bluuebunny/crossref_metadata_2025 huggingface dataset:
Eigenvalue distribution of large dilute random matrices
Authors: Khorunzhy A. , Rodgers G. J.
Published: July 2002

We study the eigenvalue distribution of dilute N×N random matrices HN that in the pure (undiluted) case describe the Hopfield model. We prove that for the fixed dilution parameter a the normalized counting function (NCF) of HN converges as N→∞ to a unique σa(λ). We find the moments of this distribution explicitly, analyze the 1/a correction, and study the asymptotic properties of σa(λ) for large |λ|. We prove that σa(λ) converges as a →∞ to the Wigner semicircle distribution (SCD). We show that the SCD is the limit of the NCF of other ensembles of dilute random matrices. This could be regarded as evidence of stability of the SCD to dilution, or more generally, to random modulations of large random matrices.
Constrained quantization on symplectic manifolds and quantum distribution functions
Authors: Jorjadze G.
Published: July 2002

A quantization scheme based on the extension of phase space with application of constrained quantization technique is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar product on the reduced Hilbert space is investigated and a possible solution to this problem is given. Generalization of the Gupta–Bleuler-like conditions is done by minimization of quadratic fluctuations of quantum constraints. The scheme for the construction of generalized coherent states is considered and relation with Berezin quantization is found. The quantum distribution functions are introduced and their physical interpretation is discussed.
An algebraic algorithm for calculating Clebsch–Gordan coefficients; application to SU(2) and SU(3)
Authors: Rowe D. J. , Repka J.
Published: July 2002

A recent paper gave an explicit construction for inducing shift tensors of a compact reductive Lie group from shift tensors of a suitably defined subgroup. The shift tensors were defined on model spaces of holomorphic vector-coherent-state wave functions. In this paper, we use these shift tensors to obtain an algorithm for computing Clebsch–Gordan coefficients. The approach reproduces the known analytical results for SU(2) and gives a simple algorithm for computing SU(3) coefficients. The algorithm is shown to yield analytical expressions for the multiplicity-free SU(3) couplings of type (λ20)⊗(λ10).
Reduction formula for moments of stochastic integrals
Authors: Bertini L. , Cancrini N.
Published: July 2002

We show how moments of stochastic integrals can be expressed explicitly as expectation values of ordinary Lebesgue integrals. This result generalizes the well known relationship for the second moment.
Zeta function regularization in de Sitter space: The Minkowski limit
Authors: Chodos Alan , Kaiser András
Published: July 2002

We study an integral representation for the zeta function of the one-loop effective potential for a minimally coupled massive scalar field in D-dimensional de Sitter space–time. By deforming the contour of integration we present it in a form suitable for letting the de Sitter radius tend to infinity, and we demonstrate explicitly for the case D=2 that the quantities ζ(0) and ζ′(0) have the appropriate Minkowski limits.
Fermionic q-Fock space and braided geometry
Authors: Majid S.
Published: July 2002

We write the fermionic q-Fock space representation of Uq(sl̂n) as an infinite extended braided tensor product of finite-dimensional fermionic Uq(sln)-quantum planes or exterior algebras. Using braided geometrical techniques developed for such quantum exterior algebras, we provide a new R-matrix approach to the Kashiwara–Miwa–Stern action of the Heisenberg algebra on the q-fermionic Fock space, obtaining the action in detail for the lowest nontrivial case [b2, b−2]=2((1−q−4n)/(1−q−4)).
Dynamics of Brownian particles in a potential
Authors: Streater R. F.
Published: July 2002

Let f(x,t) be the density of a cloud of particles, and T(x,t) the temperature at x∈Rd at time t. Let f̊∈L1(Rd)∩Lp(Rd) and T̊, measurable uniformly positive and exponentially bounded in Rd, be given. We study the coupled system ∂f/∂t=divκ(∇f+f∇V/T), ∂T/∂t=κ′∂2T/∂x2+κ∇V⋅(∇f+f∇V/T), with initial data f(x,0)=f̊(x) and T(x,0)=T̊(x). We show that there is a unique solution for small times if the conditions p>d, ∇V∈L∞ and ΔV∈L∞ hold.
A model of continuous polymers with random charges
Authors: Buffet E. , Pulé J. V.
Published: July 2002

We study a model of polymers with random charges; the possible shapes of the polymer are represented by the sample paths of a Brownian motion, and the cumulative charge distribution along a polymer is modeled by a realization of a Brownian bridge. Charges interact through a general positive-definite two-body potential. We study the infinite volume free energy density for a fixed realization of the Brownian motion; this is not self-averaging, but shows on the contrary a sample dependence through the local time of the Brownian motion. We obtain an explicit series representation for the free energy density; this has a finite radius of convergence, but the free energy is nevertheless analytic in the inverse temperature in the physical domain.
Riemannian space-times of Gödel type in five dimensions
Authors: Rebouças M. J. , Teixeira A. F. F.
Published: July 2002

The five-dimensional (5D) Riemannian Gödel-type manifolds are examined in light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by two essential parameters m2 and ω: identical pairs (m2,ω) correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian Gödel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that apart from the (m2=4ω2,ω≠0) and (m2≠0,ω=0) classes the homogeneous Riemannian Gödel-type manifolds admit a seven-parameter maximal group of isometry (G7). The special class (m2=4ω2,ω≠0) and the degenerated Gödel-type class (m2≠0,ω=0) are shown to have a G9 as maximal group of motion. The breakdown of causality in these classes of homogeneous Gödel-type manifolds are also examined.
Algebraic solutions for point groups: The tetrahedral group for the group chain T⊃D2⊃C2
Authors: Chen Jin-Quan , Fan Peng-Dong
Published: July 2002

A factorization lemma is discovered for the irreducible symmetry operators (ISO’s) of a semidirect product group of two abelian groups. By means of it, simple algebraic expressions of the T⊃D2 single-valued irreducible matrices, ISO’s and symmetry adapted functions are derived. Using the double-induced technique, the algebraic solutions for the double-valued representations of group T in the group chain T⊃C2 are also obtained. The simplicity and elegance of the algebraic solution of the point group can be compared with that of the analytic solution of the rotation group.
Expansion of the hydrogen-like wave functions in the inverse principal quantum number, for the discrete and continuous spectra
Authors: Blaive Bruno , Cadilhac Michel
Published: July 2002

An expansion with respect to the inverse principal quantum number n−1 has been derived recently for the hydrogen-like wave functions of the discrete spectrum. The basic functions of this expansion were Bessel functions multiplied by a power rk of the distance r to the origin. We show that this expansion remains valid for the continuous spectrum, with minor changes. For the wave function corresponding to the energy E=+1/(2n2) a.u. of the continuum, the pure imaginary number −in (positive real n) must be substituted for the integer n in the expansion for the discrete spectrum, and a normalizing factor must be introduced.
SU(2) quantum kinematics: Rotation-observable versus angular-momentum generalized commutation relations
Authors: Krause J.
Published: July 2002

The canonical commutation relations of quantum mechanics are generalized to the case where appropriate dynamical variables are angular-momentum, rotation-angle, and rotation-axis observables. To this end, SU(2) is “quantized” on the compact group manifold, according to the standard procedure of non-Abelian quantum kinematics. Quantum-kinematic invariant operators are introduced, and their commutation relations with the rotation variables are found in an explicit manner. The quantum-kinematic invariants yield superselection rules in the form of eigenvalue equations of an isotopic structure (which one should solve in the applications, in order to get multiplets that carry the irreducible representations of the underlying quantum kinematic models). A wide range of applicability of SU(2) quantum kinematics is suggested.
Instability of a pseudo-relativistic model of matter with self-generated magnetic field
Authors: Griesemer Marcel , Tix Christian
Published: July 2002

For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant. This is true no matter whether this interaction is accounted for by the Breit potential, by an external magnetic field which is chosen to minimize the energy, or by the quantized radiation field.
Darboux method and search of invariants for the Lotka–Volterra and complex quadratic systems
Authors: Cairó Laurent , Feix Marc R. , Llibre Jaume
Published: July 2002

The Darboux method introduces algebraic solutions quite useful to obtain invariant and first integrals of polynomial differential systems. Here we study the 2D Lotka–Volterra (LVS) and the complex quadratic system (QS) using straight lines for both and conics for the LVS. The conditions needed to obtain these invariants are given and a study of the phase space portrait is done.
Weyl anomaly in higher dimensions and Feynman rules in coordinate space
Authors: Ichinose Shoichi , Ikeda Noriaki
Published: July 2002

An algorithm to obtain the Weyl anomaly in higher dimensions is presented. It is based on the heat-kernel method. Feynman rules, such as the vertex rule and the propagator rule, are given in (regularized) coordinate space. A graphical calculation is introduced. The six-dimensional scalar-gravity theory is taken as an example, and its explicit result is obtained.
Attractors for the Klein–Gordon–Schrödinger equation
Authors: Wang Bixiang , Lange Horst
Published: July 2002

In this paper we deal with the asymptotic behavior of solutions for the Klein–Gordon–Schrödinger equation. We prove the existence of compact global attractors for this model in the space Hl×Hl×Hl−1 for each integer l⩾1.
Anisotropic fluid spherically symmetric space–times admitting a kinematic self-similarity
Authors: Benoit Patricia M. , Coley Alan A.
Published: July 2002

Anisotropic fluid spherically symmetric space–times admitting a kinematic self-similar vector are investigated. The geodesic case is considered, and some special subcases in which the anisotropic fluid satisfies additional physical conditions are investigated in detail. A number of other special cases are studied. Particular attention is focused on the possible asymptotic behavior of the models, and it is shown that the models considered always asymptote towards an exact homothetic solution, which is in general either a perfect fluid model or a static solution.
SU
(N)
- and SO(N)-invariant chiral fields: One- and two-dimensional subspaces
Authors: Matos Tonatiuh , Nucamendi Ulises , Wiederhold Petra
Published: July 2002

Applying the harmonic map ansatz we find new classes of SU(N) and SO(N) chiral fields. We write the corresponding one-dimensional subgroups of SU(N) and SO(N) chiral fields in terms of one and two harmonic maps and the corresponding two-dimensional subgroups in terms of SU(2) and SO(3) chiral fields. In other words, we reduce the SU(N) and SO(N) chiral equations to harmonic maps in one- and two-dimensional spaces.
Comment on phase-space representation of quantum state vectors
Authors: Mo/ller Klaus B.
Published: July 2002

A simple approach to phase-space representation of quantum state vectors using the displacement-operator formalism is presented. Although the resulting expressions for the fundamental operators (position and momentum) are equivalent to those obtained by other methods, this approach provides both alternative mathematical foundation as well as physical interpretation of phase-space representation of quantum state vectors.
On the dynamics of the Holstein model from the anticontinuous limit
Authors: Bambusi Dario
Published: July 2002

We consider the Holstein model describing an electron interacting with a lattice of identical oscillators. We remark that the on site system (i.e., the system in which the interaction between the different sites of the lattice vanishes) is integrable and anisocronous. This allows us to apply some recent Nekhoroshev-type results to show that corresponding to the majority of initial data in which the electron probability is concentrated on a finite number of sites, the electron probability distribution is approximatively constant for times growing exponentially with the inverse of the coupling parameter. Moreover, for the same times, the total energy of the oscillator system is approximatively constant.
Soliton stability in a Z(2) field theory
Authors: Veerman J. J. P. , Bazeia D. , Moraes Fernando
Published: July 2002

We investigate the stability of the coupled soliton solutions of a two-component Z(2) vector field model, in contraposition to similar solutions of a Z(2)×Z(2) model recently introduced. We demonstrate that the coupled soliton solutions of the Z(2) model are classically unstable.
The spectrum of the Liouville–von Neumann operator in the Hilbert–Schmidt space
Authors: Antoniou I. , Shkarin S. A. , Suchanecki Z.
Published: July 2002

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.
Hopf algebra extension of a Zamolochikov algebra and its double
Authors: Ding Jintai
Published: July 2002

The particles with a scattering matrix R(x) are defined as operators Φi(z) satisfying the relation ∑i′,j′Ri,jj′,i′(x1/x2)Φi′(x1)Φj′(x2)=Φi(x2)Φj(x1). The algebra generated by those operators is called a Zamolochikov algebra. We construct a new Hopf algebra by adding half of the Faddeev–Reshetikhin–Takhtajan–Semenov-Tian-Shansky (FRTS) construction of a quantum affine algebra with this R(x). Then we double it to obtain a new Hopf algebra such that the full FRTS construction of a quantum affine algebra is a Hopf subalgebra inside. Drinfeld realization of quantum affine algebras is included as an example.
Nonlinear Hamiltonian equations with fractional damping
Authors: Seredyńska M. , Hanyga A.
Published: July 2002

Existence and uniqueness are proved for a class of Hamiltonian nonlinear differential equations of second order with a Caputo fractional derivative of order λ∈]0,2[. For noninteger λ the rate of convergence of solutions to a critical point is algebraic. For 0<λ⩽1 a non-negative dissipation function is constructed. For λ=2 the equation is Hamiltonian. The solution is an analytic function of λ for 0<λ<1 and for 1<λ<2. Numerical studies of nonlinear pendulum and the Duffing equation with a fractional derivative term replacing the usual damping show striking differences between ordinary differential and fractional differential equations.
A particle-field Hamiltonian in relativistic quantum electrodynamics
Authors: Arai Asao
Published: July 2002

We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F≔[⊕4L2(R3)]⊗Frad, where Frad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a deformation parameter connecting the Hamiltonian with the “dipole approximation” (τ=0) and the original Hamiltonian (τ=1). We first discuss the self-adjointness problem of Hτ(V,g). Then we consider Hτ≔Hτ(0,g), the Hamiltonian without the external potential. It is shown that, under a general condition on g, the closure of Hτ is unitarily equivalent to a direct integral ∫R3⊕Hτ(p)¯dp with a fiber Hamiltonian Hτ(p) acting in the four direct sum ⊕4Frad of Frad, physically the polaron Hamiltonian of the Dirac particle with total momentum p∈R3.
New electromagnetic bound states
Authors: Reitz John R. , Mayer Frederick J.
Published: July 2002

We formulate a Dirac Hamiltonian for an electron in the field of a charged magnetic dipole, which can be solved exactly in a central field approximation. While we find no scattering resonances, we do find three categories of bound-state solutions for this Hamiltonian which may represent new electron/positron states or possible new electromagnetic composites. One category of solution is a state with very strong binding energy (greater than the electron rest mass) but with only a small amount of kinetic energy. This state corresponds to a classical orbit picture in which the electric and magnetic forces are opposed and are almost balanced. No bound states are found if the central magnetic dipole is uncharged.
The U(1)-invariant field theories with normal field operators
Authors: Śniady Piotr , Zygmunt Marcin
Published: July 2002

In this paper we consider a very general U(1)-invariant field theory such that a field operator commutes with its adjoint, that corresponds to a theory of a charged bosonic particle. We show that from such an invariance follows the existence of particles and antiparticles associated with the same physical state. The field operator always turns out to be the sum of a particle creation and an antiparticle annihilation operator. We study in detail the case when creation and annihilation operators factorize and show that such operators are closely related to q-deformed commutation relations.
Transition from strong to weak electron localization in a percolating gold film under the influence of an electric field
Authors: Belevtsev B. I. , Belyaev E. Yu. , Komnik Yu. F. , Kopeichenko E. Yu.
Published: July 2002

The low-temperature (0.5–55 K) conductivity of a semicontinuous gold film near the percolation threshold is studied. It is found that the film resistance is very sensitive to the applied voltage U. By varying U, the film can be reversibly transformed from the insulating to the metallic type conductivity. This makes it possible to study the metal–insulator transition (MIT) by tuning the electric field. For low U⩽0.05 V, the film behaves as an insulator with the sheet resistance R□ up to 10 MΩ. In this state, the dependences R(T)∝exp(1/T) (for T⩽20 K) and R(U)∝exp(1/U) (for T⩽1 K and U>0.1 V) are observed. At high voltages (U≃10 V), the film has the resistance R□≃5 kΩ and behaves like a “dirty” metal. The magnetoresistance (MR) in the metallic state is positive and corresponds to the weak localization effect. In the insulating state, the MR is negative and is described by the formula ΔR(H)/R(0)∝−H2/T. The negative MR manifests itself for nearest-neighbor hopping. Such behavior is unusual, and its nature is unclear. The dependences of resistance on temperature, voltage, and magnetic field as well as the general nature of the observed MIT are considered on the basis of the obtained results.
Deviations from the classical Kolmogorov theory of the inertial range of homogeneous turbulence
Authors: Yakhot Victor , She Zhen-Su , Orszag Steven A.
Published: July 2002

Deviations from classical scaling behavior are shown to result in flattened energy and dissipation–fluctuation inertial-range spectra in fully developed turbulence.
Instability and fingering in a rotating Hele–Shaw cell or porous medium
Authors: Schwartz Leonard W.
Published: July 2002

The simplified mathematical model for two-phase displacement in a Hele–Shaw cell, i.e., slow flow between closely spaced parallel plates, has been extended to include effects arising from a constant rate of rotation of the system. A linear stability analysis for an initially concentric circular drop reveals that it is unstable both to translation and, depending on the rotation rate, to a number of fingering modes. The nonlinear evolution with time of two of these modes is traced using a boundary-integral numerical scheme. Ultimately, the liquid mass will break up into a number of drops. Apart from small distortion due to the Coriolis force, the patterns formed are essentially independent of both the liquid viscosity and the cell plate spacing or porous-medium permeability. Potential application areas include certain aspects of coating flows, mold filling, and a class of liquid-filled spinning projectiles with permeable packing.
Stability of a viscous liquid between sliding pipes
Authors: Preziosi L. , Rosso F.
Published: July 2002

A numerical investigation of the eigenvalue problems related to both the energy and the linear theory of stability of a Newtonian liquid between sliding pipes is presented. An enlargement of the region of nonlinear stability is shown as the radii ratio is increased. On the other hand, the flow always turns out to be linearly stable.
Direct simulation of vortex shedding in dilute gas flows past an inclined flat plate
Authors: Koura Katsuhisa
Published: July 2002

The vortex shedding in dilute gas flows past an inclined flat plate is studied using the null-collision direct-simulation Monte Carlo (DSMC) method. It is shown that the DSMC method is capable of generating large-scale vortices even for the collision-cell size considerably greater than the mean free path, provided that an average molecular number per cell is sufficiently large. There exists the cell-size effect that the vortex structure becomes more obscure and the decay length of large-scale vortices becomes shorter with an increase in the collision-cell size. The Strouhal number evaluated from the vortex shedding process for the free-stream Mach number M∞=0.7 and Knudsen number Kn∞= (1)/(60) and (1)/(200) , for which the Reynolds number Re∞=69.2 and 231, respectively, is about 0.2. It is found that large-scale vortices disappear at a rather small Mach (M∞≳2 for Kn∞= (1)/(60) ) or Knudsen (Kn∞≳0.1 for M∞=0.7) number.
Secondary fluid flow in a rotating narrow cylindrical annulus heated from the side
Authors: Kropp M. , Busse F. H.
Published: July 2002

The problem of bifurcations in the manifold of solutions for fluid flow in the narrow gap between two corotating coaxial vertical cylinders is considered in the case when one of the cylindrical walls is heated, the other is cooled. This problem can be regarded as an extension to the rotating case of the well-known problem of the flow between two parallel vertical walls kept at different temperatures. The influence of rotation modifies the mechanisms of monotonic and oscillatory instabilities and introduces a new instability. Spiraling rolls instead of axisymmetric motions describe the onset of secondary flows. The Coriolis force leads to a strong reduction of the critical Grashof number. Linear and weakly nonlinear properties of the instabilities are discussed in dependence on the rotation parameter, the Grashof number, and the Prandtl number.
Stabilization against Küppers–Lortz instability by a magnetic field
Authors: Das Supreeti , Bhattacharjee Jayanta K.
Published: July 2002

Küppers–Lortz instability is considered for a conducting fluid in an external magnetic field. It is found that the effect of the magnetic field is to stabilize the system against this instability. The angle at which the perturbing rolls grow when the instability sets in is weakly dependent on the magnetic field.
Similarity between turbulent kinetic energy and temperature spectra in the near-wall region
Authors: Antonia R. A. , Kim J.
Published: July 2002

The similarity between turbulent kinetic energy and temperature spectra, previously confirmed using experimental data in various turbulent shear flows, is validated in the near-wall region using direct numerical simulation data in a fully developed turbulent channel flow. The dependence of this similarity on the molecular Prandtl number is also examined.
The Fokker–Planck closure for turbulent molecular mixing: Passive scalars
Authors: Fox R. O.
Published: July 2002

A turbulent-molecular-mixing closure for passive scalar mixing is derived based on the theory of diffusion in layerlike lamellar structures. The closure is formulated in terms of the Fokker–Planck (FP) equation (or an equivalent stochastic differential equation), and is to be employed in conjunction with the probability density function (pdf) balance equation appearing in the pdf methods for modeling turbulent reactive flows. Like the mapping closure, the FP closure predicts a limiting Gaussian pdf for the passive scalar concentration in isotropic turbulence. In addition, the FP closure models the joint pdf of the scalar concentration and the scalar gradient and thus predicts the scalar dissipation rate. The closure predictions for the scalar rms concentration, the marginal pdf, and the joint pdf as well as other relevant statistics have been studied by Monte Carlo simulation. The shape and temporal evolution of the marginal pdf for the scalar concentration compare favorably with published results found from direct numerical simulations and from the mapping closure. Finally, unlike the mapping closure, the FP closure is shown to easily extend to the case of multiple scalar mixing.
The evolution of small-scale structures in homogeneous isotropic turbulence
Authors: Ruetsch G. R. , Maxey M. R.
Published: July 2002

Using direct numerical simulations of homogeneous isotropic turbulence, the temporal evolution of small-scale vorticity and passive scalar structures has been examined. Visualization of small-scale vorticity structures indicates a process where vortex sheets may roll up into intense vortex tubes through a Kelvin–Helmholtz-type instability. The ability of these vortex structures to mix a passive scalar has also been examined. The regions of intense scalar gradient form sheets which are found to occur in regions of persistent straining flow, such as between neighboring vortex structures of approximately equal circulation. The magnitude of vorticity of these structures is usually not large, as persistent straining is most commonly found in connection with regions of moderate vorticity. Scalar gradient sheets are also found between low intensity regions of antiparallel vorticity, which are also observed to produce persistent straining.
Nonlocal triad interactions and the dissipation range of isotropic turbulence
Authors: Domaradzki J. Andrzej
Published: July 2002

Detailed transfer functions T(k‖p,q), which express turbulent energy transfer rate to modes k caused by their nonlinear interactions with modes p and q, are analyzed using results of direct numerical simulations of homogeneous turbulence. A previously found phenomenological scaling for the functions T(k‖p,q), which brings them into a self-similar form, is used to deduce the form of the energy spectrum in the dissipation range proportional to k−2 exp(−ak) and the transfer spectrum proportional to exp(−ak). A physical mechanism of the energy transfer process consistent with the self-similarity scaling is proposed.
Pattern selection for the oscillatory onset in thermosolutal convection
Authors: Renardy Yuriko Yamamuro
Published: July 2002

A layer of fluid lies between two parallel horizontal walls and the solute concentration and temperature are higher at the bottom wall. The onset of time-periodic instability in this double diffusion problem in three dimensions is analyzed. Periodicity with respect to the hexagonal lattice is assumed. The no-slip condition is imposed at the top and bottom boundaries. There are 11 bifurcating solutions, and their stability is presented. For relatively low solutal and thermal Rayleigh numbers, the solutions are found to be unstable. For the heating of salty water, situations are presented where the standing rolls, the standing patchwork quilt, and either the standing hexagons or the standing regular triangles, may be stable.
Turbulent transport in wall-bounded flows. Evaluation of model coefficients using direct numerical simulation
Authors: Cazalbou J. B. , Bradshaw P.
Published: July 2002

The modeling of the turbulent diffusion of quantities such as the turbulent kinetic energy and its dissipation rate in the outer part of wall-bounded flows is examined with the aid of simulation data. The channel-flow data of Mansour et al. [J. Fluid Mech. 194, 15 (1988)] and those of Spalart [J. Fluid Mech. 187, 61 (1988)] for a flat-plate boundary layer with zero pressure gradient are used to examine the differences between turbulent flows with and without a free-stream edge. The ratio of the diffusivity of the above-mentioned turbulent quantities to the diffusivity of momentum is roughly constant, as assumed in most models, and little affected by the presence of the free-stream edge. However, the diffusivity ratios are found to deviate significantly from so-called ‘‘standard’’ values. Furthermore, current models for the momentum diffusivity fail badly at the edge of the boundary layer: the modeling constant Cμ used in the (k,ε) and related models exhibits a rapid rise there. In this respect, the simulation data confirm earlier experimental studies. The consequences of these findings for turbulence modeling are briefly examined.
Scale invariance and ε expansion in the RNG theory of stirred fluids
Authors: Carati D. , Chriaa K.
Published: July 2002

The influence of a ‘‘nonscale invariant’’ forcing is investigated in the renormalization group theory of stirred fluids. It is shown that such forcings introduce a free parameter in the theory. However, the difficulties inherent in the use of the ε expansion remain when the results are applied to real turbulence.
Chaotic bubbling
Authors: Tritton D. J. , Egdell C.
Published: July 2002

A short set of experiments on bubbling from a submerged orifice has been carried out to investigate whether the fact that bubbling is sometimes regular and sometimes irregular may be related to modern concepts of chaotic dynamics. A period-doubling sequence leading to chaotic behavior has been observed, followed by further developments in which intermittency of varying intermittency factor and ‘‘period-3’’ patterns are prominent.
An exact nonlinear cylindrical surface wave solution
Authors: Stenflo L. , Yu M. Y.
Published: July 2002

An exact solution for strongly nonlinear electrostatic surface waves on a cylindrical boundary of a plasma medium is presented. The effective nonlinear dielectric constant turns out to be dependent upon the geometry as well as the electric field amplitude.
Statistical mechanics of a two-field model of drift wave turbulence
Authors: Gang F. Y. , Scott B. D. , Diamond P. H.
Published: July 2002

The absolute equilibrium statistical mechanics of a two-field model of drift wave turbulence is investigated with emphasis on predicting the direction of spectral transfer, and on exploration of the role of density-potential correlation (cross-correlation) in constraining the nonlinear transfer process. The results indicate that departure from the adiabatic relation ñ/n0=eφ̃/Te allows transfer of total energy to small scales in fully developed turbulence. This prediction is in distinct contrast to intuition based on the one-field Hasegawa–Mima model [Phys. Fluids 21, 87 (1978)].
Modeling of a cylindrically expanding hydrogenlike fluorine x-ray laser
Authors: Eder D. C.
Published: July 2002

Modeling results are presented for a hydrogenlike fluorine soft x-ray amplifier experiment performed at Rutherford Appleton Laboratory [Plasma Phys. Controlled Fusion 30, 35 (1988)] in which a gain coefficient of 4.4 cm−1 was observed. Simulations using various values of the flux limiter, f (used to inhibit heat transport), and the amount of resonance absorption, RA, are compared to the experimental results. The maximum calculated gain coefficient is 2 cm−1 for f=0.1 and RA=1%. For this choice of hydrodynamic modeling parameters the dependence of gain on intensity is in qualitative agreement with the experimental data. It is shown that the experiment can be modeled adequately in one dimension by comparing to a two-dimensional calculation. The use of escape probabilities in an expanding cylindrical medium is discussed. General modeling techniques useful in modeling cylindrically symmetric systems are presented.
Effect of negative ions on stimulated Raman scattering in a plasma
Authors: Cho Guan Sik
Published: July 2002

In the linear theory of stimulated Raman scattering based on the three-fluid model, the effect of negative ions is reflected in the growth rate through simple functions of P (the relative fraction of negative ions in the number of negatively charged particles in a plasma). The Raman instability is weakened by negative ions, when the pump intensity is well above the threshold, while it is strengthened close to the threshold.
Relaxation processes in a turbulent compressible magnetofluid
Authors: Ghosh S. , Matthaeus W. H.
Published: July 2002

The compressible extensions of time asymptotic relaxation states of incompressible two-dimensional magnetohydrodynamic turbulence are studied. A polytropic equation of state is used with viscous and resistive dissipation. The incompressible case is known to allow three distinct time asymptotic types of behavior: magnetic energy dominated relaxation, kinetic energy dominated relaxation, and cross helicity dominated relaxation. At low Mach numbers the incompressible scenario is reproducible from the compressible simulations, and compressibility plays only a secondary role. At moderate, but still subsonic, Mach numbers the distinct incompressible processes are still recognizable, but strong compressibility features dominate the high-wave-number regime of several simulations. In particular, the magnetic and kinetic energy dominated simulations display regions of strong acoustic turbulence near the dissipation scale.
Conversion of laser light into soft x rays. Part I: Dimensional analysis
Authors: Sigel R. , Eidmann K. , Lavarenne F. , Schmalz R. F.
Published: July 2002

The conversion of laser light into soft x rays by irradiation of a high-Z material is theoretically investigated for open, planar geometry. The material may be subdivided into a hot, low-density conversion layer, optically thin for the x rays, and a dense, optically thick reemission zone. The two layers are coupled through radiation only. Dimensional analysis yields asymptotic expressions for the x-ray conversion efficiency and the reemission coefficient and hence for the total converted flux from the target.
Effects of a nonuniform equilibrium electric field on ion temperature gradient instabilities
Authors: Migliuolo S. , Sen A. K.
Published: July 2002

A nonuniform equilibrium electric field oriented in the direction perpendicular to the magnetic field, and parallel to the density and temperature gradients, is considered. The effects of electric field gradients on the behavior of ion temperature gradient instabilities are examined. Electrostatic modes are considered in the local approximation for a shearless slab geometry, with phase velocities much lower than the characteristic electron thermal speed. The adiabatic response of electrons to the perturbing potential precludes the existence of Kelvin–Helmholtz (driven by velocity shear) and Rayleigh–Taylor (driven, e.g., by a centrifugal acceleration) instabilities. The velocity shear, caused by the nonuniform equilibrium electric field, has two principal effects. The first, proportional to the gradient of the velocity shear, causes both the well-known finite Larmor radius (FLR) modification to the E×B drift, as well as distortions of the particle unperturbed orbits. The second, proportional to both first and second spatial derivatives of the E×B drift velocity, shifts the cyclotron frequency, thereby modifying the effective FLR parameter, k⊥ ρi. Generally, electric field profiles with a positive second derivative in x (the radial coordinate in a slab geometry) have a stabilizing influence.
Two-dimensional compressible magnetohydrodynamic simulation of the driven reconnection process
Authors: Jin S.-P. , Ip W.-H.
Published: July 2002

A two-dimensional compressible magnetohydrodynamic code is developed to provide simulations of the driven reconnection process in conducting plasma. For a fixed value of the plasma inflow at the boundary (Alfvénic Mach number MA=0.15 ) and a ratio of 2:1 for the two sides of the simulation box, the dependence of the reconnection effect as a function of time on the magnetic Reynolds number is investigated by examining a range of Rm value (400–2500). The size of the current sheet is generally found to cover the horizontal length of the whole simulation box. It is found that as Rm increases, the plasma system will evolve from a configuration of one single X-line formation to a multiple X-line formation. Unlike the former situation, the multiple X-line formation is characterized by quasiperiodic generation of secondary magnetic islands (or plasmoids) of high temperature and dense mass. These two states are separated by a critical value of R*m=2000 for the plasma parameters considered. The occurrence of the flux tube transfer events (FTEs) at the magnetopause might be related to the nonstationary driven reconnection with high Rm value as found here.
Time-resolved measurements of laser-induced shock waves in deuterated polystyrene porous targets by x-ray backlighting
Authors: Kodama R. , Tanaka K. A. , Nakai M. , Nishihara K. , Norimatsu T. , Yamanaka T. , Nakai S.
Published: July 2002

Experimental studies are presented of laser-driven shock waves in deuterated polystyrene porous targets observed with x-ray streak shadowgraphy. Using two different target-mass densities of 0.1 g/cm3 and 0.2 g/cm3, the density dependence of the shock velocity was obtained as vs∝ρ−0.45±0.02 and agreed well with a simple scaling obtained from the Hugoniot relation. X-ray shadowgraphy has shown a shock formation in porous targets and analysis suggests that there are two parts to compression waves: a shock front and a following pileup zone of multiple shock waves. Temporal histories of the pressure, the temperature, and the compression were estimated from the measured shock velocities and the opacities. It was found that the pressure peak due to the shock front was retarded to that by the pileup zone. The pileup zone had a higher compression and followed a thermodynamic condition closer to an adiabat than the shock front.
Energy extraction from intense electron beams in hot plasmas by electron cyclotron waves
Authors: Maroli C. , Petrillo V. , Lampis G. , Basilico F.
Published: July 2002

A hot weakly relativistic plasma in a magnetic field is considered in the slab description with an electron distribution which is the sum of an isotropic Maxwellian function plus a second shifted Maxwellian function describing an electron population drifting along the external magnetic field. The interaction of such a beam–plasma system with ordinary and extraordinary electron cyclotron waves propagating in a direction perpendicular to the external magnetic field and to the beam is studied. The physical system is analyzed in the geometrical optics limit and also by means of a wave-dynamical treatment. A resonance layer due to the beam appears where the condition ωce=γω is verified, where γ=(1−v02/c2)−1/2 and v0 is the beam drift velocity. If the electron beam has a sufficiently high density, an ordinary wave coming from the high-field side can be converted into an extraordinary mode precisely at ωce=γω, propagating then up to the upper-hybrid layer where electron Bernstein waves are generated. When the beam density exceeds a definite threshold value, a multiple conversion process also directly involving the Bernstein waves takes place at ωce=γω. The excitation of the Bernstein modes enhances the amplification of the injected waves. For definite values of the relevant parameters of the problem, the injected electromagnetic waves are strongly amplified, the electrostatic field associated to the Bernstein mode bunching the electrons of the beam in a direction perpendicular to that along which the beam is flowing.
Analytical solution for the mode conversion equations with steep exponential density profiles
Authors: Alava M. J. , Heikkinen J. A.
Published: July 2002

A general analytical solution for the converted power from the fast magnetosonic wave to an ion Bernstein wave in a magnetized plasma with an exponential steeply increasing density profile is given in the closed form. The solution covers both the conversion at the lower-hybrid resonance and the conversion through the density gradient for small parallel wave numbers. As an application, the conversion coefficients at the scrape-off layer plasma are estimated in the context of ion cyclotron heating of a tokamak plasma.
Solitary surface-wave structures in a semi-infinite plasma
Authors: Gradov O. M. , Stenflo L. , Yu M. Y.
Published: July 2002

A physical model for the plasma boundary layer is used to verify the standing solitary surface-wave envelope structure on a cold semi-infinite plasma.
The spectral signatures of a Langmuir soliton instability
Authors: Hadžievski Lj. R. , Škorić M. M.
Published: July 2002

Two-dimensional simulation of a soliton instability in a weakly magnetized plasma is performed in the Zakharov model of strong Langmuir turbulence. Growth rate spectra are calculated showing the suppression of a magnetic-field effect with a growing soliton strength. Time resolved spectra of the Langmuir energy and electric-field components are exposed with important nonlinear effects of a nonlinear frequency shift and spectral broadening observed already in an early stage.
Fast magnetic reconnection and the coalescence instability
Authors: Rickard G. J. , Craig I. J. D.
Published: July 2002

The magnetic reconnection that occurs during the nonlinear development of the coalescence instability is considered. The structure of the reconnection region at the time of maximum current as a function of the resistivity η is analyzed in detail using a compressible magnetohydrodynamic fluid code. It is shown that the numerical results concur remarkably well with a simple scaling analysis which predicts the dependence of the reconnection region structure on η. It is argued that the flow topology is crucial in maintaining the ‘‘fast’’ reconnection rate. The results indicate a flux pileup solution in which the flux annihilation rate is approximately independent of η, whereas the Ohmic dissipation rate scales as η−1/3. The possibility that these scalings break down at lower values of η is discussed.
Quasilinear theory of the ponderomotive force: Induced stability and transport in axisymmetric mirrors
Authors: D’Ippolito D. A. , Myra J. R.
Published: July 2002

A kinetic theory of the ponderomotive force density produced by an electromagnetic cyclotron wave is developed within the quasilinear approximation. The theory is applied to identify the effects of the rf-plasma interaction in equilibrium, stability and transport in paraxial, axisymmetric mirror geometry. The force caused by nonresonant particles is shown to modify the usual magnetohydrodynamic interchange stability drive, and the corresponding arbitrary-m ballooning equation is derived. Resonant particle contributions to the force are shown to arise from the absorption of photon momentum and spin. This effect produces a radial particle flux, modifies the radial ambipolar potential profile, and couples transport and stability.
Induced emission of radiation near 2ωe by a synchrotron-maser instability
Authors: Wu C. S. , Zhou G. C. , Gaffey J. D.
Published: July 2002

In the literature, the emission of radiation at 2ωe , where ωe denotes the electron plasma frequency, is usually explained as having been produced by the nonlinear interaction of two Langmuir waves via a backscattering process. Since the emission is frequently observed in solar radio bursts, the mechanism has attracted considerable theoretical interest. In the present paper a model is proposed based on a synchrotron-maser instability excited by a hollow beam of moderately relativistic electrons in a plasma, in which the plasma frequency is much higher than the gyrofrequency. An important conclusion is that, as a result of this instability, unpolarized electromagnetic waves with frequencies near 2ωe may be amplified.
Nonlinear interaction of tearing modes: A comparison between the tokamak and the reversed field pinch configurations
Authors: Holmes J. A. , Carreras B. A. , Hender T. C. , Hicks H. R. , Lynch V. E. , An Z. G. , Diamond P. H.
Published: July 2002

The multiple helicity nonlinear interaction of resistive tearing modes is compared for the tokamak and reversed field pinch configurations using the magnetohydrodynamic equations. Unlike the case of the tokamak disruption, for which this interaction is destabilizing when islands overlap, the nonlinear coupling of the dominant helicities is shown to be a stabilizing influence in the reversed field pinch. The behavior of the coupled instabilities in the two configurations can be understood as a consequence of the stability properties of the nonlinearly driven modes. In the case of the tokamak disruption, quasilinear effects linearly destabilize the dominant driven mode, which then feeds energy to the driving mode. For the reversed field pinch the driven modes remain stable, acting as a brake on the growth of the dominant instabilities. Furthermore, for the reversed field pinch configuration, numerical results indicate that nonlinear coupling of different helicities results in noticeably more rapid saturation of the dominant instabilities than was observed in single helicity studies.
The Karman vortex trail and flow behind a circular cylinder
Authors: Sirovich Lawrence
Published: July 2002

Recent measurements by Sreenivasen [Frontiers in Fluid Mechanics (Springer, New York, 1985), pp. 41–67] have shown the presence of temporal frequencies (other than the shedding frequency) in the vortex wake generated by a circular cylinder. It is shown here that these modes of oscillation can be described in terms of the classical analysis of the von Karman vortex trail. A comparison of theory with experiment identifies the individually excited modes.
Increased particle confinement observed with the use of an external dc bias field in a spheromak experiment
Authors: Barnes Cris W. , Hoida H. W. , Henins I. , Fernández J. C. , Jarboe T. R. , Marklin G. J.
Published: July 2002

Spheromaks are formed in a mesh flux conserver in the presence of an external dc bias magnetic field. The particle confinement is improved when the spheromak separatrix is put inside the metal mesh by the application of positive bias flux. The spheromaks remain stable to tilt instabilities with ratios of bias-to-spheromak flux of up to 47±7%.