bluuebunny/crossref_metadata_2025 huggingface dataset:
Can Monte Carlo simulation describe dynamics? A test on Lennard-Jones systems
Authors: Huitema H. E. A. , van der Eerden J. P.
Published: July 2002

A new estimation of physical time in Monte Carlo simulations is derived from the requirement that the self-diffusion coefficient measured by Monte Carlo and molecular dynamics simulations have the same value. The dynamics of the particles using both simulation methods are compared by measuring velocity autocorrelation functions. Simulations of pure Lennard-Jones liquids and a binary Lennard-Jones solution show that at small time scales the particle dynamics are different, but at larger time scales they become similar. As a critical test crystal growth from the melt is simulated using the proposed time scale. Both for Monte Carlo and molecular dynamics a linear dependence of the growth rate on undercooling is found and the measured proportionality constant (the kinetic coefficient) is equal to within 6%, i.e., within the statistical error of both methods.
The structures, electron affinities, and energetic stabilities of TiOn and TiOn− (n=1–3)
Authors: Walsh Mary B. , King Rollin A. , Schaefer Henry F.
Published: July 2002

By use of density functional and coupled cluster methods, we report energetic and structural information concerning the ground states of TiOn and TiOn− (n=1–3), much of which has not previously been observed experimentally or predicted theoretically. This study establishes the following geometrical symmetries and electronic ground states: X̃ 1A′ TiO3 (Cs), X̃ 2A2′ or B22 TiO3− (D3h or C2v), and X̃ 2A1 TiO2− (C2v). In addition, the electronic ground state of TiO− is established as Δ,2 arising from the 9σ21δ configuration. This finding is contrary to the suggestion of Wu and Wang, contained in their report of recent photoelectron experiments, that ground state TiO− has a 9σ1δ2 electronic configuration and Σ−4 symmetry. The ground state minimum-energy structure for TiO3− contains no oxygen–oxygen bonds and has D3h or C2v symmetry. The first theoretical adiabatic electron affinities, as predicted by the CCSD(T)//B3LYP level of theory, for TiO, TiO2, and TiO3 are 1.25 eV, 1.60 eV, and 3.34 eV, while Wu and Wang’s photoelectron measurements for these were 1.30 eV, 1.59 eV, and 4.2 eV, respectively. The results for the mon- and dioxide cases are in excellent accord with experiment; however, the experimental result for TiO3 is approached with similar accuracy only when compared with our CCSD(T)//B3LYP value for the vertical detachment energy for TiO3− of 4.02 eV. The latter prediction reflects the fact that the theoretical structures for TiO3 and TiO3− are qualitatively different. Finally, several of the lowest-lying minima on the potential energy surfaces of TiO3 and TiO3− are elucidated.
Short-range orientational correlation in the disordered crystal of 1-chloro-4-iodobenzene
Authors: Meriles C. A. , Pérez S. C. , Wolfenson A. E. , Brunetti A. H.
Published: July 2002

p-chlorobromobenzene (PCBB) and p-chloroiodobenzene (PCIB) crystallize in the centrosymmetric space group P21/c, Z=2. Since the molecules do not possess an inversion center, the crystals exhibit orientational disorder, in other words, the electrical dipoles of regularly distributed molecules irregularly point in opposite directions. In this study, the temperature dependence of the nuclear quadrupole resonance (NQR) line shape for PCBB and PCIB and the spin-lattice relaxation time (T1) for PCIB have been measured. Both compounds exhibit an inhomogeneously broadened spectrum, as is expected for this kind of disorder. However, the measured NQR profile strongly depends on temperature, particularly that of PCIB. To explain this behavior, each orientation of the molecular dipoles has been considered as a component of what we call a binary orientational alloy. Within this framework it is shown that the minimum free energy of the system always corresponds to a centrosymmetric array, but that short-range orientational correlations may arise, depending on the difference in binding energy between a parallel and an antiparallel pair of neighboring molecules. In this way, the overall temperature dependence of the experimental profile can be succesfully reproduced if a one-dimensional orientational correlation among molecules is considered. At high temperatures, 180° molecular reorientations completely destroy the short range order and the measured spectra can be reproduced in terms of a pure random disordered model. The presence of molecular reorientations has been inferred from the measured temperature dependence of the nuclear spin-lattice relaxation time. In addition, the effect of short-range orientational correlations on T1(T) has also been calculated and discussed.
Decay rate of concentration fluctuations in microemulsions
Authors: Nonomura Makiko , Ohta Takao
Published: July 2002

Using a variational method, we derive a set of equations of motion for ternary fluids with oil, water, and surfactant. The equations are written in terms of two local concentrations of the components and a local average velocity field. Choosing the free energy functional suitable for microemulsions, we study the dynamics of concentration fluctuations. The time-correlation function of the concentration fluctuations is shown to be generally given by two exponential functions due to the dynamic cross coupling between the two concentration fields. A formula of the stress tensor and the explicit form of the effective diffusion constant arising from the hydrodynamic interaction are also obtained.
Electronic and vibrational structure of thin films of bithiophene: Undoped and alkali-doped states
Authors: Schatzmayr M. , Koller G. , Kardinal I. , Ramsey M. G. , Stafström S. , Netzer F. P.
Published: July 2002

The complete electronic (occupied and unoccupied states) and vibrational structure of thin films of bithiophene in undoped form and after alkali doping have been investigated experimentally and theoretically. The ultraviolet (UV) photoemission and inverse photoemission spectra demonstrate clearly the filling of the LUMO of bithiophene in the doping process due to charge transfer from the alkali atoms, and density functional theory (DFT) calculations confirm the formation of dianion (bipolaronlike) states in the HOMO–LUMO band gap at high doping levels, respectively. High-resolution electron energy loss spectra (HREELS) have been used to probe the vibrational structure of the bithiophene films, and the formation of a quinoidic structure on Cs doping is well reflected in HREELS by the advent of an intense vibrational structure at 206 meV, which is due to the stiffened C–C interring bond as also predicted by theory.
Comparison of atomistic simulations and pseudopotential calculations of the MgO{100}/Ag{100} and MgO{110}/Ag{110} interfaces
Authors: Purton J. A. , Bird D. M. , Parker S. C. , Bullett D. W.
Published: July 2002

Both first principles pseudopotential calculations and atomistic simulations have been employed to study the MgO{100}/Ag{100} and MgO{110}/Ag{110} interfaces. For both interfaces the most stable structure was determined to be where the Ag atoms are situated above the O2− ion. The binding energy for the {110} interface is approximately three times greater than for the {100} interface. The relative binding energies for the two interfaces is reflected in the Ag to O2− distance and the electron distortion on the Ag atom. The binding energies have been determined with the local density approximation and generalized gradient approximation GGA to the exchange-correlation energy. The binding energies calculated using an atomistic simulation model are similar to the GGA results. However, the calculation of short-range potentials using the electron gas method is an oversimplification.
Trajectory dependence of scattered Ne+ and recoiled S− ion fractions from the Cd- and S-terminated CdS{0001} surfaces
Authors: Houssiau L. , Rabalais J. W. , Wolfgang J. , Nordlander P.
Published: July 2002

Scattered Ne+ and recoiled S− ion fractions resulting from 4 keV Ne+ and 4 keV Kr+ impingement, respectively, on both the Cd- and S-terminated surfaces of CdS{0001} have been measured. The absolute values of these ion fractions as well as their dependence on surface structure and electron density have been determined. Using a density functional approach, a clear correlation has been demonstrated between these Ne+ and S− ion fractions and the lateral variation of the electrostatic potential along the outgoing trajectories of the scattered and recoiled atoms. The observed anisotropy in the ion fractions is a result of the variations in surface to atom electron transfer rates due to tunneling barriers introduced by the electrostatic potentials. Both the Ne+ and S− ion fractions are higher on the Cd-terminated surface than on the S-terminated surface and their azimuthal patterns are different due to the spatial modulation of the electron tunneling rates on the surface caused by the electrostatic barriers. The azimuthal anisotropies of electrons ejected during the collision indicate that they are emitted only from collisions whose impact parameters are less than a threshold value, consistent with a kinetic electron emission mechanism.
State-specific excitation function for Cl(2P)+H2 (v=0,j): Effects of spin-orbit and rotational states
Authors: Lee Shih-Huang , Lai Lih-Huey , Liu Kopin , Chang Hua
Published: July 2002

By exploiting different sources for both reagents, the state-specific excitation function was deduced for the title reaction for the first time. It was found that for reactions with the ground state Cl(2P3/2) atom, the rotation of the H2 reagent has little effect on reactivity at low collision energies, but plays a beneficial role in promoting the reaction at higher Ec’s; in contrast to a recent QCT prediction on the G3 surface. Evidence was presented for non-negligible reactivity from the spin-orbit excited Cl*(2P1/2) atom. The ratio of the cross sections for a rotating H2 to a nonrotating one appears to be larger for reaction with the ground state Cl than with the excited Cl*, σ(j>0)/σ(j=0)>σ*(j>0)/σ*(j=0).
Observation of several new electronic transitions of the SrOH free radical
Authors: Beardah Matthew S. , Ellis Andrew M.
Published: July 2002

We report four new electronic transitions of the SrOH free radical, the C̃ 2∏–X̃ 2∑+, D̃ 2∑+–X̃ 2∑+, Ẽ 2∑+–X̃ 2∑+, and F̃ 2∏–X̃ 2∑+ transitions. SrOH was prepared in a supersonic jet by laser ablation and spectra were recorded using laser-induced fluorescence. The C̃ 2∏–X̃ 2∑+ excitation spectrum shows complex vibronic structure which is attributed, at least in part, to Renner–Teller activity in the excited electronic state. This is supported by dispersed fluorescence spectra which show substantial bending mode activity in the emission from several different excited vibronic levels. It is suggested that the prominence of nominally forbidden vibrational features arises from a large change in permanent electric dipole moment between the X̃ and C̃ states. In turn, this suggests that the C̃ 2∏ state of SrOH is the analogue of the “reverse-polarized” ∏ states known for the alkaline-earth monohalides, i.e., the highest occupied π orbital points towards the O atom. The D̃ 2∑+–X̃ 2∑+, Ẽ 2∑+–X̃ 2∑+, and F̃ 2∏–X̃ 2∑+ spectra are much simpler than the C̃–X̃ system, being dominated by regular structure in the Sr–O stretching vibration.
Potential energy surface for the proton transfer in 8-hydroxyimidazo[1,2-a]pyridine
Authors: Naundorf H. , Organero J. A. , Douhal A. , Kühn O.
Published: July 2002

An all Cartesian reaction surface Hamiltonian for the title reaction is calculated using density functional theory. Two reaction coordinates are chosen to model the motion of the proton in the plane of the pyridine and imidazole rings. The remaining degrees of freedom of the molecular scaffold are described by orthogonal normal modes. The reorganization energy of the latter is determined and the modes which are most strongly coupled to the proton transfer are analyzed. Based on this multidimensional potential energy surface the applicability of different schemes for ultrafast laser controlled isomerization is discussed.
Thermalization process after the relaxation of electronically excited states: Intramolecular proton transfer systems studied by the transient grating method
Authors: Okazaki Toshiya , Hirota Noboru , Terazima Masahide
Published: July 2002

Photophysical and thermalization processes after photoexcitation of 2-(2′-hydroxy-5′-methylphenyl)benzotriazole (HMPB) in cyclohexane and 2-hydroxybenzophenone (HBP) in various solvents were investigated by the transient grating (TG) method. From the time profiles of the population grating (PG) signals, two distinct kinetics were observed for HMPB and HBP. For HMPB, the faster (600 fs) kinetics is attributed to the back proton transfer reaction in the ground state, and the faster process of HBP (400 fs) is attributed to the vibrational cooling in the S1 state. The slower one (∼30 ps) of both compounds is assigned to the vibrational cooling in the S0 state. In ethanol (hydrogen bonding solvent), the PG signal originated from the T1 state of HBP is apparent. However, the thermal energy from the T1 state is negligibly small and the triplet quantum yield was found to be less than 0.05. The photoexcited HBP relaxes to the ground state by the internal conversion dominantly even in ethanol. The thermalization rates of these molecules were measured from a point of view of the translational energy of solvents by the acoustic peak delay method of the TG signal. The results show that in the early step of the thermalization, there is a very fast cooling process (less than a few ps) which is due to the energy transfer from the photoexcited solute to (several) effectively coupled solvent molecule(s), and then the heated solvent molecule becomes cool by the thermal diffusion to the bulk solvents. The thermalization processes depend on both of the solute and solvent properties. The time development of the temperature calculated based on this thermalization model explains the experimental observations.
Fluctuating charge model for polyatomic ionic systems: A test case with diatomic anions
Authors: Ribeiro Mauro C. C. , Almeida Luiz C. J.
Published: July 2002

The fluctuating charge (FQ) model proposed by Rick et al. [(J. Chem. Phys. 101, 6141 (1994)] for molecular dynamics (MD) simulation of water is applied to a test case for polyatomic ionic systems. A system resembling alkali cyanide crystals, with two partial charges on the atomic sites of the polarizable anions, is considered. The need for charge fluctuation considerations in such a simple system is demonstrated by ab initio calculations of the partial charges in the cyanide ion with different orientations within a fixed octahedral environment of sodium ions. It is shown that the charge distributions in the crystal obtained with the FQ model are sensitive to changes in the environment in such a way that the anions become more polarizable as the lattice parameter increases. Conversely, the charge distributions shrink with increasing repulsive short-range interactions. Furthermore, a well-known polarization effect, that is, the reduction in the frequencies of longitudinal optic modes of the crystal, is also obtained with the FQ model.
The breaking of the backward–forward symmetry in the angular distribution of mj-selected photofragments
Authors: Pe’er Asaf , Shapiro Moshe , Balint-Kurti Gabriel G.
Published: July 2002

We present calculations on the angular distributions of mj-selected photofragments (with mj being the projection of the fragments’ internal angular momentum on a space-fixed z-axis). We show that the proper analysis of such experiments [based on G. G. Balint-Kurti and M. Shapiro, Chem. Phys. 61, 137 (1981)], involves coherent λ≠λ′ terms (with λ—the “helicity”—being the projection of the fragment angular momentum on the recoil direction). The involvement of these coherent terms leads, amongst other things, to the creation of “orientation,” i.e., the backward–forward asymmetry, in the fragments’ angular distributions. Thus we demonstrate that the detection of polarization in one (internal) variable—the internal rotation, creates a correlated orientation in another (external) variable—the recoil angular distribution.
Modeling analysis of molecular chiral effect detected by Maxwell-displacement-current measurements
Authors: Zhao Wei , Wu Chen-Xu , Iwamoto Mitsumasa , Zhong-can Ou-Yang
Published: July 2002

Based on Maxwell displacement current (MDC) and surface pressure measurements by monolayer compression, the physicochemical properties of chiral and racemic phospholipid [α-phosphatidylcholine dipalmitoyl (DPPC)] monolayers at the air–water interface were investigated. It was found that at a temperature of 20 °C, the chiral and racemic phospholipid monolayers exhibited similar pressure-area isotherms with a pressure plateau between 65 and 85 Å2, usually attributed to the two-dimensional (2D) phase transition from expanded monolayer to condensed one. Nevertheless, with MDC measurement some critical peaks in the 2D pressure plateau region with different amplitude and sign were detected related to the chirality of the phospholipid samples. This result clearly demonstrates that microscopic chirality affects the electrical properties of monolayers. To investigate the chiral effect theoretically, a twist-conformation molecular model was raised by a modification of the simple rodlike model and biaxial rodlike model, which were developed in our previous work. The analysis based on this modified model reveals that the monolayer properties, especially the MDC behavior by compression, are profoundly influenced by the chirality of molecules.
Radiative lifetime measurement of the a 3Σ+ metastable state of NO+ using a new type of electrostatic ion trap
Authors: Wester R. , Bhushan K. G. , Altstein N. , Zajfman D. , Heber O. , Rappaport M. L.
Published: July 2002

A new type of ion trap is used to measure the radiative lifetime of the NO+(a 3Σ+) metastable state. The ion trap is designed to store ion beams with an energy of a few keV and is well suited for the study of metastable states. The measured value for the radiative lifetime is τr=760±30 ms, in good agreement with the last experimental values of Calamai and Yoshino [J. Chem. Phys. 101, 9480 (1994)], and with the theoretical value of Kuo et al. [J. Chem. Phys. 92, 4849 (1990)].
Rotational diffusion and dielectric relaxation of linear molecules in a cubic potential
Authors: Déjardin J. L. , Kalmykov Yu. P.
Published: July 2002

The dielectric relaxation of molecular impurities in cubic crystals is treated by averaging the Langevin equation for noninertial rotational Brownian motion of a linear rotator in a cubic potential, so that the system of linear differential-recurrence equations for the appropriate equilibrium correlation functions is derived without recourse to the diffusion (Smoluchowski) equation. The solution of this system is expressed in terms of matrix continued fractions that allows us to evaluate the dielectric relaxation time τ and the low frequency spectrum of the complex susceptibility χ(ω). The behavior of τ and χ(ω) is investigated for all ranges of the anisotropy energy (σ) parameter. The results obtained are compared both with previously available solutions and asymptotic estimates based on the Kramers escape rate theory in the overdamped limit. It is shown that the relaxation processes in a cubic potential are very similar to those in a double-well potential. They are governed and can be described by two distinct mechanisms — overbarrier and intrawell relaxation. Simple analytic formulas for χ(ω) and τ are also presented.
Homocoordination preference in NaCs and LiNa liquid alloys by first principles molecular dynamics
Authors: Costa Cabral B. J. , Martins J. L.
Published: July 2002

We present structural and dynamics results based on Hellman–Feynman molecular dynamics for the liquid phase of the NaCs alloy at two Na concentrations (cNa=0.6 and 0.8) and for the Li0.61Na0.39 zero alloy at two temperatures (T=590 K and 690 K). For NaCs the calculated structure factor S(k) is in very good agreement with data from neutron scattering experiments and the partial structure factors are compared to semiexperimental, theoretical and classical molecular dynamics predictions. We predict similar values for the self-diffusion coefficients of Na and Cs atoms in the Na0.6Cs0.4 alloy. For LiNa the concentration–concentration structure factor is in good agreement with experimental data and our results for the dynamics are compared with data from classical molecular dynamics simulations.
Effects of the heterogeneous energetic topography on the collective motion of adsorbed particles
Authors: Bulnes F. M. , Pereyra V. , Riccardo J. L. , Zgrablich G.
Published: July 2002

Collective surface diffusion of adsorbed particles on correlated heterogeneous surfaces is studied by Monte Carlo simulation, in the framework of the Kubo–Green theory. The energetic disordered surface is described through the dual site-bond model (DSBM) introduced by Mayagoitia et al. [Surf. Sci. 221, 394 (1989)]. The influence of the energetic correlation on the jump (DJ) and collective (D) diffusion coefficients is analyzed by simulating the coverage fluctuations in the grand canonical ensemble and the mean-square displacements of particles in the canonical ensemble. The topography is shown to strongly affect the coverage dependence of the transport coefficient. The effects of nearest-neighbor lateral interactions is also discussed.
Analysis of long range dispersion and exchange interactions between one Na atom and one K atom
Authors: Zemke Warren T. , Stwalley William C.
Published: July 2002

This article critically surveys spectroscopic data for the two lowest states (X 1Σ+ and a 3Σ+) of NaK. These states both dissociate to ground state Na and K atoms. Since both states are known precisely to near dissociation, they can be used to determine experimental values of the separate Coulombic and exchange contributions to the long-range interaction potentials, which agree reasonably well with theory. We also discuss the dissociation energy of both of the states and recommend De(X 1Σ+)=5273.65±0.10 cm−1 and De(a 3Σ+)=207.79±0.10 cm−1.
Behavior of a random heteropolymer in mixed solvents
Authors: Chakraborty Arup K.
Published: July 2002

I use a Landau theory to study the behavior of A–B heteropolymers with disordered sequences immersed in a binary solvent mixture. Segments of type A are preferentially solvated in one type of solvent, and those of type B prefer the other type of solvent. At high temperatures, the behavior is qualitatively the same as that in a single solvent. As the temperature approaches the critical temperature for solvent demixing, however, the chain conformational statistics change dramatically. A phase transition occurs driven by the long-range solvent density fluctuations. The transition is one where on scales larger than a preferred length the chain is collapsed and microphase ordered. On shorter scales it is disordered and exhibits self-avoiding walk statistics. In many circumstances this domain size acquires a limiting value and the system cannot order on shorter length scales by reducing temperature. The ordering disappears when the critical point is approached too closely. Predictions are made for scattering profiles that may be observed in neutron-scattering experiments.
Long-range effects in optimizing the geometry of stereoregular polymers. II. Hydrogen fluoride chains as a working example
Authors: Jacquemin Denis , André Jean-Marie , Champagne Benoı̂t
Published: July 2002

We use linear hydrogen fluoride chains to evaluate the efficiency of the long-range approach developed in the first paper of this series. A wide panel of tests and comparisons are carried out in order to understand the influence of the parameters on the quality of the forces and the accuracy of the optimized geometry. The long-range corrections are demonstrated to be essential for tight optimizations as well as to fasten the calculation procedure.
Probing nanoscale photo-oxidation in organic films using spatial hole burning near-field scanning optical microscopy
Authors: Credo G. M. , Lowman G. M. , DeAro J. A. , Carson P. J. , Winn D. L. , Buratto S. K.
Published: July 2002

Spatial hole burning near-field scanning optical microscopy (SHB–NSOM) is used to locally photopattern three species of organic thin films, poly(2-methoxy, 5-(2′-ethyl hexyloxy)–p-phenylene vinylene) (MEH–PPV), tris-8-hydroxyquinoline aluminum (Alq3) and dye-functionalized polyelectrolyte self-assembled layers, on a 100 nm length scale. In SHB–NSOM the film is illuminated with light from a stationary NSOM tip to induce photo-oxidation. The reduction in the fluorescence yield resulting from this exposure is then mapped using fluorescence NSOM (FL–NSOM). We have examined the localized photo-oxidation as a function of time, position, and environment free from the limits of far-field spatial averaging. In all of the thin film materials studied we find that the long-time diameter of the dark spot is much larger than the tip diameter and is a signature of energy migration. Characteristic lengths of the energy migration are extracted from this data by a simple diffusion model and are found to be of the order of a few hundred nanometers for each of the films studied.
Diffusion-influenced controlled reaction in an inhomogeneous medium: Small concentration of reagents
Authors: Buján-Nuñez M. C. , Miguel-Fernández A. , López-Quintela M. A.
Published: July 2002

We report a computer simulation study of diffusion influenced reactions in a disorder medium constituting by immobile spherical obstacles when the concentration of reagents is smaller than the concentration of obstacles. We found that the compartmentalization of the embedding medium leads to a strong decrease of the rate of the first collision between reagents and a strong increase of the rate of recollision after a no-reactive encounter. The behavior of the full rate of reaction depends on the probability that a collision leads to reaction (value of the activation energy) and on the relationship between the decrease of the rate of collision and the increase of the rate of recollision. Thus, totally diffusion controlled reactions are always unfavored in these mediums, while partially diffusion controlled reactions with very high activation energy are more favored in mediums with a bigger degree of compartmentalization.
A comparative ab initio and DFT study of neutral aniline oligomers
Authors: Lim S. L. , Tan K. L. , Kang E. T. , Chin W. S.
Published: July 2002

Comparative ab initio restricted Hartree–Fock (RHF) and density functional theory (DFT) calculations were performed to investigate the geometric and electronic structures of various neutral aniline oligomers. These oligomers were selected to model polyaniline (PANI) in different intrinsic oxidation states, with an aim to study the applicability and extendibility of the theoretical methods to conjugated polymers. In general, we found that DFT calculations produce results that are in good agreement with observations from x-ray diffraction, ultraviolet-visible absorption, ultraviolet photoelectron and x-ray photoelectron spectroscopy. The DFT method has reproduced well the ∼4.0 eV π–π* transition of leucoemeraldine base and the ∼2.0 eV Peierls gap transition of pernigraniline base. The valence band structure and the ∼1.2 eV energy separation of nitrogen core levels of emeraldine base are also correctly predicted. On the other hand, large discrepancies with experimental measurements are predicted by the RHF method. Single-point MP2 calculations show that the DFT-optimized structures are all at lower energy than the RHF-optimized ones.
Higher-order interaction energies for a system of N arbitrary molecules in the light of spherical tensor theory
Authors: Piecuch Piotr
Published: July 2002

The Rayleigh–Schrödinger perturbation treatment accompanied by a multipole expansion of the interaction potential can be used in the quantum-mechanical studies of long-range intermolecular forces. The total third-order interaction energy in a system of N molecules separates into several induction and dispersion categories. Only some of them are purely pairwise additive. In the present paper the closed expressions for all possible categories of the third-order anisotropic interaction energy in a collection of N arbitrary molecules are derived, in which the orientational dependence is pushed to its limits. The derivation is based on the spherical tensor formalism. The formulas for the induction energies are directly related to the spherical multipole moments and irreducible (hyper)polarizabilities of the interacting molecules in body-fixed frames. The same is achieved for the dispersion categories after employing some simple approximations. The present paper can be treated as an extension of the spherical tensor description of the two-body long-range molecular interactions for the most important quantum-mechanical pairwise nonadditive forces.
Spinor structures on spheres and projective spaces
Authors: Dabrowski Ludwik , Trautman Andrzej
Published: July 2002

An explicit construction of spinor structures on real, complex, and quaternionic projective spaces is given for all cases when they exist. The construction is based on a theorem describing the bundle of orthonormal frames of a homogeneous Riemannian manifold. This research is motivated by a remarkable coincidence of spinor connections on low-dimensional spheres with simple, topologically nontrivial gauge configurations.
An infinite number of infinite hierarchies of conserved quantities of the Federbush model
Authors: Kersten P. H. M. , Ten Eikelder H. M. M.
Published: July 2002

The construction of two Lie–Bäcklund transformations is given, which are Hamiltonian vector fields leading to an infinite number of hierarchies of conserved functionals and associated Lie–Bäcklund transformations.
Calculation of radiated gravitational energy using the second-order Einstein tensor
Authors: Habisohn Chris X.
Published: July 2002

In general relativity there is a well-defined prescription for defining a quantity that represents the radiated energy of an exact, asymptotically flat solution of Einstein’s equation. This quantity is called the Bondi energy flux. However, in linearized gravity off a stationary and asymptotically flat background, the second-order Einstein tensor has been used as a stress-energy tensor for the perturbed gravitational field, enabling one to calculate the energy radiated away in gravitational radiation. It is natural to ask how this method compares to the exact method for calculating the Bondi energy flux. In this paper, it is shown that if the metric perturbation satisfies certain falloff and gauge conditions, then the radiated energy calculated using the second-order Einstein tensor equals the second-order contribution to the Bondi energy flux associated with the perturbation. As an application, the second-order Einstein tensor is used to demonstrate gravitational superradiance from a Kerr black hole. Also, the Appendix contains a theorem that makes precise the notion that if ∇(aξb) and its derivative is ‘‘small,’’ then ξa is close to a Killing field.
Cosmological models in globally geodesic coordinates. I. Metric
Authors: Hongya Liu
Published: July 2002

A thought method of measuring distances and recording times by using light signals and the observer’s own clock is introduced into cosmological models of homogeneous and isotropic universes. From this a coordinate transformation that brings the Robertson–Walker metric into a new coordinate system is derived. It is found that this system is a globally geodesic coordinate system that reduces to a local inertial frame at the position of the observer who is moving freely with the cosmological fluid.
Canonical commutation relations on the interval
Authors: Lassner G. , Lassner G. A. , Trapani C.
Published: July 2002

On the Hilbert space ℋ=ℒ 2 (0,L), where (0,L) is a bounded interval of R1, the domain for the canonical commutation relation (CCR) and the CCR quasi-*-algebra is constructed. It is shown that the Bogolubov inequality for a Bose gas (in a box) is fulfilled.
Composite variational principles and the determination of conservation laws
Authors: Caviglia G.
Published: July 2002

Sufficiently regular systems of partial differential equations can always be derived from a composite variational principle via the introduction of a suitable set of adjoint variables. By applying an appropriate formulation of Noether’s theorem to such composite variational principles, an operative procedure leading to the determination of the conservation laws of the given system is determined. As an application, conservation laws for a viscous incompressible fluid and an inviscid barotropic compressible fluid are examined in detail. In particular, new conservation laws for Euler flows are found.
Gauge anomalies on S2 and group extensions
Authors: Carey Alan , Palmer John
Published: July 2002

A geometric connection is established between the group cocycle used by Mickelsson [Topological and Geometrical Methods in Field Theory (World Scientific, Singapore, 1986), pp. 117–131] to realize the Kac–Moody extension of the group of loops in SU(n) as the quotient of a topologically trivial extension of maps from the disk into SU(n) and the gauge anomaly for Quillen’s determinant bundle over the Cauchy–Riemann operators on the spin bundle over S2.
Unbounded partial Hilbert algebras
Authors: Ekhaguere G. O. S.
Published: July 2002

A notion of an unbounded partial Hilbert algebra is introduced and some properties and examples of such an algebra are furnished. Noncommutative versions of Arens Lω spaces over partial Hilbert algebras are formulated and shown to be unbounded partial Hilbert algebras. Moreover, necessary and sufficient conditions for the Lω spaces to be pure unbounded partial Hilbert algebras are established.
Bound on the mass gap for a stochastic contour model at low temperature
Authors: Thomas Lawrence E.
Published: July 2002

A two-dimensional stochastic contour model is considered in which the state space consists of simple closed lattice contours about a fixed origin and the evolution in the state space is a continuous time reversible jump process. An upper bound is obtained on the mass gap for the model, which goes rapidly to zero, in a low temperature limit. A connection between this model and statistical mechanical and droplet models is discussed.
Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series
Authors: Bose Asok
Published: July 2002

The infinite series for log(exp X exp Y) for noncommuting X and Y is expressible in terms of iterated commutators of X and Y except for the linear term X+Y. Dynkin derived an explicit expression for the terms as a sum of iterated commutators over a certain set of sequences. This paper presents a practical algorithm for applying Dynkin’s formula and gives several illustrative examples.
The relations among a special type of solutions in some (D+1)-dimensional nonlinear equations
Authors: Lou Sen-yue , Ni Guang-jiong
Published: July 2002

Among a special type of solutions of some kinds of nonlinear equations in (D+1) dimensions such as the cubic nonlinear Klein–Gordon, sine–Gordon, double sine–Gordon, Ginzburg–Landau equations, etc., some mapping relations exist that allow one to find a solution of one system from a solution of another. Furthermore, one can find some new solutions from a known one within the same system. Some new N-kinklike solutions are also presented.
A note on the existence of a solution for a model of Mc Laughlin, Moloney, and Newell for optical ring cavities
Authors: Merle Frank
Published: July 2002

A problem that arises in a model introduced by McLaughlin, Moloney, and Newell [Phys. Rev. Lett. 51, 75 (1983)] concerning the theory of optical ring cavities is solved. Namely, the equation i ∂v/∂t=Δv−‖v‖2v+ε0‖v‖4v, ε0>0, v(0,⋅)=φ(⋅), where v(t,x): R×R2→C, is considered. The solution of this equation is denoted by vφ(t,x). In addition, let T∈R, Θ∈R, 0<R<1, and a(⋅): R2→C. It is proved that there exists a φ such that a(⋅)+Rvφ(T,⋅) =φ(⋅). Finally, the properties of such a φ are examined and various extensions are given.
Conformal branching rules from Kac̆–Moody automorphisms
Authors: Walton Mark A.
Published: July 2002

The branching rules for the conformal subalgebra SU(2)N×SO(N)4⊆Ŝp(2N)1 is calculated. The method used relies on the outer automorphisms of affine Kac̆–Moody algebras, and was first applied by the author to the conformal subalgebra SU(p)q×SU(q)p⊆SU(pq)1. The results presented here demonstrate the general applicability of the method.
Killing–Yano tensors and variable separation in Kerr geometry
Authors: Kalnins E. G. , Miller W. , Williams G. C.
Published: July 2002

A complete analysis of the free-field massless spin-s equations (s=0, (1)/(2) ,1) in Kerr geometry is given. It is shown that in each case the separation constants occurring in the solutions obtained from a potential function can be characterized in an invariant way. This invariant characterization is given in terms of the Killing–Yano tensor admitted by Kerr geometry.
A Mellin transform technique for the heat kernel expansion
Authors: Malbouisson A. P. C. , Monteiro M. A. R. , Simão F. R. A.
Published: July 2002

It is shown, for a wide class of operators, that the solution to the associated heat equation may be obtained as a series. This is accomplished using the inverse Mellin transform of the kernel of the sth power of the operator, together with the analytic properties of the kernel in the complex s plane.
Symmetrized powers of the fundamental irrep of E6
Authors: Wybourne B. G.
Published: July 2002

The resolution of all possible antisymmetrically symmetrized powers of the fundamental irrep (27) is given. This reduces the problem of plethysms of the fundamental irrep to the evaluation of ordinary Kronecker products of E6 irreps.
Symmetries in predictive relativistic mechanics
Authors: Droz-Vincent Philippe , Nurowski Pawel
Published: July 2002

Symmetries of a two-body relativistic harmonic oscillator and a two-body relativistic Coulomb system are considered. It is shown that, in the harmonic case, the Lie algebra of first integrals includes Poincaré algebra and u(3). In the Coulomb case, the Lie algebra of first integrals includes Poincaré algebra and one of the algebras so(1, 3), so(4), or the algebra corresponding to the group of rigid motions in R3. In both cases, the algebra generated by internal symmetry together with the complete space-time symmetry is infinite dimensional.
Norms of Bethe wave functions for the nonlinear Schrödinger model of spin-1/2 particles
Authors: Pang Gen-di , Pu Fu-cho , Zhao Bao-heng
Published: July 2002

A formula for scalar products of Bethe wave functions in the nonlinear Schrödinger model of spin- (1)/(2) particles is proposed. It is shown, in addition, that one can replace conjugate states by dual eigenfunctions to calculate correlation functions for integrable systems.
Classification of all star irreps of gl(m‖n)
Authors: Gould M. D. , Zhang R. B.
Published: July 2002

All the finite-dimensional star irreps of gl(m‖n) are classified in terms of their highest weights, thereby completing the classification of all finite-dimensional star irreps of the basic classical Lie superalgebras. The lowest weights of such irreps are determined explicitly and it is shown that the contravariant and covariant tensor irreps of gl(m‖n) are star irreps of type (1) and (2), respectively. This explains the applicability of the Young diagram method to these two classes of representations. However, it is shown that one-parameter families of typical star irreps occur that are intrinsically different from the tensorial irreps.
The electroweak interaction as a relativistic symmetry
Authors: Hannabuss K. C.
Published: July 2002

The electroweak gauge group arises naturally in a theory that uses an antilinear instead of a linear Dirac operator.
Scattering and inverse scattering for the 1-D Schrödinger equation with energy-dependent potentials
Authors: Aktosun Tuncay , van der Mee Cornelis
Published: July 2002

The one-dimensional Schrödinger equation with a potential k2V(x) proportional to energy is studied. This equation is equivalent to the wave equation with variable speed. When V(x)<1, is bounded below, and satisfies two integrability conditions, the scattering matrix is obtained and its asymptotics for small and large energies are established. The inverse scattering problem of recovering V(x) when the scattering matrix is known is also solved. By proving that all the solutions of a key Riemann–Hilbert problem have the same asymptotics for large energy, it is shown that the potential obtained is unique.
Moyal quantization of 2+1-dimensional Galilean systems
Authors: Ballesteros A. , Gadella M. , Del Olmo M. A.
Published: July 2002

Stratonovich–Weyl kernels are constructed for some of the coadjoint orbits of the two-dimensional extended Galilean group G(2+1). As an intermediate step, the unitary irreducible representations associated with a given group orbit are obtained by using the Kirillov–Mackey theory. Star products are defined, in the sense of Moyal, for functions on each of these orbits. The central extension of G(2+1) with parameter k is also analyzed, which results from the commutator between the generators of boosts, to conclude that it originates a sort of nonrelativistic remainder of the Thomas precession.
Autocatalytic reactions as dynamical systems on the interval
Authors: Rondoni Lamberto
Published: July 2002

Single chemical reactions that preserve the total number of molecules in a system are considered, and this is expressed by saying that such reactions are stoichiometrically balanced. The study is restricted to those systems whose forward and backward rate constants are equal. The resulting time evolution, for the concentrations of the chemicals, defines a dynamical system (with discrete or continuous time) that is governed by a polynomial map of the interval [B,C], where B≥0 and C≤1.
The trace of the heat kernel on a compact hyperbolic 3-orbifold
Authors: Cognola Guido , Vanzo Luciano
Published: July 2002

The heat coefficients related to the Laplace–Beltrami operator defined on the hyperbolic compact manifold H3/Γ are evaluated in the case in which the discrete group Γ contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.
Nonlinear random wave equations
Authors: Elshamy Maged
Published: July 2002

Nonlinear wave equations describing forced vibrations of a string subject to random perturbations of intensity ε are studied herein. Two kinds of random perturbations are considered; one is Gaussian in the form of initial white noise and the other is a non-Gaussian random forcing which involves the formal derivative of a Brownian sheet. The solutions uε(t,x) of the complete forced equation are a stochastic process in space and time which has a unique stochastic equilibrium. The time variable t varies in a finite interval I:=[0, T], where T is a fixed positive time, and the space variable x varies in an interval J. Assuming that the initial conditions are of sufficient regularity, the fluctuations uε(t,x) from u0(t,x), the unperturbed solution, are analyzed as the intensity of perturbation ε↓0.
On the group theory of the polarization states of a massless field
Authors: Shnerb N. , Horwitz L. P.
Published: July 2002

It is shown that the theory of representations of the Poincaré group applied to the vector potentials of a massless field yields in a simple and direct way (without assuming that the field is a gauge field, and without detailed assumption on the form of the equation of motion), the structure of the polarizations, the Gupta–Bleuler condition, and gauge invariance of the theory. The method is shown to apply to the Maxwell field and to a five-dimensional generalization of the Maxwell field (which properly contains the Maxwell theory) associated with manifestly covariant dynamics.
Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation
Authors: Lou Sen-yue , Weng Jian-ping
Published: July 2002

The formal series symmetry approach is applied to the conditionally integrable nonlinear evolution equation. A set of infinitely many symmetries for a 3+1-dimensional model, Jimbo–Miwa equation with a conditional equation (Kadomtsev–Petviashvilli equation), are obtained by an explicitly constructable formula. Similar to the usual KP equation, these symmetries constitute a generalized W∞ symmetry algebra.
Symmetries and tau function of higher dimensional dispersionless integrable hierarchies
Authors: Takasaki Kanehisa
Published: July 2002

A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ‘‘phase space’’ variables (k,x) of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions compactified to a two (or any even) dimensional torus. Integrability of this hierarchy and the existence of an infinite dimensional of ‘‘additional symmetries’’ are ensured by an underlying twistor theoretical structure (or a nonlinear Riemann–Hilbert problem). An analogue of the tau function, whose logarithm gives the F function (‘‘free energy’’ or ‘‘prepotential’’ in the context of matrix models and topological conformal field theories), is constructed. The infinite dimensional symmetries can be extended to this tau (or F) function. The extended symmetries, just like those of the dispersionless KP hierarchy, obey an anomalous commutation relations.
Asymptotic eigenvalue degeneracy for a class of three-dimensional Fokker–Planck operators
Authors: Carlini Alessandra , Mazzotti Angelo Alessandro , Recchioni Maria Cristina , Zirilli Francesco
Published: July 2002

In this paper, the spectrum of a class of three-dimensional Fokker–Planck operators is studied. Asymptotic eigenvalue degeneracy is proved when the diffusion constant ε goes to zero. A lower bound on the gap between the ground state and the first eigenvalue in each l channel is given.
Dimension formulas for the Lie superalgebra sl(m/n)
Authors: Van der Jeugt J.
Published: July 2002

Although character formulas for simple finite-dimensional modules of the Lie superalgebra sl(m/n) are not known in general, they are known in the cases of so-called typical and of singly atypical modules. For singly atypical modules, however, the character formula is such that the classical limiting procedure yielding a dimension formula from a character formula does, in general, not work. In this article, another approach is presented yielding an explicit dimension formula for all singly atypical modules of sl(m/n) in terms of the highest weight labels.
On the distribution of gravitational energy in the de Sitter space
Authors: Maluf José W.
Published: July 2002

We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized gravitational energy that naturally arises in the framework of the teleparallel equivalent of general relativity. We find that the gravitational energy can only be defined within the cosmological horizon and is largely concentrated in regions far from the center of spherical symmetry, i.e., in the vicinity of the maximal spacelike radial coordinate R=√3/Λ. The smaller the cosmological constant, the farther the concentration of energy. This result complies with the phenomenological features of the de Sitter solution, namely, the existence of a radial acceleration directed away from the center of symmetry experienced by a test particle in the de Sitter space. Einstein already contemplated the de Sitter solution as a world with a surface distribution of matter, a picture which is in agreement with the present analysis.