bluuebunny/crossref_metadata_2025 huggingface dataset:
Flow of zero-point energy and exploration of phase space in classical simulations of quantum relaxation dynamics
Authors: Stock Gerhard , Müller Uwe
Published: July 2002

Necessary conditions under which a classical description will give the correct quantum relaxation behavior are analyzed. Assuming a nonequilibrium preparation, it is shown that the long-time mean values of observables can be expressed in terms of the spectral density and state-specific level densities of the system. Any approximation that reproduces these quantities therefore yields the correct expectation values at long times. Apart from this rigorous condition, a weaker but more practical criterion is established, that is, to require that the total level density is well approximated in the energy range defined by the spectral density. Since the integral level density is directly proportional to the phase-space volume that is energetically accessible to the system, the latter condition means that an appropriate classical approximation should explore the same phase-space volume as the quantum description. In general, however, this is not the case. A well-known example is the unrestricted flow of zero-point energy in classical mechanics. To correct for this flaw of classical mechanics, quantum corrections are derived which result in a restriction of the classically accessible phase space. At the simplest level of the theory, these corrections are shown to correspond to the inclusion of only a fraction of the full zero-point energy into the classical calculation. Based on these considerations, a general strategy for the classical simulation of quantum relaxation dynamics is suggested. The method is (i) dynamically consistent in that it refers to the behavior of the ensemble rather than to the behavior of individual trajectories, (ii) systematic in that it provides (rigorous as well as minimal) criteria which can be checked in a practical calculation, and (iii) practical in that it retains the conceptional and computational simplicity of a standard quasiclassical calculation. Employing various model problems which allow for an analytical evaluation of the quantities of interest, the virtues and limitations of the approach are discussed.
Structure and vibrational dynamics of the benzene dimer
Authors: Špirko Vladimı́r , Engkvist Ola , Soldán Pavel , Selzle Heinrich L. , Schlag Edward W. , Hobza Pavel
Published: July 2002

Point-wise evaluated coupled-cluster single double triple [CCSD(T)] stabilization energies are used to parameterize the nonempirical model (NEMO) empirical intermolecular potential of the benzene dimer in the ground electronic state. The potential is used for theoretical interpretation of the dimer structure and the dynamics of its intermolecular motions. Only one energy minimum, corresponding to the T-shaped structure, is found. A parallel displaced structure is the first-order transition structure separating the molecular symmetrically equivalent T-shaped structures. Due to a relatively high transition barrier (∼170 cm−1), the interconversion tunneling is unimportant in the energy region spanned by the available rotational spectra and is thus neglected (accordingly, the molecular symmetry group which is used for interpretation of the available experimental spectra is related to the T-shaped structure with two feasible internal rotations and nonequivalent monomers). The dimer undergoes a nearly free internal rotation along the axis connecting the benzene centers of mass in the T-shaped equilibrium geometry and a hindered internal rotation (the barrier being ∼46 cm−1) along the axis that is perpendicular to the “nearly free” internal rotation axis. The tunneling splittings observed in the rotational spectrum are likely due to this hindered rotation. An analysis assuming the latter rotation as an independent motion and using purely vibrational tunneling splittings (obtained by extrapolating to zero values of the rotational quantum numbers) indicates that the genuine value of the hindered rotation barrier is nearly twice higher than its ab initio value. Similarly, the difference ΔR=0.25 Å between the ab initio (equilibrium) and experimental (ground state) values for the distance of the mass centers of the benzene monomers is strong evidence that our theoretical potential is much shallower than the genuine one. The Raman bands observed at the 3–10 cm−1 region seem to involve states associated with the nearly free rotation and the “energy minimum path” bending motion. Unambiguous assigning of the weaker Raman features is infeasible, partly due to limitations in the accuracy of the theoretical potential, and partly due to the lack of knowledge of the polarizability tensor of the dimer and temperature at which the spectra were taken.
Physical and mathematical content of coupled-cluster equations. III. Model studies of dissociation processes for various reference states
Authors: Jankowski K. , Kowalski K.
Published: July 2002

The structure and physical significance of the full set of solutions to coupled-cluster (CC) equations at various stages of the dissociation process and the impact of the choice of reference functions on these solutions have been studied for the first time. The equations for the CC method involving double excitations (CCD) are obtained for the P4 model consisting of two H2 molecules in a rectangular nuclear configuration determined by a geometry parameter α. We consider equations for the reference states |ΦA〉, |ΦQ〉, and |ΦB〉 corresponding to the lowest, highest, and intermediate Hartree–Fock (HF) energies, respectively. The first two states provide a size-consistent description of the dissociation process. For the compact-molecule geometries (α<10.0) the sets of complete solutions to the standard CCD equations [based on molecular orbitals (MOs) of D2h symmetry] in the spin–orbital and spin–symmetry-adapted versions always consist of 20 and 12 entries, respectively. For |ΦA〉 and |ΦB〉 in the dissociation limit (α→∞) only for the latter version the solutions can be attained by homotopy method. In this case we have reformulated the standard spin–symmetry-adapted CCD equations to a version based on the use of localized orbitals (LO) which is extremely simple and can be solved analytically providing an understanding of the unexpected peculiarities of the solutions for α→∞. For |ΦA〉 and |ΦQ〉, there are only two regular solutions. For the remaining 10 solutions, the CCD wave functions are meaningless despite the fact that the corresponding CCD energies are equal to the exact values.
Etching effects during the chemical vapor deposition of (100) diamond
Authors: Battaile C. C. , Srolovitz D. J. , Oleinik I. I. , Pettifor D. G. , Sutton A. P. , Harris S. J. , Butler J. E.
Published: July 2002

Current theories of CVD growth on (100) diamond are unable to account for the numerous experimental observations of slow-growing, locally smooth (100)(2×1) films. In this paper we use quantum mechanical calculations of diamond surface thermochemistry and atomic-scale kinetic Monte Carlo simulations of deposition to investigate the efficacy of preferential etching as a mechanism that can help to reconcile this discrepancy. This etching mechanism allows for the removal of undercoordinated carbon atoms from the diamond surface. In the absence of etching, simulated growth on the (100)(2×1) surface is faster than growth on the (110) and (111) surfaces, and the (100) surface is atomically rough. When etching is included in the simulations, the (100) growth rates decrease to values near those observed experimentally, while the rates of growth on the other surfaces remain largely unaffected and similar to those observed experimentally. In addition, the etching mechanism promotes the growth of smooth (100) surface regions in agreement with numerous scanning probe studies.
The averaged density matrix in the coordinate representation: Application to the calculation of the far-wing line shapes for H2O
Authors: Ma Q. , Tipping R. H.
Published: July 2002

The far-wing line shape theory within the binary collision and quasistatic framework developed previously for linear molecules using the coordinate representation has been generalized to symmetric- and asymmetric-top molecular systems. However, due to more variables needed to specify the orientation of these complicated molecules, one has to evaluate multidimensional integrals with higher dimensionality and this would be intractable for practical calculations. In cases where the anisotropic interaction contains cyclic coordinates, one can carry out the integration of the density matrix over these coordinates analytically and obtain the “averaged” density matrix. This reduces the dimensionality of the multidimensional integrals and thus dramatically reduces the computational time necessary to obtain converged results. In addition, a new interpolation method that enables one to treat more realistic potential models has been formulated. Using these results, calculations for the band-average far-wing line shapes and corresponding absorption coefficients in the spectral range 300–1100 cm−1 have been carried out for H2O–H2O and H2O–N2 pairs for a few temperatures. These results improve the agreement with experimental data over previous calculations that were limited in the number of states that could be included and in the sophistication of the anisotropic interaction potential model that was used.
Doppler-free optical–optical double resonance polarization spectroscopy of the K8539Rb 1 1Π and 2 1Π states
Authors: Kasahara Shunji , Fujiwara Chizuru , Okada Naoko , Katô Hajime , Baba Masaaki
Published: July 2002

High resolution spectra of the 1 1Π(v′=13–69,J′)←X 1Σ+(v″,J″) and 2 1Π(v′=0–13,J′)←X 1Σ+(v″,J″) transitions of the K8539Rb molecule have been measured with the technique of Doppler-free optical–optical double resonance polarization spectroscopy (OODRPS). Molecular constants of the 1 1Π(v=13–69) and 2 1Π(v=0–13) levels have been determined, and potential energy curves constructed by the RKR method. The RKR potential of the 1 1Π state was found to have a distortion at outer wall, which originates from an avoided crossing of two  1Π states. The perturbations between the 1 1Π(v1,J) and 2 1Π(v2,J) levels were found from the energy shifts of the rotational levels. The magnitude of the nonadiabatic interaction between the 1 1Π(v1=54) and 2 1Π(v2=9) levels, 〈1 1Π(v1=54)|TN|2 1Π(v2=9)〉, was evaluated to be 2.2 cm−1 by a least squares fitting to the energy shifts of the 1 1Π(v1=54,J=20–33) levels. The line intensities were observed to change dramatically around the maximum energy shift. These intensity anomalies are interpreted as an interference effect, which occurs when two interacting levels have comparable transition moments. A remarkable line broadening was observed for the transitions to the 1 1Π(v⩾63) levels, and it was identified as originating from the predissociation to K(4s2S1/2)+Rb(5p2P1/2) atoms. The dissociation energies of the X 1Σ+, 1 1Π, and 2 1Π states have been determined to be 4217.4±0.8, 2021.5±0.8, and 1050.0±0.8 cm−1, respectively.
On the nature of thermal diffusion in binary Lennard-Jones liquids
Authors: Reith Dirk , Müller-Plathe Florian
Published: July 2002

The aim of this study is to understand deeper the thermal diffusion transport process (Ludwig–Soret effect) at the microscopic level. For that purpose, the recently developed reverse nonequilibrium molecular dynamics method was used to calculate Soret coefficients of various systems in a systematic fashion. We studied binary Lennard-Jones (LJ) fluids near the triple point (of one of the components) in which we separately changed the ratio of one of the LJ parameters mass, atomic diameter, and interaction strength while keeping all other parameters fixed and identical. We observed that the magnitude of the Soret coefficient depends on all three ratios. Concerning its sign we found that heavier species, smaller species, and species with higher interaction strengths tend to accumulate in the cold region whereas the other ones (lighter, bigger or weaker bound) migrate to the hot region of our simulation cell. Additionally, the superposition of the influence of the various parameters was investigated as well as more realistic mixtures. We found that in the experimentally relevant parameter range the contributions are nearly additive and that the mass ratio often is the dominating factor.
Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations
Authors: Weiss John
Published: July 2002

We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painlevé property, a Bäcklund transformation is defined in terms of an expansion about the singular manifold. This Bäcklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Bäcklund transformations of the modified equations provides a method for the iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev–Petviashvili equation and the Hirota–Satsuma equations.
On the one- and two-dimensional Toda lattices and the Painlevé property
Authors: Gibbon J. D. , Tabor M.
Published: July 2002

The Toda lattice and the two-dimensional Toda lattice (2-DTL) are shown to possess a type of ‘‘Painlevé property’’ that is based on the use of separate ‘‘singular manifolds’’ for each dependent variable. The isospectral problem for the 2-DTL found by both Mikhailov and by Fordy and Gibbons can be simply and logically derived from this analysis. Some remarks are made about the connection between our work and independent work of Kametaka and Airhault on the relationship between the Toda lattice and the second Painlevé transcendent.
Ermakov and non-Ermakov systems in quantum dissipative models
Authors: Nassar Antônio B.
Published: July 2002

Via the hydrodynamical formulation of quantum mechanics, a unified protocol to treat the quantum time-dependent harmonic oscillator with friction is presented, described by two different models: an explicitly time-dependent, linear Schrödinger equation (Caldirola–Kanai model) and a logarithmic nonlinear Schrödinger equation (Kostin model). For the former model, an Ermakov system that makes it possible to obtain an invariant of Ermakov–Lewis-type is derived. For the latter model, a non-Ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of Ermakov–Lewis-type exists.
First-order conserved densities for gas dynamics
Authors: Verosky John M.
Published: July 2002

For a certain choice of pressure the equations of gas dynamics can be diagonalized, making it easy to calculate some first-order conserved densities of the system. Using the Hamiltonian structure of these equations, third-order symmetries are seen to exist by the Noether correspondence. Such higher-order phenomena are usually associated with a linearization, but in this case, no linearization is obvious.
Bäcklund transformations for the Caudrey–Dodd–Gibbon–Sawada–Kotera equation and its λ-modified equation
Authors: Chan W. L. , Zheng Yu-kun
Published: July 2002

A λ-modified equation for the Caudrey–Dodd–Gibbon–Sawada–Kotera equation is introduced. A new Bäcklund transformation for this equation is derived from the invariance property of the scattering problem for the Caudrey–Dodd–Gibbon–Sawada–Kotera equation under a Crum transformation [Q. J. Math. 6, 121 (1955)]. This, in turn, gives rise to a new Bäcklund transformation for the Caudrey–Dodd–Gibbon–Sawada–Kotera equation.
A class of connections governing parallel transport along density matrices
Authors: Dittmann Jochen , Rudolph Gerd
Published: July 2002

A class of connections governing parallel transport along nondegenerate density matrices is discussed. These connections are given by certain analytic functions. We develop a calculus for operator-valued differential forms, which enables us to calculate the curvature of these connections. The class under consideration contains a non-Abelian generalization of Berry’s phase recently proposed by Uhlmann.
Wronskian solutions of the constrained Kadomtsev–Petviashvili hierarchy
Authors: Oevel Walter , Strampp Walter
Published: July 2002

The integrable Kadomtsev–Petviashvili (KP) hierarchy is compatible with generalized k-constraints of the type (Lk)−=∑i qi∂−1xri. A large class of solutions—among them solitons—can be represented by Wronskian determinants of functions satisfying a set of linear equations. In this paper we shall obtain additional conditions for these functions imposed by the constraints.
Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach
Authors: Rañada Manuel F.
Published: July 2002

The properties of superintegrable systems in two degrees of freedom, possessing three independent globally defined constants of motion, are studied using as an approach, the existence of hidden symmetries and the generalized Noether’s theorem. The potentials are obtained as solution of a system of two partial differential equations. First the case of standard Lagrangians is studied and then the method is applied to the case of Lagrangians with a pseudo-Euclidean kinetic term. Finally, the results are related with other approaches and with a family of potentials admitting a second integral of motion cubic in the velocities obtained by Drach.
Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions
Authors: Pelinovsky Dmitry
Published: July 2002

A general approach to constructing the polynomial solutions satisfying various reductions of the Kadomtsev–Petviashvili (KP) hierarchy is described. Within this approach, the reductions of the KP hierarchy are equivalent to certain differential equations imposed on the τ-function of the hierarchy. In particular, the l-reduction and the k-constraint as well as their generalized counterparts are considered. A general construction of the rational solutions to these reductions is found and the particular solutions are explicitly derived for some typical examples including the KdV and Gardner equations, the Boussinesq and classical Boussinesq systems, the NLS and Yajima–Oikawa equations. It is shown that the degenerate rational solutions of the KP hierarchy are related to stationary manifolds of the Calogero–Moser (CM) hierarchy of dynamical systems. The scattering dynamics of interacting particles in the CM systems may become complicated due to an anomalously slow fractional-power rate of the particle motion along the stationary manifolds.
Determinant formula for the six-vertex model with reflecting end
Authors: Tsuchiya Osamu
Published: July 2002

Using the quantum inverse scattering method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six-vertex model with reflecting end.
The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model
Authors: Hou Bo-yu , Yang Wen-Li
Published: July 2002

From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars–Schneider model (cf. Ruijsenaars). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero–Moser model.
Classical and quantum mechanics with time-dependent parameters
Authors: Sardanashvily G.
Published: July 2002

We show that composite bundles Q→Σ→R, where Σ→R is the parameter bundle, provide the adequate mathematical description of mechanical systems with time-dependent parameters both in classical and quantum mechanics. In particular, the Berry phase phenomenon is described in terms of connections on composite Hilbert space bundles.
On the generation of helical waves in circular pipe flow
Authors: Landman Michael J.
Published: July 2002

The question of the existence of helical waves in fluid flow through a circular pipe is discussed. In the case of pipe flow forced only by an axial pressure gradient, direct simulations have failed to find any self-sustaining helical waves. The effect of residual swirl in the inlet flow is investigated, by performing linear stability calculations and direct simulations of a forced basic flow. The results are qualitatively similar to that of flow in a rotating pipe, in which stable helical waves are known to exist. These results suggest that residual rotation may be an important mechanism in triggering laminar-turbulent transition in circular pipe flow.
The outer region of a turbulent boundary layer
Authors: Phillips W. R. C. , Ratnanather J. T.
Published: July 2002

Matched asymptotic expansions are used as a framework from which to derive differential equations that describe the mean velocity and turbulence fields in the outer region of a zero-pressure-gradient turbulent boundary layer. Attention is focused upon solutions to these equations in the very outer region or superlayer, where the boundary layer merges with the outer flow. It is found that both the velocity and turbulence fields approach their free-stream values exponentially fast as Townsend [The Structure of Turbulent Shear Flow (Cambridge U.P., Cambridge, 1976)] had foreseen, but not necessarily in the detailed manner he conjectured. These details are used to help construct approximate solutions for the mean velocity and turbulence fields in the outer region that display the correct asymptotic form both in the logarithmic region and the superlayer. The resulting solution for mean velocity is closely in accord with Coles’ law of the wake and accurately reproduces data over the complete Reynolds number range for which the boundary layer is turbulent; likewise the profiles for the turbulence intensities. It is further shown that the turbulence intensities conform to a law analogous to the law of the wake.
Fingering instability of a gravitationally driven contact line
Authors: Jerrett John M. , de Bruyn John R.
Published: July 2002

Results of an experimental study of the flow of a viscous fluid down an inclined plane are presented. The contact line at the front of the flow is straight in the early stages of the flow, then becomes unstable to the formation of fingers. From measurements of the contact line position as a function of time for angles of inclination α in the range 0°<α≤32°, the flow is analyzed before and after the instability occurs, and the development of the finger pattern is parametrized.
Confinement of multiply charged ions in an electron cyclotron resonance heated mirror plasma
Authors: Petty C. C. , Goodman D. L. , Smatlak D. L. , Smith D. K.
Published: July 2002

Multiply charged ions are studied in the Constance B quadrupole mirror experiment [Phys. Rev. Lett. 59, 1821 (1987)] in order to better understand the ion physics of electron cyclotron resonance (ECR) high charge-state ion sources. By measuring the ion densities and end loss fluxes, the parallel confinement times for the first five charge states of oxygen plasmas are determined. The parallel ion confinement times increase with charge state and peak on axis, both indications of an ion-confining potential dip created by the hot electrons. The radial profile of ion end loss is normally hollow, with the peak fluxes occurring at the edge of the ECR zone. An attempt is made to increase the end loss flux of a selected ion species by decreasing its parallel confinement time using minority ion cyclotron resonance heating (ICRH). In addition, an ion model is developed to predict the ion densities, end loss fluxes, and confinement times using the ion particle balance equations, the quasineutrality condition, and theoretical confinement time formulas. The model generally agrees with the experimental data to within experimental error.
Doppler-shifted cyclotron resonance maser driven by an electrostatic pumped beam
Authors: Spassovsky I. P. , Nikolov N. A. , Kostov K. G. , Spassov V. A. , Velichkov J. N. , Yovchev I. G. , Loza O. T.
Published: July 2002

A Doppler-shifted cyclotron resonance maser experiment using a 500 keV, 30 nsec high-current electron beam emitted by a Blumlein pulse accelerator has produced approximately 20 and 8 MW at frequencies of 13 and 37 GHz in TE01 and TE03 waveguide modes, respectively. The beam has been electrostatically pumped by means of a strongly inhomogeneous electrostatic field created in the diode region. The experimental results are in a good agreement with the numerical calculations of a cold system electrostatic field and with simulation studies of beam propagation. The transverse electron velocity has been estimated on the basis of the performed computations and experimental measurements.
Non-Spitzer heat flow in a steadily ablating laser-produced plasma
Authors: Bell A. R.
Published: July 2002

Electron energy transport in a laser-produced ablating plasma is modeled by the Vlasov–Fokker–Planck equation for electrons and the fluid equations for cold ions. These equations are solved using approximations which maintain good accuracy but allow faster computational solution than was previously possible. It is found that the spatial profiles for temperature and density in planar geometry differ very little from those calculated from the Spitzer conductivity. At high laser intensities, the plasma flow diverges as it flows away from the solid target and the effects of nonplanar flow are important. This is modeled by the adoption of spherical geometry, and it is found that the Spitzer conductivity breaks down and the temperature and density profiles differ significantly from those calculated using the Spitzer conductivity.
Convection transitions within a vertical cylinder heated from below
Authors: Figliola R. S.
Published: July 2002

Flow visualization experiments were conducted on a confined vertical column of fluid heated from below. The experiments were performed using a high Prandtl number fluid at Rayleigh numbers up to 118 000 in an apparatus having a height-to-width ratio of unity. An axisymmetric motion was documented at the onset of convection, followed by two distinct three-dimensional motions as the Rayleigh number was increased.
Equilibrium for radiation in a homogeneous plasma
Authors: Caflisch Russel E. , Levermore C. David
Published: July 2002

Entropy increase and comparison principles are found for the Fokker–Planck equation for the radiation field in a homogeneous plasma with constant electron temperature. When emission– absorption is neglected, this is used to find equilibrium distributions that have the form of a Planck distribution plus a δ function at zero photon energy. For distributions below the Planck and with emission–absorption included, a rate of entropy increase is obtained. Numerical results confirm these conclusions.
Current in wave-driven plasmas
Authors: Karney Charles F. F. , Fisch Nathaniel J.
Published: July 2002

A theory for the generation of current in a toroidal plasma by radio-frequency waves is presented. The effect of an opposing electric field is included, allowing the case of time varying currents to be studied. The key quantities that characterize this regime are identified and numerically calculated. Circuit equations suitable for use in ray-tracing and transport codes are given.
The stability of a stratified shear layer
Authors: Satyanarayana P. , Lee Y. C. , Huba J. D.
Published: July 2002

The stability of a stratified shear layer is investigated using an exponential density profile and a laminar shear flow with a continuous velocity distribution. It is shown that an exact stability boundary can be obtained for an inhomogeneous inviscid fluid under the action of gravity without the need to impose the Boussinesq approximation. The stability boundary is given by J=k̂2(1−β2/4−k̂2), where β is the ratio of the velocity and density gradient scale sizes, J is the Richardson number, and k̂ is the perpendicular wavenumber normalized to the velocity gradient scale size; this reduces to the stability boundary derived by Drazin [J. Fluid Mech. 4, 214 (1958)] in the limit β=0. The solution allows for c=β/2, where c is the normalized phase velocity.
Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation
Authors: Kim H. J. , Durbin P. A.
Published: July 2002

Vortex shedding and instability wave frequencies have been measured in the wakes of spheres in the Reynolds number range 500<Re<60 000. The effect of acoustic excitation was examined and an interaction between the two frequency modes was found at the lower Reynolds numbers; through this interaction, external forcing at the instability frequency could change the vortex shedding frequency. The development of the mean wake was manipulated by forcing near to the dominant shear layer instability frequency. With this forcing, the separated shear layer moved closer to the surface of the sphere and the reversed flow region of the wake was shortened. Concomitantly, the base pressure decreased and drag increased.
On the behavior of two-equation models at the edge of a turbulent region
Authors: Cazalbou J. B. , Spalart P. R. , Bradshaw P.
Published: July 2002

The flow structure predicted in the vicinity of free-stream edges by two-equation eddy-viscosity turbulence models is examined. Analytical expansions, previously used by several authors, are shown to be weak solutions to the pure nonlinear diffusion problem, connecting with trivial solutions in the nonturbulent region. They remain locally valid solutions to the full one-dimensional system of model equations in the vicinity of the edge, provided that some constraints on the turbulent ‘‘Prandtl numbers’’ are satisfied. Calculations performed with the (k,ε) turbulence model for a time-evolving mixing layer and a flat-plate boundary layer in zero pressure gradient are fully consistent with the analysis. In contradiction of a prior study by Lele [Phys. Fluids 28, 64 (1985)], the modeled turbulent-kinetic-energy, dissipation-rate, and shear-stress fronts are found to propagate into the nonturbulent region at the same velocity, with no need for any special relationship between the model constants. Implications related to the calibration of models are discussed.
Turbulent vortex breakdown
Authors: Sarpkaya Turgut
Published: July 2002

Reported herein is a cone-shaped turbulent vortex breakdown in noncavitating swirling flows at high Reynolds numbers in a slightly diverging cylindrical tube. The turbulent conical form is in addition to the well-known double-helix, spiral, and nearly axisymmetric or ‘‘bubble’’-type breakdowns.
Linear two-dimensional stability of a Burgers vortex layer
Authors: Beronov Kamen N. , Kida Shigeo
Published: July 2002

A linear stability analysis is presented for a stationary Burgers vortex layer in irrotational straining flow, to normal mode disturbances invariant in the direction of main flow vorticity. The whole neutral curve is calculated by combining numerical and asymptotic analysis. It is similar to that for free mixing layers which are always unstable, except that there is unconditional stability below a critical Reynolds number, in agreement with the long-wave asymptotic result by Neu [J. Fluid Mech. 143, 253 (1984)]. The Reynolds number compares shear flow vorticity versus stretching rate and diffusion, so both latter factors are stabilizing if strong enough. Neutral disturbances represent standing waves.
High-frequency acoustic noise emitted by initial impact of solid sphere falling onto liquid surface
Authors: Likhterov L.
Published: July 2002

The high-frequency part of the sound wave spectrum generated by an initial impact of a solid sphere falling onto a quiescent liquid surface is considered. At the initial stage of the process, when a sphere hits the liquid vertically, the usual equations of continuity, momentum, and state (in Tait’s form) are used for a lower half-space. Moreover, the Kirkwood and Bethe hypothesis is used, too. This approximation allows the pressure field to be obtained and then the Fourier transform can be calculated for determination of the sound spectrum. It is shown that, in the first row approximation, the spectral density of the acoustic energy emitted by falling sphere diminishes approximately 4.3 decibels per octave.
A new flow regime in a Taylor–Couette flow
Authors: Lim T. T. , Chew Y. T. , Xiao Q.
Published: July 2002

In this Brief Communication, we report a new finding on a Taylor–Couette flow in which the outer cylinder is stationary and the inner cylinder is accelerated linearly from rest to a desired speed. The results show that when the acceleration (dRe/dt) is higher than a critical value of about 2.2 s−1, there exists a new flow regime in which the flow pattern shows remarkable resemblance to regular Taylor vortex flow but is of shorter wavelength. However, when the acceleration is lower than 2.2 s−1, a wavy flow is found to occur for the same Reynolds number range. To our knowledge, this is probably the first time that such a phenomenon has been observed. For completeness, the case of a decelerating cylinder is also investigated, and the results are found to be almost the same.
Double-helical pairing in plane mixing layers
Authors: Estevadeordal Jordi , Kleis Stanley J.
Published: July 2002

Double-helical pairing is identified in the second vortex pairing of a spanwise-unforced plane mixing layer. Phase-locked measurements using two-dimensional (2D) periodic acoustic excitation reveal that as the rollers of the second pairing approach each other, three-dimensional (3D) modes become amplified in each roller. Rollers then revolve around each other, forming a double helix with spanwise wavelength on the order of the streamwise lengthscale. Some spanwise areas exhibit a more advanced pairing stage than others, producing “branched” vortex patterns.
Anticonvection in systems with heat release on the interface
Authors: Nepomnyashchy A. A. , Simanovskii I. B. , Braverman L. M.
Published: July 2002

The generation of anticonvection in the presence of heat sources (or sinks) homogeneously distributed on the interface in layers with finite thickness, is studied in the framework of linear theory. The general transformation formula, which predicts the existence of anticonvection in any fluid system, is derived. This formula is applied to a system of real fluids.
Piston flow in a two-dimensional channel
Authors: Katopodes Fotini V. , Davis A. M. J. , Stone H. A.
Published: July 2002

A solution using biorthogonal eigenfunctions is presented for viscous flow caused by a piston in a two-dimensional channel. The resulting infinite set of linear equations is solved using Spence’s optimal weighting function method [IMA J. Appl. Math. 30, 107 (1983)]. The solution is compared to that with a shear-free piston surface; in the latter configuration the fluid more rapidly approaches the Poiseuille flow profile established away from the face of the piston.
X-ray radiographic imaging of hydrodynamic phenomena in radiation-driven materials—Shock propagation, material compression, and shear flow*
Authors: Hammel B. A. , Kilkenny J. D. , Munro D. , Remington B. A. , Kornblum H. N. , Perry T. S. , Phillion D. W. , Wallace R. J.
Published: July 2002

One- and two-dimensional, time-resolved x-ray radiographic imaging at high photon energy (5–7 keV) is used to study shock propagation, material motion and compression, and the effects of shear flow in solid density samples which are driven by x-ray ablation with the Nova laser. By backlighting the samples with x rays and observing the increase in sample areal density due to shock compression, the trajectories of strong shocks (∼40 Mbars) in flight are directly measured in solid density plastic samples. Doping a section of the samples with high-Z material (Br) provides radiographic contrast, allowing a measurement of the shock-induced particle motion. Instability growth due to shear flow at an interface is investigated by imbedding a metal wire in a cylindrical plastic sample and launching a shock in the axial direction. Time-resolved radiographic measurements are made with either a slit-imager coupled to an x-ray streak camera or a pinhole camera coupled to a gated microchannel plate detector, providing ∼10 μm spatial and ∼100 ps temporal resolution.
A dispersion function for plasmas containing superthermal particles
Authors: Mace R. L. , Hellberg M. A.
Published: July 2002

It is now well known that space plasmas frequently contain particle components that exhibit high, or superthermal, energy tails with approximate power law distributions in velocity space. Such nonthermal distributions, with overabundances of fast particles, can be better fitted, for supra- and superthermal velocities, by generalized Lorentzian or kappa distributions, than by Maxwellians or one of their variants. Employing the kappa distribution, with real values of the spectral index κ, in place of the Maxwellian we introduce a new plasma dispersion function expected to be of significant importance in kinetic theoretical studies of waves in space plasmas. It is demonstrated that this function is proportional to Gauss’ hypergeometric function 2F1[1,2κ+2;κ+2;z] enabling the well-established theory of the hypergeometric function to be used to manipulate dispersion relations. The reduction, for integer values of κ, to the less general so-called modified plasma dispersion function [Phys. Fluids B 3, 1835 (1991)] is demonstrated. An example illustrating the use of the function is presented.
Dynamic modeling of magnetically insulated transmission line systems
Authors: Mendel C. W. , Rosenthal S. E.
Published: July 2002

Negative conductors in vacuum transmission lines used in multiterrawatt applications emit electrons freely. These lines are efficient only because the self-magnetic field of the power flow forces the electrons to flow parallel to the electrodes. Excepting numerical simulations, dynamic modeling of systems of these transmission lines has generally either ignored electron flow, or has included only those electrons that cross immediately to the anode at the front of the forward wave. In this paper we describe an analytic model that includes flowing electrons and the effects of these flows on line voltage and on the reduction of magnetic flux. Axial electron currents are modeled using simple, measurable, and calculable parameters. Transverse electron currents are modeled using general patterns found empirically from simulation data. These currents are in turn related by an expanded set of Telegrapher equations. An example of the use of the model is compared to two-dimensional, time-dependent particle-in-cell simulations.
Observation of space-charge driven beam instabilities in a radio frequency photoinjector
Authors: Dowell D. H. , Joly S. , Loulergue A. , de Brion J. P. , Haouat G.
Published: July 2002

This article describes an experimental determination of the correlated, longitudinal phase-space electron distribution produced by a radio frequency photoinjector. Measurements of the electron beam energy spectra and pulse shapes are analyzed to deduce the longitudinal phase space at the exit of the photoinjector rf cavity. Data were obtained for micro-pulse charges of 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 nC, and show different phenomena in the low-charge and high-charge regimes. At low beam charge, the uncorrelated energy spread increases with increasing charge density, while rf bunching appears to cancel any pulse-length elongation due to the space-charge forces. At high beam charge, the data show that the micro-pulse separates into three distinct sub-pulses of nearly equal charge, and with a temporal separation proportional to the relativistic plasma frequency. These effects are compared with the space-charge generated instabilities and virtual-cathode phenomena observed in lower voltage devices. The implications that these results have upon the fundamental limits of beam brightness and magnetic pulse compression limitations are discussed.
The electron-acoustic mode in a plasma with hot suprathermal and cool Maxwellian electrons
Authors: Mace R. L. , Amery G. , Hellberg M. A.
Published: July 2002

The electron-acoustic wave, in a plasma with hot suprathermal, kappa-distributed electrons and cool, Maxwellian electrons, is investigated. This model is a generalization of those that have been investigated previously, and through its parametrization by κ, can be reduced to many previous models of the stable wave. It is found that the hot suprathermal electrons significantly increase the Landau damping of the wave at small wave numbers, i.e., in its acoustic regime. Results from a survey of parameter space, which help to identify parameters for which the stable mode will be only weakly Landau damped, are presented. The dependence of the Landau damping on the fraction of suprathermal electrons, which is related to the index, κ, of the hot electron distribution, is investigated in detail.
Theory of perturbed equilibria for solving the Grad–Shafranov equation
Authors: Zakharov L. E. , Pletzer A.
Published: July 2002

The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad–Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.
Flow impedance in a uniform magnetically insulated transmission line
Authors: Mendel C. W. , Seidel D. B.
Published: July 2002

In two recent publications [C. W. Mendel, Jr. and S. E. Rosenthal, Phys. of Plasmas 2, 1332 (1995), C. W. Mendel, Jr. and S. E. Rosenthal, Phys. of Plasmas 3, 4207 (1996)] relativistic electron flow in cylindrical magnetically insulated transmission lines was analyzed and modeled under the assumption of negligible electron pressure. The model allows power flow in these lines to be accurately calculated under most conditions. The model was developed for coaxial right circular cylindrical electrodes. It is shown here that the model applies equally well to arbitrary cylindrical systems, i.e., systems consisting of electrodes of arbitrary cross section.
Broadly tunable infrared parametric oscillator using AgGaSe2
Authors: Eckardt R. C. , Fan Y. X. , Byer R. L. , Marquardt C. L. , Storm M. E. , Esterowitz L.
Published: July 2002

The first successful operation of a AgGaSe2 infrared parametric oscillator is reported. Continuous tuning ranges of 1.6–1.7 μm, 6.7–6.9 μm, and 2.65–9.02 μm were achieved using 1.34-μm neodymium and 2.05-μm holmium pump lasers. Pulse energies exceeding 3 mJ, peak powers near 100 kW, and conversion efficiencies of 18% were obtained. Operation of the parametric oscillator was possible well below the 13–40 MW/cm2 surface damage threshold of this nonlinear material.
Optical probing of the mechanical impulse response of a transducer
Authors: Royer D. , Dieulesaint E.
Published: July 2002

The mechanical impulse response of a piezoelectric transducer has been plotted by using an optical interferometric heterodyne probe. The sensitivity of this Mach–Zehnder type probe is better than 10−4 Å/(Hz)1/2. Transient displacements of a few angstroms have been detected in a single sweep with a 20-MHz bandwidth.
Raman scattering in Ga0.47In0.53As/InP superlattices grown by metalorganic vapor phase epitaxy
Authors: Davey S. T. , Spurdens P. C. , Wakefield B. , Nelson A. W.
Published: July 2002

Raman scattering in two Ga0.47In0.53As/InP superlattices is reported. Scattering by folded longitudinal acoustic phonons has been observed and interpreted using the elastic continuum theory. The data yield superlattice periods of 18.0 and 12.1 nm. The optical phonon energies are observed to be different from bulk values.
Electroabsorption of highly confined systems: Theory of the quantum-confined Franz–Keldysh effect in semiconductor quantum wires and dots
Authors: Miller D. A. B. , Chemla D. S. , Schmitt-Rink S.
Published: July 2002

Semiconductor quantum wells are known to show large electroabsorption (e.g., the quantum-confined Stark effect) that results in low-energy optical modulating and switching devices. We show theoretically that the electroabsorption and associated electrorefraction in lower dimensional structures could be much larger, suggesting very low energy devices. We illustrate the theory with specific calculations for hypothetical GaAs-like quantum wires and dots.
Excimer laser induced oxidation of ion-implanted silicon
Authors: Fogarassy E. , White C. W. , Slaoui A. , Fuchs C. , Siffert P. , Pennycook S. J.
Published: July 2002

We have investigated laser-induced oxidation of ion-implanted Si using a repetitively pulsed ArF laser, working at low-energy density (100–500 mJ/cm2). Oxidation is observed at energy densities between the melt threshold and that required for epitaxial recrystallization of the amorphous layer. At these energy densities, oxidation is not observed on virgin silicon. The factors that influence the oxidation process are discussed.
Archimedean solids: Transition metal mediated rational self-assembly of supramolecular-truncated tetrahedra
Authors: Leininger Stefan , Fan Jun , Schmitz Marion , Stang Peter J.
Published: July 2002

A family of nanoscale-sized supramolecular cage compounds with a polyhedral framework is prepared by self-assembly from tritopic building blocks and rectangular corner units via noncovalent coordination interactions. These highly symmetrical cage compounds are described as face-directed, self-assembled truncated tetrahedra with Tdsymmetry.
Asymptotic solution of the cylindrical nonlinear Poisson–Boltzmann equation at low salt concentration: Analytic expressions for surface potential and preferential interaction coefficient
Authors: Shkel Irina A. , Tsodikov Oleg V. , Record M. Thomas
Published: July 2002

The analytic solution to the nonlinear Poisson–Boltzmann equation describing the ion distributions surrounding a nucleic acid or other cylindrical polyions as a function of polyion structural quantities and salt concentration ([salt]) has been sought for more than 80 years to predict the effect of these quantities on the thermodynamics of polyion processes. Here we report an accurate asymptotic solution of the cylindrical nonlinear Poisson–Boltzmann equation at low to moderate concentration of a symmetrical electrolyte (≤0.1 M 1:1 salt). The approximate solution for the potential is derived as an asymptotic series in the small parameter ɛ
−1
, where ɛ ≡ κ
−1
/
a
, the ratio of the Debye length (κ
−1
) to the polyion radius (
a
). From the potential at the polyion surface, we obtain the coulombic contribution to the salt–polyelectrolyte preferential interaction (Donnan) coefficient (Γ

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) per polyion charge at any reduced axial charge density ξ. Γ

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is the sum of the previously recognized low-salt limiting value and a salt-dependent contribution, analytically derived here in the range of low-salt concentrations. As an example of the application of this solution, we obtain an analytic expression for the derivative of the midpoint temperature of a nucleic acid conformational transition with respect to the logarithm of salt concentration (

dT
m

/
d
ln[salt]) in terms of [salt] and nucleic acid structural quantities. This expression explains the experimental observation that this derivative is relatively independent of salt concentration but deviates significantly from its low-salt limiting value in the range 0.01–0.1 M.