bluuebunny/crossref_metadata_2025 huggingface dataset:
Semiclassical approximation for bound states of the Schrödinger equation with a Coulomb-like potential
Authors: Zhevandrov Peter N.
Published: July 2002

The eigenvalue problem for the radial Schrödinger equation with an ‘‘almost’’ Coulomb potential is considered. This problem provides the simplest example of a system whose classical trajectories have singularities. Thus the standard semiclassical quantization procedure (in the sense of Einstein–Brillouin–Keller–Maslov) cannot be applied straightforwardly to this situation. The equation under consideration has two transition points on the half axis 0<x<∞: a regular singular point at the origin and a turning point for some x0≳0; these points coalesce at low energy levels. The well-known comparison equation method provides uniform asymptotics for equations of this kind, but has the following shortcomings: it does not appeal to the corresponding classical mechanical problem and the formulas for the eigenvalues and eigenfunctions contain phase integrals which are not analytic with respect to the parameter characterizing the closeness of the transition points. In the present article we derive new formulas for the eigenfunctions in the form of inverse Fourier transforms of rapidly oscillating exponentials multiplied by some powers of x, together with simple formulas for the eigenvalues. These formulas are directly connected with the classical trajectories and do not have the shortcomings of the comparison equation method, i.e., all the functions entering the asymptotic expansions are analytic in x and energy. As a by-product, an asymptotic expansion of integrals having two stationary phase points which coalesce for some value of the parameter and tend to infinity when the parameter tends to zero is obtained.
Holonomy groups and holonomy representations
Authors: McInnes Brett
Published: July 2002

The holonomy group of a Riemannian manifold always arises in geometry through a particular representation, not as an abstract group. One can therefore ask whether there exist pairs of (compact, locally irreducible) manifolds with holonomy groups which are isomorphic, yet distinct, because the holonomy representations are not equivalent. A theorem of Besse asserts that this is not possible in the simply connected case; however, it is possible for certain nonsimply connected manifolds. Here we identify all of these manifolds (up to space form problems) in the case where the Ricci curvature is not negative. This allows us to solve the holonomy classification problem for all compact, locally irreducible Riemannian manifolds of positive Ricci curvature.
The structure of quasi-exactly solvable systems
Authors: Brihaye Y. , Giller S. , Gonera C. , Kosinski P.
Published: July 2002

The linear, differential operators that preserve the N-dimensional vector space whose entries are polynomials of fixed, but arbitrary, degrees in one variable are considered herein. They are relevant for the classification of quasi-exactly solvable systems of equations. Generating elements are explicitly constructed and rules for ordering their products are derived. Some examples of equations that can be reduced to such systems are discussed.
Density correlation inequalities analogous to Bell’s
Authors: Kanter Marek
Published: July 2002

The usual Bell-type inequalities involve correlations between observables. Inequalities of the Bell-type are presented which involve correlations between the probabilities associated with states and which can be used as a test for hidden variables in quantum mechanics independent of the Bell inequalities. The inequalities are universal in the sense that they are valid for all separable metric state spaces, as opposed to the usual Bell inequalities whose specific form is a function of the state space of the candidate classical model. The inequalities are harder to prove than the usual Bell-type inequalities because no essential restrictions on the state space are made.
Passage from quantum systems with continuous spectrum to quantum Poisson processes on Hilbert modules
Authors: Lu Yun-Gang
Published: July 2002

The present article is devoted to the explanation of the irreversible behavior of quantum systems as a limiting case (in a sense to be made precise) of usual quantum dynamics. One starts with a system, whose Hamiltonian has a continuous spectrum, interacting with a reservoir and studies the limits of quantities related to the whole compound system. A macroscopic equation is obtained for the limit of the compound system, which is a quantum stochastic differential equation of Poisson type on some Hilbert module (no longer a space) and whose coefficients are uniquely determined by the one-particle Hamiltonian of the original system and whose driving noises are the creation, annihilation, and number (or gauge) processes living on the Fock module over this module.
Energy levels of double-well potentials in a three-dimensional system
Authors: Witwit M. R. M.
Published: July 2002

The renormalized inner product perturbation technique is used to compute the energy levels for a double-well potential V(x,y,z;Z2,λ)=−Z2[x2+y2+z2] +λ[axxx4+ayyy4+azzz4 +2axyx2y2+2axzx2z2 +2ayzy2z2] in the three-dimensional system. Results are produced for a wide range of parameters Z2, λ and of state numbers (nx,ny,nz). Comparison is made with results obtained by other means.
Integral expressions of the derivatives of the small-angle scattering correlation function
Authors: Ciccariello S.
Published: July 2002

The integral expressions of the derivatives of the small-angle scattering correlation function are obtained in terms of the parametric equations of the interphase surfaces. For each derivative, its integral expression is the surface average of a loop integral of a vectorial field that is the only quantity depending on the derivative order. The field relevant to the nth derivative is obtained by letting a suitable differential operator act (n-2) times on the field relevant to the second derivative. Both the differential operator and the last vectorial field are given in terms of the interface parametric equations. Starting from these expressions, the limiting values of the derivatives of the correlation function as r → 0 are studied by a procedure similar to the one used by Kirste and Porod [Kolloid-Z. 184, 1 (1962)] and Wu and Schmidt [J. Appl. Crystallogr. 4, 224 (1971)]. In this way, the conjecture put forth by Wu and Schmidt that, when the interfaces are sufficiently smooth, all even-order derivatives of the correlation function are null at the origin is proven to be true.
Quantum Poincaré group without dilatation and twisted classical algebra
Authors: Chaichian M. , Demichev A. P.
Published: July 2002

A quantum deformation of a Poincaré group was constructed using as a starting point SU(2,2) conformal group and twistorlike definition of the Minkowski space. This leads to a pure twisted quantum Poincaré group. The relative simplicity of the q deformation permits one to find out the important properties of the q groups of the space–time transformations. In particular, it is shown that the geometrical meaning of the twisting is the transition to the another space–time coordinates frame, so that one can freely choose the most convenient deformation among the ones related to each other by twists. The small subgroup used in the induced representation construction is proven to be twisted with respect to initial q group. This last fact means that commutation relations for creation and destruction operators are not strongly defined by the q group of the space–time transformations.
Toward discrete wavelets with irrational scaling factor
Authors: Gazeau Jean Pierre , Spiridonov Vyacheslav
Published: July 2002

Scaling equations determining Haar-type wavelets are considered for three Pisot numbers β=(1+√5)/2, 1+√2, 2+√3 appearing as dilation factors in scale invariance of observed diffraction patterns of quasicrystals. Simple summation formulas for exponentials of the corresponding β integers are derived.
On localization and regularization
Authors: Miettinen Mauri
Published: July 2002

Different regularizations are studied in localization of path integrals. We discuss the effect of the choice of regularization by evaluating the partition functions for the harmonic oscillator and the Weyl character for SU(2). In particular, we solve the Weyl shift problem that arises in path integral evaluation of the Weyl character by using the Atiyah–Patodi–Singer η-invariant and the Borel–Weil theory.
Quantum mechanics of charged particles in random electromagnetic fields
Authors: Truman A. , Zhao H. Z.
Published: July 2002

In this paper we consider the ℏ→0 asymptotics for the solutions to stochastic Schrödinger equations for quantum mechanical particles in random electromagnetic fields in Rn. We obtain semi-classical expansions for their solutions up to any order in L2(Rn) a.s. by using a stochastic Hamilton Jacobi equation and a stochastic continuity equation. We conclude that as ℏ→0 the stochastic quantum mechanics with random electromagnetic fields tends to stochastic classical mechanics.
Energy extremes and spin configurations for the one-dimensional antiferromagnetic Ising model with arbitrary-range interaction
Authors: Douthett Jack , Krantz Richard
Published: July 2002

The one-dimensional antiferromagnetic spin-1/2 Ising model is investigated using the formalism of Maximally/Minimally Even sets. The salient features of Maximally/Minimally Even set theory are introduced. Energy and spin content vectors are defined to facilitate the use of interval spectra used in Maximally/Minimally Even set theory. It is shown that Maximally Even sets of up- and down-spins minimize the configurational energy per spin and that Minimally Even sets maximize configurational energy per spin. An exponentially decreasing antiferromagnetic pairwise interaction of arbitrary range is used as an example interaction. The asymptotic (N→∞) configurational energy per spin and the energy per spin calculated for seven-near neighbors are compared.
Algebraic proof of the symmetric space theorem
Authors: Daboul C.
Published: July 2002

I give a relatively elementary proof of the symmetric space theorem, due to Goddard, Nahm and Olive [Phys. Lett. B 160, 111–116 (1985)]. Unlike their original proof, which involves the quark-model construction, I only use elementary algebraic techniques.
Discrete Weyl–Heisenberg transforms
Authors: Zak J.
Published: July 2002

The concepts of von Neumann lattices and tight frames are used for defining discrete quantum mechanical transforms in the phase plane. These transforms are obtained by finite shifts la and mb in the coordinate x and momentum p, respectively, of the Weyl–Heisenberg group, and they are called the discrete Weyl–Heisenberg transforms ψ(la,mb). Here ab=h/N with h the Planck constant, l and m integers, and N a positive integer. A construction is carried out of ψ(la,mb) for a general Weyl–Heisenberg set by using the kq-representation, in which a useful formula is established for the frame operator. The construction is illustrated on an example of the ground state of a harmonic oscillator. It is shown that any physical quantity can be described by the discrete Weyl–Heisenberg transform. Connections are established between ψ(la,mb), the Bargmann representation, and the Husimi distribution function.
A unified treatment of the characters of SU(2) and SU(1,1)
Authors: Bal Subrata , Shajesh K. V. , Basu Debabrata
Published: July 2002

The character problems of SU(2) and SU(1,1) are re-examined from the standpoint of a physicist by employing the Hilbert space method which is shown to yield a completely unified treatment for SU(2) and the discrete series of representations of SU(1,1). For both the groups the problem is reduced to the evaluation of an integral which is invariant under rotation for SU(2) and Lorentz transformation for SU(1,1). The integrals are accordingly evaluated by applying a rotation to a unit position vector in SU(2) and a Lorentz transformation to a unit SO(2,1) vector which is time-like for the elliptic elements and space-like for the hyperbolic elements in SU(1,1). The details of the procedure for the principal series of representations of SU(1,1) differ substantially from those of the discrete series.
On the noncommutative Riemannian geometry of GLq(n)
Authors: Georgelin Y. , Madore J. , Masson T. , Mourad J.
Published: July 2002

A recently proposed definition of a linear connection in noncommutative geometry, based on a generalized permutation, is used to construct linear connections on GLq(n). Restrictions on the generalized permutation arising from the stability of linear connections under involution are discussed. Candidates for generalized permutations on GLq(n) are found. It is shown that, for a given generalized permutation, there exists one and only one associated linear connection. Properties of the linear connection are discussed, in particular its bicovariance, torsion, and commutative limit.
Solving the constrained KP hierarchy by gauge transformations
Authors: Chau Ling-Lie , Shaw Jiin-Chang , Tu Ming-Hsien
Published: July 2002

We solve the constrained Kadomtsev–Petviashvili (cKP) hierarchy by using the gauge transformation technique. We show that there are two kinds of gauge transformations which preserve the form of the Lax operator of the cKP hierarchy. One of them is differential type and the other is integral type. Through two such gauge transformations we obtain not only the Wronskian-type τ-functions for the cKP hierarchy, but also the binary-type τ-functions which have not been obtained before.
Stable singularities of wave-fronts in general relativity
Authors: Low Robert
Published: July 2002

A wave-front in a space-time M is a family of null geodesics orthogonal to a smooth spacelike two-surface in M; it is of some interest to know how a wave-front can fail to be a smoothly immersed surface in M. In this paper we see that the space of null geodesics N of M, considered as a contact manifold, provides a natural setting for an efficient study of the stable singularities arising in the time evolution of wave-fronts.
Integral equation formulation of the spinless Salpeter equation
Authors: Brau F.
Published: July 2002

The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. These kinds of equations are well known and can be more easily handled. We also present some analytical results concerning the spinless Salpeter equation and the action of the square-root operator.
Miura transformation between two non-linear equations in 2+1 dimensions
Authors: Cerveró J. M. , Estévez P. G.
Published: July 2002

A Dispersive Wave equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave equation (GLDW). Using Singularity Analysis and techniques based upon the Painlevé Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW equation into the GLDW equation. Through this Miura transformation we shall also present the Lax pair of the 2LDW equation as well as some interesting reductions to several already known integrable systems in 1+1 dimensions. As the 2LDW equation arises from a Miura transformation we propose that it should be treated conventionally as a Modified Equation. In this case, we propose its designation as The MGLDW Equation.
Symbolic calculus on the time-frequency half-plane
Authors: Bertrand J. , Bertrand P.
Published: July 2002

This study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.
On the classification of subalgebras of the conformal algebra with respect to inner automorphisms
Authors: Barannyk L. F. , Basarab-Horwath P. , Fushchych W. I.
Published: July 2002

We give a complete justification of the classification of inequivalent subalgebras of the conformal algebra with respect to the inner automorphisms of the conformal group, and we perform the classification of the subalgebras of the conformal algebra AC(1,3).
On the representations of a Q-oscillator algebra
Authors: Guichardet A.
Published: July 2002

We give a classification of all irreducible representations of the Arik–Coon oscillator algebra without the assumption that the number operator has a discrete nondegenerate spectrum.
Symplectic gravity models in four, three and two dimensions
Authors: Kechkin Oleg , Yurova Maria
Published: July 2002

A class of the D=4 gravity models describing a coupled system of n Abelian vector fields and the symmetric n×n matrix generalizations of the dilaton and Kalb–Ramond fields is considered. It is shown that the Peccei–Quinn axion matrix can be entered and the resulting equations of motion possess the Sp(2n,R) symmetry in four dimensions. The stationary case is studied. It is established that the theory allows a σ-model representation with a target space which is invariant under the Sp[2(n+1),R] group of isometry transformations. The chiral matrix of the coset Sp[2(n+1),R]/U(n+1) is constructed. A Kähler formalism based on the use of the Ernst (n+1)×(n+1) complex symmetric matrix is developed. The stationary axisymmetric case is considered. The Belinsky–Zakharov chiral matrix depending on the original field variables is obtained. The Kramer–Neugebauer transformation, which algebraically maps the original variables into the target space ones, is presented.
On harmonic maps into gauge groups
Authors: Ding Qing
Published: July 2002

We continue the work of the paper [J. Math. Phys. 37, 4076 (1996)] on the existence of globally defined harmonic maps from the Minkowski plane R1,1 into an infinite-dimensional Hilbert Lie group. We prove that the Cauchy problem for harmonic maps from R1,1 into Hilbert loop groups Hs(LG) can be solved globally for all remaining cases 12<s⩽34 and we obtain similar results for harmonic maps from R1,1 into certain Hilbert Lie gauge groups Hs(Sn,G) (n⩾2). These answer the two questions remaining from the above paper.
A new scaling property of the Casimir energy for a piecewise uniform string
Authors: Brevik I. , Elizalde E. , Sollie R. , Aarseth J. B.
Published: July 2002

An unexpected and very accurate scaling invariance of the Casimir energy of the piecewise uniform relativistic string is pointed out. The string consists of 2N pieces of equal length, of alternating type I/type II material, endowed with different tensions and mass densities but adjusted such that the velocity of transverse sound equals c. If EN(x) denotes the Casimir energy as a function of the tension ratio x=TI/TII, it turns out that the ratio fN(x)=EN(x)/EN(0), which lies between zero and one, will be practically independent of N for integers N⩾2. Physical implications of this scaling invariance are discussed. Finite temperature theory is also considered.
Rectangular well as perturbation
Authors: Dudek Mariusz , Giller Stefan , Milczarski Piotr
Published: July 2002

We discuss a finite rectangular well of a depth λ2 as a perturbation for the infinite one with λ as a perturbation parameter. In particular, we consider a behavior of energy levels in the well as functions of complex λ. It is found that all the levels of the same parity are defined on infinitely sheeted Riemann surfaces whose topological structures are described in detail. These structures differ considerably from those found in models investigated earlier. It is shown that perturbation series for all the levels converge what is in a contrast with the known results of Bender and Wu. The last property is shown to hold also for the infinite rectangular well with the Dirac delta barrier as a perturbation considered earlier by Ushveridze.
Transfer matrices for scalar fields on curved spaces
Authors: Prodan E.
Published: July 2002

We apply Nelson’s technique of constructing Euclidean fields to the case of classical scalar fields on curved spaces. It is shown how to construct a transfer matrix and, for a class of metrics, the basic spectral properties of its generator are investigated. An application concerning the decoupling of a nonconvex disjoint region is given.
Static Bondi energy in the teleparallel equivalent of general relativity
Authors: Maluf J. W. , da Rocha-Neto J. F.
Published: July 2002

We consider Bondi’s radiating metric in the context of the teleparallel equivalent of general relativity (TEGR). This metric describes the asymptotic form of a radiating solution of Einstein’s equations. The total gravitational energy for this solution can be calculated by means of pseudotensors in the static case. In the nonstatic case, Bondi defines the mass aspect m(u), which describes the mass of an isolated system. In this paper we express Bondi’s solution in asymptotically spherical 3+1 coordinates, not in radiation coordinates, and obtain Bondi’s energy in the static limit by means of the expression for the gravitational energy in the framework of the TEGR. We can either obtain the total energy or the energy inside a large (but finite) portion of a three-dimensional spacelike hypersurface, whose boundary is far from the source.
Quantum description of rigidly or adiabatically constrained four-particle systems and supersymmetry
Authors: Baloı̈tcha E. , Hounkonnou M. N.
Published: July 2002

A general formalism for the quantum description of many-body systems is developed, using the principal-axis hyperspherical parametrization of coordinates. This formalism is applied to four-particle systems for which the exact kinetic energy operator is derived using a model constraints and dynamical constraints. Then, using the supersymmetry and shape invariance approach, we obtained in a closed form the eigenvalues and eigenfunctions of a wide class of noncentral potentials for the adiabatically constrained four-particle systems.
A new type of loop independence and SU(N) quantum Yang–Mills theory in two dimensions
Authors: Fleischhack Christian
Published: July 2002

The expectation values of Wilson loop products for the pure Euclidean Yang–Mills theory on R×R given by Ashtekar et al. in the article “SU(N) Quantum Yang–Mills Theory in Two Dimensions: A Complete Solution” [J. Math. Phys. 38, 5453 (1997)] are determined directly for all piecewise analytic loops. For that purpose we enlarge their calculations from quadratic lattices to general floating lattices introducing a new kind of loop independence and slightly modifying the regularization scheme.
Green’s function for the five-dimensional SU(2) MIC–Kepler problem
Authors: Pletyukhov M. V. , Tolkachev E. A.
Published: July 2002

The Green’s function for the five-dimensional counterpart of the MIC–Kepler problem [Kepler potential plus SU(2) Yang–Mills instanton plus Zwanziger-like 1/R2 centrifugal term] is constructed on the basis of the Green’s function for the eight-dimensional harmonic oscillator.
Single point interactions, quantization by parts, and boundary conditions
Authors: Trueman Colin , Wan K. K.
Published: July 2002

Traditionally point interaction problems in quantum mechanics are treated in the physics literature by solving the Schrödinger equation containing an appropriate potential term. In this paper we discuss a systematic quantization scheme, known as the method of quantization by parts, which provides a general method for dealing with single point interactions in one dimension, namely by reducing the problem to boundary conditions. Our method can also be applied to superconducting systems like those concerning Josephson and the recently discovered π-junctions, and single electron circuit systems.
Contraction of superintegrable Hamiltonian systems
Authors: Calzada Juan A. , Negro J. , del Olmo Mariano A. , Rodrı́guez Miguel A.
Published: July 2002

We investigate the contraction of a class of superintegrable Hamiltonians by implementing the contraction of the underlying Lie groups. We also discuss the behavior of the coordinate systems that separate their equations of motion, the motion constants, as well as the corresponding solutions along such a process.
A comparison of internal energy calculation methods for diatomic molecules
Authors: Liu Yen , Shakib Farzin , Vinokur Marcel
Published: July 2002

Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schrödinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasibound states is presented. For N2 molecules, all vibrational–rotational states of 11 available electronic potentials are computed and summed to obtain the exact internal energy function with temperature. The total computation required 314 sec of CPU time on NASA’s Cray 2 computer. Various approximate models are discussed and compared with exact calculations. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.
On boundary conditions for velocity potentials in confined flows: Application to Couette flow
Authors: Marqués Francisco
Published: July 2002

The representation of solenoidal fields by means of two scalar potentials can be a very useful method for a wide range of problems, in particular for the incompressible Navier–Stokes equations, though in finite containers boundary conditions may not be easily handled. The differential equations for the potentials are of an order higher than the original Navier–Stokes ones. As a consequence additional boundary conditions are needed to solve them. These differential equations and the corresponding boundary conditions for any geometry have been derived and the equivalence with the original problem has been proved. Special emphasis has been laid on domains with nontrivial geometry in which integral boundary conditions appear. As an example, the results have been applied to the periodic Couette flow. In this case the integral boundary conditions can be avoided by an appropriate change of variables, hence reducing the order of the equations obtained.
Vortex motion, sound radiation, and complex time singularities
Authors: Kimura Yoshifumi , Zawadzki Ireneusz , Aref Hassan
Published: July 2002

The equations of motion for interacting point vortices can be embedded in a system of ordinary differential equations with polynomial couplings and thus subjected to the ‘‘Painlevé test’’ for integrability. The arrays of singularities produced by this analysis confirm well known results on integrability and chaos in few-vortex systems, and are shown by further numerical experiments to predict qualitative features of the low Mach number sound radiation from the vortex system. The correspondence between singularity distribution, vortex trajectory pattern, time series of far-field pressure, and sound spectrum are illustrated and discussed based on a parametric numerical survey of some simple three- and four-vortex motions. The results suggest a physical interpretation of the Painlevé singularities.
Dynamics of fluid mixing in separated flows
Authors: Leder A.
Published: July 2002

The dynamics of the flow in the separated region and near wake of a vertical flat plate was analyzed with the phase-locked laser-Doppler technique at Reynolds number Re=2.8×104. The flow exhibits an intense quasiperiodic component at a Strouhal frequency of St=0.14. The vortex shedding process was resolved into six phases, resulting in a time difference between consecutive phases of Δt=0.02 sec. Interactions between the free shear layers, emanating from the model edges, lead to nonlinear dynamics of the flow. The distributions of the Reynolds stresses indicate that maximal amplitudes in the normal stresses 〈u′2〉 and 〈v′2〉 as well as in the shear stress term 〈u′v′〉 are provoked by positive pressure gradients in the shear layer flows upstream of saddle points. Saddles are quasiperiodically formed by interactions between the two free shear layers. Regions with enhanced Reynolds stresses and saddles are convectively transported within the flow field.
A branching liquid jet
Authors: Lin S. P. , Woods D. R.
Published: July 2002

A new phenomenon of successive branchings of a liquid jet injected from a nozzle into the atmosphere is reported. It is observed that an intact jet can be made to bifurcate successively into a two-, three-, and multiple-pronged jet by oscillating the nozzle along its axis at a successively higher critical frequency. While the two- and three-pronged jets are found to be structurally stable in certain frequency ranges, the different branches in a multiple-pronged jet appear to merge and split among themselves chaotically without any discernible periodicity.
Similarity transformation of the Boltzmann equation
Authors: Nishitani Toshiyuki
Published: July 2002

A kind of similarity transformation is considered for the nonlinear Boltzmann equation with an external force term. The equation is reduced by the transformation to the Boltzmann equation without the external force term and without spatial variables as well. Some exact solutions of the Boltzmann equation having an external force term are derived by applying the present transformation to the solution obtained by Bobylev [Sov. Phys. Dokl. 20, 820 (1976)], and Krook and Wu [Phys. Rev. Lett. 36, 1107 (1976); Phys. Fluids 20, 1589 (1977)].
Stabilizing and destabilizing effects of a solid-body rotation on quasi-two-dimensional shear layers
Authors: Lesieur Marcel , Yanase Shinichiro , Métais Olivier
Published: July 2002

The effect of a solid-body rotation, characterized by an angular velocity Ω, on a two-dimensional mixing layer (in a plane perpendicular to Ω) of relative vorticity ω2D, upon which is superposed a small three-dimensional turbulent perturbation, is considered. Using the Kelvin theorem in the frame rotating with Ω, and with the aid of arguments based on the straining of absolute vortex filaments by the basic velocity, it is shown that the rotation is always stabilizing (with respect to the nonrotating case) in the cyclonic case. In the anticyclonic case, a slight rotation is destabilizing. At a local Rossby number R0=‖ω2D‖/2‖Ω‖ of the order of 1, the anticyclonic rotation disrupts catastrophically the coherent structures of the mixing layer. Anticyclonic rotation becomes stabilizing again for R0<0.5. Also presented are three-dimensional numerical simulations which support the theory, and agree qualitatively with experimental results. The consequences for oceanic and atmospheric vortices are briefly discussed.
Poiseuille flow driven by an external force
Authors: Alaoui M. , Santos A.
Published: July 2002

The steady planar Poiseuille flow generated by a constant external force is analyzed in the context of the nonlinear Bhatnagar–Gross–Krook kinetic equation for a gas of Maxwell molecules. An exact solution is found for a particular value of the force parameter. At a hydrodynamic level, the solution is characterized by a parabolic profile of the flow velocity with respect to a space variable scaled with the local collision frequency, a parabolic profile of the temperature with respect to the same variable, and a constant pressure. The (dimensionless) ratios between the quadratic coefficients and the external force are equal to 146 for the flow velocity and 65 for the temperature, as compared with the values 1/2 and 0, respectively, in the Navier–Stokes order. The fluxes of momentum and energy are explicitly evaluated. The anisotropy of the velocity distribution is made evident by the diagonal elements of the pressure tensor: Pyy/Pxx=0.031, Pzz/Pxx=0.081. Finally, the velocity distribution function is obtained in terms of quadratures.
Planarization during spin coating
Authors: Stillwagon L. E. , Larson R. G.
Published: July 2002

A recently proposed two-stage flow/shrinkage model of leveling (or planarization) of uneven substrate topography during spin coating [Stillwagon and Larson, Phys. Fluids A 2, 1937 (1990)] is extended to account qualitatively for solvent evaporation. In the first, or flow, stage of the model, the film profile over a feature is assumed to be controlled by a balance of centrifugal and capillary forces within the lubrication approximation. This stage persists until solvent evaporation makes the film viscous enough that fluid rearrangement over a substrate feature is no longer possible. In the second, or shrinkage, stage, the film shrinks without flow by further evaporative drying. The transition between the two stages is assumed to occur abruptly at a polymer concentration φp1. This model is tested in spin coating studies with a series of polystyrene solutions spun on substrates with ideal trenchlike features, where the polymer molecular weight, the initial polymer concentration φp0, the spinning speed ω, the trench width w, and the radial distance r0 of the trench from the center of the substrate are varied. It is found that, except at low polymer concentrations, the model correctly predicts the dependence of the planarization on a dimensionless spinning speed proportional to ω2w3r0, and correctly predicts that φp1 is independent of spinning speed ω, but dependent on polymer concentration and on the ratio r0/w. The dependence of φp1 on initial polymer concentration and molecular weight correlates reasonably well with theoretical predictions, if a single fitting parameter is allowed.
Magnetohydrodynamic stability of cylindrical liquid bridges under a uniform axial magnetic field
Authors: Nicolás J. A.
Published: July 2002

The effect of a uniform axial magnetic field on the stability of cylindrical liquid bridges of negligible viscosity and resistivity is examined in this paper, in the limit case when magnetic forces dominate inertia forces. The analysis yields the bifurcation curve and the growth factor in the neighborhood of the stability limit points as a function of two dimensionless parameters: Λ, the slenderness of the bridge and M, a nondimensional quantity proportional to the magnetic field. It is found that bridges of any slenderness can be stabilized by magnetic fields when M≳1/√2. The results are compared to those existing for capillary liquid jets, showing that the stability curves coincide and that the stabilizing effects are greater for liquid bridges than for infinite columns.
Behavior of turbulence in the near wake of a thin flat plate at low Reynolds numbers
Authors: Hayakawa Michio , Iida Sei-ichi
Published: July 2002

Conventional hot-wire measurements have been made in the turbulent developing wake of a thin flat plate. The data obtained are primarily concerned with turbulence characteristics in the near-wake region. Turbulence properties in the inner wake first increase up to a streamwise distance of 200–300 times the initial wall-layer length scale, followed by a gradual decay farther downstream. The mechanism of this overshoot phenomenon is inferred from space-time correlation data. Quasiperiodic motion similar to that in the far wake is observed as early as near the end of the near wake.
The steady thermocapillary-driven motion of a large droplet in a closed tube
Authors: Wilson S. K.
Published: July 2002

In this paper the steady thermocapillary-driven motion of a large fluid droplet in a closed tube subject to a constant temperature gradient in both two and three dimensions is analyzed. In particular, expressions are obtained for the velocity of the droplet in both cases. An error in the work of Hasan and Balasubramaniam [J. Thermophys. 3, 87 (1989)], who solved the same problem in the special case of an inviscid droplet, is identified and corrected.
Some asymmetric Stokes flows that are structurally similar
Authors: Davis A. M. J.
Published: July 2002

This paper considers the creeping flows generated by a disk moving edgewise parallel to a rigid wall or free surface, a disk oscillating edgewise in unbounded fluid and a hole in the rigid plane that bounds a shear flow excited by a parallel moving plane. The analyses for the three cases follow a similar pattern and several simplifying strategies are introduced to obtain significant improvements on the presentations suggested by previous work on such flows. Indeed, the resulting integral equations for the first disk problem are similar to those solved for the corresponding broadside motion. The drag force is shown to slowly approach its limit value as the disk is placed nearer to the free surface. The oscillatory hydrodynamic force is shown to have only Stokes and Basset components. The error in previously assuming the shear flow to extend to infinity is shown to be of order H−3, where H is the separation distance between the bounding planes.
Damping of lower hybrid waves by low-frequency drift waves
Authors: Krall Nicholas A.
Published: July 2002

The conditions under which a spectrum of lower hybrid drift waves will decay into low-frequency drift waves (LFD) are calculated. The purpose is to help understand why lower hybrid drift waves are not seen in all field-reversed configuration (FRC) experiments in which they are predicted. It is concluded that if there is in the plasma a LFD wave amplitude above a critical level, lower hybrid waves will decay into low-frequency drift waves. The critical level required to stabilize TRX-2 [Phys. Fluids 30, 1497 (1987)] is calculated and found to be reasonably consistent with theoretical estimates.
The Pierce diode with an external circuit. II. Chaotic behavior
Authors: Lawson William S.
Published: July 2002

The existence of the strange attractor discovered by Godfrey [Phys. Fluids 30, 1553 (1987)] in the neighborhood of α=3π for the Pierce diode is verified, and his numerical results are refined. The theory of Feigenbaum for the sequence of period-doubling bifurcations [J. Stat. Phys. 19, 25 (1975)] is tested with good agreement, despite the strong assumptions made by that theory. The evolution of this attractor is then followed as an external capacitance is introduced, producing a family of bifurcation diagrams. Examination of these diagrams produces one result that should be of interest to mathematical physicists: The existence of an unstable equilibrium in the neighborhood of the strange attractor is strongly implicated in both the existence and destruction of the attractor. The reversibility of the equations of evolution is also discussed, but no clear-cut conclusion is reached.
Theory of neoclassical pressure-gradient-driven turbulence
Authors: Kwon O. J. , Diamond P. H. , Biglari H.
Published: July 2002

The nonlinear evolution and saturation of neoclassical pressure-gradient-driven turbulence (NPGDT), evolving from linearly unstable bootstrap-current modes, are investigated. The theoretical model is based on ‘‘neoclassical magnetohydrodynamic (MHD) equations’’ that are valid in the banana-plateau regimes of collisionality. Modes with poloidal wavelengths shorter than radial wavelengths are shown to be suppressed. From nonlinear saturation conditions, the turbulent pressure diffusivity is determined as an eigenvalue of the renormalized equations. Levels and radial scales of turbulence are determined from the pressure diffusivity and are shown to exceed mixing-length estimates by powers of a nonlinear enhancement factor. The problem of the electron heat transport resulting from stochastic magnetic fields driven by NPGDT is revisited. The reconsideration of the radial structure of magnetic flutter leads to estimates of the electron heat transport and magnetic fluctuation levels that differ qualitatively and quantitatively from previous calculations.
Time-dependent sheath response to abrupt electrode voltage changes
Authors: Calder A. C. , Laframboise J. G.
Published: July 2002

Results are presented of particle simulations of the time-dependent behavior of the plasma sheath surrounding an electrode whose potential is abruptly changed from 0 to some positive value. The surrounding plasma is assumed isotropic and collisionless and the electrode is a sphere or infinite cylinder. Potential steps in the range 10 to 104kT/e are considered. The transient behavior of the collected electron current is examined. For small (≲25kT/e) potential steps, the current quickly settles to a value consistent with existing static probe theory. Persistent Langmuir oscillations launched by larger potential steps significantly perturb the collected current, with the result that static probe theory predictions are in some cases exceeded for times as long as 1000ω−1p after the step. Trapping of electrons during all or part of an oscillation cycle is evident in many cases. The oscillations themselves are examined and evidence for beating between modes at ωp and at the sheath–plasma parallel resonance frequency is discussed. In some cases, the oscillations are driven to large amplitudes by the ion–electron two-stream instability.
Three-dimensional numerical simulations of simple electron drift wave turbulence in a sheared and curved magnetic field
Authors: Waltz R. E.
Published: July 2002

A three-dimensional code is used to study the scaling of an electrostatic electron drift wave turbulence with respect to shear and curvature of the magnetic field as well as the driving strength. The electrons are modeled with a simple formula for the deviation from a near Boltzmann response and the ions are modeled as a nonlinear fluid. For sheared slab geometry suppressing curvature (or toroidal) effects, the turbulence level and transport scale according to the mixing length rules with the mixing length given by the linear normal mode widths and the poloidal wavelengths scaled to the ion gyroradius. Toroidal coupling results in a more complex behavior. Some evidence for nonlocal or convective turbulence effects is found.
Near-surface sputtered particle transport for an oblique incidence magnetic field plasma
Authors: Brooks J. N.
Published: July 2002

Near-surface sputtered particle transport has been analyzed numerically using models of sputtering, sheath parameters, and impurity collisions with a background D–T plasma. Tungsten and carbon sputtering was examined, for tokamak divertor plasma conditions. Redeposited ion parameters computed include the charge state, transit time, energy, and angle of incidence. A regime of operation for finite self-sputtering of tungsten has been identified. This regime is broader than previous estimates. Results for energetically sputtered and thermally sputtered carbon are compared.
The bootstrap current in stellarators
Authors: Boozer Allen H. , Gardner Henry J.
Published: July 2002

A method of calculating the bootstrap current in asymmetric devices, such as the stellarator, is developed. The features that determine the bootstrap current are the variation of the magnetic-field strength within a magnetic surface and the rotational transform. The shape of the magnetic surfaces is shown to be irrelevant. If the fraction of trapped particles is small, the device dependence of the bootstrap current is determined by a single constant which can be calculated by integrations of the field strength along the field lines. The relative dependence of the bootstrap current on the density and the temperature gradients is the same in any device with a small fraction of trapped particles as in a large aspect ratio tokamak.
Plasma evolution from laser-driven gold disks. I. Experiments and results
Authors: Gabl E. F. , Failor B. H. , Busch Gar. E. , Schroeder R. J. , Ress D. , Suter L.
Published: July 2002

Gold disk targets were irradiated with green (λ=0.53 μm) laser light at intensities between 0.5 and 5×1014 W/cm2 using shaped laser pulses. Plasma conditions near and below critical density (nc≂4×1021/cm3) were determined from three diagnostics. Streaked one-dimensional images of the M-band emission (2–3.5 keV) along the laser axis yield the peak emission trajectory. Temporally and spatially averaged measurements of the hard x-ray spectrum (4–25 keV) were used to determine the average coronal electron temperature. Holographic interferometry was used to determine the electron density profiles and scale lengths along the laser axis. The peak emission trajectory, electron temperature, and scale lengths are all in good agreement with simulations, but the magnitudes of the electron density profiles are not, as discussed in an accompanying paper [Phys. Fluids B 2, 2448 (1990)].
Effects of compressibility, diamagnetic drift, and thermal conduction on resistive ballooning modes in the second stability regime
Authors: Kim Jin-Yong , Choi D.-I. , Van Dam J. W. , Horton W.
Published: July 2002

The stabilizing effects of various terms such as compressibility, diamagnetic drift, and parallel thermal conduction are investigated on the type of resistive ballooning modes whose driving force comes from the resistive region, which are known to be unstable in the high-beta second stability regime when analyzed in the incompressible limit. It is found that compressibility gives a significant stabilizing effect mainly through the perpendicular magnetic compression, which suggests the possibility of a second stable window for these resistive ballooning modes. The diamagnetic drift terms slightly reduce the growth rate in the incompressible limit, but, with finite compressibility, lead to fairly strong stabilization. The compression due to ion polarization, which becomes significant at large diamagnetic drift, contributes to this stabilization. On the other hand, parallel thermal conduction and perpendicular magnetic compression, which enter through the equation for temperature evolution, are shown to have a negligible effect on the stability of these modes.
Experiments on Korteweg–de Vries solitons in a positive ion–negative ion plasma
Authors: Cooney Jamie L. , Gavin Matthew T. , Lonngren Karl E.
Published: July 2002

Experiments on the propagation of ion acoustic solitons that propagate in a positive ion–negative ion plasma are described. The solitons are launched from a solid metal disk to which a small negative step voltage [Δφ≊−2(Te/e) V] is applied. The mechanism for the excitation of the soliton, the identification of the fast and the slow modes in such a plasma, and the observation of a transient sheath are presented.
Production of very large, sub-tenth-critical plasmas for laser-fusion research
Authors: Batha S. H. , Montgomery D. S. , Drake R. P. , Estabrook Kent , Remington B. A.
Published: July 2002

The development of a plasma environment that is appropriate for the study of low-gain processes in laser-fusion plasmas is reported. These plasmas have long scale lengths, low densities, and no quarter-critical or critical-density surfaces. The plasmas were created by two-sided irradiation of CH foils with 15 kJ of 351 nm laser light. When the peak electron density in the plasma had decayed to about 2×1020 cm−3, the parabolic density profile was estimated to have a full width at half-maximum of 3 mm and the electron temperature was estimated to be 1 keV. Probe lasers of different wavelengths were used to measure the peak electron density via stimulated scattering processes and odd half-harmonic generation. Sufficiently accurate modeling of the laser-irradiation conditions led to improved agreement between the experiment and two-dimensional (2-D) computer simulations.