bluuebunny/crossref_metadata_2025 huggingface dataset:
Spinodal decomposition in multicomponent polymer blends
Authors: Lin C. C. , Jeon H. S. , Balsara N. P. , Hammouda B.
Published: July 2002

Spinodal decomposition in multicomponent mixtures of two homopolymers and a block copolymer was studied by a combination of neutron and light scattering experiments. Mixtures of nearly monodisperse polyolefins—polymethylbutylene (Mw=1.7×105 gm/mol), polyethylbutylene (Mw=2.2×105 gm/mol), and a symmetric polymethylbutylene-block-polyethylbutylene (Mw=4.6×104 gm/mol) were studied, following relatively deep quenches into the spinodal region −χ/χs ranged from 1.7 to 2.4 (χ is the Flory–Huggins interaction parameter at the experimental temperature and χs is the Flory–Huggins interaction parameter at the spinodal temperature). The ratio of homopolymer volume fractions was kept constant at unity, and the block copolymer volume fraction was varied from 0.0 to 0.2. The evolution of structure was followed over five decades of real time—1 min to 1 month. During this time, the characteristic length scale of the phase separated structure increased from 10−1 to 10 μm. The early stages of spinodal decomposition, captured by time-resolved neutron scattering, were compared with theoretical predictions based on the random phase approximation (RPA). Qualitative agreement was obtained. The intermediate and late stages, studied by light scattering, followed classic signatures of binary spinodal decomposition. Experimental evidence indicates that the block copolymer is uniformly distributed throughout the sample during all stages of the decomposition.
The nature of flexible linear polyelectrolytes in salt free solution: A molecular dynamics study
Authors: Stevens Mark J. , Kremer Kurt
Published: July 2002

We present results of molecular dynamics simulations of linear polyelectrolytes in solution. The fundamental model for polyelectrolytes in solution is studied. Specifically, simulations are performed for multichain systems of a flexible chain model of charged polymers. The full Coulomb interactions of the monomers and counterions are treated explicitly. Experimental measurements of the osmotic pressure and the structure factor are reproduced. The simulations reveal a new picture of the chain structure based on calculations of the structure factor, persistence length, end-to-end distance, etc. We present a detailed discussion of the chain structure and a comparison with present theories. In contrast to the predicted dilute limit of rodlike chains, we find that the chains have significant bending at very low densities. Furthermore, the chains contract significantly before they overlap. We also show that counterion condensation dramatically alters the chain structure.
Bound states in electrolyte solutions: Theory of ion association
Authors: Kremp Dietrich , Beskrownij Walerij
Published: July 2002

A new concept of ion association in electrolyte solutions is presented in this paper. The starting point for our theory is the activity expansion of osmotic pressure in the physical picture and the energetic definition of bound states in the phase space of ions. The weight function describing the contributions of the bound states to the second cluster coefficients is calculated. It is established that ion screening has a substantial influence on the formation of bound states. The equation of state is written in the chemical picture by splitting the two-particle screened cluster coefficient into bound and free parts. We show that the bound part of the cluster coefficient in the physical picture can be identified with the association constant in the chemical picture. The mass action law is derived in a self-consistent way.
Growth and collapse of structural patterns in the hydrogen bond network in liquid water
Authors: Shiratani Eli , Sasai Masaki
Published: July 2002

Intermittent and chaotic motions of the hydrogen bond network are studied with the molecular dynamics (MD) simulation. By analyzing the fluctuation in the radial distribution function, it is shown that individual water molecule alternately goes through two different periods; the structured period during which the local structure around the molecule is developed more than the average and the destructured period during which the local structure is less developed. At room temperature the lifetime of each period is hierarchically distributed from a few hundreds fsecs to several psecs. This intermittent structural fluctuation is quantitatively analyzed by defining a new quantity, local structure index (LSI). Molecules which have the large LSI value have tendency to be close to each other to form clusters. Temporal and spatial correlations of the structural order are studied with this new method. The analyses of the structural fluctuation provide a new perspective to study the collective motion of water molecules.
A Debye–Hückel theory for electrostatic interactions in proteins
Authors: Ullner Magnus , Woodward Cliff E. , Jönsson Bo
Published: July 2002

The site–site Ornstein–Zernike equation with a simple mean spherical closure is used to study electrostatic interactions of proteins. Using a Debye–Hückel approximation for the correlation functions of the bulk electrolyte and a simple basis expansion for the protein–salt direct correlation functions, we obtain a very simple variational expression for the electrostatic component of the excess chemical potential of a protein in an electrolyte solution. The predictions of the theory are tested on a model of the protein calbindin D9k. Our calculations for calcium binding affinities and protein acidity constants are found to be in excellent agreement with the results of computer simulations.
Perturbation-dependent atomic orbitals for the calculation of spin-rotation constants and rotational g tensors
Authors: Gauss Jürgen , Ruud Kenneth , Helgaker Trygve
Published: July 2002

Spin-rotation constants and rotational g tensors can be evaluated as second derivatives of the energy with respect to the rotational angular momentum and nuclear spin or angular momentum and external magnetic field, respectively. To overcome problems with the slow basis set convergence and the unphysical (gauge-)origin dependence in quantum chemical calculations of these two properties, we suggest the use of perturbation dependent atomic orbitals (rotational London orbitals), which depend explicitly on the angular momentum and the external magnetic field and are a generalization of the conventional London orbitals (also known as gauge-including atomic orbitals). It is shown that calculations of spin-rotation constants and rotational g tensors based on rotational London orbitals are closely related to London-orbital computations of nuclear shieldings and magnetizabilities. Test calculations at the Hartree–Fock self-consistent-field level for HF, N2, CO, and CH2O demonstrate the superior convergence to the basis set limit provided by the rotational London orbitals. They suggest that future calculations employing rotational London orbitals in conjunction with highly correlated wave functions will be able to provide results of unprecedented accuracy for spin-rotation constants and rotational g tensors.
A reactant-product decoupling method for state-to-state reactive scattering
Authors: Peng Tong , Zhang John Z. H.
Published: July 2002

We propose a general and computationally attractive method that decouples the reactant from the product for state-to-state dynamics calculation in quantum reactive scattering with multiproduct arrangements. In this decoupled approach, the full wave function is divided into the reactant and product components that are connected through absorbing potentials. Using this method, the overall computational effort for state-to-state calculation is essentially the sum of those for the reactant and product arrangements separately. This method solves, to a large extent, the notorious problem of the choice of coordinates in quantum reactive scattering. Although the application of this decoupling method is specifically presented for time-dependent implementation in this communication, the basic methodology should also be applicable in the time-independent application as well.
An instantaneous normal mode description of relaxation in supercooled liquids
Authors: Keyes T. , Vijayadamodar G. V. , Zurcher U.
Published: July 2002

Relaxation in supercooled liquids is formulated from the instantaneous normal modes (INM) point of view. The frequency and temperature dependence of the unstable, imaginary frequency lobe of the INM density of states, 〈ρu(ω,T)〉 (for simplicity we write ω instead of iω), is investigated and characterized over a broad temperature range, 10⩾T⩾0.42, in the unit density Lennard-Jones liquid. INM theories of diffusion invoke Im-ω modes descriptive of barrier crossing, but not all imaginary frequency modes fall into this category. There exists a cutoff frequency ωc such that modes with ω<ωc correspond to “shoulder potentials,” whereas the potential profiles include barrier-crossing double wells for ω>ωc. Given that only modes with ω>ωc contribute to diffusion, the barrier crossing rate, ωh, and the self diffusion constant D, are shown to be proportional to the density of states evaluated at the cutoff frequency, 〈ρu(ωc,T)〉. The density of states exhibits crossover behavior in its temperature dependence such that the exponential T-dependence of D(T) crosses over from Zwanzig–Bassler exp(−E2/T2) behavior at low T to Arrhenius exp(−E/T) behavior at high T; the exponential may be too weak to be observed, in which case D(T) is a power law. Based on the properties of LJ, a general INM description of strong and fragile liquids is presented, with a physical interpretation in terms of the “landscape” of the potential energy surface.
Application of symplectic integrator to stationary reactive-scattering problems: Inhomogeneous Schrödinger equation approach
Authors: Takahashi Kin’ya , Ikeda Kensuke S.
Published: July 2002

The FFT-symplectic integrator (SI) scheme devised for solving the wave packet propagation problem is applied to stationary reactive-scattering problems. In order to relate the stationary problem to the time-dependent problem, a class of Schrödinger equation with an inhomogeneous wave source term is introduced. By using the equivalence between the stationary scattering eigenstate and the equilibrium state of the inhomogeneous Schrödinger equation, the scattering eigenstates can be computed by integrating the inhomogeneous Schrödinger equation with the FFT-SI scheme. A Gaussian wave source is proposed as an efficient wave source exhibiting rapid relaxation toward the eigenstate. Our method is tested by a one-dimensional example which has an analytical solution, and great numerical accuracy is confirmed. It is further examined by an example of time-dependent scattering and by a two-dimensional example of chaotic tunnel-scattering.
Quantum mechanical exchange in a transition metal hydride complex: NMR data for [cp(PPh3)IrH3]+ fitted by a two-dimensional model
Authors: Scheurer Ch. , Wiedenbruch R. , Meyer R. , Ernst R. R. , Heinekey D. M.
Published: July 2002

A two-dimensional model for hydrogen pair exchange in transition metal trihydrides is used to interpret NMR data observed for [cp(PPh3)IrH3]+. Inspired by quantum chemical results for [cp(PH3)IrH3]+, the model describes a combined process of rotational tunneling and IrH2 bending that merges into an H2 “lift-off’’ motion at a small proton–proton distance. The condensed environment with which the tunneling system interacts is represented by a heat bath. A second-order perturbation treatment yields a master equation for the populations of the vibrational states within each of the rotational symmetry species A and B and for the respective AB coherences. A theoretical basis is provided for the evolution of the tunneling (AB) coherence as a damped oscillation in agreement with an independent treatment very recently published by Szymanski [J. Chem. Phys. 104, 8216 (1996)]. A simplified model assumption, containing one adjustable parameter, is made for the system–bath interaction. The temperature-dependent frequency of the tunneling process is found to be close to the Boltzmann average of the tunnel frequencies in the individual vibrational states. Both the calculated temperature-dependent coherence damping-rate constant and the tunnel frequency fit the experimental data after adjustment of three parameters describing the potential energy surface and of the parameter representing the system–bath interaction strength.
Ion scattering and recoiling from liquid surfaces
Authors: Tassotto Michael , Gannon Thomas J. , Watson Philip R.
Published: July 2002

We have shown that ion beams can be used to probe the surface composition and molecular orientation of liquid surfaces. Time-of-flight analysis of the kinetic energy of scattered inert gas ions and recoil atoms ejected from the surface reveals the identity of atoms in the topmost atomic surface layer of the liquid. In this report we describe the first scattering/recoil experiments on surfaces of a liquid siloxane and glycerol using helium, neon and argon ions in the 2–3 keV energy range. Analysis of peak intensities as a function of experimental parameters can be used to infer average molecular orientations in the surface. Spectra from the liquid siloxane are similar to that reported by Bertrand et al. [J. Phys. Chem. 97, 131 788 (1993)] for the long-chain hydrocarbon hexatriacontane deposited as oriented solid films on Si wafers. Our data indicates that the siloxane backbone is effectively shielded by the attached hydrocarbon groups, and for incoming ions the molecule effectively resembles a hydrocarbon. Recent sum-frequency generation spectroscopy experiments [J. Phys. Chem. B 101, 4607 (1997)] suggest that a glycerol molecule in the liquid is, on average, oriented with the carbon backbone normal to the surface. Our data is consistent with this result, but scattering/recoiling simulations are needed to definitively determine the orientation.
The HH̄1Σg state of the hydrogen molecule
Authors: Wolniewicz L.
Published: July 2002

Born–Oppenheimer potential and adiabatic corrections for the HH̄1Σg+ state of the hydrogen molecule are given for internuclear distances up to 80 a.u. Term values in the outer well are computed for J⩽5. A comparison with experiment shows that the theoretical total energies are too low by about 1 cm−1. The source of this discrepancy is briefly discussed.
A quantum statistical mechanical study of the enthalpy of formation of the water dimer
Authors: Schenter Gregory K.
Published: July 2002

Monte Carlo simulations of quantum statistical mechanical properties using the Feynman path integral method were carried out over a temperature range from 50 to 400 K to study the energetics of the water dimer (H2O)2. These results were then used to understand the relation between estimates of the enthalpy of formation obtained from recent ab initio electronic structure calculations and estimates of the enthalpy of formation deduced from experimental measurements of thermal conductivity, second virial coefficients and submillimeter spectroscopy. The full quantum mechanical and anharmonic theoretical results were compared to results obtained from classical mechanical simulation and those obtained from a quantum mechanical harmonic analysis. In performing the analysis for temperatures above 200 K, the definition of a water dimer becomes poorly defined as thermal activation leading to dissociation becomes more probable. The calculated enthalpy of the dimer is strongly dependent on the manner in which trapped and independent monomer species are defined. To address these issues we employ an energy threshold as a dividing surface to separate trapped dimers from those that eventually dissociate on the time scale of an experiment. Approximate quantum mechanical expressions that are consistent with an energy definition of the water dimer were introduced and used in the simulation. It is found that experimental observations are consistent with theoretical calculations once a characteristic time scale for the experimental technique is identified.
Dynamical aspects of mixing schemes in ethanol–water mixtures in terms of the excess partial molar activation free energy, enthalpy, and entropy of the dielectric relaxation process
Authors: Sato Takaaki , Chiba Akio , Nozaki Ryusuke
Published: July 2002

Dielectric relaxation measurements on the ethanol–water mixture for the entire concentration range in very small increments were carried out using TDR in the frequency range from 300 MHz to 25 GHz at 20 °C, 22.5 °C, and 25 °C. The activation enthalpy ΔH and entropy ΔS for the mixtures were separated from the activation free energy ΔG, and hence the excess partial molar activation free energy, enthalpy, and entropy for ethanol, ΔGEAE, ΔHEAE, and ΔSEAE, and those for water, ΔGWE, ΔHWE, and ΔSWE were calculated. The concentration dependence of these partial molar quantities shows the existence of two regions bound at X (molar fraction of ethanol) ∼0.18. In the water-rich region of X<0.1, ΔHEAE and ΔSEAE take large positive values, exhibiting two sharp maxima at X=0.04 and X=0.08, which is clearly attributed to structural enhancement of the hydrogen bond network of water by ethanol, the so-called hydrophobic hydration. From a standpoint of dynamics, mixing schemes of ethanol and water around the two points X=0.04 and X=0.08 seem to be qualitatively different. On the other hand, in the region of X>0.18, the values of ΔHEAE and ΔSEAE take nearly zero. This means that ethanol molecules in the mixtures are in almost the same environment as those are in pure ethanol, forming chainlike clusters surrounded or exothermically attached to by water molecules.
On the calculation of reaction rate constants in the transition path ensemble
Authors: Dellago Christoph , Bolhuis Peter G. , Chandler David
Published: July 2002

We present improved formulas for the calculation of transition rate constants in the transition path ensemble. In this method transition paths between stable states are generated by sampling the distribution of paths with a Monte Carlo procedure. With the new expressions the computational cost for the calculation of transition rate constants can be reduced considerably compared to our original formulation. We demonstrate the method by studying the isomerization of a diatomic molecule immersed in a Weeks–Chandler–Andersen fluid. The paper is concluded by an efficiency analysis of the path sampling algorithm.
Structures, energetics, and spectra of fluoride–water clusters F−(H2O)n, n=1–6: Ab initio study
Authors: Baik Jiwon , Kim Jongseob , Majumdar D. , Kim Kwang S.
Published: July 2002

F − (H 2 O) n  (n=1–6) clusters have been studied using ab initio calculations. This is an extensive work to search for various low-lying energy conformers, for example, including 13 conformers for n=6. Our predicted enthalpies and free energies are in good agreement with experimental values. For n=4 and 6, both internal and surface structures are almost isoenergetic at 0 K, while internal structures are favored with increasing temperature due to the entropic effect. For n=5, the internal structure is favored at both 0 and 298 K under 1 atm. These are contrasted to the favored surface structures in other small aqua–halide complexes. The ionization potential, charge-transferto-solvent (CTTS) energy, and O–H stretching vibrational spectra are reported to facilitate future experimental work. Many-body interaction potential analyses are presented to help improve the potential functions used in molecular simulations. The higher order many-body interaction energies are found to be important to compare the energetics of the various conformers and compare the stability of the internal over the surface state.
Unexpected phase behavior of an asymmetric diblock copolymer
Authors: Papadakis Christine M. , Almdal Kristoffer , Mortensen Kell , Vigild Martin E. , Štěpánek Petr
Published: July 2002

We report on measurements of the transmitted depolarized light intensity and on small-angle neutron scattering (SANS) measurements on a compositionally asymmetric poly(ethylene propylene)-poly(dimethylsiloxane) diblock copolymer studied in the bulk. SANS measurements were made both on isotropic and on shear oriented samples. Apart from the disordered phase, three different ordered morphologies were identified as a function of temperature: the body-centered cubic structure at the lowest temperature, a noncubic, slightly birefringent intermediate phase, and a cubic high-temperature structure which may be body-centered cubic. The available data cannot, however, finally prove this. These findings are in contrast to both available theories and to expectations based on analogous experiments on related diblock copolymer systems.
Global potential energy surfaces for the H3+ system. Analytical representation of the adiabatic ground-state 1 1A′ potential
Authors: Aguado Alfredo , Roncero Octavio , Tablero César , Sanz Cristina , Paniagua Miguel
Published: July 2002

Adiabatic global potential energy surfaces, for singlet and triplet states of A′ and A″ symmetries, were computed for an extensive grid for a total of 8469 conformations of H3+ system at full configuration interaction ab initio level and using an extended basis set that has also been optimized for excited states. An accurate (root-mean-square error lower than 20 cm−1) global fit to the ground-state potential is obtained using a diatomics-in-molecules approach corrected by several symmetrized three-body terms with a total of 96 linear parameters and 3 nonlinear parameters. This produces an accurate global potential which represents all aspects of ground-state H3+ including the absolute minimum, the avoided crossing and dissociation limits, satisfying the correct symmetry properties of the system. The rovibrational eigenstates have been calculated up to total angular momentum J=20 using hyperspherical coordinates with symmetry adapted basis functions. The infrared spectra thus reproduced is within 1 cm−1 with respect to the experimental values for several transitions.
Collision induced desorption by “hot” atoms: Desorption of O2 from Ag(110)
Authors: Zeiri Yehuda
Published: July 2002

A detailed study, using molecular dynamics, of O2 desorption from Ag(110) following a collision with “hot” oxygen atoms is presented. The interactions in the system are described by semiempirical model potentials. The variation of desorption yield and desorbate angular and energy distributions as a function of “hot” atom energy and surface coverage is examined. The computational results clearly show that the collision induced desorption, following photo-induced dissociation of O2, is a plausible explanation of the experimental findings. The coverage dependence of collision induced desorption cross section and the angular distribution of desorbates agree well with the corresponding measured quantities.
First principles analysis of hydrogen chemisorption on Pd–Re alloyed overlayers and alloyed surfaces
Authors: Pallassana Venkataraman , Neurock Matthew , Hansen Lars B. , Nørskov Jens K.
Published: July 2002

Gradient corrected periodic density functional theory (DFT–GGA) slab calculations were used to examine the chemisorption of atomic hydrogen on various Pd–Re alloyed overlayers and uniformly alloyed surfaces. Adsorption was examined at 33% surface coverage, where atomic hydrogen preferred the three-fold fcc sites. The binding energy of atomic hydrogen is observed to vary by as much as 0.7 eV due to Pd–Re interactions. The computed adsorption energies were found to be between −2.35 eV [for monolayer Pd-on-Re, i.e., PdML/Re(0001)] and −3.05 eV [for Pd33 Re66/Pd(111)]. A d-band weighting scheme was developed to extend the Hammer–Nørskov surface reactivity model [Surf. Sci. 343, 211 (1995)] to the analysis of bimetallic Pd–Re alloyed systems. The hydrogen chemisorption energies are correlated linearly to the surface d-band center, which is weighted appropriately by the d-band coupling matrix elements for Pd and Re. The farther the weighted d-band center is shifted below the Fermi energy, the weaker is the interaction of atomic hydrogen with the alloyed Pd–Re surface.
Thermal composition fluctuations near the isotropic Lifshitz critical point in a ternary mixture of a homopolymer blend and diblock copolymer
Authors: Schwahn Dietmar , Mortensen Kell , Frielinghaus Henrich , Almdal Kristoffer , Kielhorn Lars
Published: July 2002

We have studied thermal composition fluctuations of a ternary symmetric homopolymer/diblock copolymer system of PEE/PDMS/PEE-PDMS [PEE and PDMS being poly(ethyl ethylene) and poly(dimethyl siloxane), respectively] in its disordered state with small angle neutron scattering for concentration Φ of diblocks up to 15%. The phase diagram shows three characteristic regimes; (1) below the Lifshitz concentration ΦLL≅9%; (2) in the very near vicinity of the Lifshitz concentration; and (3) above ΦLL. In the regime (1) of low diblock content the maximum neutron intensity is obtained at Q=0 and phase separation into macroscopic large domains is observed at low temperatures. With increasing diblock content the thermal fluctuations indicate a crossover from 3d-Ising to isotropic Lifshitz critical behavior with critical exponents of the susceptibility γ=(1.62±0.01) and correlation length ν=(0.99±0.04) appreciably larger than in the 3d-Ising case. In the structure factor this crossover is accompanied by a strong reduction of the Q2 term leading to the dominance of the Q4 term; the restoring force of the thermal fluctuations is strongly reduced as the Q2 term is proportional to the surface energy. Near the Lifshitz critical temperature a further crossover was observed leading to the appreciably larger critical exponents γ=(2.44±0.08) and ν=(1.22±0.08) and a stabilization of the disordered regime visible through a decrease of the phase boundary by nearly 10 K. This crossover is interpreted by the formation of fluctuation induced inhomogeneous diblock distribution at the interface of the thermal fluctuations. (2) In the intermediate regime between 9% and 12% diblock content the Lifshitz line was crossed twice upon increasing the temperature from low to high temperatures; at low and high temperatures the structure factor S(Q) shows diblock character (maximum of S(Q) at Q≠0) while at intermediate temperature blendlike character (maximum of S(Q) at Q=0). At low temperatures a transition to a bicontinuous microemulsion phase is proposed. (3) At diblock content of 15% a weak order-disorder transition was observed. The data in the Lifshitz critical range and larger than the Lifshitz line could be interpreted by a recently developed theory of Kielhorn and Muthukumar who considered the effect of thermal fluctuations in ternary homopolymer/diblock copolymer samples and from which the Flory–Huggins parameter could be evaluated.
First principles study of thermal decomposition of alkyl–gallium and tertiary butylarsine
Authors: Boero Mauro , Morikawa Yoshitada , Terakura Kiyoyuki , Ozeki Masashi
Published: July 2002

We present a first principles molecular dynamics study of the decomposition processes of alkyl–gallium and tertiary butylarsine at the experimental pyrolysis temperatures. The good agreement of the theoretical results with available data allows us to link the microscopic picture offered by the simulations to the experimental findings. Furthermore, we investigate the β–H elimination processes which represent an important rate limiting step directly influencing the epitaxial film growth.
The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches
Authors: Kowalski Karol , Piecuch Piotr
Published: July 2002

This paper is the first in a series of papers on the new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC). A hierarchy of MMCC approximations, including the renormalized and completely renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) methods, which can be viewed as generalizations of the well-known perturbative coupled-cluster CCSD[T], CCSD(T), CCSD(TQf), and CCSDT(Qf) schemes, is introduced. In this initial study, an emphasis is placed on the ability of the MMCC approach to describe bond breaking and large effects due to connected triples and quadruples by modifying the standard noniterative CC approaches, such as the popular CCSD(T) method. The performance of selected MMCC approaches, including the renormalized and completely renormalized CCSD[T], CCSD(T), and CCSD(TQ) schemes, is illustrated by the results of pilot calculations for the HF and H2O molecules.
Turing patterns in a self-replicating mechanism with a self-complementary template
Authors: Tsai Leo L. , Hutchison Geoffrey R. , Peacock-López Enrique
Published: July 2002

A variety of nonlinear chemical models, such as the Selkov–Schnakenberg, exhibit Turing patterns. The Templator, which is based on a minimal autocatalytic monomer–dimer system, is a newer two-variable model also able to show Turing patterns. Here we find that the dynamic behavior of the Templator is quite similar to other models with cubic nonlinearities. This is demonstrated through a series of computer simulations in two dimensions utilizing the cellular automata approach. The selection of parameter values is based on linear stability analysis, which provides a relatively simple method of predicting Turing pattern formation. The simulations reveal spot, labyrinth, and striped patterns, in agreement with the predictions of the analysis. Other behaviors, such as honeycomb patterns, are also observed. For some parameter values, we study transient spot replication. Our findings strongly suggest that the Templator may belong to the same class of models previously studied by Pearson.
Maximal and minimal eigenvalues and their associated nonlinear equations
Authors: Ashbaugh Mark S. , Harrell Evans M.
Published: July 2002

The spectral theory of uniformly elliptic operators A under perturbations V giving rise to operators of the form HV=A+V(x) on a bounded or unbounded region, such as Schrödinger operators, are considered. Suppose that ∥V∥p is constrained, but V is otherwise unspecified. The theory of the potentials V that maximize or minimize the eigenvalues of HV is presented. The optimizing potentials are typically determined by equations of the form −Δu+W(x)u=±cuα+Λu. The optimization of eigenvalues also turns out to be related to the determination of the best constants in Sobolev’s inequality, and, in its one-dimensional simplification, to a classical oscillator problem with ‘‘instanton’’ properties.
The Zakharov–Shabat inverse spectral problem for operators
Authors: Bauhardt Wolfgang , Pöppe Christoph
Published: July 2002

Many soliton equations, their solutions and their properties, can be deduced from simpler (essentially linear) equations involving more complicated objects, e.g., integral operators. The deduction process from the operator-valued equation to the scalar one amounts to some rather simple procedure like taking a trace or a determinant. This is described for the class of soliton equations solvable with the Zakharov–Shabat spectral transform.
Controlling quantum motion
Authors: Fernández C. David J. , Mielnik Bogdan
Published: July 2002

The techniques of controlling the free evolution of a nonrelativistic charged particle by time-dependent magnetic fields are proposed and the possibility of more general operations upon the Schrödinger wave packet is discussed. It is found that a properly programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to ‘‘go back in time’’ to recover its past shape. Our manipulation prescriptions hold also for nonrelativistic particles of arbitrary spin.
Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates
Authors: Sánchez-Ruiz Jorge
Published: July 2002

The problem of calculating the information entropy in both position and momentum spaces for the nth stationary state of the one-dimensional quantum harmonic oscillator reduces to the evaluation of the logarithmic potential Vn(t)=−∫−∞∞(Hn(x))2 ln |x−t|e−x2 dx at the zeros of the Hermite polynomial Hn(x). Here, a closed analytical expression for Vn(t) is obtained, which in turn yields an exact analytical expression for the entropies when the exact location of the zeros of Hn(x) is known. An inequality for the values of Vn(t) at the zeros of Hn(x) is conjectured, which leads to a new, nonvariational, upper bound for the entropies. Finally, the exact formula for Vn(t) is written in an alternative way, which allows the entropies to be expressed in terms of the even-order spectral moments of the Hermite polynomials. The asymptotic (n≫1) limit of this alternative expression for the entropies is discussed, and the conjectured upper bound for the entropies is proved to be asymptotically valid.
Path integral solution by sum over perturbation series
Authors: Lin De-Hone
Published: July 2002

A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov–Bohm–Coulomb system is obtained by the method. Different from the earlier treatment based on the space–time transformation and infinite multiple-valued trasformation of Kustaanheimo–Stiefel in order to perform path integral, the method developed in this contribution involves only the explicit form of a simple Green’s function and an explicit path integral is avoided.
A separation bound for non-Hamiltonian differential equations with proper first integrals
Authors: Gascón F. G. , Salas D. Peralta , Sancho J. Ruiz
Published: July 2002

It is shown that when a dynamical system X0 with a proper set of global first integrals is perturbed, the phase space region accessible to the orbits of the perturbed vector field X0+Xp is bounded (we are assuming here that the time variable runs over a finite interval). A polynomial new bound is obtained for the separation between the solutions of X0 and X0+Xp. Perturbations near an equilibrium point of X0 are also considered.
A generalization of the geodesic notion
Authors: Chauvineau B.
Published: July 2002

It is well known that the conservation and geodesic equations can be derived from the null divergence of an energy-momentum tensor. This derivation involves the existence of a metric defined on the space–time. We show in this paper that these equations can be generalized to the case where a probability field is considered, instead of a vector field. It is shown that the null-divergence condition of a particular density field leads to the generalized conservation and geodesic equations. This derivation is made without the help of any metric field.
Static stringlike solutions in five-dimensional relativity. II
Authors: Gravel Pierre
Published: July 2002

In this paper we find five-dimensional static strings solutions to Einstein’s equations in the context of the induced-matter approach to higher dimensional relativity. This is done by separating Einstein’s equations for a metric depending on a radius and the extra coordinate. Extending previous work, we consider the cases where the separation constants do not vanish. We find all elements of a decomposition of the four-dimensional induced-matter energy-momentum tensor necessary to identify perfect, heat and viscous parts. Corresponding metrics are found.
On the extension of the Obukhov theorem in non-Riemannian gravity. I
Authors: Scipioni R.
Published: July 2002

This is the first paper of a series in which we give some generalizations of the Dereli–Obukhov–Tucker–Wang theorem in the Tucker–Wang approach to metric-affine gravity in which we consider more general actions containing scalar and in general fields which do not depend on the metric or connection.
Orthogonal polynomial method and odd vertices in matrix models
Authors: Minguzzi Ettore
Published: July 2002

We show how to use the method of orthogonal polynomials for integrating, in the planar approximation, the partition function of one-matrix models with a potential with even or odd vertices, or any combination of them.
Einstein–Weyl spaces and third-order differential equations
Authors: Tod K. P.
Published: July 2002

The three-dimensional null-surface formalism of Tanimoto [M. Tanimoto, “On the null surface formalism,” Report No. gr-qc/9703003 (1997)] and Forni et al. [Forni et al., “Null surfaces formation in 3D,” J. Math Phys. (submitted)] are extended to describe Einstein–Weyl spaces, following Cartan [E. Cartan, “Les espaces généralisées et l’integration de certaines classes d’equations différentielles,” C. R. Acad. Sci. 206, 1425–1429 (1938); “La geometria de las ecuaciones diferenciales de tercer order,” Rev. Mat. Hispano-Am. 4, 1–31 (1941)]. In the resulting formalism, Einstein–Weyl spaces are obtained from a particular class of third-order differential equations. Some examples of the construction which include some new Einstein–Weyl spaces are given.
Quasiwaves in superconductors
Authors: Bezuglyi E. V. , Boichuk A. V.
Published: July 2002

Temperature dependence of the amplitude and ballistic velocity of a high-frequency signal (quasiwave) in a superconductor, associated with the energy dependence of the velocity of electron excitations, is studied theoretically. The spatial distribution of the quasiwave field and the transformation coefficient are calculated for quasiwave excitation by an electromagnetic wave as well as by longitudinal or transverse elastic deformation. The obtained results are in accord with the data on electron sound velocity measurements in the superconducting states of Ga, Mo, and Al.
Dynamic characteristics of adsorbents for adsorption pumps of dilution refrigerators
Authors: Shcherbachenko R. I. , Grigor’ev V. N.
Published: July 2002

The data on adsorption isotherms of He4 in synthetic adsorbents are obtained at 4.2 K in the pressure range 1–10−2 torr. The dependence of pressure on the amount of adsorbed gas in adsorption pumps is studied under conditions simulating the pump operation in dilution refrigerators. It is found that the pressure in the pump is practically independent of the amount of adsorbed helium for a constant pumping rate in the interval 10−6−10−4 mole/s, over a wide pressure range. The obtained characteristics can be used for designing and developing pumps for dilution refrigerators.
Electromagnetic waves in layered conductors and superlattices in a magnetic field
Authors: Gvozdikov V. M. , Vega-Monroy R.
Published: July 2002

The collective electromagnetic wave excitations in layered conductors in an external quantizing magnetic field are studied theoretically. A set of coupled equations for the electric field components and the Green’s functions describing collective electromagnetic modes in such a system within the linear-response approach are obtained on the basis of a model of conducting planes embedded into a dielectric matrix. These equations, written in the layer-site representation, provide a basis for studies of the electromagnetic waves in the general case which does not imply either the spatial uniformity across the layers or the homogeneity within the conducting planes. The dispersion relations are obtained for the uniform and homogeneous layered conductors, which give a rich structure of collective electromagnetic modes in layered conductors in an external magnetic field. The dispersion and damping of helicons in layered conductors in the regimes of conventional and quantum Hall effects have been studied, both analytically and numerically. Two new modes propagating perpendicular to the magnetic field with frequencies of the order of the plasma frequency have been found.
Phase transitions in antiferromagnetic cobalt fluoride
Authors: Cherpurnykh G. K. , Medvedovskaya O. G. , Nikitina O. A.
Published: July 2002

The phase transitions in cobalt fluoride (at T≪TN=38 K) in a longitudinal magnetic field are investigated theoretically, and it is shown that the field-induced transition of the magnetic subsystem from an antiferromagnetic phase can occur only to a canted phase and that it is a first-order transition. The character of this transition is due to the “sign” of the Dzyaloshinskiı̆ interaction, and this affords an opportunity to determine experimentally the “sign” of the Dzyaloshinskiı̆ interaction. The field of the transition to the spin-flop phase (when the total magnetic moment becomes parallel to the easy axis) coincides with the field of the transition to the spin-flip phase (when the antiferromagnetism vector becomes equal to zero).
Spin polarization of quasiparticle states in S/F structures with a finite transparency of the SF interface
Authors: Koshina E. A. , Krivoruchko V. N.
Published: July 2002

The proximity effect between a massive superconductor (S) and a mesoscopic layer of a normal ferromagnetic metal (F) is investigated for arbitrary transparency of the SF interface and arbitrary value of the proximity effect. For the case of high transparency of the SF interface and a low value of the proximity effect, the spatial distribution of the order parameter in the S layer and the densities of quasiparticle states at the interface for the S and F layers are found analytically as functions of the exchange field. It is shown that in mesoscopic S/F structures the single-particle excitations are polarized in both the F and S metals.
Some influences of particle shape on drag and heat transfer
Authors: Dwyer H. A. , Dandy D. S.
Published: July 2002

A study has been carried out on some of the influences of particle shape and orientation on the drag, lift, and heat transfer characteristics of nonspherical particles at intermediate Reynolds numbers, 10≤Re≤66. The geometry that has been employed in the investigation has been an ellipsoid of revolution with variation in angle of attack, and the aspect ratio (ratio of the major to the minor axis) has been varied by a factor of 3. The method of solution consists of a second-order, finite volume formulation of the Navier–Stokes equations, which is capable of being extended to time-dependent and variable density low Mach number flows. For relatively small increases in the ratio of major to minor axis the behavior of the pressure and skin friction distributions becomes substantially different in both qualitative and quantitative ways. The skin friction distribution as well as the heat flux to the particle surface exhibit a maxima near the major axis of the ellipsoid regardless of orientation, and the total friction drag and the total particle heat transfer exhibit a strong correlation. The total drag coefficient and the lift coefficient behave in a much different manner and they are strongly influenced by the Reynolds number, aspect ratio, and angle of attack. It appears that the total drag and lift force depend strongly on the particle shape, and it appears difficult to develop simple correlation schemes. The numerical methods that have been used performed well and they will be extended to more complex problems in the future.
Bulk viscosity of a dilute polyatomic gas
Authors: Emanuel George
Published: July 2002

Theoretical and experimental knowledge of the bulk viscosity for a dilute gas is briefly reviewed. Neither area is satisfactory; the lack of experimental data for polyatomic gases over a broad temperature range is particularly acute. There is one circumstance where this deficiency is especially detrimental, namely, high-speed entry into planetary atmospheres.
Symmetry of interacting modes in a cylinder wake
Authors: Mansy Hussein , Williams David R.
Published: July 2002

The cross-flow symmetry properties of interacting nonlinear disturbances have been studied experimentally in the wake of a circular cylinder. It is shown using modal decomposition that the interaction between two symmetric or two antisymmetric modes produces symmetric combination modes, while the interaction between a symmetric and an antisymmetric mode produces antisymmetric combination modes.
Effect of bulk viscosity on a hypersonic boundary layer
Authors: Emanuel George
Published: July 2002

The bulk viscosity μb is generally set equal to zero (Stokes’ hypothesis). For certain gases, such as CO2, μb/μ exceeds 103, where μ is the shear viscosity. In this circumstance, the bulk viscosity may substantially alter a hypersonic boundary layer. A general, nonsimilar, laminar, boundary-layer formulation is provided in which the bulk viscosity terms are included as a correction. To obtain explicit results, flow over a flat plate is considered. In addition to the heat transfer, the transverse pressure gradient inside the boundary layer is not zero, whereas the skin friction is unaltered by the bulk viscosity. This analysis is relevant to aerogravity-assisted maneuvers in planetary atmospheres that largely consist of CO2.
Two-dimensional simulations of a charge-neutral plasma beam injected into a transverse magnetic field
Authors: Livesey W. A. , Pritchett P. L.
Published: July 2002

Two-dimensional (three-velocity component) electrostatic simulations are performed to study charge-neutral beam injection across a uniform vacuum magnetic field. Parameters are chosen that allow the beam to penetrate across the magnetic field by the polarization drift mechanism. Upon injection, the beam polarizes by virtue of the Lorentz force, forming space-charge boundary layers, and continues to propagate across the field at the injection velocity. The beam path curves in the direction opposite to that of ion gyration. Ions gyrating out of the positive space-charge layer allow a net electron current to flow from the head of the beam to its source. The resulting j×B force is of the correct direction and magnitude to account for the observed beam deflection. The presence of a tenuous (np/nb =1/100) ambient plasma enhances the shielding of the ions in the positive space-charge layer and permits their escape in greater quantities. The j×B force exceeds that of the vacuum case, and a more pronounced beam curvature is observed. In the presence of a marginally dense (np/nb =1/10) ambient plasma, the beam deflects sharply and partially separates into ion and electron streams. The streams then recombine, and the reconstituted beam deflects in the opposite direction.
High-frequency instability of the sheath–plasma resonance
Authors: Stenzel R. L.
Published: July 2002

Coherent high-frequency oscillations near the electron plasma frequency (ω≲ωp) are generated by electrodes with positive dc bias immersed in a uniform Maxwellian afterglow plasma. The instability occurs at the sheath–plasma resonance and is driven by a negative rf sheath resistance associated with the electron inertia in the diodelike electron-rich sheath. With increasing dc bias, i.e., electron transit time, the instability exhibits a hard threshold, downward frequency pulling, line broadening, and copious harmonics. The fundamental instability is a bounded oscillation caused by wave evanescence, but the harmonics are radiated as electromagnetic waves from the electrodes acting like antennas. Wavelength and polarization measurements confirm the emission process. Electromagnetic waves are excited by electrodes of various geometries (planes, cylinders, spheres), which excludes other radiation mechanisms such as orbitrons or beam–plasma instabilities. The line broadening mechanism has been identified as a frequency modulation via the electron transit time by dynamic ions. Ion oscillations at the sheath edge give rise to burstlike rf emissions. These laboratory observations of a new instability are important for antennas in space plasmas, generation of coherent beams with diodes, and plasma diagnostics.