bluuebunny/crossref_metadata_2025 huggingface dataset:
The formulation of quantum statistical mechanics based on the Feynman path centroid density. III. Phase space formalism and analysis of centroid molecular dynamics
Authors: Cao Jianshu , Voth Gregory A.
Published: July 2002

The formulation of quantum statistical mechanics based on the path centroid variable in Feynman path integration is generalized to a phase space perspective, thereby including the momentum as an independent dynamical variable. By virtue of this approach, operator averages and imaginary time correlation functions can be expressed in terms of an averaging over the multidimensional phase space centroid density. The imaginary time centroid-constrained correlation function matrix for the phase space variables is then found to define the effective thermal width of the phase space centroid variable. These developments also make it possible to rigorously analyze the centroid molecular dynamics method for computing quantum dynamical time correlation functions. As a result, the centroid time correlation function as calculated from centroid molecular dynamics is shown to be a well-defined approximation to the exact Kubo transformed position correlation function. This analysis thereby clarifies the underlying role of the equilibrium path centroid variable in the quantum dynamical position correlation function and provides a sound theoretical basis for the centroid molecular dynamics method.
Direct inversion in the iterative subspace-induced acceleration of the ridge method for finding transition states
Authors: Ionova Irina V. , Carter Emily A.
Published: July 2002

We extend the application of the direct inversion in the iterative subspace (DIIS) technique to the ridge method for finding transition states (TS). The latter is not a quasi-Newton-type algorithm, which is the only class of geometry optimization methods that has been combined with DIIS. With this new combination, we obtain a factor of two speedup due to DIIS, similar to the DIIS-related speedup achieved in other methods including quasi-Newton geometry optimization and self-consistent field iterations. We also demonstrate that DIIS is useful even in cases where optimization is started far from the quadratic region of the TS, provided that only one previous iteration is used in the DIIS expansion. We compare the performance of the new ridge-DIIS method to that of the TS algorithm utilized in GAUSSIAN 92. We find that the computational cost of the former is similar (when both methods converge) to that of the latter. The examples considered in the paper include a novel TS found for an isomerization of a cluster of six Na atoms. Locating such a TS poses a known problem for second-derivatives-based algorithms that fail on very flat potential energy surfaces. Thus, the gradient-based ridge-DIIS method is the only TS search method that is robust, does not need second derivatives and/or an initial guess for the TS geometry, and whose performance matches or exceeds that of a second-derivatives-based algorithm.
Droplets formed in helium free-jet expansions from states near the critical point
Authors: Harms J. , Toennies J. P. , Knuth E. L.
Published: July 2002

Droplets formed in 4He free jets expanded from source stagnation states in the vicinity of the critical point (Tc=5.2 K, Pc=2.3 bar) are investigated using a mass-spectrometer time-of-flight (TOF) technique. Depending on the source conditions, three different TOF peaks are identified: (a) atoms, (b) droplets formed by condensation from the gas phase, and (c) droplets formed by disintegration of the liquid phase. The latter show the lowest ever observed 4He cluster speeds, about 50 m/s, at a source pressure of 1.5 bar and a source temperature of 4–5 K, just below the critical pressure and temperature. The TOF distributions at the critical point are very broad and this may be due to critical-point fluctuations during the averaging period (2–10 min) of the individual measurements.
Thermodynamically driven incompressible fluid mixtures
Authors: Otto Felix , E Weinan
Published: July 2002

We compare two models describing the dynamics of phase separation of incompressible mixtures: A local model proposed by de Gennes, and a nonlocal model proposed by E and Palffy-Muhoray. We find that in the interfacial regime, the local model gives rise to interfacial motion via the Mullins-Sekerka law for moderate quenches, and surface diffusion for deep quenches. The interface dynamics is slowed down sharply as the quench depth is increased. The nonlocal model, on the other hand, has an additional convective mechanism which gives rise to motion by Hele-Shaw dynamics. This additional mechanism is insensitive to the quench depth. While both models explain qualitatively the observed pinning phenomenon for deeply quenched off-critical mixtures, only the nonlocal model predicts the correct dependence of the coarsening rate on the quench depth.
Capture of lithium by 4He clusters: Surface adsorption, Penning ionization, and formation of HeLi+
Authors: Scheidemann Adi A. , Kresin Vitaly V. , Hess Henry
Published: July 2002

We investigate the capture of lithium atoms by a beam of large cold helium clusters and subsequent ion production by electron impact. Li atoms are efficiently picked up by the He droplets, although with a cross section significantly lower than that for other atoms and molecules. The mass spectrum reveals the presence of Li atom and dimer ions, as well as the weakly bound complex HeLi+, confirming that capture by He-cluster beams can be used for efficient soft ionization of fragile species. The electron-energy dependence of the Li+, Li2+, and HeLi+ yield shows that they are formed primarily by Penning ionization in a collision with a metastable He atom in the droplet. This leads to the conclusion that lithium metal atoms are not submerged in the helium clusters but locate on the surface, corroborating theoretical predictions for bulk helium surfaces and spectroscopic measurements.
Viscous fingering in periodically heterogeneous porous media. I. Formulation and linear instability
Authors: De Wit A. , Homsy G. M.
Published: July 2002

We are generally interested in viscously driven instabilities in heterogeneous porous media for a variety of applications, including chromatographic separations and the passage of chemical fronts through porous materials. Heterogeneity produces new physical phenomena associated with the interaction of the flow with the heterogeneity on the one hand, and the coupling between the flow, the concentration of a passive scalar, and the physical properties (here the viscosity) on the other. We pose and solve a model in which the permeability heterogeneity is taken to be periodic in space, thus allowing the interactions of the different physical mechanisms to be carefully studied as functions of the relevant length and time scales of the physical phenomena involved. In this paper, Paper I of a two-part study, we develop the basic equations and the parameters governing the solutions. We then focus on identifying resonant interactions between the heterogeneity and the intrinsic viscous fingering instability. We make analytical progress by limiting our attention to the case of small heterogeneity, in which case the base state flow is only slightly disturbed from a uniform flow, and to linear instability theory, in which the departures from the base state flow are taken to be small. It is found that a variety of resonances are possible. Analytic solutions are developed for short times and for the case of subharmonic resonance between the heterogeneities and the intrinsic instability modes. A parametric study shows this resonance to increase monotonically with the viscosity ratio i.e., with the strength of the intrinsic instability, and to be most pronounced for the case of one-dimensional heterogeneities layered horizontally in the flow direction, as expected on simple physical grounds. When axial variation of the permeability field is also considered, a damping of the magnitude of the response generally occurs, although we find some evidence of local resonances in the case when the axial forcing is commensurate with a characteristic dispersive time. The response exhibits a high frequency roll-off as expected. These concepts of resonant interaction are found to be useful and to carry over to the strongly nonlinear cases treated by numerical methods in Paper II [J. Chem Phys. 107, 9619 (1997)].
The spectroscopy of the CdCH3 radical and its positive ion
Authors: Panov Sergey I. , Powers David E. , Miller Terry A.
Published: July 2002

Resonantly enhanced multiphoton ionization, REMPI (2 color, 1+1′), and zero electron kinetic energy-pulsed field ionization, ZEKE-PFI, spectra are reported for the first organometallic radical, CdCH3. The combined REMPI and ZEKE-PFI data have necessitated a change of assignment for one of the bands of the Ã2E←X̃ 2A1 electronic transition of the neutral radical. The new assignment and the revised molecular parameters are reported. The ZEKE-PFI spectrum yields the adiabatic ionization potential for the CdCH3 radical and four of the six possible vibrational frequencies of its cation. Clearly resolved rotational (K level) structure is observed in some bands of the ZEKE-PFI spectrum, providing a unique experimental test for newly extended ZEKE-PFI rotational selection rules.
Pressure-induced change of the stereochemical activity of a lone electron pair
Authors: Winkler Björn , Milman Victor , Lee Ming-Hsien
Published: July 2002

Ab initio total energy calculations based on density functional theory and the generalized gradient approximation in conjunction with a constant pressure minimization algorithm have been used to demonstrate that the pressure-induced phase transition from a rhombohedrally distorted into an ideal cubic structure of CsGeCl3 involves a change in the stereochemical activity of the lone electron pair from “active” to “inert.”
Ionic distribution around simple B-DNA models II. Deviations from cylindrical symmetry
Authors: Montoro Juan Carlos Gil , Abascal José L. F.
Published: July 2002

The structure of the ions around two B-DNA models with added monovalent salt at the continuum solvent level is investigated by computer simulation. The salt concentrations cover a wide range, from 0.05 to 4.5 M. The simplicity of the so-called grooved primitive model (unit electron charges at the phosphate positions of canonical DNA and the grooves shape approximated by means of simple geometric elements) enables a detailed study of the counterion and coion distributions with a very small statistical noise. The inhomogeneity of the ionic distributions is noticeable along the axial direction up to distances of about 20 Å from the DNA axis. The counterions deeply penetrate into the DNA grooves even at very low added salt concentrations. In the minor groove, the counterions are preferentially located in its center whereas they lie at the sides of the major groove, close to the phosphate positions. The coions also enter within the major groove, especially in the systems at high added salt concentrations for which regions of absolute negative charge can be found within the groove. This can be explained in terms of an arrangement of ions with alternating charges. The grooved primitive model has also been solved in the context of the finite difference Poisson–Boltzmann theory. The theory accurately describes the ionic structure around DNA at low salt concentrations but the results deteriorate with increasing salt missing important qualitative features at or above molar concentrations. The other model investigated differs from the more detailed one in that the shape of DNA is not taken into account; a soft cylinder is used instead. The counterions accumulate in this model in front of the phosphates and the axial inhomogeneity of the distribution quickly vanishes. These results together with those of previous investigations lead to the conclusion that the coupling of the discrete description of the DNA charge with the steric effects due to the presence of the grooves is the primary determinant of the final ionic distribution, especially at high salt concentrations. This effect may play a decisive role in those DNA properties which are strongly dependent on the salt concentration, like the B- to Z-DNA conformational transition.
Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation
Authors: Sun Xiong , Wang Haobin , Miller William H.
Published: July 2002

A linearized approximation to the semiclassical initial value representation (SC-IVR), referred to herein as the LSC-IVR, was used by us in a recent paper [J. Chem. Phys. 108, 9726 (1998)] to calculate reactive flux correlation functions for a model of a chemical reaction on a single potential energy surface. This paper shows how the LSC-IVR—which is much easier to apply than the full SC-IVR because it linearizes the phase difference between interfering classical trajectories—can be applied to electronically nonadiabatic processes, i.e., those involving transitions between different potential-energy surfaces. Applications to several model problems are presented to show its usefulness: These are the nonadiabatic scattering problems used by Tully to test surface-hopping models, and also the spin–boson model of coupled electronic states in a condensed phase environment. Though not as accurate as the full SC-IVR, the LSC-IVR does a reasonably good job for all these applications, even describing correctly Stuckelberg oscillations (interference between nonadiabatic transitions) and the transition between coherent and incoherent behavior in the spin–boson example.
Semiclassical study of electronically nonadiabatic dynamics in the condensed-phase: Spin-boson problem with Debye spectral density
Authors: Wang Haobin , Song Xueyu , Chandler David , Miller William H.
Published: July 2002

The linearized semiclassical initial value representation (LSC-IVR) [H. Wang, X. Sun and W. H. Miller, J. Chem. Phys. 108, 9726 (1998)] is used to study the nonadiabatic dynamics of the spin-boson problem, a system of two electronic states linearly coupled to an infinite bath of harmonic oscillators. The spectral density of the bath is chosen to be of the Debye form, which is often used to model the solution environment of a charge transfer reaction. The simulation provides a rather complete understanding of the electronically nonadiabatic dynamics in a broad parameter space, including coherent to incoherent transitions along all three axes (the T-axis, the η-axis, and the ωc-axis) in the complete phase diagram and the determination of rate constants in several physically interesting regimes. Approximate analytic theories are used to compare with the simulation results, and good agreement is found in the appropriate physical limits.
Superposition formulas for rectangular matrix Riccati equations
Authors: del Olmo M. A. , Rodríguez M. A. , Winternitz P.
Published: July 2002

A system of nonlinear ordinary differential equations allowing a superposition formula can be associated with every Lie group–subgroup pair G⊇G0. We consider the case when G=SL(n+k,C) and G0=P(k) is a maximal parabolic subgroup of G, leaving a k-dimensional vector space invariant (1≤k≤n). The nonlinear ordinary differential equations (ODE’s) in this case are rectangular matrix Riccati equations for a matrix W(t)∈Cn×k. The special case n=rk (n,r,k∈N) is considered and a superposition formula is obtained, expressing the general solution in terms of r+3 particular solutions for r≥2, k≥2. For r=1 (square matrix Riccati equations) five solutions are needed, for r=n (projective Riccati equations) the required number is n+2.
Diffusive limits for particle transport in stochastic mixtures
Authors: Sammartino M. , Malvagi F. , Pomraning G. C.
Published: July 2002

Under the assumption of weak spatial and temporal gradients as well as weak absorption and sources, it is well known that the classic kinetic equation describing linear particle transport has a diffusion equation as an asymptotic limit. Considered here is such particle transport in a stochastic Markovian mixture of two immiscible fluids. It is shown that a variety of asymptotic diffusive limits exist under the scaling indicated above, depending upon the additional scaling introduced for the Markov transition lengths. These lengths are indicative of the mean chord lengths of the fluid packets in the stochastic mixture, and it is thus found that the details of the diffusive limits are strongly dependent upon the presumed sizes of the fluid packets. Asymptotically consistent initial and boundary conditions are also derived for each diffusion description obtained.
Representations and traces of the Hecke algebras H
n(q) of type A
n−1
Authors: King R. C. , Wybourne B. G.
Published: July 2002

The notion of the connectivity class of minimal words in the algebra Hn(q) is introduced and a method of explicitly constructing irreducible representation matrices is described and implemented. Guided by these results, the connection between the Ocneanu trace on Hn(q) and Schur functions is exploited to derive a very simple prescription for calculating the irreducible characters of Hn(q). They appear as the elements of the transition matrix relating certain generalized power sum symmetric functions to Schur functions. Their evaluation involves the use of the Littlewood–Richardson rule, which is proved to apply to Hn(q) just as it does to Sn. Both representation matrices and characters are tabulated.
Maurer–Cartan forms and equations for two-dimensional superdiffeomorphisms
Authors: Gieres François
Published: July 2002

Explicit expressions for the Maurer–Cartan forms of the superdiffeomorphism group associated to a super-Riemann surface are presented. As an application to superconformal field theory, these forms are used to evaluate the effective action for the factorized superdiffeomorphism anomaly.
Searchlight on a target with diffuse background. I
Authors: Wang Alan P. , Ueno Sueo
Published: July 2002

A mathematical model of a searchlight on a target with diffused background is constructed based on three-dimensional radiative transfer and integral operators. The main result is the recovery of the true target reflection from the measured reflection which consists of background light and multiscattering between atmospheric layer and the earth surface. An exact solution is solved and approximations are obtained by use of the assumption that the searchlight is strong and focused and the background light is weak and uniform in space in a given narrow frequency band of intensity.
A q-analog of the quantum central limit theorem for SUq(2), q complex
Authors: Lenczewski Romuald
Published: July 2002

A q-analog of the central limit theorem for SUq(2), ‖q‖■{0,1} is studied. It is shown that in the q-quantum central limit sense SUq(2) converges to the algebra of complex quantum q-oscillator.
Consideration of the general state which minimizes the Nth order minimum uncertainty product
Authors: Lynch R. , Mavromatis H. A.
Published: July 2002

This paper considers the problem of whether mixed states can arise in the Nth order minimum uncertainty expression UN=<Ψ‖‖x‖N‖Ψ≳<Ψ‖‖p‖N‖Ψ≳. Using a method due to R. Jackiw [J. Math. Phys. 9, 339 (1968)], and finding the extremum of the appropriate functional, a set of equations is derived which must be satisfied by such a mixed state. It is easily shown that a sufficient condition that the equations have a solution is that the mixed state in fact reduces to a pure state. It does not appear possible to rigorously prove that such a reduction is necessary, although the authors present approximate calculations which make such a conclusion plausible. In the course of the approximate calculations generalized Nth order ‘‘squeezed state’’ values for UN are also obtained which are of some interest in and of themselves.
Imploding scalar fields
Authors: Roberts M. D.
Published: July 2002

Static spherically symmetric uncoupled scalar space–times have no event horizon and a divergent Kretschmann singularity at the origin of the coordinates. The singularity is always present so that nonstatic solutions have been sought to see if the singularities can develop from an initially singular free space–time. In flat space–time the Klein–Gordon equation ⧠φ=0 has the nonstatic spherically symmetric solution φ=σ(v)/r, where σ(v) is a once differentiable function of the null coordinate v. In particular, the function σ(v) can be taken to be initially zero and then grow, thus producing a singularity in the scalar field. A similar situation occurs when the scalar field is coupled to gravity via Einstein’s equations; the solution also develops a divergent Kretschmann invariant singularity, but it has no overall energy. To overcome this, Bekenstein’s theorems are applied to give two corresponding conformally coupled solutions. One of these has positive ADM mass and has the following properties: (i) it develops a Kretschmann invariant singularity, (ii) it has no event horizon, (iii) it has a well-defined source, (iv) it has well-defined junction condition to Minkowski space–time, and (v) it is asymptotically flat with positive overall energy. This paper presents this solution and several other nonstatic scalar solutions. The properties of these solutions which are studied are limited to the following three: (i) whether the solution can be joined to Minkowski space–time, (ii) whether the solution is asymptotically flat, (iii) and, if so, what the solutions’ Bondi and ADM masses are.
Coherent state path-integral representation of supersymmetric lattice models
Authors: Chang Zhe
Published: July 2002

A kind of high-temperature superconductivity related lattice model is investigated within the framework of supergroup coherent state path-integral representation. Symmetry properties are analyzed and the Hamiltonians are written in the symmetric form explicitly in terms of generators of the supergroup U(N/M). By a standard approach, general supergroup coherent states are constructed. Holstein–Primakoff realizations of the supergroup U(N/M) on the coset space U(N/M)/[U(1)⊗U(N−1/M)] are obtained. Vacuum persistence amplitudes are expressed in terms of parameters on the coset space U(2/M)/[U(1)⊗U(1/M)]. Symmetry-breaking terms in the Hamiltonian are taken into account separately. The Lagrangians of these models are quadratic in Grassmann variables. Thus fermionic fields can be integrated out. The nonlinear σ model is arrived at as effective continuum field theory describing the low-energy excitations of the supersymmetric lattice models.
Two-body wave equations in curved space–time
Authors: Droz-Vincent Philippe
Published: July 2002

Two scalar particles undergoing mutual interaction are considered in a prescribed curved space–time. Both masses are finite (recoil is not neglected). For a description of this system we propose a pair of coupled Klein–Gordon equations; they involve two-body-sector extensions of the Laplace–Beltrami operator, plus a term that takes mutual interaction into account. Besides the problem of compatibility, we discuss several requirements that seem more or less necessary from a physical point of view. Particular attention is devoted to the preservation of space–time symmetries (isometric invariance). Composition of curvature with mutual interaction is a nonlinear problem, but it can be explicitly solved in a toy model of static orthogonal space–time. Moreover, we check that isometric invariance and other physical requirements are satisfied in this example.
Remarks on the universal central extension of sdiff(T2)loc
Authors: Òdúndún Wolé
Published: July 2002

In a paper by C. N. Pope and K. S. Stelle [Phys. Lett. B 226, 257–263 (1989)], it was shown that the algebra of local area-preserving diffeomorphisms on the torus is equivalent to su(∞). In this paper we present a few remarks on the universal central extension of this infinite dimensional Lie algebra, and construct, for this case, in analogy to the situation in which the affine Lie algebra has an underlying finite-dimensional Lie algebra, the nontrivial universal central extension.
Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equations
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

The one-dimensional Schrödinger equation and two of its generalizations are considered, as they arise in quantum mechanics, wave propagation in a nonhomogeneous medium, and wave propagation in a nonconservative medium where energy may be absorbed or generated. Generically, the zero-energy transmission coefficient vanishes when the potential is nontrivial, but in the exceptional case this coefficient is nonzero, resulting in tunneling through the potential. It is shown that any nontrivial exceptional potential can always be fragmented into two generic pieces. Furthermore, any nontrivial potential, generic or exceptional, can be fragmented into generic pieces in infinitely many ways. The results remain valid when Dirac delta functions are included in the potential and other coefficients are added to the Schrödinger equation. For such Schrödinger equations, factorization formulas are obtained that relate the scattering matrices of the fragments to the scattering matrix of the full problem.
Exact semiclassical expansions for one-dimensional quantum oscillators
Authors: Delabaere Eric , Dillinger Hervé , Pham Frédéric
Published: July 2002

A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh–Schrödinger series is Borel resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of “multi-instanton expansions.”
The influence of oxygen content on the Tc of HTS Hg-1245
Authors: Itskevich E. S.
Published: July 2002

We have observed an extraordinary behavior of the HgBa2Ca4Cu5O12+δ layered HTS (phase 1245) in the overdoped state. Earlier we have synthesized the phase Hg-1245 with different oxygen content and consequently different values of the lattice parameter a. We have observed a coincidence of a values when the Tc(a) cupolas reach their maxima for phases Hg-1223, 1234, and 1245, and a merging of their overdoped parts together with abrupt falling off of the Tc values. The Hg-1245 phase has shown the most unusual behavior. Contrary to other phases, this one contains three types of CuO2 layers in a unit cell. We supposed that, in the case of the Hg-1245 phase, the holes coming from the reservoir, which is the Hg–O plane, cannot reach the “far” CuO2 layer which is notable for this phase. We have calculated the hole concentration for each layer for 1223, 1234, and 1245 phases. The results obtained confirm our assumption. The hole concentration appears negligibly small for the overdoped 1245 phase. We can consider the “fifth” CuO2 layer as not taking part in superconductivity. The analysis of the behavior of the Tc(a) cupolas for the phases with different number of CuO2 layers and of hole density distribution between the layers has been carried out.
A crossover in the temperature behavior of the perpendicular upper critical magnetic field of layered superconductors and thin films
Authors: Gvozdikov V. M.
Published: July 2002

A mechanism which relates the upturn of the perpendicular upper critical magnetic field Hc2⊥(T) in layered superconductors and thin films with the structural inhomogeneity in the bulk of the sample, provided that the local critical temperature Tc* inside the inhomogeneity is higher than in the rest of the sample (Tc) is proposed. Within the Ginzburg–Landau approach an equation which describes two types of experimentally observed nonlinearities in Hc2⊥(T) near Tc for ISN (insulator-superconductor-normal metal) and NSN layer configurations, is found. In the NSN case a crossover from the linear branch Hc2⊥(T)∝(Tc−T), for fields H⩽Hm, to the nonlinear branch with the upturn, if H>Hm, takes place. The crossover field Hm is inversely proportional to the local enhancement of the critical temperature (Tc*−Tc) and the distance R to the surface (the nearest surface, in case of a thin film). In the ISN case the upturn holds for H<Hm, whereas for higher fields Hc2⊥(T) crosses over to the linear branch. In the ISI case the Hc2⊥(T) is a linear function.
Probability distribution of a passive scalar: A soluble example
Authors: Goldhirsch I. , Yakhot A.
Published: July 2002

The probability distribution, in space, of a passive scalar advected by a model, divergence-free, velocity field is analytically calculated. It is found to have a logarithmic singularity at the origin and a quasi-Gaussian decay away from it. The significance of this result for the general case of convection of passive scalars and the relation to a recent theory of Yakhot and Sinai [Phys. Rev. Lett. 63, 1962 (1989)] are discussed.
Kinetic theory for a monodisperse gas–solid suspension
Authors: Koch Donald L.
Published: July 2002

The fluid-dynamic and solid-body interactions among a suspension of perfectly elastic particles settling in a viscous gas are studied. The Reynolds number of the particles, Re≡ρfUa/μ, is small but their Stokes number St≡mŪ/(6πμa2) is large, indicating that particle inertia and viscous forces in the fluid are important. Here, ρf is the density of the fluid, m is the mass of a particle, Ū is the average velocity of the particles, a is their radius, and μ is the fluid viscosity. Equations for the particle velocity distribution and averages of the fluid and particle velocities are derived. For very large Stokes numbers, St≫φ−3/2, where φ is the particle volume fraction, solid-body collisions lead to a nearly Maxwellian velocity distribution. On the other hand, at smaller Stokes numbers, St≪φ−3/2, fluid-dynamic interactions play a more important role in determining the particle velocity distribution and the distribution is not Maxwellian. The amount of energy contained in the particle velocity fluctuations is determined by a balance involving fluid-dynamic interactions, even in the case where the solid-body collisions lead to a nearly Maxwellian velocity distribution. The viscous interactions are found to be similar to those in a fixed bed at high Stokes numbers, St≫φ−3/4, where the particles do not respond quickly to changes in the local fluid velocity. A stability analysis of the averaged equations indicates that the suspension is unstable to particle density waves for St≫φ−3/2. The inertia of the particles is destabilizing, while the energy introduced into the fluctuating motions of the particles by viscous flow interactions is stabilizing.
The origin of a characteristic frequency in hard thermal turbulence
Authors: Vincent Alain P. , Hansen Ulrich , Yuen David , Malevsky Andrei V. , Kroening Sherri E.
Published: July 2002

New methods are proposed for filtering the time series of heat flux which is useful for detecting the characteristic frequencies in hard turbulent convection. High-resolution solutions have been obtained for a Rayleigh (Ra) of 108 and infinite Prandtl number in a box with an aspect ratio of 1.8, in which the finest grid consisting of 140×400 bicubic splines was used. Successively higher temporal derivatives and high-pass spectral filtering of the Nusselt number at this high Ra reveal the existence of bursts. They are closely related to the presence of plumes in the thermal boundary layer in that there is a relative absence of activity in the boundary layer just before the onset of a burst and, on the other hand, there is a period of intense activity shortly before the end of a burst. These bursts are spaced evenly in time, thus yielding a single characteristic frequency, which may be related to a period associated with a pulsation mechanism in hard turbulent convection.
The effect on an acoustic wave as it traverses an unsteady expansion
Authors: Paull A. , Stalker R. J.
Published: July 2002

The shift in fundamental frequency that occurs in acoustic waves is obtained for waves traversing an unsteady expansion. It is shown analytically that downstream of the unsteady expansion all frequencies approach one of an infinite number of discrete frequencies independent of the frequency upstream of the unsteady expansion. This theoretical analysis is used to accurately predict the period of noise observed in an expansion tube when operated at low enthalpies.
A criterion for vortex street breakdown
Authors: Marshall J. S.
Published: July 2002

A new theoretical development for vortex street wakes, which includes viscous dissipation, is used to derive an analytical criterion for breakdown of the street. The analysis shows that beyond a certain critical distance downstream of the wake-generating cylinder, a perturbation in wavelength will rapidly grow, destroying the periodicity of the vortex street. This event is identified with vortex street breakdown, and a simple expression is given for the minimum downstream distance at which the breakdown may occur. The results are consistent with existing experimental data and qualitative observations of the vortex street breakdown phenomenon.
Chaotic behavior of finite inertia particles in ABC flow
Authors: Peskin Richard L. , Tanz Jonathan M.
Published: July 2002

Lagrangian trajectories in ABC flow have been studied by Dombre et al.1 for the purpose of analyzing chaos in three-dimensional Hamiltonian systems. In this paper we report on the study of finite particles (i.e., particles with inertia and dissipation) embedded in an ABC flow. Both linear and nonlinear drag models were examined. Because the dynamics must be represented in a six-dimensional phase space (rather than three dimensions for the pure Lagrangian ABC flow), and such high dimension spaces are difficult to visualize, we use a three-dimensional projection to study individual particle trajectories. Specially developed interactive graphics tools were used to facilitate the search for strange attractor regions, and computations were done on a 128 processor hypercube computer. The system is dissipative, and the expected folding appears; trajectories fold in about the unstable stagnation points in the flow. These regions of folding are outside the principal vortices, and the folding regions appear to be bounded by the KAM surfaces that would be associated with the Hamiltonian ABC flow. Strange attractors are, observed in the steady-state trajectories. As the drag becomes very small, both the linear and nonlinear models approach the limiting case of ABC flow. While this seems reasonable, the ‘‘zero drag’’ limit is singular, in the sense that the six-dimensional phase space problem would have to become a three-dimensional problem in the limit of point particles. When released in a periodic or quasiperiodic region, a particle with a linear drag force retains trajectory regularity, even if it crosses a chaotic region. This was not true for the nonlinear drag model. The introduction of particles can be thought of as a perturbation of ABC flow, and as drag increases this perturbed flow exhibits increasing breakdown of KAM-like surfaces, leading to larger chaotic regions. Future work will concentrate on the particle perturbations to the base ABC flow, and more examination of the phase space projections which may possibly give information on basins of attraction.
Sharp boundary analysis of electrostatic flute modes
Authors: Lemons Don S.
Published: July 2002

A linear, electrostatic, stability analysis of a magnetized cross-field drifting plasma with a sharp boundary is presented. The analysis corrects an error in a previously published sharp boundary theory [Phys. Fluids 19, 882 (1976)] and extends another theory [Geophys. Res. Lett. 14, 60 (1987)] to include finite electron mass and non-neutral perturbations. The instability’s long wavelength structure is associated with the classical flute instability, while the peak of the growth rate curve, at much shorter wavelengths, is a Buneman-like instability.
Measurements of the toroidal plasma rotation velocity in TFTR major-radius compression experiments with auxiliary neutral beam heating
Authors: Bitter M. , Wong K. L. , Scott S. , Hsuan H. , Grek B. , Johnson D. , Tait G.
Published: July 2002

The time history of the central toroidal plasma rotation velocity in Tokamak Fusion Test Reactor (TFTR) experiments [Phys. Rev. Lett. 55, 2587 (1985)] with auxiliary heating by neutral deuterium beam injection and major-radius compression has been measured from the Doppler shift of the emitted Ti XXI Kα line radiation. The experiments were conducted for neutral beam powers in the range 2.1–3.8 MW and line-averaged densities in the range 1.8–3.0×1019 m−2. The observed rotation velocity increase during compression is consistent with theoretical estimates.
Transition from reactive to kinetic electromagnetic instabilities generated by ring-beam ions
Authors: Ziebell L. F. , Yoon Peter H. , Wu C. S.
Published: July 2002

The dispersion relation for the low-frequency electromagnetic waves propagating parallel to the ambient magnetic field is studied for a plasma comprised of energetic ring-beam distribution of ions and a background population. Detailed properties of the dispersion relation are studied for various physical parameters with particular emphasis placed on the transition from the cold case to the thermal regime. In addition, the stability characteristics are investigated for different values of α, where tan α is the ratio between the ring and the beam velocity, ranging from α=0 (pure beam) to α=90° (pure ring). The unstable modes are studied in further detail, and the dependence of the growth rate on several parameters, such as the density of the ring-beam ions and thermal speeds associated with the background and the ring-beam ions, is discussed.
Simulations of constant poloidal beta experiments on ZT-40M using a one-dimensional multispecies transport model
Authors: Veerasingam Ramana , Klevans Edward H. , Werley Kenneth A. , Nebel Richard A. , Weber Paul G.
Published: July 2002

A one-dimensional (1-D) multispecies transport model for the reversed-field pinch plasma, which includes neutral deuterium and a coronal nonequilibrium model for impurities, is used to simulate a set of ZT-40M [Fusion Technol. 10, 307 (1986)] experiments. In these experiments, the radiation fraction is varied from 15% to 95% by use of krypton seeding, while the plasma operating parameters Iφ and ne are constrained to within a small variation from a fixed operating point. In effect, these experiments maintain an almost constant βθe on axis for the range of radiation fractions. The simulations match experimental estimates of particle, energy, and nonradiative confinement times, and of the electron poloidal beta. The results show that the anomalous thermal transport needed to reproduce the observed experimental behavior, i.e., constant βθe on axis, can be modeled by use of a small amount of parallel thermal conduction. Such a model phenomenologically accounts for anomalous heat transport due to fluctuations or stochastic field line diffusion. This model is also used for parametric studies on the design conditions of ZTH [Bull. Am. Phys. Soc. 31, 1546 (1984)]. To achieve the ZTH design values it is necessary for particle and thermal diffusivities to improve by a factor of 10–15 over ZT-40M.
80 kV, 8.9 kJ plasma focus experiments
Authors: Fishbine B. H. , Mather J. W. , Woodall D. M.
Published: July 2002

High-voltage, low-energy, Mather-geometry plasma focus experiments were performed to study large sheath formation input power, fast rundown, and current optimization and stabilization during collapse and pinch. For the parameters of these experiments, large bank impedance and short implosion time lead to small pinch current depression. Double-peaked x-ray emission data correlates with I-dot compression spikes; Cu Kα radiation is believed to dominate. I-dot data indicate that on-axis sheath bouncing occurs. Center electrode damage, reduced compression dynamics, and sheath bouncing suggest the use of larger electrode radius for these operating parameters. B-dot probe data indicate a rundown current sheath full-width-half-maximum thickness of 7.4 mm.
General solution for an asymmetric snowplow in Z-pinch-like geometry
Authors: Salberta E. , Parks D. , Waisman E.
Published: July 2002

The simple snowplow model has been extended into two dimensions in an x-y geometry for the study of radially imploding plasmas with azimuthal density asymmetries. When reduced to dimensionless form à la Krall and Trivelpiece [Principles of Plasma Physics (McGraw-Hill, New York, 1973), pp. 123–128], the resultant family of solutions depend upon two parameters rather than one. A numeric algorithm for the solution of these equations has been developed and solutions for several choices of the parameters are shown.
Simultaneous measurement of velocity and temperature by the use of a laser Doppler velocimeter
Authors: Sano Osamu , Takaki Ryuji
Published: July 2002

A simple, new method of measuring velocity and temperature simultaneously without imparting any disturbances to the fluid is developed. The key idea is to use a certain liquid that undergoes thermochromism as a test fluid, the temperature of which can be observed directly by its color change or measured quantitatively by a suitable optical method. If a laser Doppler velocimeter is used, the temperature at the measuring point, in addition to the velocity, can be determined simultaneously and instantaneously by detecting the otherwise discarded intensity of the transmitted light of the laser beams. This method was applied to measurements of distributions of velocity and temperature of a plume in a Hele–Shaw cell. Results were in fairly good agreement with similarity laws derived theoretically in this paper.
Lightning return stroke. A numerical calculation of the optical radiation
Authors: Paxton A. H. , Gardner R. L. , Baker Louis
Published: July 2002

A numerical model for a lightning channel that includes a multigroup treatment of radiative transport was used to calculate the optical output corresponding to an assumed current waveform. The calculation compares well with the experimental data that are available. The time development of the temperature, pressure, density, and electrical conductivity profiles across the channel were investigated, as was the energy balance for the process.
Generation of lower-hybrid noise by superthermal cross-field ion currents
Authors: Barbosa D. D.
Published: July 2002

A kinetic model for generating lower-hybrid waves by a low-density, superthermal ion beam directed across a magnetic field is investigated. Growth rate calculations demonstrate the salient features of the process, in particular, the small threshold drift of several background ion thermal speeds required for instability. The mechanism is suitable for collisionless dissipation in systems which evince the characteristics of anomalous resistivity in the presence of relatively small electrical currents.
Magnetic islands at the field reversal surface in reversed field pinches
Authors: Pinsker R. I. , Reiman A. H.
Published: July 2002

In the reversed field pinch (RFP), magnetic field perturbations having zero poloidal mode number and any toroidal mode number are resonant at the field reversal surface. Such perturbations are a particular threat to the RFP because of their weak radial dependence at low toroidal mode number, and because the toroidal field ripple is essentially of this type. The widths of the resulting islands are calculated in this paper. The self-consistent plasma response is included through the assumption that the plasma relaxes to a Taylor force-free state. The connection with linear tearing mode theory is established for those limits where arbitrarily large islands result from infinitesimal perturbations. Toroidal effects are considered, and application of the theory to RFP experiments is discussed.
Oscillatory instabilities in the Rayleigh–Bénard problem with a free surface
Authors: Benguria R. D. , Depassier M. C.
Published: July 2002

The linear stability theory of the Rayleigh–Bénard problem when the fluid is bounded above by a free deformable surface is studied numerically. When the free surface is thermally insulated and the lower surface is isothermic the marginal curve for the onset of oscillatory convection lies below the marginal curve for the exchange of stabilities.
Anisotropic pressure tokamak equilibrium and stability considerations
Authors: Salberta E. R. , Grimm R. C. , Johnson J. L. , Manickam J. , Tang W. M.
Published: July 2002

Investigation of the effect of pressure anisotropy on tokamak equilibrium and stability is made with a magnetohydrodynamic model. Realistic perpendicular and parallel pressure distributions, P⊥(ψ,B) and P∥(ψ,B), are obtained by solving a one-dimensional Fokker–Planck equation for neutral beam injection to find a distribution function f (E,v∥/v) at the position of minimum field on each magnetic surface and then using invariance of the magnetic moment to determine its value at each point on the surface. The shift of the surfaces of constant perpendicular and parallel pressure from the flux surfaces depends strongly on the angle of injection. This shift explains the observed increase or decrease in the stability conditions. Estimates of the stabilizing effect of hot trapped ions indicate that a large fraction must be nonresonant and thus decoupled from the bad curvature before it becomes important.
The onset of plume dynamics in the spectral space
Authors: Vincent Alain P. , Yuen David A.
Published: July 2002

Time-dependent convection for infinite Prandtl number fluids has been investigated hitherto in the physical domain. Dynamics of plumelike structures resulting from boundary-layer instabilities can be interpreted in the spectral domain as having both direct and inverse cascades of energy taking place. In the physical domain only a small part of the spectrum is discernible. But the rest of the spectrum is needed for properly describing the nonlinear process. Only a relatively few modes, fewer than ten, are actually required for describing the essential features associated with the onset of plume dynamics.
The decay of axisymmetric homogeneous turbulence
Authors: Chasnov J. R.
Published: July 2002

The decay of a homogeneous turbulence generated by an axisymmetric distribution of random impulsive forces acting at the initial instant is studied by means of large-eddy simulations. The impulsive forces may be either parallel or perpendicular to the symmetry axis. For impulsive forces, which result in a k4 low wave number energy spectrum of the turbulence, it is determined that the flow approaches isotropy on all scales of motion at long times, provided the Reynolds number is large. However, for the type of impulsive forces originally proposed by Saffman [J. Fluid Mech. 27, 581 (1967)], in which a k2 low wave number energy spectrum is produced, the turbulence approaches isotropy only at the smallest scales, and remains significantly anisotropic at the largest and energy-containing scales. Nevertheless, a similarity state of the flow field establishes itself asymptotically, in which the kinetic energy per unit mass of the turbulence decays as t−6/5.