bluuebunny/crossref_metadata_2025 huggingface dataset:
Stress-energy-momentum tensors in constraint field theories
Authors: Sardanashvily Gennadi A.
Published: July 2002

We observe no conventional energy-momentum conservation law in classical field theory, but relations involving different stress-energy-momentum tensors which differ from each other in currents of Noether type. They can be conserved if some internal symmetries present. The key point is that different solutions of the same constraint field model require different stress-energy-momentum tensors. We show that the stress-energy-momentum of affine-metric gravity as like as the Noether current in gauge theory is reduced to a superpotential on shell.
Analytic regularization of the Yukawa model at finite temperature
Authors: Malbouisson A. P. C. , Svaiter B. F. , Svaiter N. F.
Published: July 2002

We analyze the one-loop fermionic contribution for the scalar effective potential in the temperature-dependent Yukawa model. In order to regularize the model a mix between dimensional and analytic regularization procedures is used. We find a general expression for the fermionic contribution in arbitrary space–time dimension. It is found that in D=3 this contribution is finite.
Integral equations of fields on a rotating black hole
Authors: Masuda Takahiro , Suzuki Hisao
Published: July 2002

It is known that the radial equation of the massless fields with spin around Kerr black holes cannot be solved by special functions. Recently, the analytic solution was obtained by use of the expansion in terms of the special functions, and various astrophysical application have been discussed. It was pointed out that the coefficients of the expansion by the confluent hypergeometric functions are identical to those of the expansion by the hypergeometric functions. We explain the reason of this fact by using the integral equations of the radial equation. It is shown that the kernel of the equation can be written by the product of confluent hypergeometric functions. The integral equation transforms the expansion in terms of the confluent hypergeometric functions to that of the hypergeometric functions and vice versa, which explains the reason why the expansion coefficients are universal.
On toroidal Green’s functions
Authors: Bates Jason W.
Published: July 2002

Green’s functions are valuable analytical tools for solving a myriad of boundary-value problems in mathematical physics. Here, Green’s functions of the Laplacian and biharmonic operators are derived for a three-dimensional toroidal domain. In some sense, the former result may be regarded as “standard,” but the latter is most certainly not. It is shown that both functions can be constructed to have zero value on a specified toroidal surface with a circular cross section. Additionally, the Green’s function of the biharmonic operator may be chosen to have the property that its normal derivative also vanishes there. A “torsional” Green’s function is derived for each operator which is useful in solving some boundary-value problems involving axisymmetric vector equations. Using this approach, the magnetic vector potential of a wire loop is computed as a simple example.
The Z2-graded Schouten–Nijenhuis bracket and generalized super-Poisson structures
Authors: de Azcárraga J. A. , Izquierdo J. M. , Perelomov A. M. , Pérez-Bueno J. C.
Published: July 2002

The super or Z2-graded Schouten–Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors Λ of even order. The corresponding super “Jacobi identities” are expressed by stating that these tensors have a zero super Schouten–Nijenhuis bracket with themselves [Λ,Λ]=0. As a particular case, we provide the linear generalized super-Poisson structures which can be constructed on the dual spaces of simple superalgebras with a non-degenerate Killing metric. The su(3,1) superalgebra is given as a representative example.
On the moment methods and irreversible thermodynamics
Authors: Chen M.
Published: July 2002

In this paper we investigate the kinetic foundation of irreversible thermodynamics by means of the moment methods proposed by Grad and by Eu, respectively. First we show that the moment methods yield a weak solution of the Boltzmann equation. On the other hand, the entropy balance equation can be satisfied only by the strong solution of the Boltzmann equation. Second, we reformulate the energy balance equation in an alternative form where dissipative energy as well as a generalized work 1-form are included in this new equation. Assume that the dissipative energy is semi-positive definite. The local form of the second law of thermodynamics is then formulated in terms of the inaccessibility condition of Caratheodory. We then show that our new formulation of the second law is equivalent to Kelvin’s principle and Clausius’ principle. Finally we obtain a calotropy balance equation where the calotropy density function is a state function in the thermodynamic space.
Properties of eigenstates of the six-vertex model with twisted and open boundary conditions
Authors: Fan Heng , Hou Bo-yu , Shi Kang-jie
Published: July 2002

We use the method proposed by Izergin and Korepin to discuss the Bethe ansatz equations of the six-vertex model with twisted and open boundary conditions. Let two parameters of the Bethe wave functions be equal, then an additional Bethe ansatz equation arises. For the open boundary condition case, we also have discussed the dual pseudovacuum state and have written out the simplest scalar products of the Bethe wave function.
Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis
Authors: Dobrev V. K. , Truini P.
Published: July 2002

An explicit realization of the U≡Uq(sl(3)) Gel’fand–(Weyl)–Zetlin (GWZ) basis as polynomial functions in three variables (real or complex) is given. This realization is obtained in two complementary ways. First, a known correspondence is used between the abstract GWZ basis and explicit polynomials in the quantum subgroup U+ of the raising generators. Then an explicit construction is used of arbitrary lowest weight (holomorphic) representations of 𝒰 in terms of three variables on which the generators of 𝒰 are realized as q-difference operators. The application of the GWZ corresponding polynomials in this realization of the lowest weight vector (the function 1) produces the first realization of this GWZ basis. Another realization of the GWZ polynomial basis is found by the explicit diagonalization of the operators of isospin Î2, third component of isospin Îz, and hypercharge Ŷ, in the same realization as q-difference operators. The result is that the eigenvectors can be written in terms of q-hypergeometric polynomials in the three variables. Finally an explicit scalar product is constructed by adapting the Shapovalov form to this setting. The orthogonality of the GWZ polynomials with respect to this scalar product is proven using both realizations. This provides a polynomial construction for the orthonormal GWZ basis. The results here are for generic q, leaving the root of unity case for a following paper. It seems that the results are new also in the classical situation (q=1).
On Lie algebra extensions in a symplectic framework
Authors: Fernandez Javier , Zuccalli Marcela
Published: July 2002

It is shown that the construction carried out by Cariñena and Ibort [J. Math. Phys. 29, 541–545 (1988)] involving nonsymplectic actions of Lie groups gives rise to “true” noncentral extensions of the corresponding Lie algebras.
Path space measures for Dirac and Schrödinger equations: Nonstandard analytical approach
Authors: Nakamura Toru
Published: July 2002

A nonstandard path space  * -measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space–time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schrödinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a  * -path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant.
Ladder operators for isospectral oscillators
Authors: Seshadri S. , Balakrishnan V. , Lakshmibala S.
Published: July 2002

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed “distorted” Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the nonlocal operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock–Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.
Zeta functions on a product of Einstein manifolds, and the multiplicative anomaly
Authors: Bytsenko Andrei A. , Williams Floyd L.
Published: July 2002

The global additive and multiplicative properties of Laplace-type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and of the multiplicative anomaly is derived.
Lax representation, r-matrix method, and separation of variables for the Neumann-type restricted flow
Authors: Zhou Ruguang
Published: July 2002

The r-matrix method and the method of separation of variables for restricted flows with Neumann constraints are considered. Restricted Jaulent–Miodek flows are taken as illustrative examples. Lax representations are obtained from the adjoint representation of the corresponding soliton hierarchy; the r-matrix formula, based on this Lax representation, is derived; and the separation of variables for the Hamilton–Jacobi equation are performed.
Irreducible representations of the Heisenberg algebra in Krein spaces
Authors: Mnatsakanova M. , Morchio G. , Strocchi F. , Vernov Yu.
Published: July 2002

The representations of the Heisenberg algebra in Krein spaces, more generally in weakly complete inner product spaces, are classified under general regularity and irreducibility conditions. Besides the Fock representation, two other types appear; one with negative, the other with a two-sided discrete spectrum of the number operator.
Adler–Kostant–Symes scheme for face and Calogero–Moser–Sutherland-type models
Authors: Jurčo Branislav , Schupp Peter
Published: July 2002

We give the construction of quantum Lax equations for IRF models and the difference version of the Calogero–Moser–Sutherland model introduced by Ruijsenaars. We solve the equations using factorization properties of the underlying face Hopf algebras/elliptic quantum groups. This construction is in the spirit of the Adler–Kostant–Symes method and generalizes our previous work to the case of face Hopf algebras/elliptic quantum groups with dynamical R matrices.
A Poincaré–Birkhoff–Witt theorem for generalized Lie color algebras
Authors: Bautista César
Published: July 2002

A proof of the Poincaré–Birkhoff–Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative) parts of the quantized universal enveloping algebras of type An and Mp,q,ε(n,K), which is a nonstandard quantum deformation of GL(n). In particular, we get, for both algebras, a unified proof of the Poincaré–Birkhoff–Witt theorem, and we show that they are genuine universal enveloping algebras of certain generalized Lie algebras.
On a class of Robin boundary value problems in physical geodesy
Authors: Ritter Stefan
Published: July 2002

In physical geodesy one considers several (exterior) Robin boundary value problems for the Laplace equation in three dimensions. The ellipsoidal Stokes problem, which occurs in context of gravimetric determination of the geoid, belongs to this class. Up to now, this and related problems have been treated with high order series expansions of spherical and spheroidal harmonics. In this article we investigate the nullfield method for this class of boundary value problems. An integral equation formulation is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. For the case that the underlying surface is a triaxial ellipsoid or an oblate spheroid, explicit expressions for the eigenvalues and eigenfunctions for the boundary integral operator are provided.
Formal improvements in the solution of the wavelet-transformed Poisson and diffusion equations
Authors: Lewalle Jacques
Published: July 2002

Hermitian wavelets’ relation to the Laplace operator leads to a natural measure of the scale factor that emphasizes the largest component wave number. For the Poisson equation (e.g. the pressure equation in Navier–Stokes turbulence), the wavelet transform of the solution at a given location and scale depends on the wavelet transform of the source field at the same location and at nearby and larger scales. For the diffusion problem, the Hamiltonian formulation is simplified through a canonical transformation.
Closure of field operators, asymptotic Abelianness, and vacuum structure in hyperfunction quantum field theory
Authors: Brüning E. , Nagamachi S.
Published: July 2002

Though, in contrast to standard quantum field theory (QFT), the tensor-algebra over the test-function space of hyperfunction quantum field theory has no local structure, the localization properties of states on this algebra can be used to derive asymptotic Abelianness in spacelike directions. Again, in contrast to standard QFT, the closure of (Hermitian) field operators can destroy localization properties. This problem is addressed in a natural modification of the definition of the closure, called the local closure. This allows one, in conjunction with asymptotic Abelianness, to define a proper reduction of the field algebra to the subspace of the translation invariant states, and to investigate the dimension of this subspace.
Gravitating brane systems: Some general theorems
Authors: Bronnikov K. A.
Published: July 2002

Multidimensional gravity interacting with intersecting electric and magnetic p-branes is considered for fields depending on a single variable. Some general features of the system behavior are revealed without solving the field equations. Thus, essential asymptotic properties of isotropic cosmologies are indicated for different signs of spatial curvature; a no-hair-type theorem and a single-time theorem for black holes are proved (the latter makes sense in models with multiple time coordinates). The validity of the general observations is verified for a class of exact solutions known for the cases when certain vectors, built from the input parameters of the model, are either orthogonal in minisuperspace, or form mutually orthogonal subsystems. From the nonexistence of Lorentzian wormholes, a universal restriction is obtained, applicable to orthogonal or block-orthogonal subsystems of any p-brane system.
Existence and nonexistence in Chern–Simons–Higgs theory with a constant electric charge density
Authors: Chae Dongho , Han Jongmin , Imanuvilov Oleg Yu.
Published: July 2002

In this paper we are devoted to proving the existence and nonexistence of self-dual equations arising in Chern–Simons–Higgs theory with a constant electric charge density. There are three kinds of boundary conditions that admit solitonic structures. It is shown that there exist solutions in two cases of them. In the other case, we prove that there is a critical electric charge density with negative value such that above the value there exists a solution and below it we have no solution. We also study asymptotic behaviors for solutions as the electric charge density goes to zero. It is found that they converge to solutions of a topological Chern–Simons system without constant electric charge density.
Propagation estimates for dispersive wave equations: Application to the stratified wave equation
Authors: Pravica David W.
Published: July 2002

The plane-stratified wave equation (∂t2+H)ψ=0 with H=−c(y)2∇z2 is studied, where z=x⊕y, x∈Rk, y∈R1 and |c(y)−c∞|→0 as |y|→∞. Solutions to such an equation are solved for the propagation of waves through a layered medium and can include waves which propagate in the x-directions only (i.e., trapped modes). This leads to a consideration of the pseudo-differential wave equation (∂t2+ω(−Δx))ψ=0 such that the dispersion relation ω(ξ2) is analytic and satisfies c1⩽ω′(ξ2)⩽c2 for c*>0. Uniform propagation estimates like ∫|x|⩽|t|αE(UtP±φ0)dkx⩽Cα,β(1+|t|)−β∫E(φ0)dkx are obtained where Ut is the evolution group, P± are projection operators onto the Hilbert space of initial conditions φ∈H and E(⋅) is the local energy density. In special cases scattering of trapped modes off a local perturbation satisfies the causality estimate ‖P+ρΛjSP−ρΛk‖⩽Cνρ−ν for each ν<1/2. Here P+ρΛj (P−ρΛk) are remote outgoing/detector (incoming/transmitter) projections for the jth (kth) trapped mode. Also Λ⋐R+ is compact, so the projections localize onto formally-incoming (eventually-outgoing) states.
Inverse Laplace transform and perturbation theory
Authors: Biswas T. , Joglekar Satish D.
Published: July 2002

We prove an extension of the result on the inverse Laplace transform. This extension will help toward making the applications of Borel techniques to perturbation theory in Quantum Field Theories be placed on a more rigorous foundation.
The study of dromion interactions of (2+1)-dimensional integrable systems
Authors: Ruan Hang-Yu , Chen Yi-Xin
Published: July 2002

Starting from a two-line soliton solution of an integrable (2+1)-dimensional system in bilinear form, one can find a dromion solution that is localized in all directions for a suitable potential. The interaction between two dromions is studied in detail through the method of figure analysis for a (2+1)-dimensional modified Korteweg–deVries (KdV) system, sine–Gordon system and Sawada–Kotera system. Except for a phase shift, there are no changes in the shape and velocity of the dromions after interactions for these models. The interactions of dromions for these models are not only elastic (there is no exchange of energy) but also irrotational (there is no exchange of angular momentum).
Quantum field theory of partitions
Authors: Bender Carl M. , Brody Dorje C. , Meister Bernhard K.
Published: July 2002

Given a sequence of numbers {an}, it is always possible to find a set of Feynman rules that reproduce that sequence. For the special case of the partitions of the integers, the appropriate Feynman rules give rise to graphs that represent the partitions in a clear pictorial fashion. These Feynman rules can be used to generate the Bell numbers B(n) and the Stirling numbers S(n,k) that are associated with the partitions of the integers.
Generalized adiabatic product expansion: A nonperturbative method of solving the time-dependent Schrödinger equation
Authors: Mostafazadeh Ali
Published: July 2002

We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding time-dependent Schrödinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum system, a time-dependent classical harmonic oscillator, and a degenerate system consisting of a spin 1 particle interacting with a time-dependent electric field E⃗(t) through the Stark Hamiltonian H=λ(J⃗⋅E⃗)2.
Unitary deformations and complex soliton equations
Authors: Varga Péter
Published: July 2002

The generalized Lax-equation L̇=i(AL−LB) leaves the spectrum of L*L invariant if A and B are self-adjoint operators. Consequently such equations possess many conversed quantities. With the help of this scheme, complex equations of Korteweg–de Vries type are derived.
A finite-dimensional integrable system associated with the three-wave interaction equations
Authors: Wu Yongtang , Geng Xianguo
Published: July 2002

Under a constraint between the potentials and the eigenfunctions, the 3×3 AKNS matrix spectral problem and its adjoint spectral problem associated with the three-wave interaction equations are nonlinearized so as to be a new finite-dimensional Hamiltonian system. A general scheme for generating involutive systems of conserved integrals and their two new generators are proposed, by which the finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Moreover, the involutive solutions of the three-wave interaction equations are given.
Dimensionally continued Oppenheimer–Snyder gravitational collapse: Solutions in odd dimensions
Authors: Ilha Anderson , Kleber Antares , Lemos José P. S.
Published: July 2002

The Lovelock gravity extends the theory of general relativity to higher dimensions in such a way that the field equations remain of second order. The theory has many constant coefficients with no a priori meaning. Nevertheless, it is possible to reduce them to two: the cosmological constant and Newton’s constant. In this process one separates theories in even dimensions from theories in odd dimensions. In a previous work, gravitational collapse in even dimensions was analyzed. In this work attention is given to odd dimensions. It is found that black holes also emerge as the final state of gravitational collapse of a regular dust fluid.
Two-parameter nonstandard deformation of 2×2 matrices
Authors: Çelik Salih , Çelik Sultan A.
Published: July 2002

We introduce a two-parameter deformation of 2×2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang–Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup GLp,q(1|1) by a transformation.
Invariant Painlevé analysis and coherent structures of two families of reaction-diffusion equations
Authors: Tanriver Ugur , Choudhury S. Roy
Published: July 2002

Exact closed-form coherent structures (pulses/fronts/domain walls) having the form of complicated traveling waves are constructed for two families of reaction–diffusion equations by the use of invariant Painlevé analysis. These analytical solutions, which are derived directly from the underlying PDE’s, are investigated in the light of restrictions imposed by the ODE that any traveling wave reduction of the corresponding PDE must satisfy. In particular, it is shown that the coherent structures (a) asymptotically satisfy the ODE governing traveling wave reductions, and (b) are accessible to the PDE from compact support initial conditions. The solutions are compared with each other, and with previously known solutions of the equations.
A representation space for minimal coupling
Authors: Wichnoski Bruno
Published: July 2002

Sternberg’s construction of the phase space for minimal coupling combines the phase space of a classical mechanical system with a principal fibre bundle with connection (gauge potential) and a Hamiltonian G-space. Using geometrical quantization data for a classical system and a Hamiltonian G-space we construct a representation space for the minimal coupling space.
Gauge-invariant covariant Hamiltonians
Authors: Fernández Antonio , Garcı́a Pedro L. , Masqué J. Muñoz
Published: July 2002

Given an Ehresmann connection γ on a fibered manifold p:E→M, a covariant Hamiltonian density Hγ is then associated to each Lagrangian density ℒ on J1E. Assume E is the bundle of connections of a principal bundle and that ℒ is gauge invariant. Our goal in this paper is to determine conditions on γ under which Hγ is also gauge invariant. The general conclusion is that there is no gauge-invariant Ehresmann connection but there is plenty of such connections providing gauge-invariant covariant Hamiltonians. The relevant cases of U(1) bundles and SU(2) bundles are discussed in detail.
The Markovian limit in a nonlinear quantum kinetic theory
Authors: Madureira Justino R.
Published: July 2002

Within the framework of a nonlinear quantum kinetic theory for dissipative far-from-equilibrium systems, based on a nonequilibrium ensemble formalism, a rigorous derivation of the Markovian limit is given. This is done in the framework of the nonequilibrium statistical operator method, and resorting to Zubarev’s approach.
Analysis of the cosmological Oppenheimer-Volkoff equations
Authors: Winter Dale
Published: July 2002

We formulate the Oppenheimer–Volkoff equations with nonzero cosmological constant, Λ. We analyze the behavior of solutions (under mild assumptions on the equation of state). We prove that solutions of the cosmological Oppenheimer–Volkoff equations are either singularity-free or else M(r)<0 for some r>0. [Here M(r) represents the total mass inside radius r.] We show that this behavior is independent of the magnitude of Λ when Λ⩽0. In the case where Λ>0, we show that these conclusions hold provided that the solution is contained within a ball of radius 1/Λ. We prove that if M(r)<0 for some r>0 then the pressure tends to infinity before r=0.
Tensor operators and Wigner–Eckart theorem for Uq→0(sl(2))
Authors: Marotta V. , Sciarrino A.
Published: July 2002

Crystal tensor operators, which transform under Uq→0(sl(2)), in analogous way as the vectors of the crystal basis, are introduced. The Wigner–Eckart theorem for the crystal tensor is defined: the selection rules depend on the initial state and on the component of the tensor operator; the transition amplitudes to the states of the same final irreducible representation are all equal.
Existence of Majorana fermions for M-branes wrapped in space and time
Authors: Chamblin Andrew
Published: July 2002

We show that it is possible to define Majorana (s)pinor fields on M-branes which have been identified under the action of the antipodal map on the adS factor of the throat geometry, or which have been wrapped on two-cycles of arbitrary genus. This is an important consistency check, since it means that one may still take the generators of supertranslations in superspace to transform as Majorana fermions under the adjoint action of Spin(10,1) even though the antipodally identified M2-brane is not space-orientable. We point out that similar conclusions hold for any p-branes which have the generic (adS)×(Sphere) throat geometry.
Absolute instability of a liquid jet in a gas
Authors: Lin S. P. , Lian Z. W.
Published: July 2002

The effect of the ambient gas density on the onset of absolute instability in a viscous liquid jet is examined. The critical Weber number, above which the instability is convective and below which the instability is absolute, is determined as a function of Reynolds number and the density ratio of gas to liquid. It is shown that the gas density has the effect of raising the critical Weber number. It also raises the cutoff wavenumber below which disturbances are spatially amplified and above which they are damped.
Computational reducibility of unsteady viscous flows
Authors: Triantafyllou George S. , Karniadakis George Em.
Published: July 2002

It is shown by direct numerical simulation of the incompressible Navier–Stokes equations that the vortex wakes of bluff objects can be reproduced by only knowing the time-average flow at one specific location behind the object, where it is most unstable according to linear instability theory.
Light scattering measurements of a hard-sphere suspension under shear
Authors: Wagner Norman J. , Russel William B.
Published: July 2002

The device described measures a two-dimensional projection of the light scattered from a sheared, optically clear colloidal suspension and decomposes the pattern to identify quantitatively the effects of shear on the structure of the dispersion. The evolution of the nonequilibrium structure for a hard-sphere suspension is traced from low to high shear rates at moderate to dense concentrations and is related qualitatively to rheological properties. At high shear rates shear induces order in dense suspensions. Comparison of the measured nonequilibrium structure factor at low shear rates to theoretical predictions based on pairwise additive interactions confirms the importance of many-body hydrodynamics, as suggested by similar discrepancies between measurements of the steady shear viscosity and predictions from the same theory. Scalings that correlate the shear rate dependence of the viscosity appear to work for the microstructure as well. Measurements of a similar suspension with weak long-range repulsions demonstrates the sensitivity of the nonequilibrium microstructure to the form of the interparticle potential.
Stokes drag on a disk sedimenting toward a plane or with other disks; additional effects of a side wall or free surface
Authors: Davis A. M. J.
Published: July 2002

For comparison with recent experimental results, a concise analytical method is presented for the sedimentation of a disk moving toward a plane wall in the presence of a parallel free surface or axisymmetric cylindrical container. In each case the problem is reduced to the numerical solution of dual integral equations and computed values of the normalized drag coefficient are displayed. The method is also applied to an array of sedimenting disks, possibly within a circular pipe, and then there is usually a larger number of integral equations to be solved. However, a clear pattern for the construction of the kernels emerges from the sample cases considered.
Transport equations from the Liu model
Authors: Garzó V.
Published: July 2002

Transport equations are developed by applying the Hilbert method to the Liu model [Phys. Fluids A 2, 277 (1990)]. The pressure tensor and the heat flux vector are calculated to Burnett hydrodynamic order for potentials of the form r−μ. The results are compared with those obtained from the Boltzmann equation.
A technique to trigger repeatable vortex wake configurations from bluff bodies
Authors: Seto Mae , Ahlborn Boye , Lefrançois Marcel
Published: July 2002

The initial configuration of a vortex street behind an impulsively started cylinder in a towing tank is usually subject to small-scale perturbations in the flow. It was found that the presence of a trigger plate, mounted normal to the towing direction on one side of the trajectory, induces an early bias to the wake vortex configuration. The phase of shedding, as inferred from lift force measurements, becomes quite repeatable. Steady-state wake oscillations can be induced early so that the length of vortex street in a given towing facility is increased.
Response of a solid–gas solidification interface to bulk heat sources
Authors: Zappoli Bernard
Published: July 2002

The response of a solid–gas solidification interface to uneven, time-dependent heat sources in the compressible mother phase is studied. The low Mach number 1-D compressible Navier–Stokes equations coupled with the transport equation of the species that reacts at the interface are solved by using a matched asymptotic expansion technique. The solution obtained shows that the density disturbance produced in the bulk by the heat source is responsible for the mass transfer at an isothermal solidification interface. It is also shown that the order of magnitude of the corresponding velocity of the gas at the interface may be of the same order of magnitude as the Stephan Wind that occurs during typical growth experiments.
Linear stability analysis of Bénard–Marangoni convection in fluids with a deformable free surface
Authors: Pérez-García Carlos , Carneiro Graciela
Published: July 2002

Linear stability analysis of the Bénard–Marangoni problem in a layer of fluid with a deformable free surface is considered. The analysis is restricted to fixed values of the Prandtl and the Biot numbers in order to determine the role of the Crispation number on convection. For a deformable upper interface both stationary and oscillatory instabilities are obtained. These two kinds of instabilities have been studied separately and the corresponding critical wave numbers kc and critical Rayleigh numbers Rc have been obtained numerically. The conditions under which two stationary states, an overstable mode and stationary mode, or two overstable modes can coexist simultaneously are determined. In the last case the possibility to obtain a strong resonance between two overstable modes is also discussed.
Ionization and edge-density gradient effects on MARFE instabilities in tokamak plasmas
Authors: Roy Choudhury S. , Kaw P. K.
Published: July 2002

Ionization and edge-density gradient effects on the long-wavelength radiative condensation (MARFE) instability in tokamak edge plasmas are considered. A self-consistent coupled equilibrium is derived from the continuity and temperature equations including the effects of radiation and ionization. In the limit relevant to edge plasmas, a modification of the temperature equilibrium derived earlier [Phys. Fluids 30, 2429 (1987)] is obtained due to the rapid edge-density variations. The critical radiation (density) limit is enhanced and results in significantly larger growth rates for the pure radiative mode than previously reported. Ionization processes affect the MARFE through a source term in the continuity equation, and produce an effect which qualitatively depends on the edge temperature TL. For TL less than a critical temperature, ionization phenomena weaken the MARFE instability. This behavior reverses at higher temperatures.
Ion cyclotron emission from energetic fusion products in tokamak plasmas—A full-wave calculation
Authors: Batchelor D. B. , Jaeger E. F. , Colestock P. L.
Published: July 2002

A full-wave ion cyclotron resonant heating (ICRH) code has been modified to allow calculation of cyclotron emission from energetic ions in tokamaks. The immediate application is to fusion alpha particles in near-ignition devices. This permits detailed evaluation of proposed alpha particle diagnostics [Proceedings of the Thirteenth European Conference on Controlled Fusion and Plasma Heating, Schliersee, Federal Republic of Germany, 1986, edited by G. Briffod and M. Kaufmann (European Physical Society, Petit-Lancy, Switzerland, 1986), Part 1, Vol. 2, p. 37.] This full-wave approach automatically takes into account wall reflections, standing waves, and plasma absorption and overcomes the difficulties inherent in attempting to apply conventional geometrical optics to long wavelengths. By calculating the coherent radiation field caused by an ensemble of localized current sources (and retaining the phase information), the directivity of pickup antennas is correctly represented. This method also promises to be useful for studying other kinds of plasma radiation, such as that produced by instabilities.
Formation studies of field-reversed configurations in a slow field-reversed theta pinch
Authors: Slough J. T. , Hoffman A. L. , Milroy R. D.
Published: July 2002

Field-reversed configurations (FRC’s) have been successfully formed in a field-reversed theta pinch in a regime where there was little or no radial shock heating. It has been observed that even with the elimination of radial shock heating there remains sufficient resistive and compressional heating to burn through any radiation barriers caused by the low Z contaminates introduced during formation. The equilibrium behavior of the FRC was not influenced by the loss of radial shock heating other than yielding a lower equilibrium flux for a given initial reverse flux. With the slower reversal of the axial field, it was possible to exert considerable control over the formation dynamics through the use of end control coils. Two modes of formation have been identified wherein either the equilibrium flux was maximized (slingshot mode), or, plasma heating was maximized and formation dynamics were minimized (bubble mode).
Nonlocal theory of the Rayleigh–Taylor instability in the limit of unmagnetized ions
Authors: Huba J. D. , Hassam A. B. , Satyanarayana P.
Published: July 2002

A nonlocal theory of the Rayleigh-Taylor instability is developed that applies to both magnetized and unmagnetized ion systems. The distinction between these two regimes is the time scale of the instability: for γ<Ωi the ions can be considered to be magnetized, and for γ>Ωi the ions can be considered to be unmagnetized, where γ is the growth rate and Ωi is the ion gyrofrequency. Both analytical and numerical results are presented that contrast the behavior of the Rayleigh-Taylor instability in these two regimes. In the long wavelength limit (kyLn≪1, where ky is the wavenumber and Ln is the density gradient scale length), it is found that the growth rate of the Rayleigh-Taylor instability in the unmagnetized ion limit is γ≂(kyg/A)1/2, where A is the Atwood number; this is quite different from the growth rate in the magnetized ion limit which is γ=(kygA)1/2. Another distinction between the two limits is that in the unmagnetized ion regime the fastest growing mode is not the lowest-order mode; again this is different from the magnetized ion regime in which the fastest growing mode is the lowest order mode. Finally, these results are applied to recent experimental observations (e.g., AMPTE [J. Geophys. Res. 92, 5777 (1987)], NRL laser experiment [Phys. Rev. Lett. 59, 2299 (1987)]).
Kelvin–Helmholtz vortex formation and particle transport in a cross-field plasma sheath. I. Transient behavior
Authors: Theilhaber K. , Birdsall C. K.
Published: July 2002

The time-dependent behavior of a transversely magnetized, two-dimensional plasma–wall sheath has been studied through particle simulations, with the aim of modeling plasma behavior in the vicinity of the limiters and walls of magnetized plasma devices. The model assumes a magnetic field perfectly parallel to the confining surfaces. The simulations have shown that the cross-field sheath between a wall and a plasma is a self-sustaining turbulent boundary layer, with strong potential fluctuations and anomalous particle transport. The driving mechanism for this turbulence is the Kelvin–Helmholtz instability, which arises from the sheared particle drifts created near the wall. In this paper, the transient behavior leading to the turbulent steady state is presented, and the processes of linear growth, vortex saturation, and vortex coalescence are examined. An analytic model for the boundary Kelvin–Helmholtz instability is derived and shown to correctly predict the growth rates of the long-wavelength modes. In a companion paper, the steady-state structure and behavior of the cross-field sheath will be discussed in detail.
Numerical simulations of axisymmetric erosion processes in ion-focused regime-transported beams
Authors: Krall Jonathan , Nguyen Khanh , Joyce Glenn
Published: July 2002

Erosion rates for a relativistic electron beam propagating through a low-density plasma channel in the ion-focused regime are computed via axisymmetric particle simulation. Steady-state inductive (Ohmic) erosion rates are found that are in quantitative agreement with new theoretical results, which correctly account for the relativistic dynamics of electrons at the beam head. In cases where the finite emittance of the beam is expected to be the dominant loss mechanism, the beam does not develop steady-state erosion, as suggested by previous analyses. Asymptotically, such a beam is characterized by a low-emittance population at the beam head, a long rise length, and an erosion rate that tends toward zero.
Experimental study of the hot electron plasma equilibrium in a minimum-B magnetic mirror
Authors: Chen Xing , Lane B. G. , Smatlak D. L. , Post R. S. , Hokin S. A.
Published: July 2002

The Constance B mirror [in Plasma Physics and Controlled Nuclear Fusion Research 1984 (IAEA, Vienna, 1985), Vol. II, p. 285] is a single cell quadrupole magnetic mirror in which high-beta (typically 0.3), hot electron plasmas (Te≂400 keV) are created with up to 4 kW of fundamental electron cyclotron resonance heating (ECRH). Details of the plasma equilibrium profile are quantitatively determined by fitting model plasma pressure profiles to the data from four complementary measurements: diamagnetic loops and magnetic probes, x-ray pinhole cameras, visible light TV cameras, and thermocouple probes. The experimental analysis shows that the equilibrium pressure profile of an ECRH generated plasma in a baseball magnetic mirror is hollow and the plasma is concentrated along a baseball-seam-shaped curve. The hollowness of the hot electron density profile is 50%±10%. The baseball-seam-shaped equilibrium profile coincides with the drift orbit of deeply trapped electrons in the quadrupole mirror field. Particle drift reversal is predicted to occur for the model pressure profile that best fits the experimental data under the typical operating conditions. When the ECRH resonance is just above the magnetic minimum, the plasma pressure closely approaches the mirror mode beta limit.
Estimation of the electrical resistivity in field-reversed configuration plasmas from detailed interferometric measurements
Authors: Okada S. , Kiso Y. , Goto S. , Ishimura T.
Published: July 2002

Electrical resistivity at the magnetic axis η(R) and at the separatrix η(rs) of a field-reversed configuration (FRC) plasma produced by theta pinch machines are estimated from detailed interferometric measurements, assuming that the temperature is uniform within the separatrix. The ratio f0[=η(R)/η(rs)] increases with the beta value at the separatrix βs, which is consistent with the fact that f0 decreases when xs (separatrix radius normalized by the inner radius of a theta pinch coil) increases [Phys. Fluids 28, 888 (1985)]. This tendency is a natural consequence of the transport properties of the FRC plasma when the particle confinement time is nearly equal to the decay time of the trapped reversed magnetic flux, as is normally the case. Theoretical expectations of the anomaly of η(rs) over the classical resistivity η0 increases and decreases slightly with βs for the case of the lower hybrid drift and the low-frequency drift instability, respectively. On the other hand, the observed η(rs)/η0 decreases substantially with βs. [The value of η(rs)/η0 changes from about 15 to 5 as βs changes from 0.45 to 0.6.]
Experimental study of a stellatron accelerator using plasma start-up
Authors: Ishizuka H.
Published: July 2002

Formation and acceleration of a high-current electron beam in a stellatron were studied. The apparatus had a 41 cm major radius and 4 cm minor radius torus, which was pumped down to 10−7 Torr. Plasma was injected into the torus and confined in a rising stellarator field. A runaway current of up to a few kiloamperes was induced when applying the betatron field. Beams of over 1 kA and with a current density of approximately 1 kA/cm2 were accelerated to several million electron volts with little loss. A 1 kA, 10 MeV beam was observed by initially forming a 2 kA beam. The loss was associated with negative-mass instability and high-mode orbital resonances.
Ion temperature gradient mode in the weak density limit
Authors: Shukla P. K.
Published: July 2002

Including the Righi–Leduc ion heat flux in the energy equation, the ion temperature gradient mode (ITG mode) is reconsidered for flat density profiles in a plasma with inhomogeneous ion temperature and magnetic field gradients. The stability boundary is (re)derived and is compared with those derived recently using either an ad hoc model or the numerical analysis of the kinetic dispersion relation. The impact of ITG mode turbulence on the ion energy confinement in tokamaks is discussed.
Mode conversion between Alfvén wave eigenmodes in axially inhomogeneous two-ion-species plasmas
Authors: Roberts D. R. , Hershkowitz N. , Tataronis J. A.
Published: July 2002

The uniform cylindrical plasma model of Litwin and Hershkowitz [Phys. Fluids 30, 1323 (1987)] is shown to predict mode conversion between the lowest radial order m=+1 fast magnetosonic surface and slow ion-cyclotron global eigenmodes of the Alfvén wave at the light-ion species Alfvén resonance of a cold two-ion plasma. A hydrogen (h)–deuterium (d) plasma is examined in experiments. The fast mode is efficiently excited by a rotating field antenna array at ω∼Ωh in the central cell of the Phaedrus-B tandem mirror [Phys. Rev. Lett. 51, 1955(1983)]. Radially scanned magnetic probes observe the propagating eigenmode wave fields within a shallow central cell magnetic gradient in which the conversion zone is axially localized according to nd/nh. A low radial-order slow ion-cyclotron mode, observed in the vicinity of the conversion zone, gives evidence for the predicted mode conversion.
Electron cyclotron resonance heating in tandem-mirror end cells
Authors: Rognlien T. D. , Matsuda Y. , Stallard B. W. , Stewart J. J.
Published: July 2002

A relativistic Fokker–Planck code is used to study the formation of non-Maxwellian electron velocity distributions in the end cell of a tandem mirror from the combined effects of Coulomb collisions and electron cyclotron radio-frequency (rf) heating. Axial electrostatic potential profiles consistent with thermal-barrier operation are assumed which lead to reasonable electron density profiles. The presence of the potentials results in four populations of electrons occupying different regions of phase space, three of which are solved for self-consistently; the fourth is the passing electron distribution from the center cell that is fixed as a Maxwellian. It is found that the second-harmonic barrier rf near the bottom of the magnetic well, together with rf cavity fields, give a good correspondence to the behavior of the hot electrons in the TMX-U experiment [IEEE Trans. Plasma Sci. PS-16, 1 (1988)]. The behavior of the fundamental rf in the plug region part way up the magnetic well shows poor correlation with experimental results.
X-ray laser beam propagation in double-foil targets
Authors: Boswell B. , Shvarts D. , Boehly T. , Yaakobi B.
Published: July 2002

Refraction effects on the gain of an x-ray laser propagating in a convex (lateral) plasma density profile have been studied previously. Here the corresponding case of concave density profile is studied theoretically. Experimentally, the convex profile is obtained by irradiating a single (exploding) foil target; the concave case can be realized by various two-beam irradiation configurations. Such geometries have been studied experimentally at the Laboratory for Laser Energetics (LLE) [SPIE Proceedings (SPIE, Bellingham, WA, 1987), Vol. 831, Paper 40, p. 283; Paper 42, p. 305]. The concave profile has a waveguiding effect on the propagation of the x-ray laser and can reduce the deleterious effects of refraction. The output power, its dependence on the length of the amplifying medium, and its angular distribution are studied and compared with the convex profile case. An amplifier mode (in which a collimated beam is incident on an amplifying medium) is compared with an amplified spontaneous emission mode (where spontaneous emission sources exist throughout the amplifying medium).
Interaction of plasma vortices with resonant particles
Authors: Jovanović D. , Pécseli H. L. , Rasmussen J. Juul
Published: July 2002

Kinetic effects associated with the electron motion along magnetic field lines in low-beta plasmas are studied. Using the gyrokinetic description of electrons, a kinetic analog of the reduced magnetohydrodynamic equations is derived, and it is shown that in the strongly nonlinear regime they possess localized solutions in the form of dipolar vortices, which can efficiently interact with resonant electrons. In the adiabatic limit, evolution equations are derived for the vortex parameters, describing exchange of the energy, enstrophy, and of the Poynting vector between the vortex and resonant particles. The evolution equations indicate the possibility of excitation of plasma vortices by electron beams.