–Trautman. These examples will be useful in testing numerical evolution codes. The geometric gauge freedom consists of an arbitrary boost and rotation at each coordinate sphere—and this freedom may be used to normalise the coordinate to an “inertial” frame.
Development of the method of potentials for the problems of gravitation-electromagnetic conversion
Authors: Denisova Irene P. , Dalal Mahavir
Published: July 2002

In this work, the problem of generation of electromagnetic waves by gravitational wave propagating in external stationary electromagnetic field has been studied. It is shown that the equation of this process can be transformed into much simpler equations for superpotentials of electromagnetic field. The exact solutions for the superpotentials in the case of plane and spherical gravitational waves have been found.
SU(N) meander determinants
Authors: Di Francesco P.
Published: July 2002

We propose a generalization of meanders, i.e., configurations of non-self-intersecting loops crossing a line through a given number of points, to SU(N). This uses the reformulation of meanders as pairs of reduced elements of the Temperley–Lieb algebra, a SU(2)-related quotient of the Hecke algebra, with a natural generalization to SU(N). We also derive explicit formulas for SU(N) meander determinants, defined as the Gram determinants of the corresponding bases of the Hecke algebra.
A method for solving Riemann–Hilbert boundary value problems in nonreciprocal wave propagation
Authors: Uehara Masahiro , Yashiro Ken’ichiro , Ohkawa Sumio
Published: July 2002

A new method for solving periodic boundary value problems in nonreciprocal wave propagation is described. A characteristic function χ0 and its complementary function χ̃0 are introduced after the particular problem has been reduced to a Riemann–Hilbert boundary value problem based on complex variable theory. The Taylor coefficients νn and ν̃n of χ0 and χ̃0,respectively, compose a system of linear equations to deduce a characteristic equation. A numerical example is presented for magnetostatic surface waves propagating in a ferrite film on which metallic stripes are deposited periodically.
The inverse loop transform
Authors: Thiemann T.
Published: July 2002

The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections modulo gauge transformations. Since this space is a compact Hausdorff space, conversely, we know from the Riesz–Markov theorem that every positive linear functional on the space of continuous functions thereon qualifies as the loop transform of a regular Borel measure on the moduli space. In the present article we show how one can compute the finite joint distributions of a given characteristic functional, that is, we derive the inverse loop transform.
Improving the convergence and estimating the accuracy of summation approximants of 1/D expansions for Coulombic systems
Authors: Elout Melchior O. , Goodson David Z. , Elliston Carl D. , Huang Shi-Wei , Sergeev Alexei V. , Watson Deborah K.
Published: July 2002

The convergence of large-order expansions in δ=1/D, where D is the dimensionality of coordinate space, for energies E(δ) of Coulomb systems is strongly affected by singularities at δ=1 and δ=0. Padé–Borel approximants with modifications that completely remove the singularities at δ=1 and remove the dominant singularity at δ=0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F(δ)=∑jEj′/j!, where Ej′ are the the expansion coefficients of the energy with singularity structure removed at δ=1, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H2+ are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using Fm(δ)=∑jEj′/Γ(j+1−m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy.
Static stringlike solutions in five-dimensional relativity
Authors: Gravel Pierre
Published: July 2002

We exhibit a family of static cylindrically symmetric solutions to (4+1) Kaluza–Klein gravity which are separable functions of the spatial radial coordinate x2=r and the extra coordinate x5=ψ. These contain solutions other than radiative and, when interpreted as string solutions, display behaviors which differ from the standard (3+1)-dimensional static strings. All of those solutions with nonvanishing mass density obey the relativistic matter equation of state.
Electromagnetic fields in air of traveling-wave currents above the earth
Authors: Margetis Dionisios
Published: July 2002

The problem of the electromagnetic field created by a thin, straight conductor of infinite length carrying a forward traveling-wave current with a complex propagation constant γ above a homogeneous and isotropic planar earth of wave number k1 is formulated in terms of contour integrals. In the limit where γ becomes equal to the free-space wave number k0, the component of the magnetic field in air normal to both conductor and interface is evaluated in closed form in terms of known special functions while the remaining components of the field in air are expressed as series expansions in δ=k02(k14−k04)−1/2 via the application of a contour integration technique. The new analytical formulas involve familiar transcendental functions and are valid at any distance from the source. The analysis sheds light on the intricate nature of low-frequency electromagnetic fields generated by transmission lines in the presence of a conducting or a dielectric half-space.
The osp(1,2)-covariant Lagrangian quantization of irreducible massive gauge theories
Authors: Geyer B. , Lavrov P. M. , Mülsch D.
Published: July 2002

The osp(1,2)-covariant Lagrangian quantization of general gauge theories is formulated which applies also to massive fields. The formalism generalizes the Sp(2)-covariant Batalin–Lavrov–Tyǔtin (BLT) approach and guarantees symplectic invariance of the quantized action. The dependence of the generating functional of Green’s functions on the choice of gauge in the massive case disappears in the limit m→0. Ward identities related to osp(1,2) symmetry are derived. Massive gauge theories with closed algebra are studied as an example.
Reduction of constrained systems with symmetries
Authors: Cantrijn Frans , de León Manuel , Marrero Juan Carlos , Martı́n de Diego David
Published: July 2002

A general model is proposed for constrained dynamical systems on a symplectic manifold which covers, among others, the description of Lagrangian and Hamiltonian systems with nonholonomic constraints and the canonical description of mechanical systems with a singular Lagrangian. The reduction properties of these systems in the presence of symmetry are investigated within this general framework.
Rigorous probabilistic analysis of equilibrium crystal shapes
Authors: Bodineau T. , Ioffe D. , Velenik Y.
Published: July 2002

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results that have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.
Geometric variational problems of statistical mechanics and of combinatorics
Authors: Shlosman Senya
Published: July 2002

We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.
Mutual influence of quantum vortices and heat pulses in superfluid helium
Authors: Kondaurova L. P. , Nemirovskiı̆ S. K. , Nedoboiko M. V.
Published: July 2002

The problem of evolution of strong heat pulses in He II interacting with quantum vortices induced by these pulses is investigated numerically on the basis of equations of hydrodynamics of superfluid turbulence. In order to study nonlinear effects, the initial equations are expanded to the second order in the amplitudes of pulses. The one-dimensional case in the absence of mass transport (second sound) is considered. The initiation of vortices was simulated by the generation term in the Vinen equation. The results on the dynamics of pulses in various temperature ranges are presented. It is shown that the Feynman–Vinen theory is applicable in the phase-transition region.
Heat and mass transport in composites of aligned slender fibers
Authors: Fredrickson Glenn H. , Shaqfeh Eric S. G.
Published: July 2002

A theory is presented to describe the time-dependent and steady transport properties of composite media containing randomly placed, aligned slender fibers. The formalism is based on a diagrammatic representation of the multiple scattering expansion for the configurational-averaged Green’s function. Several topological reductions are performed on the series to remove long-wavelength singularities and to render the theory self-consistent. Approximations based on partial summation of the renormalized series have structures that are similar to, but distinct from, effective medium theories. The present approach is systematic and retains a unique subset of the multiple scattering series at each level of approximation. The formalism is appliedto the specific cases of steady diffusion-controlled reaction and heat conduction in composites that contain slender, aligned rods. Both the dilute and semidilute regimes are investigated. Theseresults for the diffusion-controlled reaction problem are new, and known results are recovered for heat conduction in the case of highly conductive rods. However, the method has uncovered a new semidilute expansion for the latter problem. The screening of disturbances in fibrous composites is also discussed.
The stretching of a thin viscous inclusion and the drawing of glass sheets
Authors: Wilmott P.
Published: July 2002

A thin, two-dimensional inclusion of a highly viscous fluid is deformed by an external Stokes flow—a suggested mechanism by which the Earth’s oceanic crust is entrained and thinned by the mantle. The method of matched asymptotic expansions is applied with the small expansion parameter being the inverse aspect ratio of the inclusion. The kinematic condition and continuity of shear and normal stresses lead to boundary conditions for the biharmonic equation governing the outer flow in the two cases of stretching by a pure shear and by a simple shear flow. The evolution of the inclusion can then, in principle, be determined. The equations governing the drawing of glass sheets may be derived as a limiting case, and any asymmetry in the centerline of the sheet is deformed over a short time scale before stretching occurs. Several examples are computed, showing how the straightening of the sheet can be slowed down by constraints on the gradients at the two ends. It is shown that an inclusion with smooth initial data cannot break up in a finite time.
Orientational dispersion of fibers in extensional flows
Authors: Shaqfeh Eric S. G. , Koch Donald L.
Published: July 2002

A kinetic theory is presented that predicts the dispersion of particle orientation, solely as a result of hydrodynamic interactions, about the principal axis of extension in uniaxial and planar extensional flows. The mean-squared displacement of the orientation vector is calculated in both the asymptotic dilute and semidilute concentration regimes. In the dilute regime (where nL3≪1, with n the fiber number density and L the fiber length) it is found that the mean-squared displacement is O[nL3/ln2(r)], where r is the fiber aspect ratio. For semidilute suspensions (where nL3≫1) it is predicted that the dispersion is O[ln(nL3)/nL3]. Thus the dispersion increases as the concentration is increased from infinite dilution and then ultimately decreases in the semidilute regime. The physical reasons for this behavior are discussed and, in particular, the semidilute scaling is demonstrated to be a consequence of the short-range particle screening that develops in semidilute suspensions [Phys. Fluids A 1, 3 (1989); 2, 7 (1990)]. The effect of this orientational dispersion on the material properties of fiber composites is also considered.
Analysis of the boundary conditions for a Hele–Shaw bubble
Authors: Burgess D. , Foster M. R.
Published: July 2002

Effective boundary conditions are derived to be used with the classical Hele–Shaw equations in calculating the shape and motion of a Hele–Shaw bubble. The main assumptions of this analysis are that the displaced fluid wets the plates, and that the capillary number Ca and the ratio of gap width to characteristic bubble length ε are both small. In a small region at the sides of the bubble, it is found that the thin-film thickness scales with ε2/5 Ca4/5, rather than the Ca2/3 scaling that is valid over most of the thin film above and below the bubble.
On the application of the Germano identity to subgrid-scale modeling
Authors: Ronchi C. , Ypma M. , Canuto V. M.
Published: July 2002

Germano [J. Fluid Mech. 238, 325 (1992)] has recently proposed an identity that has been widely applied to several turbulent flows to dynamically compute rather than adjust the Smagorinsky coefficient. In this Brief Communication, the assumptions under which the method has been used are discussed and some conceptual difficulties in its current implementation are pointed out.
A bifurcation study of convective heat transfer in porous media. Part II: Effect of tilt on stationary and nonstationary solutions*
Authors: Ryland D. K. , Nandakumar K.
Published: July 2002

In the present work the investigation of Weinitschke et al. [Phys. Fluids A 2, 912 (1990)] on the bifurcation structure of stationary, two-dimensional solutions of the Darcy–Oberbeck–Boussinesq model equations, which governs the convection heat transfer in a porous medium, is extended. The effect of imposing a symmetry breaking geometrical perturbation, viz., a tilt, on the unfolding of the bifurcation structure, is investigated first. The symmetry breaking bifurcation points that are found at zero tilt are structurally unstable to even a slight degree of tilt, and they unfold into limit points that coalesce with the neighboring limit points as the degree of tilt is increased. Two such limit points disappear through the formation of a double limit point at very small angles of tilt. On the fold curve of such limit points are found origins of paths of Hopf points, also known as the B-point singularity. Several such B points are located on the fold curves of limit points. This is helpful in pointing to regions of parameter space, where interesting dynamical behavior with oscillatory and chaotic flow structures are possible. The dynamical behavior is explored through simulation of the governing time-dependent equations after suitable spatial discretization through the Arakawa scheme. Linear stability analysis of stationary solutions indicate that such solutions remain stable over an increasing range of Rayleigh number (Ra) as the degree of tilt is increased. The first limit point (L1), below which there is a unique solution, tends toward infinite Rayleigh number as the tilt approaches 45°. At 45° tilt, a reflective symmetry about the diagonal of a square cell is restored and the stationary solutions computed by the continuation method remain stable for Ra as high as 200 000. Results from the dynamic simulation confirm this behavior. For tilts of 5° and 10° stationary solutions lose stability at Rayleigh numbers in the range of 4000–5000. Periodic solutions interspersed with regions of chaotic behavior are observed as Ra is increased continuously. For 20°, however, periodic solutions begin only above Ra≊10 000.
Stabilization of Rayleigh–Bénard convection by means of a slow nonplanar oscillatory flow
Authors: Kelly R. E.
Published: July 2002

A new technique is proposed for delaying the onset of thermal convection in a horizontal layer of fluid. The method consists of causing the fluid in the layer to oscillate slowly about a zero mean with two horizontal velocity components that are neither in phase nor 180° out of phase. Convection rolls then experience the stabilizing effects of shear regardless of their orientation. The amount of stabilization seems likely to be substantial, especially at large values of the Prandtl number.
The effect of thermal expansion on nonlinear fourth sound
Authors: Cramer M. S. , Kluwick A.
Published: July 2002

Weakly nonlinear fourth sound waves in clamped He II are considered. The first approximation to the nonlinear speed of fourth sound is derived through the use of a well-known multiple-scales scheme. As expected, the classical result that the linearized fourth sound speed can be accurately approximated by neglecting the coefficient of thermal expansion is recovered. However, this coefficient is found to be non-negligible when Doppler shifts and nonlinear effects are considered. The influence of the thermal expansion coefficient is significant even at low to moderate pressures and becomes dominant as the lambda temperature is approached. The terms which must be retained are found to be proportional to the well-known Grüneisen parameter.
On the absence of motion in certain nonequilibrium states of gases and vapors in free-molecular regime: General considerations and pipe flow
Authors: Cercignani Carlo , Frezzotti Aldo , Kogan Mikhail N.
Published: July 2002

This paper is devoted to the discussion of certain nonequilibrium states of gases and vapors in the free-molecular regime. In spite of the presence of temperature differences and, in some cases, of evaporation and condensation processes, the gas is shown to remain at rest. The case of a vapor in a tube of condensed phase, for which some numerical solutions are also given, is treated in some detail.
Magnetohydrodynamic stability and nonlinear evolution of the m=1 mode in toroidal geometry for safety factor profiles with an inflection point
Authors: Holmes J. A. , Carreras B. A. , Charlton L. A.
Published: July 2002

Magnetohydrodynamic (MHD) stability and nonlinear evolution of the m=1 mode are studied in toroidal geometry for safety factor profiles having an inflection point at the q=1 surface. For ideally stable cases, linear growth rates of the resistive m=1 mode are decreased by any combination of the following variations: decreasing the aspect ratio, decreasing shear at the q=1 surface, increasing S, decreasing q0, and/or decreasing beta. Transitions from resistive kink to tearing mode to complete stability are accompanied by increasing localization as the mode is stabilized. The ideal stability of the m=1 mode for low-shear inflection-point profiles is broken at very low, but finite, beta by the appearance of a radially localized ideal interchange mode. As beta is increased, the m=1 mode becomes a global ideal internal kink. These ideal modes are stabilized by decreasing the aspect ratio and, to a lesser extent, by increasing shear at the q=1 surface. Nonlinear evolution of the m=1 mode is found to follow the Kadomtsev complete reconnection process or to be stable, depending on the linear stability of the mode. However, all nonlinear calculations were carried out at Lundquist number S=105 and hence contain substantial resistive kink contributions. Consequently, nonlinear evolution in the m=1 tearing mode regime is not examined. Even for cases in which ideal effects dominate the linear mode, Kadomtsev reconnection is observed. The nonlinear stability of linearly stable modes was also uniformly observed, even for several cases having large initial perturbations. Hence complete linear stabilization resulting from a combination of toroidal effects and low shear at the q=1 surface can suppress sawteeth, as described by the Kadomtsev reconnection process, in tokamaks having safety factor profiles with q0<1 at the magnetic axis; but, for the S values considered, nonlinear calculations of unstable modes result in complete Kadomtsev reconnection.
Stability of plasmas sustained by ion cyclotron wave excitation in the central cell of the Tara tandem mirror
Authors: Golovato S. N. , Brau K. , Casey J. , Gerver M. J. , Horne S. , Irby J. , Kesner J. , Lane B. , Machuzak J. , Myer R. , Post R. S. , Sevillano E. , Wang L.
Published: July 2002

The stability of plasmas produced by radio-frequency heating in the ion cyclotron frequency range (ICRF) has been studied in the central cell of the Tara tandem mirror [Nucl. Fusion 22, 549 (1982); Plasma Physics and Controlled Nuclear Fusion Research 1986, Proceedings of the 11th International Conference, Kyoto (IAEA, Vienna, 1987), Vol. II, p. 251]. Ion cyclotron wave excitation by a slot antenna provided stability against macroscopic plasma motions in an axisymmetric configuration. The maintenance of macroscopic stability depended on the ICRF power, gas fueling rate, ion cyclotron resonance location, and ω/ωci at the antenna location. The ICRF ponderomotive force model is consistent with many of the observed stability features and predicts that the E+ component of the ion cyclotron wave was responsible for the stabilization. The Alfvén ion cyclotron microinstability was observed when the plasma β⊥ and anisotropy were sufficiently high. Magnetic probe measurements of the unstable mode identified it as an ion cyclotron wave and the instability threshold was within a factor of 2 of the theoretical value.