bluuebunny/crossref_metadata_2025 huggingface dataset:
A re-examination of the phase diagram of hard spherocylinders
Authors: McGrother Simon C. , Williamson Dave C. , Jackson George
Published: July 2002

The phase transitions exhibited by systems of hard spherocylinders, with a diameter D and cylinder length L, are re-examined with the isothermal–isobaric Monte Carlo (MC-NPT) simulation technique. For sufficiently large aspect ratios (L/D) the system is known to form liquid crystalline phases: isotropic (I), nematic (N), smectic-A (Sm A), and solid (K) phases are observed with increasing density. There has been some debate about the first stable liquid crystalline phase to appear as the aspect ratio is increased from the hard-sphere limit. We show that the smectic-A phase becomes stable before the nematic phase as the anisotropy is increased. There is a transition directly from the isotropic to the smectic-A phase for the system with L/D=3.2. For larger aspect ratios, e.g., L/D=4, the smectic-A phase is preceded by a nematic phase. This means that the hard spherocylinder system exhibits I–Sm A–K and I–N–Sm A triple points, the latter occurring at a larger aspect ratio. We also confirm the simulation results of Frenkel [J. Phys. Chem. 92, 3280 (1988)] for the system with L/D=5, which exhibits isotropic, nematic, smectic-A, and solid phases. All of the phase transitions are accompanied by a discontinuous jump in the density, and are, therefore, first order. In the light of these new simulation results, we re-examine the adequacy of the Parsons [Phys. Rev. A 19, 1225 (1979)] scaling approach to the theory of Onsager for the I–N phase transition. It is gratifying to note that this simple approach gives an excellent representation of both the isotropic and nematic branches, and gives accurate densities and pressures for the I–N phase transition. As expected for such a theory, the corresponding orientational distribution function is not accurately reproduced at the phase transition. The results of the recent Onsager/DFT theory of Esposito and Evans [Mol. Phys. 83, 835 (1994)] for the N–Sm A bifurcation point are also in agreement with the simulation data. It is hoped that our simulation results will be used for comparisons with systems with more complex interactions, e.g., dipolar hard spherocylinders and hard spherocylinders with attractive sites.
Cluster analogs of binary isotopic mixtures: Path integral Monte Carlo simulations
Authors: Chakravarty Charusita
Published: July 2002

The structure of quantum clusters composed of binary isotopic mixtures is studied using Fourier path integral Monte Carlo simulations. Such clusters display a purely quantum analog of the segregation phenomenon observed in classical binary clusters with the lighter isotope preferentially located on the cluster surface and the heavier isotope in the cluster interior. A parametric multistage sampling scheme is developed to equilibrate such quantum mixtures. The behavior of a single isotopic impurity in a quantum cluster is examined as a function of impurity mass, temperature and cluster size. Isotopic segregation effects in mixed para-H2/ortho-D2 clusters are shown to be striking.
Infrared spectroscopy of the C–H stretching modes of partially F-substituted benzenes. III. The first overtone of fluorobenzene
Authors: Bassi D. , Corbo C. , Lubich L. , Oss S. , Scotoni M.
Published: July 2002

In this article we report the study of the first overtone of fluorobenzene (C6H5F) in the wave number range from about 5900 to 6100 cm−1. The absorption spectrum has been measured with both a low-temperature opto-acoustic cell and a supersonic-beam opto-thermal spectrometer. A theoretical description of the observed, high-resolution spectrum is given in the framework of the one-dimensional algebraic model, inclusive of a complete set of Fermi (anharmonic) interactions.
Molecular simulation and continuum mechanics study of simple fluids in non-isothermal planar couette flows
Authors: Khare Rajesh , de Pablo Juan , Yethiraj Arun
Published: July 2002

The behavior of simple fluids under shear is investigated using molecular dynamics simulations. The simulated system consists of a fluid confined between two atomistic walls which are moved in opposite directions. Two approaches for shear flow simulations are compared: in one case, the sheared fluid is not thermostatted and only the confining walls are maintained at a constant temperature, while in the other, a thermostat is employed to keep the entire mass of the sheared fluid at a constant temperature. In the first case the sheared fluid undergoes significant viscous heating at the shear rates investigated, consistent with experimental observations and with theoretical predictions. Most simulations to date, however, have used the second approach which is akin to studying a fluid with infinite thermal conductivity. It is shown here that results for transport coefficients are significantly affected by the thermostat; in fact, the transport properties of the fluid determined using the two methods exhibit a qualitatively different shear rate dependence. It is also shown that the temperature profiles observed in our simulations can be described by continuum mechanics, provided the temperature dependence of the viscosity and thermal conductivity is taken into account.
Properties of atoms in molecules: Atoms under pressure
Authors: Bader R. F. W. , Austen M. A.
Published: July 2002

The in situ pressure acting on the surface of an open system at the atomic level is defined and determined by the virial theorem for a proper open system, one whose spatial boundary and equations of motion are determined by the principle of stationary action. The quantum pressure is determined by the virial of the force resulting from the electronic momentum flux through the surface of the open system. A scaling procedure is used to demonstrate that the expectation value of the pressure–volume product of a proper open system is proportional to its surface virial. Previous work, in analogy with the classical virial theorem for a contained system, incorrectly relates the pressure to the external forces of constraint acting on a closed system. A neon vise consisting of a chain of three, four or five hydrogen molecules compressed between two neon atoms is used to introduce the quantum definition of pressure and study its effect on the mechanical properties of an atom and on the topology of the electron density. Pressures approaching 160 GPa have been calculated for the vise. The topology of the electron density and the homeomorphism it exhibits with the virial field are found to be invariant to an increase in pressure, the electron density accumulating to an ever increasing extent between all pairs of nuclei which serve as the sole attractors. The virial of the Ehrenfest force acting on the surface of a compressed molecule provides a measure of the increase in the electronic kinetic energy resulting from the applied pressure. The effects of pressure on the intra- and intermolecular bonding are discussed in terms of pressure-induced changes in the electron density and in the mechanical properties of the atoms.
Femtosecond photon echoes in molecular aggregates
Authors: Meier T. , Chernyak V. , Mukamel S.
Published: July 2002

Two-pulse four-wave-mixing signals from molecular aggregates, including effects of two-exciton states, static disorder, and exciton-phonon interaction represented by arbitrary spectral densities are calculated. Three types of contributions to the signal are identified. The first, reflecting exciton self-correlation, is similar to the photon echo from disordered two-level systems and dominates the signal for long time-delays. The second is related to correlations of one-exciton states, whereas the third reflects correlations between one- and two-exciton states. The information gained by completely resolving the signal field (both amplitude and phase) is analyzed using Wigner spectrograms.
Chain dynamics in entangled polymers: Power laws of the proton and deuteron spin-lattice relaxation dispersions
Authors: Kimmich R. , Fatkullin N. , Seitter R.-O. , Gille K.
Published: July 2002

Chain modes of entangled polymer melts can directly be probed in a frequency range 102 Hz<ν<108 Hz with the aid of field-cycling proton or deuteron relaxometry. The frequency dispersion of proton spin-lattice relaxation universally shows crossovers between the power laws T1∝ν0.5±0.05 (region I), T1∝ν0.25±0.05 (region II), and T1∝ν0.45±0.05 (region III) from high to low frequencies. Regions I and II are identified as limits of a theory based on the renormalized Rouse model assuming intrasegment dipolar interactions. Region III does not appear in distinct form in the deuteron T1 dispersion of perdeuterated chains. It is inferred that proton relaxation in region III is influenced by intersegment interactions which are negligible with deuterons. A corresponding formalism is given. The comparison with the experimental data suggests some multi-chain correlation of the displacement dynamics.
Suspensions of fibers in viscoelastic fluids: Rheology
Authors: Grmela Miroslav , Aı̈t-Kadi Abdellatif , Lafleur Pierre G.
Published: July 2002

Suspensions of fibers in polymeric fluids are regarded as two-component fluids. One component (the fibers) is a rigid body fluid; the second component (polymeric fluid) is a fluid composed of dumbbells. States of the suspension are chosen to be characterized by overall momentum field, configuration space distribution functions of fibers and macromolecules (or alternatively fields of conformation tensors of fibers and macromolecules), and the field of angular momentum (in the body-fixed coordinate system) of the fibers. The time evolution equations (that include expressions for the stress tensor) for these fields are formulated by following Hamiltonian modeling (GENERIC). In the process of solving the governing equations a simplified set of governing equations is derived. This simplified set of equations extends Jeffery’s equations describing suspensions in simple fluids to equations describing suspensions in polymeric fluids. The time evolution and the corresponding expression for the stress tensor are discussed for both distribution functions and conformation tensors.
Semiflexible polymer brushes: A scaling theory
Authors: Kuznetsov Dmitri V. , Chen Zheng Yu
Published: July 2002

We present a simple scaling theory to describe the conformational properties of semiflexible polymers grafted on a flat surface. For orientation-dependent interactions between polymer segments, we analyzed the physical properties of a polymer brush from the collapsed to strongly stretched regimes. Our analysis predicts first-order isotropic–nematic phase transitions between isotropically and nematically collapsed brushes, and between stretched and nematically collapsed brushes. It is also found that the orientational interactions would raise the effective θ temperature as compared with the isotropic counterparts.
Fluctuations-induced anomalous heat capacity above the smectic-A to smectic-C transition
Authors: Mukherjee Prabir K. , Deutsch M.
Published: July 2002

The anomalous part of the heat capacity of smectic-A liquid crystals above the smectic-A to smectic-C phase transition temperature is calculated using Landau’s fluctuation theory, by allowing a spatial variation of the tilt angle. The temperature dependence of the heat capacity above the transition is calculated first for a simple Gaussian model and found to be in good agreement with experiment. The quartic term in the Landau expansion, treated within perturbation theory, is shown to have a negligible contribution to the heat capacity.
Dispersion of an adsorption-induced electronic state of benzene/Cu(111)
Authors: Munakata Toshiaki
Published: July 2002

An angle resolved photoemission work for a benzene-adsorbed Cu(111) surface with a photon energy of 5.45 eV has revealed that an adsorption-induced state due to hybridization of benzene π* and copper shows dispersion with electron momentum along the surface. The dispersion is reproduced well by a parabola with an effective electron mass ratio m*/me=0.9. This suggests that the bonding state extends many copper lattice spacings from the adsorbed molecule. The bonding orbital is thought to be the origin of long range interactions of molecules on a metal surface.
Investigation of intramolecular hydrogen bonds in ortho-hydroxytropolone
Authors: Tsuji Takeshi , Hamabe Hidenori , Hayashi Yoshiyuki , Sekiya Hiroshi , Mori Akira , Nishimura Yukio
Published: July 2002

The S0–S1 electronic spectra of ortho-hydroxytropolone (o-OHTR) in supersonic jets were measured in order to study its isomerism. Only one isomer has been detected in a supersonic jet. A blue shift of electronic origin due to deuteration of two -OH groups was twice as large as that of one -OH group, suggesting that the configurations of the two -OH groups in o-OHTR are equivalent. This finding is consistent with the results of the ab initio calculations. The origin bands of the complexes with water and acetone were red-shifted from that of the bare molecule. The red-shift was explained in terms of two opposite effects of formation of an intermolecular hydrogen bond on each of two intramolecular hydrogen bonds.
Classical trajectory study of CD2OH+→CDO++HD on potential energy surfaces constructed at various quantum chemical levels: Scaling of product mode-specific energies
Authors: Moon Jeong Hee , Park Sang Tae , Kim Myung Soo
Published: July 2002

Potential energy surfaces for the title reaction have been constructed by interpolation of 40 local potentials along the intrinsic reaction coordinate obtained by quantum chemical calculations at the semiempirical, Hartree–Fock (HF), post-HF, and density functional thoery (DFT) levels of theory. Classical trajectory calculations have been carried out and the average product mode-specific energies originating from the reverse barriers have been estimated. When normalized to the reverse barrier heights, the mode-specific energies evaluated at the HF, post-HF and theory DFT levels have been found to be comparable, indicating that the energy partitioning data are scaled to the barrier heights at these levels of theory. Namely, dynamical results obtained on potential energy surfaces constructed at moderate quantum chemical levels were similar (within ∼5%) to those at higher levels. It has been found theoretically that classical dynamics on two potential energy surfaces related by simple scaling results in scaled mode-specific energies. As a guideline for general cases, the similarity factor between two potential energy surfaces has been defined, which shows a good correlation with the scalability of the energy partitioning data.
Deducing energy dissipation from rheological response
Authors: Zaloj V. , Urbakh M. , Klafter J.
Published: July 2002

We propose a method for analyzing the nonlinear response regime of confined liquids driven harmonically in measurements using surface force apparatus. The approach is based on calculating the average energy dissipation in the system, and it provides a way to deduce the microscopic parameters which are responsible for the dissipation. We compare the method with the widely used linear fourier analysis in the case of the Tomlinson model and discuss the meaning and applicability of the two approaches.
Reaction of C60 with oxygen adatoms on Pt(111)
Authors: He Hong , Swami Nathan , Koel Bruce E.
Published: July 2002

Reactions of a C60 monolayer with oxygen adatoms on the Pt(111) surface were studied by a multitechnique surface science approach in the 100–1100 K range. Temperature programmed desorption (TPD), x-ray photoelectron spectroscopy (XPS), ultraviolet (UV) photoelectron spectroscopy (UPS), and high resolution electron energy loss spectroscopy (HREELS) were used to determine the onset temperature for the initial reaction and to characterize the reaction intermediates and products. Unlike the reaction of C60 with O2(g), which begins at 370 K, reaction with oxygen adatoms on Pt(111) begins below 100 K with the formation of C=O bonds with ν(CO) at 2134 cm−1. At about 450, R–O–R species, where R=sp2-hybridized carbon atoms singly bonded to oxygen, with ν(CO)=1215 cm−1, develop and become the dominant reaction intermediates at 700–800 K. Also at these temperatures, an intense peak develops in the HREELS spectra characteristic of polymerized C60 at 1460 cm−1. The reaction products decompose to liberate gas phase CO and CO2 and form graphitic carbon. A prominent difference between the intermediates of this reaction and that of C60 with O2(g) is the absence of vibrational peaks in the 1650–1750 cm−1 region that arise from carbonyl groups. An R–O–R intermediate derived from the opening of pentagons in C60, a structure that has not been observed experimentally before but has been suggested to be stable from theoretical calculations, is most consistent with our spectroscopic results.
Femtosecond probing of exciton relaxation and transport dynamics in polybithiophene
Authors: Bock Alexander M. , Schmid Dankward , Kryschi Carola
Published: July 2002

The relaxation and transport dynamics of singlet excitons in 100 nm thick, electrochemically prepared polybithiophene films were investigated by monitoring the time evolution of photoinduced bleaching of the S0–S1 absorption and photoinduced absorption (S1–Sn) with femtosecond resolved transient absorption spectroscopy. The decay dynamics of both photoinduced bleaching and photoinduced absorption in the spectral range from 500 to 800 nm are observed to be independent of the pump pulse wavelength and can be fitted by a double exponential, the time constants of which are τ1=120±20 fs and τ2=2±0.3 ps. The fast decay process with ∼τ1=120 fs was ascribed to the transport dynamics of the initially generated free excitons migrating over parallel aligned polymer segments to structural defects acting as traps. The competing process, occurring predominantly in structurally disordered regions, is structural relaxation of the initially generated free excitons to self-trapped excitons decaying with a lifetime of about 2 ps.
Molecular dynamics simulations of dielectric relaxation of concentrated polymer solutions
Authors: Kaznessis Yiannis N. , Hill Davide A. , Maginn Edward J.
Published: July 2002

Molecular dynamics simulations are conducted for concentrated solutions of flexible polymers. The results are contrasted with literature dielectric spectroscopy data, in an attempt to elucidate the observed phenomena from a molecular level perspective. A bead-spring model is used and systems with chain sizes up to N=150 beads at reduced densities 0.5⩽ρ⩽0.8 are studied. The dimensions of the chains follow a universal behavior with ρ/ρ*, where ρ* is the crossover density demarcating the onset of chain overlapping. All the chains are found to follow random-walk behavior. The global motion of the chains is investigated in terms of the dielectric loss E″. As in dielectric spectroscopy experiments, the motion of the chains induces prominent dielectric relaxation at low frequencies. The shape of E″ broadens with increasing density, and a normal-mode analysis indicates that overlapping of the chains with increasing density progressively renders the distribution of relaxation times more heterogeneous. For denser systems a second, smaller peak appears at the high frequency end of the spectrum. This secondary peak is not identified with segmental motion, since the simulated chains lack components of the segmental dipoles perpendicular to the chain contour. Entanglement effects are investigated calculating the mean squared displacement g1(t), and the results suggest that the topological constraints of entanglements render at least two different relaxation mechanisms with disparate time scales important. An attempt to explain the shape of the spectra in terms of a phenomenological separation of the motion of chains into a rotational and a stretching mode showed that stretching plays no important role in the relaxation function and the shape of E″.
Molecular-field splitting and vibrational structure in the phosphorus 2p photoelectron spectrum of PF3
Authors: Bo/rve Knut J. , Sæthre Leif J. , Bozek John D. , True Jan , Thomas T. Darrah
Published: July 2002

The experimental phosphorus 2p spectrum of PF3 shows vibrational structure corresponding to the symmetric phosphorus-fluorine stretching mode, with a fundamental frequency of 121.7 meV. In addition, the spectrum shows that the 2p3/2 peak is a doublet split by 146 meV. This molecular-field splitting arises because the anisotropic molecular environment lifts the threefold degeneracy of the 2p orbitals. The observed vibrational structure is compared with that predicted by theory, either treating the core hole explicitly or using the equivalent-cores approximation to simulate the effects of the core hole. Ab initio calculations of the molecular-field splitting that include core-valence electron correlation predict a value in good agreement with the experimental value.
Nuclear magnetic resonance investigations into long range chain fluctuations in molten poly(ethylene-oxide)
Authors: Cohen Addad Jean-Pierre , Guillermo Armel
Published: July 2002

We studied by NMR the long range relaxation of poly-(ethylene oxide) chains, in the melt; the molecular weight was varied over the range 12–450 K. The transverse magnetic relaxation curves of protons attached to the polymer were thoroughly analyzed over the time interval 0–1 s and over the amplitude range 5×10−4 to 1. The analysis revealed three ensembles of protons clearly distinguished from one another from their different relaxation rates (≈7, 102, and 103 s−1, respectively), on the one hand, and from the differences brought about by forming so-called pseudosolid spin–echoes specific to entangled polymers, on the other hand. In this work, it is shown that the main part of the relaxation curve (relative amplitude ≈80%) can be interpreted in terms of exponential modes of isotropic chain relaxation, corresponding to the partition of one chain into Gaussian submolecules. The model provided relaxation functions in very good agreement with experimental curves: the best fits showed that the submolecule molecular weight (11 K) and its associated correlation time (1 ms) are independent of the chain molecular weight. Typical values of the terminal relaxation time, τR, of chain fluctuations were 0.002 and 0.17 s, for molecular weights equal to 55 and 450 K, respectively; correspondingly, the terminal reptation times, estimated from self-diffusion data reported in the literature, were 0.002 and 2 s, respectively. On increasing the molecular weight, the isotropic chain relaxation observed from NMR was found to occur within a time interval much shorter than viscoelastic relaxation times.
Mean field approximation for the stochastic Schrödinger equation
Authors: Prezhdo Oleg V.
Published: July 2002

A stochastic mean-field (SMF) approach to nonadiabatic molecular simulations is introduced. Based on the quantum-classical mean-field approximation, SMF extents the classical model of the environment to incorporate its quantum properties. SMF differs from the ordinary mean-field method by the presence of additional terms in the Schrödinger equation that are due to the system-environment interaction. SMF resolves the two major drawbacks of mixed quantum-classical models. First, decoherence effects in the quantum subsystem are rigorously included. Present in all open systems, decoherence is crucial for nonadiabatic transitions taking place in condensed media. Second, the correct branching of the quantum-classical trajectories is achieved. In earlier approaches, the correct branching of the trajectories was attained via ad hoc surface hopping procedures, which experienced the hop rejection problem and could produce unfavorable classical trajectories in regions of nonadiabatic transitions depending on the quantum basis. It is shown that the correct branching of the trajectories is a direct consequence of decoherence. It is argued that the hop rejection problem disappears in SMF. The decoherence operator is discussed in detail, and the properties of the SMF method are illustrated with model simulations.
A simplified force field for describing vibrational protein dynamics over the whole frequency range
Authors: Hinsen Konrad , Kneller Gerald R.
Published: July 2002

The empirical force fields used for protein simulations contain short-ranged terms (chemical bond structure, steric effects, van der Waals interactions) and long-ranged electrostatic contributions. It is well known that both components are important for determining the structure of a protein. We show that the dynamics around a stable equilibrium state can be described by a much simpler midrange force field made up of the chemical bond structure terms plus unspecific harmonic terms with a distance-dependent force constant. A normal mode analysis of such a model can reproduce the experimental density of states as well as a conventional molecular dynamics simulation using a standard force field with long-range electrostatic terms. This finding is consistent with a recent observation that effective Coulomb interactions are short ranged for systems with a sufficiently homogeneous charge distribution.
Polymer crystallization in quasi-two dimensions. I. Experimental results
Authors: Reiter Günter , Sommer Jens-Uwe
Published: July 2002

We have used atomic force microscopy to investigate the patterns obtained by isothermal crystallization of quasi-2-D monolayers of poly(ethylene oxide) adsorbed onto bare silicon wafers. These monolayers were prepared by a pseudo-dewetting process. Fingerlike branched structures were observed with a characteristic width which increased rapidly with crystallization temperature. The patterns are explained by a simple model considering the interplay of transport on the surface and the probability of attachment to the crystal. The influence of molecular weight was also studied. The average stem length increases with increasing temperature for the longer polymer. The shorter one crystallized in the (almost) fully extended form for all temperatures investigated. Temperature jumps during crystallization resulted in patterns with two different length scales.
Predicting the gas–liquid critical point from the second virial coefficient
Authors: Vliegenthart G. A. , Lekkerkerker H. N. W.
Published: July 2002

We show that whereas the critical point is very sensitive to the range of interaction, the second virial coefficient has a fairly constant value at the critical temperature. This enables us to predict the critical temperature with fair accuracy. We discuss the connection between the second virial coefficient as a predictor for the critical temperature and the second virial coefficient as predictor in crystal growth as was proposed by George and Wilson [A. George and W. W. Wilson, Acta Crystallogr., Sec. D: Biol. Crystallogr. 50, 361 (1994)].
Time-resolved observation of intermolecular vibrational energy transfer in liquid bromoform
Authors: Seifert G. , Zürl R. , Patzlaff T. , Graener H.
Published: July 2002

Efficient intermolecular energy transfer between the C–Br stretching modes ν2 and ν5 of bromoform molecules in the liquid phase has been observed directly in time-resolved experiments applying vibrational pump–probe spectroscopy with picosecond laser pulses. An analysis of results on CHBr3, CDBr3, and an isotopic mixture of both yields a typical time constant of 25±15 ps for this rather efficient, near-resonant intermolecular relaxation channel. Additional new details about the intramolecular pathways of vibrational energy relaxation have been determined for the pure substances.
Valence electron momentum spectroscopy of n-butane
Authors: Pang W. N. , Gao J. F. , Ruan C. J. , Shang R. C. , Trofimov A. B. , Deleuze M. S.
Published: July 2002

The valence electronic structure and momentum-space electron density distributions of n-butane have been studied by means of high-resolution (e,2e) electron momentum spectroscopy based on noncoplanar symmetric kinematics. Ionization spectra for the range of binding energies 6 to 32 eV and momenta described by azimuthal angles φ=0°, 2°, 4°, 6°, 8°, and 10° have been recorded and compared to the results of one-particle Green’s function calculations, performed using the third-order algebraic–diagrammatic construction [ADC(3)] approximation and series of basis sets of improving quality. Experimental electron momentum profiles have been determined from a set of 11 measurements and compared to theoretical results. It has been shown that despite the complex structure of the spectral bands and the conformational versatility of n-butane, the experimental electron momentum distributions are accurately described by the momentum-space form of orbital densities obtained from Becke three-parameter Lee–Yang–Parr (B3LYP) density functional calculations. Significant broadening of the spectral lines and the s-type angular dependence of their intensities above 24 eV have been explained by the breakdown of the one-electron picture of ionization for the 3ag molecular orbital.
Investigations on several empirical rules for entangled polymers based on a self-consistent full-chain reptation theory
Authors: Hua Chi C.
Published: July 2002

Empirical rules, including the stress-optical rule, the Cox–Merz rule, the Gleissle’s mirror relation, and the Laun’s rule, that provide important alternatives in obtaining rheological data for concentrated polymer liquids are investigated via stochastic simulations of a recently proposed full-chain reptation theory [Hua and Schieber, J. Chem. Phys. 109, 10018 (1998)] capable of treating rigorously all fundamental effects for concentrated polymer systems. Theoretical investigations of these rules are important, for they provide strict consistency checks on the predictions of existing molecular theories; at the same time, the limitations of these rules may also be explored. The current simulation implies that deviations from these empirical rules are likely to be observed when polymer chain stretching becomes significant. The effects of molecular weight and molecular weight distribution on the applicability of these rules are inferred; accordingly, we are able to explain the essential feature of the experimental finding when deviations from the Cox–Merz rule were observed. On the other hand, the theory is slightly modified to account for the proper stress-optical relation so that it can be used to simulate directly the birefringence fields of complex flows without being restricted by the validity of the stress-optical rule. Despite its remarkable success in explaining many experimental findings, the theory is found to be unable to predict satisfactorily the Cox–Merz rule and other similar empirical relationships in the power-law region. The discrepancies seem to imply that certain important effects might still be missing in existing reptation theories, and we discuss this issue within the reptation picture.
The generalized Kramers theory for nonequilibrium open one-dimensional systems
Authors: Banik Suman Kumar , Chaudhuri Jyotipratim Ray , Ray Deb Shankar
Published: July 2002

The Kramers theory of activated processes is generalized for nonequilibrium open one-dimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate. The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and nonthermal steady state activation processes.
Hyperparallel tempering Monte Carlo simulation of polymeric systems
Authors: Yan Qiliang , de Pablo Juan J.
Published: July 2002

A new hyperparallel tempering Monte Carlo method is proposed for simulation of complex fluids, including polymeric systems. The method is based on a combination of the expanded grand canonical ensemble (or simple tempering) and the multidimensional parallel tempering techniques. Its usefulness is established by applying it to polymer solutions and blends with large molecular weights. Our numerical results for long molecules indicate that the new algorithm can be significantly more efficient than previously available techniques.
A comparative study of Hamilton and overlap population methods for the analysis of chemical bonding
Authors: Glassey Wingfield V. , Hoffmann Roald
Published: July 2002

The utility of Hamilton population analysis—a partitioning of the electronic energy of a molecule—is investigated within a one-electron molecular orbital framework of the extended Hückel type. The classical Mulliken overlap population description of the valence electron density in terms of one- and two-center “atom” and “bond” contributions, respectively, provides the starting point for the development of an atom-bond energy partitioning scheme. Within an extended Hückel framework simple analytic relations exist between Hamilton populations and Mulliken overlap populations, permitting a step-by-step comparative study of the techniques. The formalism developed for population analysis of two-orbital interactions is tested by performing Hamilton and overlap population analyses of chemical bonding in the isoelectronic series of main group fluorides BrF5, [TeF5]−, [SbF5]2− and the tetrahedral P4 cluster. These molecules were specifically chosen to illustrate the circumstances under which Hamilton and overlap population descriptions of chemical bonding will differ and when they will qualitatively agree. Differences come to the fore when atoms of quite different electronegativity interact, or even in a homonuclear system with disparate atomic basis orbital energies. The significant atomic electronegativity differences in the fluorides result in substantive differences between Hamilton and overlap population descriptions of bonding in these compounds. In contrast the small s–p energy separation in phosphorus results in qualitatively similar Hamilton and overlap population descriptions of P–P bonding in P4. We argue that Hamilton population analysis, by explicitly including reference to the energies of the individual orbitals, affords a more reliable analysis of orbital interactions in molecules.
Mobility and measurements in nonlinear wave mechanics
Authors: Waniewski Jacek
Published: July 2002

The theory based on the nonlinear Schrödinger equation with an additional term λ(ψ̄ψ)αψ is investigated. The standard quantum mechanical interpretation of ψ is assumed at the beginning of the considerations. It turns out that every finite set of pure states can be transformed with the aid of an adequate time sequence of external potentials into a set of pairwise nearly orthogonal states. As a consequence, there exist measurements more selective than quantum ones. In particular, it is possible to discriminate between various mixtures of states that are equivalent in quantum mechanics. The possibility of existence of deterministic measurements is also discussed.
Direct calculation of the Berry phase for spins and helicities
Authors: Jordan Thomas F.
Published: July 2002

The Berry phase for spins or helicities is calculated in a simple way in which it appears more as a property of the spin states than of the Hamiltonian. The calculation applies to nonrelativistic particles or relativistic particles with either zero or nonzero mass. A simple way to see how the Berry phase corresponds to rotation of the electric and magnetic fields of plane-polarized light is also pointed out.
Three interacting particles in one dimension: An algebraic approach
Authors: McGuire J. B. , Hurst C. A.
Published: July 2002

An algebraic formulation of the problem of three particles in one dimension is given, where the particles interact with delta function potentials of arbitrary strength and have almost arbitrary mass. An algebraic formulation is taken to mean that the steps implied from formulation to solution involve finite algebra. The canonical example is equal mass particles interacting with equal strength delta function potentials, where the Bethe ansatz holds and the solution involves only sums of products of matrices with elements that are rational functions of a complex variable. When the Bethe ansatz fails the Sommerfeld diffraction ansatz is satisfied if a condition of internal consistency is met. This condition of internal consistency requires the solution to a Riemann–Hilbert functional equation with an algebraic coefficient. The solution to this functional equation is an analytic, but not generally a meromorphic function. It is demonstrated that an asymptotic solution may be constructed within the domain of algebraic functions.
Nonlocal symmetries and Bäcklund transformations for the self-dual Yang–Mills system
Authors: Papachristou C. J. , Harrison B. Kent
Published: July 2002

The observation is made that generalized evolutionary isovectors of the self-dual Yang–Mills equation, obtained by ‘‘verticalization’’ of the geometrical isovectors derived in a previous paper [J. Math. Phys. 28, 1261 (1987)], generate Bäcklund transformations for the self-dual system. In particular, new Bäcklund transformations are obtained by ‘‘verticalizing’’ the generators of point transformations on the solution manifold. A geometric ansatz for the derivation of such (generally nonlocal) symmetries is proposed.
Comment on the paper ‘‘An exactly soluble relativistic quantum two-fermion problem’’ [J. Math. Phys. 2
7, 3055 (1986)]
Authors: Barut A. O. , Moore R. A. , Scott T. C.
Published: July 2002

A comment is made on the separability of the center of mass and relative coordinates in the exact solution of a covariant two-body equation for two spin- 1/2 particles.
Theta function representation of modular group for SU(n)
Authors: Ardalan F. , Arfaei H. , Zarkesh M.
Published: July 2002

Matrices of the representation of the modular group acting on the space of SU(n) level k Kac–Moody algebra character are calculated explicitly. Also, a simple form is obtained for the case k=1, which is compared with the corresponding matrix elements for the character representation in the case of the toroidally compactified string theory.
Cartan-preserving automorphisms of untwisted and twisted Kac–Moody algebras
Authors: Gorman N. , O’Raifeartaigh L. , McGlinn W.
Published: July 2002

The group Ñ defined as the normalizer of the Cartan subalgebra in the group of all (inner and outer) automorphisms of affine Kac–Moody (KM) algebras is a natural extension of the Weyl group and is shown to play a fundamental role in the structure of these algebras (both untwisted and twisted). It is a (discrete) Galilean group which incorporates the affine and Weyl group structure of the KM algebra and the space-time structure of the string. It links the Virasoro and KM algebras in a nontrivial way and plays a key role in the ‘‘vertex’’ construction. Moreover, the elements of its covering group can be used to uniquely parametrize (and untwist) the pseudotwisted KM algebras.
Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models
Authors: Jaulent Marcel , Manna Miguel A. , Alonso Luis Martínez
Published: July 2002

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann–Hilbert and ∂̄ problems. When MSIM’s are written in terms of the ‘‘group coordinates,’’ some of them can be ‘‘contracted’’ into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM’s corresponding to one pole, yield the Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. Two-pole contractible MSIM’s are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2+1)-dimensional evolution equations and of quite strong differential constraints.
Octonions and subalgebras of the exceptional algebras
Authors: Buccella F. , Della Selva A. , Sciarrino A.
Published: July 2002

The vector space of the generators of E8 is realized in terms of 3×3 traceless matrices, two independent sets of octonions imaginary units, and the two G2 acting on them. In this way one gets an appropriate framework to describe in a simple way how exceptional algebras and their fundamental representations transform under their subalgebras.
A geometric approach to quantum vortices
Authors: Penna Vittorio , Spera Mauro
Published: July 2002

In this paper a geometrical description is given of the theory of quantum vortices first developed by Rasetti and Regge [Physica A 80, 217 (1975)] relying on the symplectic techniques of Marsden and Weinstein [J. Phys. D 7, 305 (1983)], and Kirillov–Kostant–Souriau geometric quantization. The RR-current algebra is interpreted as the natural Hamiltonian algebra associated to a certain coadjoint orbit of the group G=SDiff(R3), the KKS prequantization condition of which is related to the Feynman–Onsager relation. This orbit is also shown to possess a G-invariant Kaehler structure, whence, in principle, it is possible to quantize it in a natural way.
On the Levinson theorem for Dirac operators
Authors: Klaus Martin
Published: July 2002

For the Dirac equation with potential V(r) obeying ∫∞0(1+r)‖V(r)‖dr<∞ we prove a relativistic version of Levinson’s theorem that relates the number of bound states in the spectral gap [−m,m] to the variation of an appropriate phase along the continuous part of the spectrum. In the process, the asymptotic properties of the Jost function as E→±m are analyzed in detail. The connection with the nonrelativistic version of Levinson’s theorem is also established.
Integrability of difference Calogero–Moser systems
Authors: van Diejen J. F.
Published: July 2002

A general class of n-particle difference Calogero–Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. We prove the quantum integrability of the model for n=2 and present partial results for n≥ 3. In degenerate cases (rational, hyperbolic, or trigonometric limit), the integrability follows for arbitrary particle number from previous work connected with the multivariable q-polynomials of Koornwinder and Macdonald. Liouville integrability of the corresponding classical systems follows as a corollary. Limit transitions lead to various well-known models such as the nonrelativistic Calogero–Moser systems associated with classical root systems and the relativistic Calogero–Moser system.
Complex analytic realizations for quantum algebras
Authors: de Azcárraga J. A. , Ellinas D.
Published: July 2002

A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for the cases of the q oscillators (q-Weyl–Heisenberg algebra) and for the suq(2) and suq(1,1) algebras and their coproducts. They are given in terms of a series in powers of ordinary derivative operators which act on the Bargmann–Hilbert space of functions endowed with the usual integration measures. In the q→1 limit these realizations reduce to the usual analytic Bargmann realizations for the three algebras.
New family of asymptotic solutions of Helmholtz equation
Authors: Maltsev N. E.
Published: July 2002

A new family of asymptotic solutions of the Helmholtz equation can be derived. It is shown that new solutions are regular at caustics and turning points and do not require any special functions.
Nonrenormalization theorem for the Abelian anomaly within dimensional regularization
Authors: Gabadadze G. T. , Pivovarov A. A.
Published: July 2002

An approach to the calculation of the Abelian axial anomaly within the dimensional regularization is proposed. This approach allows one to make all computations consistently in the framework of a perturbation theory to any number of loops by using the ordinary dimensional regularization. Handling of the γ5 matrix in the anomaly calculation requires only the possibility of cycle permutation under the trace sign. Our procedure leads to a normalization of the axial current that differs by a finite amount from that of the corresponding vector current. The question of normalization of the axial current in relation to the π0→2γ decay amplitude is briefly considered.
Thermodynamics of vortices in the plane
Authors: Shah P. A. , Manton N. S.
Published: July 2002

The thermodynamics of vortices in the critically coupled Abelian Higgs model, defined on the plane, are investigated by placing N vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli space for N vortices, which is the same as that of N indistinguishable points on a torus, fibrates into a CPN−1 bundle over the Jacobi manifold of the torus. The volume of the moduli space is a product of the area of the base of this bundle and the volume of the fiber. These two values are determined by considering two 2-surfaces in the bundle corresponding to a rigid motion of a vortex configuration, and a motion around a fixed center of mass. The partition function for the vortices is proportional to the volume of the moduli space, and the equation of state for the vortices is P(A−4π N)=NT in the thermodynamic limit, where P is the pressure, A the area of the region of the plane occupied by the vortices, and T the temperature. There is no phase transition.
The potential constraints of the KP system and the corresponding Hamiltonian equations
Authors: Dengyuan Chen , Ningsheng Zhu , Min Zhu
Published: July 2002

In this paper all the potential constraints (with or without first-order partial derivatives) of the KP system, from which the associated linear problem can be restricted into a (1+1)-dimensional Hamiltonian equation, are obtained by using the sufficient and necessary condition for a nonlinear equation to be a Hamiltonian system. Some well-known integrable systems, such as (1+1)-dimensional AKNS system, generalized NS system, and several new Hamiltonian equations, are deduced as particular examples.
Null cone evolution of axisymmetric vacuum space–times
Authors: Gómez R. , Papadopoulos P. , Winicour J.
Published: July 2002

The details of an algorithm for the global evolution of asymptotically flat, axisymmetric space–times, based upon a characteristic initial value formulation using null cones as evolution hypersurfaces is presented. A new static solution of the vacuum field equations which provides an important test bed for characteristic evolution codes is identified. It is also shown how linearized solutions of the Bondi equations can be generated by solutions of the scalar wave equation, thus providing a complete set of test beds in the weak field regime. These tools are used to establish that the algorithm is second order accurate and stable, subject to a Courant–Friedrichs–Lewy condition. In addition, the numerical versions of the Bondi mass and news function, calculated at scri on a compactified grid, are shown to satisfy the Bondi mass loss equation to second order accuracy. This verifies that numerical evolution preserves the Bianchi identities. Results of numerical evolution confirm the theorem of Christodoulou and Klainerman that in vacuum, weak initial data evolve to a flat space–time. For the class of asymptotically flat, axisymmetric vacuum space–times, for which no nonsingular analytic solutions are known, the algorithm provides highly accurate solutions throughout the regime in which neither caustics nor horizons form.