bluuebunny/crossref_metadata_2025 huggingface dataset:
General recurrence theory of ligand binding on a three-dimensional lattice
Authors: Kong Yong
Published: July 2002

Several general conclusions are obtained for the finite linear three-dimensional lattice models which are built by replicating two-dimensional layers in the third dimension. It is shown that the linear lattice, although less symmetrical, has a simpler structure than the circular lattice where the periodical boundary condition is imposed. If the ligands bound in one layer interact with ligands on its d neighbor layers, the size of the transfer matrix M for the linear lattice is equal to the number of unique binding configurations in d consecutive layers, which is usually smaller than the size of the original transfer matrix M′ that determines the recurrence relation of the circular lattice. In certain situations a significant reduction of the matrix size can be achieved. Matrix M′ contains all the eigenvalues of matrix M in addition to other eigenvalues if the binding configurations are degenerate. The global partition functions as well as the contracted partition functions at either end of the linear lattice obey the same unique and minimum recurrence relation determined by the secular equation of M. The two ends of the linear lattice, which break the symmetry of the circular lattice, actually make the linear lattice simpler than the circular lattice. The reduced size of the transfer matrix (or the order of the recurrence relation) for the linear lattice not only makes the model more accessible, but also allows the model to describe linear systems more accurately by making the model closer to the system under study. The general theory is applied to several lattices with simple geometries that are of interest in biology and statistical mechanics.
Density functional theory study on ethanol dimers and cyclic ethanol trimers
Authors: González Leticia , Mó Otilia , Yáñez Manuel
Published: July 2002

The structure and the relative stability of the ethanol dimer and the cyclic ethanol trimer were studied using density functional theory methods. The geometries of the different dimers and trimers were optimized at the B3LYP/6-311+G(d,p) level of theory, while the final energies were obtained at the B3LYP/6-311+G(3df,2p) level. Four different (ethanol)2 complexes were found to be local minima of the potential energy surface, the global minimum being that in which both monomers exhibit a trans conformation. The hydrogen bond (HB) in ethanol dimer is slightly stronger than in methanol dimer, reflecting the enhanced intrinsic basicity of ethanol with regards to methanol. The OH donor stretch appears redshifted by 161 cm−1, while the redshifting undergone by the OH acceptor stretch is negligibly small. The relative stability of the trimers is a function of the number of monomers with a gauche conformation, the global minimum being that in which the three monomers have a trans conformation. As for water and methanol trimers, the three HBs in the cyclic ethanol trimer are not strictly equivalent. Consistently, the redshiftings of the OH stretching frequencies are different. Cooperative effects are sizably large, as reflected in the O⋯O distances, the elongation of the OH donor groups, the charge density at the bond critical points, the frequency shiftings of the OH stretches, and the additivity interaction energy. The most significant features of the vibrational spectra of the monomers, the dimers, and the trimers in the 800–1200 cm−1 region are reasonably well reproduced by our calculations.
Relating colloidal particle interactions to gel structure using Brownian dynamics simulations and the Fuchs stability ratio
Authors: Mellema M. , van Opheusden J. H. J. , van Vliet T.
Published: July 2002

Brownian dynamics simulations of aggregation of hard-sphere dispersions at intermediate volume fractions (∼3–10 vol%) have been performed. A long-range activation energy for aggregation was incorporated. The bonds formed were irreversible and flexible. Cluster growth rate and fractal properties of the gel matrix could be related to particle interactions by using a Fuchs stability ratio WF. Although this approach is expected to apply only to the very early stages of gelation, WF was shown to be a useful parameter, especially for predicting gel matrix parameters like the fractal dimensionality Df (which is a measure of the compactness of the clusters in the intermediate or fractal length scale regime) and the correlation length ξ (which is a measure of the average gel pore size). The number of aggregates, Nagg, was found to be a convenient measure of the stage of aggregation for the range of volume fractions and interactions studied. For high values of WF, the value of Df was more generic (i.e., less dependent of WF or φ). In addition, the fractal parameters were less dependent on WF at higher φ. These observations can be explained by the limited formation of (diffusion-kinetics type) depletion zones in the presence of repulsive barriers compared to purely attractive systems.
Perturbed ground state method for electron transfer
Authors: Prezhdo Oleg V. , Kindt James T. , Tully John C.
Published: July 2002

A novel ab initio method is presented for characterization of electron transfer (ET). The method utilizes perturbed ground state (PGS) properties of the ET systems in order to evaluate the electron donor–acceptor coupling and the donor–acceptor energy splitting. Since no excited states are involved in calculations, density functional implementation of the method provides an efficient way to include electron correlation effects for ET in large chemical systems. The PGS method is applied to two model systems and is compared with high-level ab initio results. The PGS method performs very well for the test systems. The method is more general than traditional techniques, providing both the ET coupling and the donor–acceptor energy splitting.
A single Lanczos propagation method for calculating transition amplitudes
Authors: Chen Rongqing , Guo Hua
Published: July 2002

A method using only a single Lanczos propagation to determine multiple transition amplitudes without the explicit calculation of the eigenstates is proposed. Comparing with methods requiring multiple propagations, this method is very attractive for large dimensional problems since the propagation is usually the most computationally intensive step. When overlaps between eigenstates and pre-specified quantum states are of interest, it is shown that the “spurious” Lanczos eigenvalues cannot be simply deleted as done in the Cullum–Willoughby procedure. Practical procedures for calculating the overlaps are provided, which take into consideration numerical behaviors of the Lanczos algorithm in finite precision arithmetic, such as the loss of global orthogonality and emergence of “spurious” eigenvalues. Numerical tests in a realistic triatomic system confirm the accuracy of the present method.
Comparison of Chebyshev, Faber, and Lanczos propagation-based methods for calculating resonances
Authors: Xie Daiqian , Chen Rongqing , Guo Hua
Published: July 2002

We compare the numerical performance of three recursive methods for calculating collisional resonances, which are characterized by complex eigenenergies of an optical potential augmented Hamiltonian. The first approach involves a modified Chebyshev propagation of a real wave packet, followed by low-storage filter-diagonalization. A similar filter-diagonalization scheme replaces the Chebyshev propagation with a more general Faber recursion associated with a specific conformal mapping in the complex plane. The complex resonance eigenenergies are also obtained using a complex-symmetric version of the Lanczos algorithm. Numerical tests for a realistic triatomic system (HCO) indicate that the Lanczos method and the low-storage filter-diagonalization based on the Chebyshev propagation are much more efficient than the Faber approach.
Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics
Authors: Leaver E. W.
Published: July 2002

The differential equation, x(x−x0)(d2y/dx2)+(B1+B2x) (dy/dx)+[ω2x(x−x0) −[2ηω(x−x0)+B3]y=0, arises both in the quantum scattering theory of nonrelativistic electrons from polar molecules and ions, and, in the guise of Teukolsky’s equations, in the theory of radiation processes involving black holes. This article discusses analytic representations of solutions to this equation. Previous results of Hylleraas [E. Hylleraas, Z. Phys. 71, 739 (1931)], Jaffé [G. Jaffé, Z. Phys. 87, 535 (1934)], Baber and Hassé [W. G. Baber and H. R. Hassé, Proc. Cambridge Philos. Soc. 25, 564 (1935)], and Chu and Stratton [L. J. Chu and J. A. Stratton, J. Math. Phys. (Cambridge, Mass.) 20, 3 (1941)] are reviewed, and a rigorous proof is given for the convergence of Stratton’s spherical Bessel function expansion for the ordinary spheroidal wave functions. An integral is derived that relates the eigensolutions of Hylleraas to those of Jaffé. The integral relation is shown to give an integral equation for the scalar field quasinormal modes of black holes, and to lead to irregular second solutions to the equation. New representations of the general solutions are presented as series of Coulomb wave functions and confluent hypergeometric functions. The Coulomb wave-function expansion may be regarded as a generalization of Stratton’s representation for ordinary spheroidal wave functions, and has been fully implemented and tested on a digital computer. Both solutions given by the new algorithms are analytic in the variable x and the parameters B1, B2, B3, ω, x0, and η, and are uniformly convergent on any interval bounded away from x0. They are the first representations for generalized spheroidal wave functions that allow the direct evaluation of asymptotic magnitude and phase.
Quotient of manifolds by discrete groups
Authors: Ardalan F. , Arfaei H.
Published: July 2002

The quotient of manifolds by discrete subgroups of their isometry group are considered. In particular, symmetry breaking due to the quotient structure, topological properties, and harmonic analysis of the resultant manifolds are discussed and illustrated by two-dimensional examples. New solutions of d=11 supergravity and the d=6 Einstein–Yang–Mills theory are thus obtained, for which alterations in their spectrum and symmetry breaking are discussed.
Spin-polarized Thomas–Fermi theory
Authors: Goldstein Jerome A. , Ruiz Rieder Gisèle
Published: July 2002

Of concern is a rigorous Thomas–Fermi theory of electron densities for spin-polarized quantum-mechanical systems. The number N↑, N↓ of spin-up and spin-down electrons are specified in advance, and one seeks to minimize the energy functional E(ρ↑,ρ↓) =c1∫R3(ρ↑(x)5/3 +ρ↓(x)5/3)dx +c2∫R3∫R3[ρ(x)ρ(y)/‖x −y‖]dx dy +∫R3V(x)ρ(x)dx, where c1, c2 are given positive constants, ρ↑ and ρ↓ are non-negative functions, ρ=ρ↑ +ρ↓ is the total electron density, ∫R3ρ↑(x)dx =N↑, ∫R3ρ↓(x)dx =N↓, and V is a given potential. These results are analogous to the classical rigorous (spin-unpolarized) Thomas–Fermi theory developed by Lieb and Simon [Phys. Rev. Lett. 33, 681 (1973)] and by Bénilan and Brezis (‘‘The Thomas–Fermi problem,’’ in preparation).
Lie algebras associated with scalar second-order ordinary differential equations
Authors: Mahomed F. M. , Leach P. G. L.
Published: July 2002

Second-order ordinary differential equations are classified according to their Lie algebra of point symmetries. The existence of these symmetries provides a way to solve the equations or to transform them to simpler forms. Canonical forms of generators for equations with three-point symmetries are established. It is further shown that an equation cannot have exactly r ∈{4,5,6,7} point symmetries. Representative(s) of equivalence class(es) of equations possessing s ∈{1,2,3,8} point symmetry generator(s) are then obtained.
The covariant linear oscillator and generalized realization of the dynamical SU(1,1) symmetry algebra
Authors: Kagramanov E. D. , Mir-Kasimov R. M. , Nagiyev Sh. M.
Published: July 2002

An exactly solvable problem for the finite-difference Schrödinger equation in the relativistic configurational space is considered. The appropriate finite-difference generalization of the factorization method is developed. The theory of new special functions ‘‘the relativistic Hermite polynomials,’’ in which the solutions are expressed, is constructed.
Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
Authors: Ma Wen-xiu
Published: July 2002

A method of constructing Lax representations for isospectral and nonisospectral hierarchies of evolution equations is proposed. It is shown that under some simple but essential conditions, the corresponding Lax operators may constitute infinite-dimensional Lie algebras with respect to the binary operation ■⋅,⋅■ given in this paper. Furthermore, the detailed analyses for the KdV couple, the AKNS couple, and a new couple of isospectral and nonisospectral hierarchies of integrable equations are presented as examples.
Linear undulator brightness: Exact analytical treatment
Authors: Dattoli G. , Giannessi L. , Mari C. , Richetta M. , Torre A.
Published: July 2002

In this paper it is shown that the calculation of linearly polarized undulator brightness can be worked out exactly using elliptic functions and multivariable generalized Bessel functions. The obtained results are shown to be valid both in nonrelativistic and ultrarelativistic regimes. The physical relevance of the obtained results are discussed and the ‘‘low-energy’’ corrections to the resonance condition are derived.
Reduced description of electric multipole potential in Cartesian coordinates
Authors: Hinsen K. , Felderhof B. U.
Published: July 2002

The electrostatic potential due to a multipole moment of order l is expressed in terms of 2l+1 independent Cartesian multipole components. The multipole expansion of the electrostatic interaction energy between two charge distributions is reduced correspondingly to the minimum number of Cartesian components.
Collineations of the Ricci tensor
Authors: Bokhari Ashfaque H. , Qadir Asghar
Published: July 2002

Ricci collineations for the Ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of Rab(r) (such that Rab≠0 for a=b). It turns out that the only collineations admitted by this tensor can be ten, six, or four and there does not appear any case in between.
Finite-dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem
Authors: Xianguo Geng
Published: July 2002

A method is developed that extends the nonlinearization procedure of eigenvalue problems to the discrete case, from which the finite-dimensional discrete systems and finite-dimensional completely integrable systems associated with the Toda hierarchy are obtained. A new model for solving discrete soliton equations is proposed, which enables one to get the solutions of the Toda lattice equations by solving the compatible systems of discrete equations and nonlinear ordinary differential equations.
Orbit–orbit branching rules for families of classical Lie algebra–subalgebra pairs
Authors: Thoma M. , Sharp R. T.
Published: July 2002

Complete orbit–orbit branching rules are derived for each classical algebra–maximal-subalgebra pair Cm+nCm⊕Cn, Bm+nDm⊕Bn, Dm+nDm⊕Dn. Since each pair is equal rank, and algebra and subalgebra Weyl sectors line up, the integrity basis in each case consists of the subalgebra orbits contained in the fundamental orbits of the algebra.
Path integral solution of the Schrödinger equation in curvilinear coordinates: A straightforward procedure
Authors: LaChapelle J.
Published: July 2002

A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schrödinger equation in curvilinear coordinates. An important feature of the formalism is that a coordinate transformation in the variables of the wavefunction does not imply a change of variable of integration in the path integral. Consequently, a transformation from Euclidean to curvilinear coordinates is simple to handle; there is no need to introduce ‘‘quantum corrections’’ into the action functional. Furthermore, the paths are differentiable: hence, issues related to stochastic paths do not arise. The procedure for constructing the path integral solution of the Schrödinger equation is straightforward. The case of the Schrödinger equation in spherical coordinates for a free particle is presented in detail.
Higher-order BRST and anti-BRST operators and cohomology for compact Lie algebras
Authors: Chryssomalakos C. , de Azcárraga J. A. , Macfarlane A. J. , Pérez Bueno J. C.
Published: July 2002

After defining cohomologically higher-order BRST and anti-BRST operators for a compact simple algebra 𝒢, the associated higher-order Laplacians are introduced and the corresponding supersymmetry algebra Σ is analyzed. These operators act on the states generated by a set of fermionic ghost fields transforming under the adjoint representation. In contrast with the standard case, for which the Laplacian is given by the quadratic Casimir, the higher-order Laplacians W are not, in general, given completely in terms of the Casimir–Racah operators, and may involve the ghost number operator. The higher-order version of the Hodge decomposition is exhibited. The example of su(3) is worked out in detail, including the expression of its higher-order Laplacian W.
Reduction theory and the Lagrange–Routh equations
Authors: Marsden Jerrold E. , Ratiu Tudor S. , Scheurle Jürgen
Published: July 2002

Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré, and others. The modern vision of mechanics includes, besides the traditional mechanics of particles and rigid bodies, field theories such as electromagnetism, fluid mechanics, plasma physics, solid mechanics as well as quantum mechanics, and relativistic theories, including gravity. Symmetries in these theories vary from obvious translational and rotational symmetries to less obvious particle relabeling symmetries in fluids and plasmas, to subtle symmetries underlying integrable systems. Reduction theory concerns the removal of symmetries and their associated conservation laws. Variational principles, along with symplectic and Poisson geometry, provide fundamental tools for this endeavor. Reduction theory has been extremely useful in a wide variety of areas, from a deeper understanding of many physical theories, including new variational and Poisson structures, to stability theory, integrable systems, as well as geometric phases. This paper surveys progress in selected topics in reduction theory, especially those of the last few decades as well as presenting new results on non-Abelian Routh reduction. We develop the geometry of the associated Lagrange–Routh equations in some detail. The paper puts the new results in the general context of reduction theory and discusses some future directions.
q
-deformed Poisson random variables on q-Fock space
Authors: Saitoh Naoko , Yoshida Hiroaki
Published: July 2002

The q-deformed Poisson distribution has been introduced as the orthogonalizing probability measure for a certain q-deformation of Charlier polynomials, which is reduced to the usual Poisson distribution in the limit q→1 and takes the free Poisson distribution in case of q=0. We give the operator on the q-Fock space, which has the q-deformed Poisson distribution with respect to the vacuum state. It is a linear combination of a q-number operator, a q-Gaussian random variable, and a scalar operator. This representation is of the same form as of Hudson and Parthasarathy on the symmetric Fock space.
Vortex pair generation and interaction with a free surface
Authors: Willmarth W. W. , Tryggvason G. , Hirsa A. , Yu D.
Published: July 2002

Two vertical, rotating flaps are used to generate a vortex pair beneath a free surface. Vortex pair formation, propagation, and interaction with a free surface are described. Numerical simulations for inviscid flow about a constant upwash sheet of vorticity beneath a free surface agree with experiment up to the time that turbulent mixing occurs during interaction with the free surface. The spacing between the vortex pairs then becomes larger than the calculated spacing. The experiments and lines of marked particles included in the simulations show fluid ingestion and transport toward the free surface.
Anomalous diffusion due to long-range velocity fluctuations in the absence of a mean flow
Authors: Koch Donald L. , Brady John F.
Published: July 2002

The dispersion of a tracer in a heterogeneous medium in which the tracer’s velocity has zero mean and a covariance that decays as x−γ with distance x is studied using nonlocal advection–diffusion theory. If the velocity covariance decays slowly, γ≤2, the tracer’s dispersive motion is non-Fickian even at long times after its release. Under these circumstances, it is not possible to predict the dispersion by assuming that the tracer samples the velocity fluctuations primarily by molecular diffusion, even if the fluctuations are weak. Instead, we develop a self-consistent theory in which the tracer samples each velocity fluctuation by the motion resulting from the other fluctuations. It is shown that in cases of anomalous diffusion, the tracer’s mean-square displacement grows faster than linearly with time—as t4/(2+γ) for 0<γ<2 and as t(ln t) 1/2 for γ≡2 as t→∞.
Steady, isentropic flows of dense gases
Authors: Cramer M. S. , Best L. M.
Published: July 2002

Steady isentropic flows of fluids in their dense gas regime are examined. It is shown that the Mach number may increase, rather than decrease, with density or pressure if the specific heats of the fluid are sufficiently large. Conditions are also reported under which isentropic expansions through converging–diverging nozzles are not possible, regardless of the imposed exit pressure. In such cases, the nozzle must be replaced with one having multiple throats. Applications to external transonic flows are briefly considered.
Shock wave effects on a turbulent flow
Authors: Rotman Douglas
Published: July 2002

A parametric study is done to investigate the change in a turbulent flow field caused by the passage of a shock wave. Two parameters are studied: the initial turbulent kinetic energy and the shock wave strength or density jump. A random or turbulent flow field is initiated within a two-dimensional box. Euler’s equations are then solved using a second-order accurate Godunov shock capturing method to calculate the change in turbulent structure and flow field parameters caused by the passage of a shock wave through the turbulent field. Two fields were analyzed, a random density field and a random velocity field. The passage of a shock through the random density field caused density and pressure variations that compare very well with experiments. Results of the shock passage through the random velocity field show that the shock causes an amplification in the turbulent kinetic energy of about 2 on a per unit mass basis. Furthermore, the length scale of the turbulent field behind the shock is smaller than that in front of the shock. Energy weighted wave numbers increase by as much as 30%. This change in length scales seems to be in disagreement with some experiments which seem to show larger time scales and larger length scales behind a shock, but in agreement with another experiment. For both results, fields containing strong shocks or weak turbulent fields yield the largest change in flow parameters. The shock wave is also affected by the turbulent field. Increasing the initial turbulent kinetic energy caused a straight shock wave to evolve into a shock containing curves and wrinkles of a size similar to the length scale of the unshocked turbulent field. These curves and wrinkles can lead to the generation of additional flow field oscillations.
Extension of the Mott-Smith method to denser gases
Authors: Orlov Alexander V.
Published: July 2002

The Mott-Smith method is used to find the shock wave solution of the Enskog equation in the linear approximation in n0σ3. The density profile, shock thickness, and nonunity asymmetry factor are found. Modified Hugoniot relations are derived.
Electromagnetic billiards
Authors: Bolcato R. , Etay J. , Fautrelle Y. , Moffatt H. K.
Published: July 2002

Moffatt has argued [J. Fluid. Mech. 218, 509 (1990)] that it should be possible to control the motion of a metallic sphere immersed in a nonconducting fluid using the electromagnetic force and couple generated by means of a traveling and/or rotating magnetic field applied externally. Such a system has been realized experimentally: one or more aluminum spheres are placed in a vessel containing fluid (air, water, or silicone oil), the whole being placed in an inductor which provides an upward-traveling magnetic field. The spheres move in response to the induced electromagnetic forces, the motion being influenced by gravity, viscous drag, vessel boundary reaction, and collisions. A range of possible behaviors, stable, unstable, and chaotic, are identified and discussed. The term ‘‘electromagnetic billiards’’ seems appropriate to describe this phenomenon.
Theory of ion temperature gradient instabilities: Thresholds and transport
Authors: Hassam A. B. , Antonsen T. M. , Drake J. F. , Guzdar P. N.
Published: July 2002

An investigation of the ion temperature gradient instability that focuses on the behavior of the mode when it is weakly unstable is presented. It is shown that ηi= (2)/(3) is the threshold for long wavelength instability, ηi being the ratio of the density gradient scale length to the ion temperature gradient scale length. For ηi>0.902, a short wavelength mode is concomitantly unstable. The transport resulting from both the short and the long wavelengths is shown to constitute a ‘‘soft’’ turn on of anomalous transport for ηi<2, with long (short) wavelengths dominating for high (weak) enough collisionality. The point ηi=2 represents a ‘‘hard’’ threshold for transport: Beyond this point, large, collisionless transport over all wavelengths is precipitated. A nonlocal collisional theory as well as a kinetic theory with a Krook collision operator are presented to describe the progression from weak to strong instability. Transport estimates, based on mixing length arguments, are given for the various regimes incorporated by the critical points ηi= (2)/(3) , 0.902, and 2.
One-dimensional relativistic Vlasov–Maxwell equilibria of charge-separation-free plasmas
Authors: Kamp Leon P. J. , Kerkhof M. J. , Sluijter F. W. , Weenink M. P. H.
Published: July 2002

The conditions under which charge separation is negligible or even absent are studied for one-dimensional relativistic Vlasov–Maxwell equilibria. These conditions are then employed to model the boundary between a vacuum magnetic field and a plasma that is free of charge separation for the cases with and without trapped particles.
Is the perpendicular resistivity in tokamaks really much greater than the Spitzer value?
Authors: Segre S. E. , Zanza V.
Published: July 2002

It has been suggested by various authors over the past 15 years, and also recently, that in tokamaks the perpendicular resistivity η⊥ is between 102 and 103 times the parallel (Spitzer) resistivity. Here it is shown that on the contrary the measurements on the FTU tokamak [Proceedings of the 16th Symposium on Fusion Technology, London, 1990 (North-Holland, Amsterdam, 1991), Vol. 1, p. 218] are consistent with η⊥/η∥=2 when the extended neoclassical theory is used (which is preferable to the conventional neoclassical theory for reasons which are here reviewed).
Effect of Hall currents on the steady convection of a current-carrying cylindrical plasma
Authors: Gomberoff K. , Gomberoff L.
Published: July 2002

The effect of Hall currents on the steady convection of a fully ionized current-carrying cylindrical plasma column surrounded by perfectly conducting walls is studied. In general, when the Hall term is large, it can affect the magnetohydrodynamic (MHD) stability problem significantly, but as long as it is small the instability persists and the marginal modes remain the same as without Hall currents. In some cases, though, even if the Hall term is large, the convective character of some modes is not changed. Thus, it is shown that convection due to the combined effect of resistivity and heat conductivity is not affected by Hall currents. However, convection due to heat conductivity and viscosity is no longer possible in the presence of Hall currents. When the combined effect of heat conductivity, resistivity, and viscosity is considered, the Hall term changes the stability properties of the system in such a way that there are no modes that are both marginal and stationary. Consequently, there are no convective modes in these conditions, except for the case of very large densities, or for very small longitudinal wave numbers, for which the Hall current term is shown to be negligible.
Weibel instability in relativistically hot magnetized electron–positron plasmas
Authors: Yang T.-Y. Brian , Gallant Yves , Arons Jonathan , Langdon A. Bruce
Published: July 2002

A linear stability analysis is carried out for the Weibel instability in relativistic magnetized electron–positron-pair plasmas, with the propagation direction parallel to the background magnetic field. The instability in the ultrarelativistic regime, with the typical Lorentz factor γ much greater than unity, is emphasized for its relevance to astrophysical sources of synchrotron radiation. Detailed stability properties are examined, in the ultrarelativistic regime, for two model distribution functions, the water-bag distribution function, and a smooth distribution function. The dispersion relations are obtained in closed analytic forms for both distribution functions. The necessary and sufficient conditions for instability are determined when the temperature along the background magnetic field is cold (T∥=0). The dispersion relations are solved numerically with T∥≠0 over a wide range of system parameters to determine the detailed dependence of the instability on the strength of the background magnetic field and the temperature anisotropy. The present analysis shows that both a decrease in temperature anisotropy and an increase in the background magnetic field can cause a significant decrease in growth rate. For the smooth distribution function, it is found that, for a given plasma density, the system stabilizes completely when the background magnetic field is stronger than the moderate threshold value [(ωp±/ωc±)2≤2/π], corresponding to T∥=0. As the temperature anisotropy decreases, the threshold magnetic field decreases.
Verification of frequency scaling laws for capacitive radio-frequency discharges using two-dimensional simulations*
Authors: Vahedi V. , Birdsall C. K. , Lieberman M. A. , DiPeso G. , Rognlien T. D.
Published: July 2002

Weakly ionized processing plasmas are studied in two dimensions using a bounded particle-in-cell (PIC) simulation code with a Monte Carlo collision (MCC) package. The MCC package models the collisions between charged and neutral particles, which are needed to obtain a self-sustained plasma and the proper electron and ion energy loss mechanisms. A two-dimensional capacitive radio-frequency (rf) discharge is investigated in detail. Simple frequency scaling laws for predicting the behavior of some plasma parameters are derived and then compared with simulation results, finding good agreements. It is found that as the drive frequency increases, the sheath width decreases, and the bulk plasma becomes more uniform, leading to a reduction of the ion angular spread at the target and an improvement of ion dose uniformity at the driven electrode.
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
Authors: Zawaideh Emad , Najmabadi Farrokh , Conn Robert W.
Published: July 2002

A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path λ to the scale length of the magnetic field gradient LB approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (λ/LB)2, are found to have errors of order (λ/Lu)2 =(λ/LB)2/(1−M2)2, where Lu is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (M≊1).
Nonlinear, dispersive, elliptically polarized Alfvén waves
Authors: Kennel C. F. , Buti B. , Hada T. , Pellat R.
Published: July 2002

The derivative nonlinear Schrödinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfvén waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg–de Vries and the modified Korteweg–de Vries solitons obtained previously for oblique propagation, but are more general. It is shown there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are charcterized.
Measurements of the collision properties of small spheres
Authors: Foerster Samuel F. , Louge Michel Y. , Chang Hongder , Allia Khédidja
Published: July 2002

An experiment to measure the properties of the collisions between two small spheres or between a small sphere and a semi-infinite flat wall are described. The apparatus releases the particles in a free-fall without initial spin. The impacts are modeled in terms of three coefficients. The first is the coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last characterizes the restitution of the tangential components of the velocity of the contact point for impacts that do not involve sliding. The coefficients are calculated from stroboscopic photographs of the ballistics of the particles near the collision. The results establish that the collision model provides an accurate description of the dynamics of the impacts.
Drop motion with surfactant transfer in a homogeneous surrounding
Authors: Rednikov Alexei Ye. , Ryazantsev Yuri S. , Velarde Manuel G.
Published: July 2002

The influence of a soluble surfactant on the stationary motion of a drop in an infinite motionless homogeneous surfactant solution is considered when the surfactant undergoes a first-order isothermal chemical reaction on the surface of the drop. The study is carried out for the asymptotic case of small Reynolds and Péclet numbers. First, the linear approximation is considered. It appears, in particular, that the hydrodynamical force acting on the drop provides either thrust or drag according to the parameter values. It also appears that the motion can be unstable and critical Marangoni numbers corresponding to instability thresholds of the motionless state of the fluids in the absence of buoyancy are provided. Emphasis is given to instability of the drop to its translations. A weakly nonlinear analysis past translational instability shows the possibility of multiple stationary states. On the one hand the hydrodynamical force dependence on the drop velocity can be nonmonotonous. Then, in particular, one may have either the rest state or self-sustained (autonomous), Marangoni-driven motion in the absence of buoyancy or any other external forcing factors. On the other hand, the velocity dependence on the hydrodynamical force can also be nonmonotonous. Then, in particular, in the absence of any external compensating forces one may have the drop levitating even under nonzero buoyancy. Finally, the relative stability of these nonlinear regimes and possible experimental observations are discussed.
Comparison of turbulent flame speeds from complete averaging and the G-equation
Authors: Embid Pedro F. , Majda Andrew J. , Souganidis Panagiotis E.
Published: July 2002

A popular contemporary approach in predicting enhanced flame speeds in premixed turbulent combustion involves averaging or closure theories for the G-equation involving both large-scale flows and small-scale turbulence. The G-equation is a Hamilton–Jacobi equation involving advection by an incompressible velocity field and nonlinear dependence on the laminar flame speed; this G-equation has been derived from the complete Navier–Stokes equations under the tacit assumptions that the velocity field varies on only the integral scale and that the ratio of the flame thickness to this integral scale is small. Thus there is a potential source of error in using the averaged G-equation with turbulent velocities varying on length scales smaller than the integral scale in predicting enhanced flame speeds. Here these issues are discussed in the simplest context involving velocity fields varying on two scales where a complete theory of nonlinear averaging for predicting enhanced flame speeds without any ad hoc approximations has been developed recently by the authors. The predictions for enhanced flame speeds of this complete averaging theory versus the averaging approach utilizing the G-equation are compared here in the simplest context involving a constant mean flow and a small-scale steady periodic flow where both theories can be solved exactly through analytical formulas. The results of this comparison are summarized briefly as follows: The predictions of enhanced flame speeds through the averaged G-equation always underestimate those computed by complete averaging. Nevertheless, when the transverse component of the mean flow relative to the shear is less than one in magnitude, the agreement between the two approaches is excellent. However, when the transverse component of the mean flow relative to the shear exceeds one in magnitude, the predictions of the enhanced flame speed by the averaged G-equation significantly underestimate those computed through complete nonlinear averaging, and in some cases, by more than an order of magnitude.
The numerical simulation of shock bifurcation near the end wall of a shock tube
Authors: Weber Y. S. , Oran E. S. , Boris J. P. , Anderson J. D.
Published: July 2002

The reflection of a normal shock wave from the end wall of a two-dimensional channel has been numerically simulated to investigate the unsteady, viscous interaction aspects of shock bifurcation. The numerical simulation implements a data-parallel version of the Flux-Corrected Transport algorithm that has been coupled to the viscous transport terms of the Navier–Stokes equations. All numerical simulations were performed on the Connection Machine, the CM-5. The results indicate that the shear layer in the bifurcation zone is unstable, and the large and small scale vortices lead to complex flow patterns. In addition, the high-speed, essentially inviscid flow, which is adjacent to the shear layer, is deflected over this region. As a result, weak shock and expansions waves are generated and a reattachment shock is formed at the trailing edge of the interaction region. The impact of heat transfer, Reynolds number, and incident shock strength on the viscous interaction is also investigated. Heat transfer to the walls weakens the interaction between the boundary layer and the reflected shock. However, the decreased Reynolds number and increased shock strength enhances the interaction.
On predicting the turbulence-induced secondary flows using nonlinear k-ε models
Authors: Mompean G. , Gavrilakis S. , Machiels L. , Deville M. O.
Published: July 2002

Low turbulent Reynolds number direct simulation data are used to calculate the invariants of the Reynolds stress and the turbulent dissipation rate in a square duct. The results show that, depending on the region where the analysis is carried out, the turbulent flow field comes close to one-, two-, and three-component states. Modeling such flows—even at higher Reynolds numbers—will require models that can approach all three states. A number of related nonlinear k-ε models are tested a priori using the direct simulation data. The numerical simulation using Reynolds averaged Navier–Stokes equations with these models was performed. Their ability to predict the secondary flows, with a low-Reynolds k-ε model, cannot be gauged from realizability.
Hypervelocity Richtmyer–Meshkov instability
Authors: Samtaney Ravi , Meiron Daniel I.
Published: July 2002

The Richtmyer–Meshkov instability is numerically investigated for strong shocks, i.e., for hypervelocity cases. To model the interaction of the flow with non-equilibrium chemical effects typical of high-enthalpy flows, the Lighthill–Freeman ideal dissociating gas model is employed. Richtmyer’s linear theory and the impulse model are extended to include equilibrium dissociation chemistry. Numerical simulations of the compressible Euler equations indicate no period of linear growth even for amplitude to wavelength ratios as small as one percent. For large Atwood numbers, dissociation causes significant changes in density and temperature, but the change in growth of the perturbations is small. A Mach number scaling for strong shocks is presented which holds for frozen chemistry at high Mach numbers. A local analysis is used to determine the initial baroclinic circulation generation for interfaces corresponding to both positive and negative Atwood ratios.
Numerical simulation of circular disks entering the free surface of a fluid
Authors: Gaudet S.
Published: July 2002

In this paper numerical simulations of the irrotational fluid flow associated with the entry of circular disks of a given mass into a semi-infinite fluid domain in the limits of very low to moderate Froude numbers are reported. This work is motivated by an experimental study performed by Glasheen and McMahon who investigated the low-Froude-number water entry of circular disks and found a linear relationship between the cavity seal depth and the Froude number and also showed that a single value of a modified drag coefficient is sufficient to predict the drag force on the disk. The numerical calculations performed in this paper confirm these experimental findings for steady cavity regimes and identify the ranges of Froude number and dimensionless mass values for which these results hold. Excellent agreement between the numerical computations and analytical velocity predictions, as well as the experimental cavity seal depth measurements, are obtained although the agreement between the measured and the computed drag coefficient values is not as good. The cavity seal depth and the drag coefficient are also found to depend on the disk mass and the numerical results in this paper show that for any disk of dimensionless mass ℳ there exists a value of the Froude number for which the cavity dynamics are steady. Also, a very low-Froude-number regime in which gravitational forces are dominant and for which the cavity dynamics are qualitatively different than for low-to-moderate-Froude-number cases is also numerically explored in this paper. Finally, a bifurcation in the cavity seal mechanism from deep seal to surface seal was found at a Froude number F=105.
Probability density functions in steady-state Burgers turbulence
Authors: Gotoh Toshiyuki
Published: July 2002

Probability density functions (PDFs) for steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers are studied by direct numerical simulation and compared to theoretical predictions. The velocity PDFs decay slightly faster than a Gaussian at large amplitudes. The putative power law exponent α of the PDF Q(ξ)∝|ξ|−α of velocity gradient ξ is examined at large Reynolds number and found to be approximately 3 or slightly greater. The tail of Q(ξ) behaves like |Rξ|−1exp(−c(|ξ|/Rξf)θ1) at large negative ξ, where ξf is a forcing parameter. The exponent θ1 is near unity, which is smaller than predicted by theory. It decreases slowly with the Reynolds number R up to R=14 000. The central parts of the PDFs of higher velocity space derivatives are found to be cusp-like, and the cusp exponents are measured. The PDF tails are stretched exponentials.
Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence
Authors: Diamessis P. J. , Nomura K. K.
Published: July 2002

The structure and dynamics of stably stratified homogeneous sheared turbulence is investigated in terms of the triadic interaction of vorticity ω, rate-of-strain S, and scalar (density fluctuation) gradient G≡∇ρ′. Results of direct numerical simulations are presented. Due to the presence of the mean velocity and scalar gradients, distinct directional preferences develop which affect the dynamics of the flow. The triadic interaction is described in terms of the direct coupling of primary mechanism pairs and influential secondary effects. Interaction of ω and S is characterized by the coupling of vortex stretching and locally-induced rotation of the S axes. Due to the intrinsic directionality of baroclinic torque, the generated ω acts to impede S axes rotation. Interaction of ω and G involves an inherent negative feedback between baroclinic torque and reorientation of G by ω. This causes baroclinic torque to act as a sink which promotes decay of ω2. Interaction of S and G is characterized by a positive feedback between differential acceleration and gradient amplification by compressive straining which promotes persistence in vertical G. In high-amplitude, rotation-dominated regions of the flow, differential acceleration effects enhance the attenuation of vertical ω while shear and baroclinic torque tend to maintain horizontal ω. This leads to a predominance of horizontal ω in these regions which manifests itself as collapsed vortex structures. As the flow develops, the third invariant of the velocity gradient tensor tends towards zero indicating locally two-dimensional flow.
Electron emission: From the Fowler–Nordheim relation to the Child–Langmuir law
Authors: Lau Y. Y. , Liu Youfan , Parker R. K.
Published: July 2002

Universal voltage-current characteristics are presented for a planar diode, showing the general transition from the Fowler–Nordheim relation to the Child–Langmuir law. These curves are normalized to the intrinsic scales that are constructed from the Fowler–Nordheim coefficients A, B. They provide an immediate assessment of the importance of the space charge effects, once the gap voltage, gap spacing, and the Fowler–Nordheim coefficients are specified. An example in the parameter regime of vacuum microelectronics is presented.