bluuebunny/crossref_metadata_2025 huggingface dataset:
On the vacuum stability in the Efimov–Fradkin model at finite temperature
Authors: Malbouisson A. P. C. , Svaiter N. F.
Published: July 2002

The behavior of the nontruncated and truncated Efimov–Fradkin models (ℒint=−∑Nn=3λnφn) at finite temperature in a generic D-dimensional flat space–time was investigated. The thermal contribution to the renormalized mass and coupling constants are obtained in the one-loop approximation by the use of a mix between dimensional and the Epstein zeta function analytic regularization and a modified minimal subtraction procedure. We proved that for Dc(N−1)≤D there is not a temperature for which at least one of the renormalized coupling constants becomes zero, where Dc(N−1) is the critical spacetime dimension for the renormalized coupling constant λN−1. For Dc(N)≤D<Dc(N−1) only the renormalized coupling constant λN−1 becomes zero at some temperature β−1N−1. For D<Dc(N) the renormalized coupling constants λN−1(β) and λN(β) become zero at temperatures β−1N−1 and β−1N, respectively. In the latter situation, for temperatures β−1N−1<β−1<β−1N the effective potential has a global minimum. For temperatures above β−1N, the system can develop a first order phase transition, where the origin corresponds to a metastable vacuum. In the nontruncated model, corresponding to a nonpolynomial Lagrange density, for D≥2 all the coupling constants remain positive for any temperature.
First order analytic difference equations and integrable quantum systems
Authors: Ruijsenaars S. N. M.
Published: July 2002

We present a new solution method for a class of first order analytic difference equations. The method yields explicit “minimal” solutions that are essentially unique. Special difference equations give rise to minimal solutions that may be viewed as generalized gamma functions of hyperbolic, trigonometric and elliptic type—Euler’s gamma function being of rational type. We study these generalized gamma functions in considerable detail. The scattering and weight functions (u- and w-functions) associated to various integrable quantum systems can be expressed in terms of our generalized gamma functions. We obtain detailed information on these u- and w-functions, exploiting the difference equations they satisfy.
An explicit construction of Casimir operators and eigenvalues. I
Authors: Karadayi H. R. , Gungormez M.
Published: July 2002

We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients gA1,A2,…,Ap. It is seen that these coefficients can be described by some rational polynomials of rank N. These polynomials are also multilinear in Cartan sub-algebra indices taking values from the set I0≡{1,2,…,N}. The crucial point here is that for each degree one needs, in general, more than one polynomial. This in fact is related to an observation that the whole set of symmetric coefficients gA1,A2,…,Ap is decomposed into some sub-sets which are in one-to-one correspondence with these polynomials. We call these sub-sets clusters and introduce some indicators with which we specify different clusters. These indicators determine all the clusters whatever the numerical values of coefficients gA1,A2,…,Ap are. For any degree p, the number of clusters is independent of rank N. This hence allows us to generalize our results to any value of rank N. To specify the general framework, explicit contructions of fourth and fifth order Casimir operators of AN Lie algebras are studied and all the polynomials which specify the numerical value of their coefficients are given explicitly.
An explicit construction of Casimir operators and eigenvalues. II
Authors: Karadayi H. R. , Gungormez M.
Published: July 2002

We provide a way of computing Casimir eigenvalues for Weyl orbits as well as for irreducible representations of Lie algebras. A κ(s) number of polynomials of rank N are obtained explicitly for AN Casimir operators of order s where κ(s) is the number of partitions of s into positive integers except 1. It is also emphasized that these eigenvalue polynomials prove useful in obtaining formulas to calculate weight multiplicities and in explicit calculations of the whole cohomology ring of classical and also exceptional Lie algebras.
Rotating dust solutions of Einstein’s equations with three-dimensional symmetry groups. III. All Killing fields linearly independent of uα and wα
Authors: Krasiński Andrzej
Published: July 2002

This is the third and last part of a series of three papers. Using the same method and the same coordinates as in papers I and II, rotating dust solutions of Einstein’s equations are investigated that possess three-dimensional symmetry groups, under the assumption that each of the Killing vectors is linearly independent of velocity uα and rotation wα at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations are solved for the components of the metric tensor in every case that arises. No progress was made with the Einstein equations in any of the cases, and no previously known solutions were identified. A brief overview of literature on solutions with rotating sources is given.
Entropy and the Segal-Bargmann transform
Authors: Sontz Stephen Bruce
Published: July 2002

The Segal-Bargmann transform A is a unitary isomorphism of the quantum mechanical configuration space L2(Rn,ν) onto the Segal-Bargmann, or phase, space HL2(Cn,μ) of entire functions square integrable with respect to μ. Here μ and ν are Gaussian measures, and for z∈Cn and measurable f:Rn→CAf(z) :=∫Rn dν(t)f(t)exp(−z2/2+√z⋅t) if the integral converges. Af is defined for all f∈Lp(Rn,ν) if 1
1+q/2 (which implies p>q) and in this case ‖A‖p→q⩽((1+q/2−p′q/2)(1−q/2))−n/2q where p′ is the dual of p. Moreover, a calculation with test functions shows that ‖A‖p→q=∞ if q>2 or p<1+q/2 (which is implied by p<q). Using an improved operator norm estimate (analogous to the Hausdorff-Young inequality) we prove Hirschman type entropy inequalities for f∈L2(Rn,ν), (p−1−2−1)S(f )⩽(q−1−2−1)S(Af )+nCp,q‖f‖22, where 1⩽q<2, p>1+q/2, Cp,q is given explicitly as a function of p and q and S(g) is the entropy of g. Examples given here show A is not entropy preserving. So these inequalities provide constraints on the change in entropy. Similarly, we get energy-entropy, or log-Sobolev, inequalities a1S(Af )+a2S(f )⩽a3‖f‖22+a4〈f,Nf〉, for f in a dense subspace of L2(Rn,ν). Here 〈f,Nf〉 is the Dirichlet form of the energy operator N in the configuration space and the ai can have various signs and are also given explicitly. The principal results of this article are generalized Heisenberg uncertainty relations, namely they are constraints on Af, the phase space representation, given information about f, the configuration space representation.
Lattice functions, wavelet aliasing, and SO(3) mappings of orthonormal filters
Authors: John Sarah
Published: July 2002

A formulation of multiresolution in terms of a family of dyadic lattices {Sj;j∈Z} and filter matrices Mj⊂U(2)⊂GL(2,C) illuminates the role of aliasing in wavelets and provides exact relations between scaling and wavelet filters. By showing the {DN;N∈Z+} collection of compactly supported, orthonormal wavelet filters to be strictly SU(2)⊂U(2), its representation in the Euler angles of the rotation group SO(3) establishes several new results: a 1:1 mapping of the {DN} filters onto a set of orbits on the SO(3) manifold; an equivalence of D∞ to the Shannon filter; and a simple new proof for a criterion ruling out pathologically scaled nonorthonormal filters.
Solutions of 1+1 relativistic field models
Authors: Degasperis A. , De Lillo S. , Tinebra F.
Published: July 2002

A class of classical relativistic nonlinear field models has been recently introduced by two of us [A. Degasperis and F. Tinebra, J. Math. Phys. 34, 2950 (1993)]; they are solvable by an explicit mapping to free field equations. Here we show the behavior of particular solutions of these models for both scalar and spinor fields. In the real spectrum we find brachion and tachion localized solutions, and we show the large-time behavior of wave packets, while in the complex spectrum we prove that the asymptotic states may contain solitons, antisolitons, and point-like charged particles (“pointons”). We report on several processes such as soliton–antisoliton pair creation and annihilation, and pointon decay in two solitons.
Dirac operator on a disk with global boundary conditions
Authors: Falomir H. , Gamboa Saraví R. E. , Santangelo E. M.
Published: July 2002

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah–Patodi–Singer. We also discuss the connection between our result and the index theorem.
Corrections to the emergent canonical commutation relations arising in the statistical mechanics of matrix models
Authors: Adler Stephen L. , Kempf Achim
Published: July 2002

We study the leading corrections to the emergent canonical commutation relations arising in the statistical mechanics of matrix models, by deriving several related Ward identities, and give conditions for these corrections to be small. We show that emergent canonical commutators are possible only in matrix models in complex Hilbert space for which the numbers of fermionic and bosonic fundamental degrees of freedom are equal, suggesting that supersymmetry will play a crucial role. Our results simplify, and sharpen, those obtained earlier by Adler and Millard.
Maximum entropy in the generalized moment problem
Authors: Frontini M. , Tagliani A.
Published: July 2002

The generalized moment problem in the framework of the maximum entropy approach is considered. A proof for the existence conditions of the solution is provided.
Lie symmetry and integrability of ordinary differential equations
Authors: Zhdanov R. Z.
Published: July 2002

Combining a Lie algebraic approach that is due to Wei and Norman [J. Math. Phys. 4, 475 (1963)] and the ideas suggested by Drach [Compt. Rend. 168, 337 (1919)], we have constructed several classes of systems of linear ordinary differential equations that are integrable by quadratures. Their integrability is ensured by integrability of the corresponding stationary cubic Schrödinger, KdV, and Harry–Dym equations. Next, we obtain a hierarchy of integrable reductions of the Dirac equation of an electron moving in the external field. Their integrability is shown to be in correspondence with integrability of the stationary mKdV hierarchy.
Timelike infinity and asymptotic symmetry
Authors: Gen Uchida , Shiromizu Tetsuya
Published: July 2002

By extending Ashtekar and Romano’s definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike three-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on asymptotically flat space–times at timelike infinity. Asymptotic flatness is characterized by the falloff rate of the energy-momentum tensor at timelike infinity, which makes it easier to understand physically what space–times are investigated. The notion of the order of the asymptotic flatness is naturally introduced from the rate. The definition gives a systematized picture of hierarchy in the asymptotic structure, which was not clear in the previous works. It is found that if the energy-momentum tensor falls off at a rate faster than ∼t−2, the space–time is asymptotically flat and asymptotically stationary in the sense that the Lie derivative of the metric with respect to ∂t falls off at the rate ∼t−2. It also admits an asymptotic symmetry group similar to the Poincaré group. If the energy-momentum tensor falls off at a rate faster than ∼t−3, the four-momentum of a space–time may be defined. On the other hand, angular momentum is defined only for space–times in which the energy-momentum tensor falls off at a rate faster than ∼t−4.
Deconstructing supersymmetry
Authors: Manton N. S.
Published: July 2002

Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in the Grassmann algebra B2 with two generators. The equations of motion are explicitly solved, and the action of the supergroup on the space of solutions is elucidated. The Lie algebra of the supergroup is the even part of the tensor product B2⊗G, where 𝒢 is the super Lie algebra of supersymmetries and time translations. For each system, the solutions with zero energy need to be constructed separately. For these Bogomolny-type solutions, the orbit of the supergroup is smaller than in the generic case.
On soliton-type solutions of equations associated with N-component systems
Authors: Alber Mark S. , Luther Gregory G. , Miller Charles A.
Published: July 2002

The algebraic geometric approach to N-component systems of nonlinear integrable PDE’s is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.
Oblique vortices on a solid wall and on an interface between two immiscible viscous fluids
Authors: Lugt Hans J.
Published: July 2002

A local three-dimensional flow analysis has been made about a singular point at the interface between two immiscible viscous fluids. A generalization has been found of a ‘‘refraction law’’ for dividing streamlines that was derived in a previous study [Phys. Fluids 30, 3647 (1987)] for two-dimensional flows. It is shown here that the inclination angle of a vortex axis with an interface lies in a plane perpendicular to the shear flow that causes the inclination. An axisymmetric stagnation-point flow is tilted in the direction of the shear flow. Superposition of both vortex and stagnation-point flow yields an angle of inclination somewhere between the planes perpendicular and parallel to the shear flow. These results are valid for slip and nonslip surface conditions.
Effective mass density of fluid suspensions
Authors: Felderhof B. U. , Ooms G.
Published: July 2002

The influence of particles suspended in a fluid on the effective mass density of the suspension is studied. It is shown how at high concentration the low-density, single-particle behavior is modified by retarded hydrodynamic interactions. To simplify the calculation we make a point particle approximation and take account only of two-body hydrodynamic interactions. It is found that the effective mass density depends on frequency.
Dynamic response of boundary-layer turbulence to oscillatory shear
Authors: Brereton G. J. , Reynolds W. C.
Published: July 2002

The temporal response of a well-developed turbulent boundary layer to the superposition of oscillatory shear has been measured experimentally, over a wide range of frequencies. The response is primarily a periodic organization in magnitude of components of the turbulent velocity field at the forcing frequency. Oscillatory production of turbulence arises predominantly as a modulation of the mean production process in the parent boundary layer. Close to the wall, the relative phases of response of components of turbulent kinetic energy indicate that temporal redistribution of turbulent kinetic energy is driven by robust coherent motions of the underlying mean flow. The local directions of redistribution deduced from these measurements indicate a wall impingement (splatting) effect, consistent with characterizations from numerical simulation.
An experimental study of the molecular mixing process in an axisymmetric laminar vortex ring
Authors: Southerland Kenneth B. , Porter John R. , Dahm Werner J. A. , Buch Kenneth A.
Published: July 2002

Results are presented from an experimental study of the molecular mixing of a dynamically passive conserved scalar quantity in an axisymmetric laminar vortex ring. The experiments are based on highly resolved laser-induced fluorescence imaging measurements of the scalar field ζ(x,t) in the diametral plane of the ring, from which the evolution of the molecular mixing rate field ∇ζ⋅∇ζ(x,t) can be directly examined. In particular, the structure and dynamics of the mixing process are addressed during the three characteristic stages in the ring evolution, namely, (i) the ring generation stage, (ii) the ring pinch-off stage, and (iii) the asymptotic stage of the ring. Results show a layering of the mixing process in which the diffusional cancellation term ∇(∇ζ):∇(∇ζ) plays a major role in setting the overall mixing rate achieved. The scalar field measurements are also used to extract detailed information about the underlying velocity field in the ring.
Motions of small particles in a turbulent simple shear flow field under microgravity condition
Authors: Ounis Hadj , Ahmadi Goodarz
Published: July 2002

Motions of small rigid spheres in a turbulent flow field in the presence of a uniform mean shear and in the absence of gravitational effect are studied. The particle equation of motion, which includes the Stokes drag and the Saffman lift force effects, is treated as a stochastic differential equation. The spectral method is used and analytical expressions relating the components of particle response statistics to that of the flow field are developed. The particle spectral intensities, autocorrelation functions, and mean-square velocities, as well as particle diffusivities for different particle relaxation times and mean shear rates are evaluated. It is shown that the presence of a mean shear field enhances the particle diffusivity in the transverse direction. Experimental observations of particle mass diffusivity greater than that of the fluid particle may then be explained by this shear induced enhancement.
Three-dimensional viscous fingering: A numerical study
Authors: Zimmerman W. B. , Homsy G. M.
Published: July 2002

Multidimensional viscous fingering is accurately simulated by an extension of the Hartley spectral methods to three dimensions. Two types of initial conditions were used in the rectilinear displacements−white noise and polygonal cells of the wave number of the mode of maximum instability identified by the linear theory. White noise initial conditions demonstrated that the mechanisms of nonlinear interaction of viscous fingers found in two-dimensional (2-D) simulations persist to three dimensions. Further, the long-time rate of advance of viscous fingers remains unchanged from two dimensions, suggesting that 2-D simulations are sufficient to capture essential features of nonlinear viscous fingering. Simulations with polygonal cellular symmetries, specifically square cells and hexagonal cells, illustrated that weak nonlinear theory cannot predict the shape selection of viscous fingers, as the mechanisms of finger interactions that dominate shape selection lack transverse symmetry and symmetry with respect to the displacement front.
Convection-induced shears for general planforms
Authors: Massaguer J. M. , Spiegel E. A. , Zahn J.-P.
Published: July 2002

Convection drives horizontal shearing modes with horizontal vorticity. For two-dimensional convection, these modes arise in a secondary bifurcation at a high Rayleigh number. When the convection is fully three dimensional, this shear arises at onset in an imperfect bifurcation with a parameter measuring the three-dimensionality as the imperfection parameter.
Influence of soluble surfactants on the motion of a finite bubble in a capillary tube
Authors: Park Chang-Won
Published: July 2002

The steady motion of a long inviscid bubble displacing a viscous fluid in a capillary tube was first analyzed by Bretherton [J. Fluid Mech. 10, 166 (1961)] in the limit of small capillary number (Ca). While his theoretical prediction for the wetting film thickness left behind the moving front of the bubble showed good agreement with experimental observations for a moderately small Ca, it underpredicted the film thickness when Ca was smaller than about 10−4. In an attempt to resolve this discrepancy, several investigators studied the Marangoni effects of surface contaminants and predicted that the film thickness could be increased by a maximum factor of 42/3 if the surfactant transport is bulk-diffusion controlled. This prediction, however, is limited to the case of a semi-infinitely long bubble. The present study examines the motion of a finite length bubble in the presence of a small amount of surfactants. Both front and rear ends of the bubble are analyzed in the limit of small capillary number. The results indicate that due to the accumulation of the surfactant at the rear end of the bubble, the film thickening effect of the surfactant occurs only when the bubble length is larger than a certain critical value. It is also shown that the total pressure drop to drive the finite bubble through the capillary tube increases linearly with the length of the bubble as long as the bubble length is smaller than the critical value. When the bubble is longer than the critical value, the pressure drop does not increase any longer but remains to be constant. It appears that these results are capable of explaining the experimental observations of Schwartz and co-workers [J. Fluid Mech. 127, 259 (1986)] in which the film-thickening behavior at low Ca was shown to be dependent on the bubble length.
The decay of a pair of point vortices in a viscous fluid
Authors: Ohring Samuel , Lugt Hans J.
Published: July 2002

The decay of two counter-rotating point vortices of equal strength in a viscous incompressible fluid is studied by solving the Navier–Stokes equations with a finite-difference technique. Solutions for Reynolds numbers 10, 50, and 100 are compared with a model presented by Cantwell and Rott. Equivorticity lines and the decay rate of translational velocity and circulation of the half-plane are presented, together with the diverging paths of the vortex pair.
Nonaxisymmetric instability in slowly swirling jet flows
Authors: Foster M. R.
Published: July 2002

Very small amounts of swirl are shown to strongly destabilize a round jet flow to large n inertial modes, where (k,n) are, respectively, the axial and azimuthal wave numbers of the disturbance. This mechanism is operative if the scale of the small swirl, ε, is O(n−1) for k=O(1). Further, viscosity is shown to exert a stabilizing influence on these modes if the Reynolds number is no larger than O(n3), hence, neutral curves have been obtained for a particular example—the slowly-swirling Squire jet. For this case, there is a very broad range of unstable wave numbers—all k between εn/2 and n. It is further determined that in the context of an initial-value problem for such a weak vortex on which is imposed a concentrated initial disturbance, the entire vortex is temporally unstable downstream of the initial disturbance.
Rosenhead’s point vortex approximation revisited
Authors: Vanden-Broeck J.-M.
Published: July 2002

The time evolution of a vortex sheet is calculated by using a simple generalization of Rosenhead’s point vortex approximation. The results confirm that the vortex sheet develops a singularity in curvature at a finite time. Numerical evidence of the rolling up of the vortex sheet is presented.
Plasma flow measurements along the presheath of a magnetized plasma
Authors: Chung K-S. , Hutchinson I. H. , LaBombard B. , Conn R. W.
Published: July 2002

Plasma flow measurements in the presheath have been performed using two types of directional electric ‘‘Mach’’ probes, in the PISCES facility at UCLA [J. Nucl. Mater. 121, 277 (1984)]. A fast scanning versatile probe combination has been developed, which operates simultaneously as a ‘‘magnetized’’ Mach probe, an ‘‘unmagnetized’’ Mach probe (with characteristic probe size greater than and smaller than ion gyroradius, respectively), and an emissive probe. Presheaths have been investigated by inserting a small object at the center of the plasma column. Variations in plasma flow velocity, density, and potential along the presheath have been deduced by fluid and kinetic theories. A comparison is made between Mach numbers obtained from the magnetized probe and the unmagnetized probe. Incorporation of shear viscosity of order ∼0.5nmiD⊥ in the cross-field transport along the presheath seems best to model the results. The cross-field diffusivity (D⊥) is found to scale approximately proportional to B−1/2, with magnitude about 4× larger than Bohm in the PISCES plasma. The effect of an electrical bias applied to the object on the presheath characteristics is discussed.
Excitation of the toroidicity-induced shear Alfvén eigenmode by fusion alpha particles in an ignited tokamak
Authors: Fu G. Y. , Van Dam J. W.
Published: July 2002

The toroidicity-induced shear Alfvén eigenmode is found to be destabilized by fusion alpha particles in an ignited tokamak plasma.
Current relaxation time scales in toroidal plasmas
Authors: Mikkelsen D. R.
Published: July 2002

An approximate normal mode analysis of plasma current diffusion in tokamaks is presented. The work is based on numerical solutions of the current diffusion equation in cylindrical geometry. Eigenvalues and eigenfunctions are shown for a broad range of plasma conductivity profile shapes. Three classes of solutions are considered that correspond to three types of tokamak operation. Convenient approximations to the three lowest eigenvalues in each class are presented, and simple formulas for the current relaxation time scales are given and applied to several cases of simple current relaxation as well as noninductive current drive. Simulations of current relaxation with and without current redistribution caused by a ‘‘sawtooth’’ model show that sawteeth can considerably shorten the relaxation time if the sawtooth region extends to r∼a/2.
Strong Langmuir turbulence and second harmonic spectra in a 1 μm laser-produced plasma
Authors: Briand J. , Berge L. , Gomes A. , Quemener Y. , Arnas C. , Armengaud M. , Dinguirard J. P. , Pesme D.
Published: July 2002

Experimental results obtained from time-resolved second harmonic spectra for a 1.06 μm laser-produced plasma are presented. These results are explained with Langmuir strong turbulence showing various stages of a Langmuir wave collapse, namely, the subsonic and supersonic regimes and the Landau damping.
Theoretical consequences of wiggler field error reduction techniques on free-electron laser performance
Authors: Marable W. P. , Esarey E. , Tang C. M.
Published: July 2002

There have been extensive studies on the effects of intrinsic field errors on the operation and performance of free-electron lasers (FEL’s) based predominantly on simple models for the spatial form and statistical properties of the field errors. In some cases, the effects of compensation magnets or steering coils have been included as a method of reducing the deleterious effects of field errors. In the present study the effects of (i) compensation magnets, (ii) general spatial forms that are more realistic models of experimental wigglers, and (iii) statistical correlations of the field errors are considered. This theoretical study has resulted in a quantitative means of measuring the relative merit of these experimental techniques for reducing wiggler field error effects. These means of comparative analysis yield important criteria for experimental design and modeling.
Peeling of convection cells and the generation of sheared flow as relaxation to minimum enstrophy
Authors: Mattor Nathan
Published: July 2002

Recent work by Drake et al. [Phys. Fluids B 4, 488 (1992)] has found that convection cells can generate large-scale shear flows by a dynamical process called ‘‘peeling.’’ Here, it is shown that this process can be viewed as a relaxation to a state where enstrophy is minimized relative to a fixed energy.
Stimulated Raman scattering: Close correspondence of Vlasov simulation and coupled modes
Authors: Reveillé T. , Bertrand P. , Ghizzo A. , Lebas J. , Johnston T. W. , Shoucri M.
Published: July 2002

The envelope equations for the coupling of modes in the stimulated Raman scattering are solved numerically and compared to the results obtained from the solution of the kinetic equations. The analysis is effected using four-mode coupled equations, in which the excitation of the Stokes and the anti-Stokes modes are both included. It is shown that the anti-Stokes mode couples to the pump and the plasma wave and plays a non-negligible role in the evolution of the system.
Numerical simulation of reversed-field pinch rising current operation
Authors: Caramana E. J. , Schnack D. D.
Published: July 2002

One of the most interesting reversed-field pinch (RFP) experimental results occurs in discharges where the toroidal current is slowly raised after toroidal field reversal is established. These discharges exhibit the RFP dynamo effect in its most unambiguous form showing the strong nonlinear coupling of the external poloidal and toroidal magnetic field circuits via the plasma-magnetic-field configuration. Three-dimensional, single-fluid resistive magnetohydrodynamic simulations of these discharges are reported. It is found that the appropriate nonlinear coupling needed to explain the experimental observations is provided by one or more helical resistive modes of long wavelength.
Nonlinear saturation of the absolute stimulated Raman scattering instability in a finite collisional plasma
Authors: McKinstrie C. J. , Simon A.
Published: July 2002

Using multiple time scale analysis, the nonlinear saturation of the absolute stimulated Raman scattering instability is examined in a finite homogeneous collisional plasma. The amplitude of the incident wave is assumed to exceed the absolute instability threshold by the fractional amount Δ(≪1). A single backscattered wave and a single plasma wave grow until time-asymptotic saturation occurs. The reflected light intensity is determined analytically and is proportional to Δ. The spatial variation of the saturated wave amplitudes is also obtained. The reflected intensity is compared to the values predicted for the convective instability, for incident intensities which are marginally less than the absolute threshold intensity. In ‘‘short’’ plasmas, i.e., ones which extend over only a few linear convective gain lengths, the reflected light intensity is found to be much higher when the absolute instability is excited.
An experimental study of helicity related properties of a turbulent flow past a grid
Authors: Kit E. , Tsinober A. , Balint J. L. , Wallace J. M. , Levich E.
Published: July 2002

Results of direct measurements of helicity density and other velocity derivative related flow properties are reported for a turbulent flow past a grid at Reλ=75. The velocity and vorticity vectors exhibit a tendency to be aligned. The flow is found to lack reflectional symmetry, which is manifested by a nonzero correlation between the velocity and vorticity vector fluctuations and considerable asymmetry in the probability density function of the cosine of the angle between the velocity and vorticity vector fluctuations. This asymmetry, as well as the tendency for alignment, increases for larger values of ‖v‖ ‖ω‖.
Analysis of the Brinkman equation as a model for flow in porous media
Authors: Durlofsky L. , Brady J. F.
Published: July 2002

The fundamental solution or Green’s function for flow in porous media is determined using Stokesian dynamics, a molecular-dynamics-like simulation method capable of describing the motions and forces of hydrodynamically interacting particles in Stokes flow. By evaluating the velocity disturbance caused by a source particle on field particles located throughout a monodisperse porous medium at a given value of volume fraction of solids φ, and by considering many such realizations of the (random) porous medium, the fundamental solution is determined. Comparison of this fundamental solution with the Green’s function of the Brinkman equation shows that the Brinkman equation accurately describes the flow in porous media for volume fractions below 0.05. For larger volume fractions significant differences between the two exist, indicating that the Brinkman equation has lost detailed predictive value, although it still describes qualitatively the behavior in moderately concentrated porous media. At low φ where the Brinkman equation is known to be valid, the agreement between the simulation results and the Brinkman equation demonstrates that the Stokesian dynamics method correctly captures the screening characteristic of porous media. The simulation results for φ≥0.05 may be useful as a basis of comparison for future theoretical work.
Evolution of nonlinear polarization in localized and finite amplitude Alfvén waves
Authors: Hoshino M.
Published: July 2002

Theoretical and computational study for a polarization change of localized and finite amplitude Alfvén waves propagating parallel to an applied magnetic field is presented using both reductive perturbation theory and numerical simulations. In the magnetohydrodynamic limit (ω≪Ωi) where right- and left-hand circularly polarized waves are degenerate, one of the transverse components of the circularly polarized Alfvén wave is stable as it propagates, but the other component is unstable to either self-focusing or diffraction effects. Consequently, the wave changes its polarization from circular to linear. In the high frequency regime (ω≳Ωi), where two circularly polarized waves (right- and left-hand circularly polarized waves) are not degenerate, two transverse components of the circularly polarized Alfvén wave are strongly coupled to each other, and there is almost no polarization change.
Atmospheric interfacial waves in the presence of two moving fluid layers
Authors: Forbes Lawrence K. , Belward Shaun R.
Published: July 2002

Atmospheric waves at the interface between two flowing layers of air are studied in this paper. The lower layer is assumed to be incompressible and to flow irrotationally, and its motion might be the result of a distant thunderstorm, for example. The upper layer is modeled as a compressible isothermal atmosphere, so that if it were stationary, its density and pressure would both decrease exponentially with height. The equations of motion in the upper layer are linearized under the assumption that the lower layer of incompressible fluid is ‘‘thin’’ (its weight is a small fraction of the total), but the possibility of large-amplitude disturbances at the interface is nevertheless allowed. A linearized theory of wave propagation in this system is discussed, and a numerical scheme is outlined for the solution of the nonlinear equations. The results confirm the predictions of a model of Forbes and Belward [Phys. Fluids A 4, 2222 (1992)], in which the upper atmosphere was assumed stationary, and demonstrate that this simpler model gives results that are likely to be useful over most of the range of values of the speed in the upper layer encountered in practice. Nonlinear waves near the limiting height are discussed, and a very significant qualitative difference between the predictions of the linearized theory and the nonlinear results concerning progressive waves is analyzed, and may be of importance in meteorology.
Direct simulation of turbulent flow in a square duct: Reynolds-stress budgets
Authors: Huser Asmund , Biringen Sedat , Hatay Ferhat F.
Published: July 2002

The data base from a direct numerical simulation of turbulent flow in a square duct is used to calculate all the terms in the Reynolds stress transport equations. The simulation of this complex turbulent flow was performed at a Reynolds number of 600 based on the friction velocity and the duct width. The distributions of the Reynolds stress budget terms along the wall bisector show similar dynamics to wall-bounded turbulent flows with one inhomogeneous direction. Budget terms in the vicinity of the corner demonstrate how transport and redistribution of energy and shear stresses between the Reynolds stress components takes place, promoting the turbulence characteristics of secondary flows of the second kind. The redistribution of energy by pressure velocity correlations can be explained by the low pressures at the cores of streamwise vortices. The data base is also used to evaluate a nonlinear turbulence model in its ability to accommodate the anisotropy of the Reynolds stress tensor in this flow. This anisotropy is known to be entirely responsible for the formation of the secondary flow in noncircular ducts and cannot be captured by linear models.
Topological fluid dynamics of interfacial flows
Authors: Bro/ns Morten
Published: July 2002

The topological description of flows in the vicinity of a solid boundary, that is familiar from the aerodynamics literature, has recently been extended to the case of flow at a liquid–gas interface or a free surface by Lugt [Phys. Fluids 30, 3647 (1987)]. Lugt’s work is revisited in a more general setting, including nonconstant curvature of the interface and gradients of surface tension, using tools of modern nonlinear dynamics. Bifurcations of the flow pattern occur at degenerate configurations. Using the theory of unfolding, this paper gives a complete description of the bifurcations that depend on terms up to the second order. The general theory of this paper is applied to the topology of streamlines during the breaking of a wave and to the flow below a stagnant surface film.
The effect of particle loading on the spatial stability of a circular jet
Authors: Sykes D. , Lyell M. J.
Published: July 2002

The spatial stability of the two-phase circular jet is investigated. Stability results are presented for mean-flow jet profiles for axisymmetric and helical modes. The variation of phase speed with particle loading is reported. The presence of particles are found to have a stabilizing effect.
Reverse flow in channel-effect of front and rear obstructions
Authors: Tulapurkara E. G. , Lakshmana Gowda B. H. , Swain Susheel K.
Published: July 2002

The occurrence of reverse flow in a channel when a bluff body is kept at the entry is already known. In the earlier investigations, attention was focused on the generation of the reverse flow with bluff bodies, such as flat plate and other geometries, having the same width as the channel. The separation of the shear layers from the obstruction at the front end and the interaction of the shear layers at the rear end are mainly responsible for the reverse flow. To gain further insight into the phenomenon, the effects of the width of the obstruction at the front and that of placing another at the rear end in tandem with the front one are examined in this study. It is observed that the reverse flow occurs even when the width of the flat plate (b) is less than the channel width (w); the lower limit being b/w=0.6. At this b/w the reverse flow velocity is small, but it increases progressively with b/w until a maximum of about 30% of the forward velocity is attained for b/w≥2.0. However, reverse flow as high as 0.6 times the free-stream velocity is obtained when another plate is kept close to the rear end in addition to the front plate. Further increase in the reverse flow to 0.83 times the free-stream velocity has been achieved by replacing the flat plate model at the rear with a semicircular scoop.
Accurate determination of the sedimentation flux of concentrated suspensions
Authors: Martin J. , Rakotomalala N. , Salin D.
Published: July 2002

Flow rate jumps are used to generate propagating concentration variations in a counterflow stabilized suspension (a liquid fluidized bed). An acoustic technique is used to measure accurately the resulting concentration profiles through the bed. Depending on the experimental conditions, we have observed self-sharpening, or/and self-spreading concentration fronts. Our data are analyzed in the framework of Kynch’s theory, providing an accurate determination of the sedimentation flux [CU(C); U(C) is the hindered sedimentation velocity of the suspension] and its derivatives in the concentration range 30%–60%. In the vicinity of the packing concentration, controlling the flow rate has allowed us to increase the maximum packing up to 60%.
Chemically reactive turbulent vortex rings
Authors: Johari H.
Published: July 2002

Employing an aqueous acid-base reaction, the minimum mixing rate of turbulent vortex rings was investigated in a water tank. Vortex rings were generated by a simple apparatus with a cylindrical geometry. The released fluid surrounding the vortex core mixed very rapidly when compared with the fluid in the toroidal core. Moreover, the fluid within the core did not mix uniformly in the azimuthal direction. The normalized distance a vortex ring must travel, in order to completely mix with the ambient fluid to a specific volumetric ratio, depends on the aspect ratio of the generating cylinder. Scaling arguments are presented that relate the above distance to the spreading rate and the generating apparatus parameters. Due to the very small net entrainment rate of vortex rings, the detrainment of core material cannot be ignored when the mixing rate of the core is considered.
Autogeneration of near-wall vortical structures in channel flow
Authors: Zhou Jigen , Adrian Ronald J. , Balachandar S.
Published: July 2002

The evolution of a symmetric pair of quasistreamwise vortical structures extracted from the two-point correlation tensor of turbulent channel flow data by a linear stochastic estimation procedure is studied through direct numerical simulation. It is observed that an Ω-shaped hairpin vortex is formed quickly from this initial structure. Sufficiently strong hairpin vortices are observed to generate a hierarchy of secondary hairpin vortices, and the mechanism of their creation closely resembles the formation of the primary hairpin vortex. New streamwise vortices are also generated, and this process provides a means for a few vortical disturbances of adequate strength to reproduce themselves and eventually populate the near-wall layer.
Direct numerical simulation of a laminar vortex ring
Authors: James S. , Madnia C. K.
Published: July 2002

Results are presented of direct numerical simulations (DNS) of a viscous, laminar ring. The effects of different generator configurations and velocity programs on the formation and post-formation characteristics of the ring are studied. It is shown that during the formation phase of the ring, total circulation and impulse in the flowfield are approximately the same for the ‘‘nozzle’’ and ‘‘orifice’’ generators. It is also found that throughout this period the slug flow model under-predicts the total circulation in the flow. During the formation phase, the simulation results for the time evolution of total circulation and location of the vortex spiral center are in agreement with the experimental findings of Didden [J. Appl. Mech. Phys. (ZAMP) 30, 101 (1979)]. The results of the flow visualization studies show that during the post-formation phase a vortex bubble is formed. As the bubble propels itself forward a wake is formed in the rear of the bubble. The impulse and vorticity from the bubble are continuously shed into this wake. It is found that the total value of the circulation in the flow varies as (t1*)−0.33 which is consistent with Maxworthy’s [J. Fluid Mech. 81, 465 (1977)] prediction of the decay of circulation for a vortex ring. The transport of a passive Shvab-Zeldovich scalar variable is used to study the mixing and to obtain the maximum product formation in a chemical reaction of the type A+B→Products in a vortex ring. It is found that as the bubble containing the fuel propels itself forward, the outside oxidizer flow is entrained into it and reacts to form a product. Some of this product then is de-entrained into the wake of the bubble.
Nonlinear feedback control of the wake past a plate: From a low-order model to a higher-order model
Authors: Cortelezzi L. , Chen Y.-C. , Chang H.-L.
Published: July 2002

A framework to estimate, with an intelligent and systematic approach, the applicability of a controller derived for a low-order model to a higher-order model is presented. This framework is applied to the test case of nonlinear feedback control of the two-dimensional unsteady separated flow past a plate perpendicular to the free-stream velocity. A hierarchy of models of increasing complexity is generated by using vortex methods. A low-order point vortex model and a high-order vortex blob model are used to simulate the roll-up of the separated shear layer. A nonlinear controller able to manipulate the wake by means of a suction point located on the downstream wall of the plate is given in closed form for the point vortex model. This controller is applied to the vortex blob model by defining a center of circulation. The topological equivalence of the phase spaces of the two models is verified. Finally, the two models are used to simulate the same flows using the same controller and the results are discussed.
Apparent slip at the surface of a small rotating sphere in a dilute quiescent suspension
Authors: Almog Y. , Brenner H.
Published: July 2002

We consider the case of a test sphere (ball) of radius a1 rotating at constant angular velocity ω in an otherwise quiescent unbounded suspension of uniformly sized spheres of radii a2 dispersed in a Newtonian fluid of viscosity μ. To the first order in the volume fraction c of suspended spheres it is shown that when the ball is small compared with the suspended spheres the suspension does not behave as regards the hydrodynamic torque L exerted on the ball like a homogeneous Newtonian fluid characterized by the usual Einstein viscosity coefficient μs=μ(1+5/2c). Explicitly, the torque on the rotating sphere does not obey Kirchoff’s law, L=8πμsa13ω for no slip. Rather, a modified form of Kirchoff’s law is obtained in which the Einstein coefficient of 5/2 is multiplied by a coefficient which is less than unity in magnitude and is functionally dependent only upon the suspended-sphere/test-sphere size ratio, λ=a2/a1. In the “continuum limit,” where λ tends to zero, one recovers Kirchoff’s law. Accordingly, the deviation from Kirchoff’s law is interpreted in terms of an apparent Knudsen-like “slip” at the rotating ball surface since this slip vanishes in the continuum limit. The existence of an apparent slip is consistent with recent experiments performed on small rotating spheres, albeit in concentrated suspensions, in which the “viscosity” of the suspension—defined via Kirchoff’s law in terms of the experimentally measured torque L as L/8πa13ω—was observed to be less than the viscosity of the suspension as measured by standard viscometric methods. Similar, although quantitatively different O(c) theoretical Knudsen-like slip results were also obtained for the “inverse” case, where the torque L on the rotating ball is held constant for all time and its mean angular velocity calculated.
A numerical study of chemical front propagation in a Hele-Shaw flow under buoyancy effects
Authors: Zhu Jingyi
Published: July 2002

We consider the propagation of chemical fronts in a Hele-Shaw flow where the front is assumed to propagate with a curvature dependent velocity. The motivation is to model some recent experiments that employ aqueous autocatalytic chemical reactions in such a device. The density change across the front in such experiments is quite small so the Boussinesq approximation can be used, and the flow field generated is exclusively due to buoyancy effects. We derive a free boundary formulation based on Darcy’s law and potential theory, and describe the evolution in terms of the θ−L formulation, in which the tangent angle and the perimeter of the closed front are followed in time. Numerical solutions are obtained for this formulation with a rising and expanding bubble. As observed in the experiments, a fingering phenomenon which is different from the surface tension associated phenomenon appears in our calculations. The mechanisms that control the wavelength selection of the fingers, and a comparison with the result of a linear stability analysis for flat fronts are discussed.