bluuebunny/crossref_metadata_2025 huggingface dataset:
Determinants of secondary structure of polypeptide chains: Interplay between short range and burial interactions
Authors: Kolinski Andrzej , Skolnick Jeffrey
Published: July 2002

The effect of tertiary interactions on the observed secondary structure found in the native conformation of globular proteins was examined in the context of a reduced protein model. Short-range interactions are controlled by knowledge based statistical potentials that reflect local conformational regularities seen in a database of three-dimensional protein structures. Long-range interactions are approximated by mean field, single residue based, centrosymmetric hydrophobic burial potentials. Even when pairwise specific long-range interactions are ignored, the inclusion of such burial preferences noticeably modifies the equilibrium chain conformations, and the observed secondary structure is closer to that seen in the folded state. For a test set of 10 proteins (belonging to various structural classes), the accuracy of secondary structure prediction is about 66% and increases by 9% with respect to a related model based on short-range interactions alone [Kolinski et al., J. Chem. Phys. 103, 4312 (1995)]. The increased accuracy is due to the interplay between the short-range conformational propensities and the burial and compactness requirements built into the present model. While the absolute level of accuracy assessed on a per residue basis is comparable to more standard techniques, in contrast to these approaches, the conformation of the chain now has a better defined geometric context. For example, the assumed spherical domain protein model that simulates the segregation of residues between the hydrophobic core and the hydrophilic surface allows for the prediction of surface loops/turns where the polypeptide chain changes its direction. The implications of having such self-consistent secondary structure predictions for the prediction of protein tertiary structure are briefly discussed.
Optical spectra of liquid water in vacuum uv region by means of inelastic x-ray scattering spectroscopy
Authors: Hayashi Hisashi , Watanabe Noboru , Udagawa Yasuo , Kao C.-C.
Published: July 2002

Inelastic x-ray scattering (IXS) spectroscopy using hard x-rays is in principle equivalent to optical spectroscopy as long as momentum transfer can be approximated to be zero. Hence IXS spectra of liquid water which corresponds to vacuum uv absorption were measured at small energy transfers with energy resolution of 0.5 eV. The loss function was derived from the spectra and its convergence for the momentum transfer smaller than 0.28 a.u. was confirmed. The reflectance spectrum and the optical oscillator strength have been calculated from the loss function. It is shown that the optical oscillator strength of liquid water differs considerably from that of gaseous water.
Molecular dynamics simulation of gas mixtures in porous media. I. Adsorption
Authors: Yi Xiaohua , Ghassemzadeh Jaleh , Shing Katherine S. , Sahimi Muhammad
Published: July 2002

In this paper and its sequel we report the results of Molecular Dynamics simulation of single component and binary gas mixtures in a porous medium with interconnected pores. The porous medium used in the study is a model pillared clay. In the present paper we study adsorption of binary gas mixtures, and investigate in detail the effect of various factors, such as the morphology of the pore space and the adsorbent-adsorbate interactions. A new mean-field statistical mechanical theory of adsorption is developed, and shown to provide very accurate predictions for the simulation results over wide ranges of the pressure, temperature and porosity of the system.
Internal surfaces of porous media studied by nuclear magnetic resonance cryoporometry
Authors: Allen S. G. , Stephenson P. C. L. , Strange J. H.
Published: July 2002

The filling processes of water and cyclohexane in porous silica (with a characteristic pore size of 60 Å) are investigated using the nuclear magnetic resonance (NMR) technique of cryoporometry. In this technique, the liquid was frozen in the pores before the temperature was raised gradually; melting the smallest particles first and then particles of increased size. The volume of the molten liquid present was measured using the height of a T2 spin echo. The experiments were performed with filling fractions ranging from 10% to 100%. The results showed distinctly different behaviors of the fluids, which depended on the surface adhesion. It was found that water (a fluid which wets the pore surface) forms small puddles—much smaller than the smallest pore size—at low filling fractions. These puddles grow in size as more water is added until all the pore volume is filled. Cyclohexane (a non-wetting fluid) on the other hand, does not form small puddles but completely fills the pores with a preference for the smaller pores. Water is found to give more accurate results for the pore size distribution than cyclohexane, in 60 Å silica.
Langevin dynamics simulations of early-stage polymer nucleation and crystallization
Authors: Liu C. , Muthukumar M.
Published: July 2002

United-atom Langevin dynamics simulations have been performed in an effort to understand early-stage polymer crystallization at the microscopic level. We have modeled the crystallization process by following the competition between the attraction among nonbonded beads and torsional energies along chain backbones. We have monitored three processes: spontaneous formation of initial nuclei and their subsequent growth in time by an isolated chain as a function of degree of undercooling, crystallization at a growth front as a function of commesurability between the thickness of the growth front and the length of crystallizing chains, and cooperative crystallization by several chains into lamellae. The details of growth kinetics here have been captured by explicit visual displays of chain conformations, radius of gyration of labeled chains and aggregates, local and global orientation order parameters, and interaction energies all as functions of time. We observe that the kinetic pathway of lamellar thickening is stepwise and quantized for small degrees of undercooling and that the lamellar thickness is inversely related to the degree of undercooling. The crystallization is found to be more efficient if chain length is an integer multiple of the thickness of the growth front. We have compared several of our key simulation results with experimentally observed results reported in the literature and found that the simulations exhibit many salient features of polymer crystallization in dilute solutions.
Approximate coupled-cluster methods employing split cluster amplitudes: Implementation of an almost-linear coupled-cluster formalism
Authors: Jankowski K. , Grabowski I. , Kowalski K.
Published: July 2002

A new approximation strategy, split-amplitude strategy, useful within the framework of the coupled-cluster (CC) methodology is proposed. It consists in representing the individual cluster amplitudes as a sum of two components, one of fixed value, which may be obtained from external sources, and the other determined from a set of modified CC equations. This approach provides new possibilities of absorbing information concerning the values of cluster amplitudes from independent calculations. By properly choosing the fixed amplitude components, one may substantially reduce the magnitudes of the most significant amplitudes to be determined for the state considered, which in turn causes that the known approximation procedures are more justifiable when applied to the modified CC equations than to the equations of the standard CC approaches. The split-amplitude strategy has been employed to setting up several almost-linear CC (AL-CC) approaches of a single reference type corresponding to the basic CC methods. These low-cost approaches seem to be useful in theories of processes involving nondynamically correlated (quasidegenerate) states. The AL-CC methods have been applied to the ground states for various geometries of the following molecular systems: H8, H2O, BH, and HF. It is found that the energies obtained for a given AL-CC approach are very close to those for the corresponding basic CC method, which is true even for strongly quasidegenerate states.
Scattering and trapping dynamics of gas-surface interactions: Vibrational excitation of CF3Br on graphite
Authors: Någård Mats B. , Marković Nikola , Pettersson Jan B. C.
Published: July 2002

We present results from molecular beam experiments and classical trajectory calculations of CF3Br scattering from graphite. Direct inelastic scattering dominates for initial translational energies Etr=0.6–3.5 eV and surface temperatures Ts=500–1170 K. An increase in the CF3Br vibrational temperature is observed in the scattered flux using the method of electron impact-induced fragmentation. The vibrational excitation depends on Etr and Ts, and a maximum vibrational temperature increase of 254±15 K is reached for Etr=3.5 eV and Ts=830 K. The vibrational excitation, angular distributions, and average translational energies are semi-quantitatively reproduced by classical trajectory calculations, indicating that the vibrational excitation can be explained by an electronically adiabatic “mechanical” process. The calculations suggest that a large fraction of the incident molecules experience multiple collisions with the surface. These transiently trapped molecules are slowly vibrationally excited while moving long distances, and are not thermalized even after 100 ps on the surface.
Generalized linear-scaling localized-density-matrix method
Authors: Liang WanZhen , Yokojima Satoshi , Chen GuanHua
Published: July 2002

A generalized linear scaling localized-density-matrix (LDM) method is developed to adopt the nonorthonormal basis set and retain full Coulomb differential overlap integrals. To examine its validity, the method is employed to evaluate the absorption spectra of polyacetylene oligomers containing up to 500 carbon atoms. The semiempirical Hamiltonian for the π electrons includes explicitly the overlap integrals among the π orbitals, and is determined from the ab initio Hartree–Fock reduced single-electron density matrix. Implementation of the generalized LDM method at the ab initio molecular orbital calculation level is discussed.
High-order multiple quantum excitation in 13C nuclear magnetic resonance spectroscopy of organic solids
Authors: Antzutkin Oleg N. , Tycko Robert
Published: July 2002

Excitation and detection of high-order multiple quantum (MQ) coherences among 13C nuclear spins in singly-13C-labeled organic solids is demonstrated experimentally. MQ signals involving at least ten quanta of spin angular momentum are observed in nuclear magnetic resonance (NMR) measurements on polycrystalline L-methionine-methyl-13C and L-alanine-1-13C, using a time-reversible multiple pulse excitation sequence modified specifically for experiments on systems with weak homonuclear dipole–dipole couplings and strong inhomogeneous interactions such as anisotropic chemical shifts. The feasibility of high-order MQ excitation and detection in 13C-labeled organic solids promises to expand significantly the range of applications of MQ NMR as a structural tool, to include such systems as 13C-labeled synthetic polymers and biopolymers.
Dielectric relaxation of water and heavy water in the whole fluid phase
Authors: Okada K. , Yao M. , Hiejima Y. , Kohno H. , Kajihara Y.
Published: July 2002

Recently we developed a new microwave spectroscopy technique in the frequency range up to 40 GHz, and measured the static dielectric constant and the dielectric relaxation time for supercritical water. In the present work we report the dielectric properties of heavy water at temperatures and pressures up to 770 K and 59 MPa, respectively. The static dielectric constant of D2O as well as H2O are well described by the Uematsu–Franck formula when the number density instead of the mass density is used as the input parameter. The dielectric relaxation time decreases rapidly with increasing temperature in liquid H2O and D2O and jumps to a large value at the liquid–gas transition. The relaxation time of D2O is longer than that of H2O in the liquid state, and the difference becomes smaller with decreasing density in the gaseous state. For both H2O and D2O the most relevant parameter determining the relaxation time is the temperature at high densities or at low temperatures, and it is the density at low densities or at high temperatures. Based upon the observation that the dielectric relaxation time becomes fairly long in the dilute limit, we have concluded that the dielectric relaxation in the gaseous state is governed by the binary collision of water molecules and explained the relaxation time quantitatively by the collision time. We have extended the interpretation of the dielectric relaxation to the liquid state by taking into account the contribution of bound water molecules that are incorporated in the hydrogen-bond network. Anomalous relaxation at low temperatures is also discussed.
Kinetic Monte Carlo simulations of the growth of polymer crystals
Authors: Doye Jonathan P. K. , Frenkel Daan
Published: July 2002

Based upon kinetic Monte Carlo simulations of crystallization in a simple polymer model we present a new picture of the mechanism by which the thickness of lamellar polymer crystals is constrained to a value close to the minimum thermodynamically stable thickness, lmin. The free energetic costs of the polymer extending beyond the edges of the previous crystalline layer and of a stem being shorter than lmin provide upper and lower constraints on the length of stems in a new layer. Their combined effect is to cause the crystal thickness to converge dynamically to a value close to lmin where growth with constant thickness then occurs. This description contrasts with those given by the two dominant theoretical approaches. However, at small supercoolings the rounding of the crystal profile does inhibit growth as suggested in Sadler and Gilmer’s entropic barrier model.
Static dipole polarizability of small mixed sodium–lithium clusters
Authors: Antoine R. , Rayane D. , Allouche A. R. , Aubert-Frécon M. , Benichou E. , Dalby F. W. , Dugourd Ph. , Broyer M. , Guet C.
Published: July 2002

We have measured the static dipole polarizability of Nay−xLix clusters (with y=2, 3, 4, and 8) by molecular beam deflection technique. For a given size, the polarizability of pure lithium clusters is smaller than the polarizability of pure sodium clusters. For mixed clusters, a smooth decrease in the polarizability is observed as the proportion of lithium atoms increases. For the NaLi molecule, both experimental permanent dipole and average polarizability have been obtained. Experimental results are compared to results of density functional theory and configuration interaction single and double (CISD) ab initio calculations.
Analytical integral equation theory for a restricted primitive model of polyelectrolytes and counterions within the mean spherical approximation. I. Thermodynamic properties
Authors: von Solms N. , Chiew Y. C.
Published: July 2002

We present an analytical integral equation theory for polyelectrolyte solutions modeled as linear freely-jointed tangent hard-sphere polyanionic chains and cationic hard-sphere monomeric counterions embedded in a continuum dielectric medium. Each hard-sphere segment on the polyelectrolyte chain and hard-sphere counterion are univalent with unit diameters. The model was formulated in the context of the multi density Ornstein–Zernike integral equation theory within the mean spherical approximation. Analytical solutions for the model were obtained using the ideal chain approximation. The contact values of the radial distribution functions, internal energy, Helmholtz energy, osmotic pressure, and activity coefficient of the system were derived as a function of chain length, density, and Bjerrum length via the energy route. Predictions from the theory were compared with computer simulation data reported in the literature, and very good agreement was found.
The rotational spectrum of rhomboidal SiC3
Authors: Apponi A. J. , McCarthy M. C. , Gottlieb C. A. , Thaddeus P.
Published: July 2002

Rhomboidal SiC3, a planar ring with C2v symmetry and a transannular C–C bond, was detected at centimeter wavelengths in a pulsed supersonic molecular beam with a Fourier transform microwave (FTM) spectrometer, and was subsequently observed in a low-pressure dc glow discharge with a free-space millimeter-wave absorption spectrometer. The rotational spectrum of SiC3 is characterized by large harmonic defects and large splitting of the K-type doublets. Lines in the centimeter-wave band were very strong, allowing the singly substituted isotopic species to be observed in natural abundance. Measurements of the normal and five isotopically substituted species with the FTM spectrometer provided conclusive evidence for the identification and yielded an experimental zero-point (r0) structure. Forty-six transitions between 11 and 286 GHz with Ka⩽6 were measured in the main isotopic species. Three rotational and nine centrifugal distortion constants in Watson’s A-reduced Hamiltonian reproduce the observed spectrum to within a few parts in 107 and allow the most intense transitions up to 300 GHz to be calculated with high accuracy. The spectroscopic constants confirm that SiC3 is a fairly rigid molecule: the inertial defect is comparable to those of well-known planar rings and the centrifugal distortion constants are comparable to molecules of similar size. The number of SiC3 molecules in our supersonic molecular beam in each gas pulse is at least 3×1011, so large that electronic transitions may be readily detectable by laser spectroscopy.
Time evolution of polymer distribution functions from moment equations and maximum-entropy methods
Authors: Poland Douglas
Published: July 2002

We use the maximum-entropy method to calculate the chain-length distribution as a function of time for cooperative polymerization models involving nucleation and growth. At least the first two moments of the distribution are required for the maximum-entropy method. To obtain the moments we use a generating function to give the moment rate equations which in general involves an infinite set of coupled differential equations which can be truncated to give a finite set by using various closure approximations. In particular we use the maximum-entropy method to treat the reversible growth of chains from a fixed concentration of initiators in which case the initial distribution is a sharp Poisson-type one that then evolves slowly to the very broad equilibrium distribution. For this model we find that there is a scaled time that reduces the time dependence of the moments to a universal set of asymptotic curves.
Energy levels in metal oxide semiconductor quantum dots in water-based colloids
Authors: Qu Fanyao , Morais P. C.
Published: July 2002

The three-dimensional Schrödinger and Poisson’s equations are used to calculate the conduction band profile, energy levels, and Fermi energy of negatively charged semiconductor quantum dots. The calculation is carried out self-consistently within the frame of the finite-difference method. Assuming the effective mass of the proton at the semiconductor–electrolyte interface, we found the conduction band profile for the spherical ZnO quantum dots dispersed as aqueous colloids very similar to the conduction band profile of symmetric modulation-doped semiconductor quantum wells. The energy levels and Fermi energy of the spherical ZnO quantum dots are obtained as a function of the band offset at the semiconductor–electrolyte interface. A comparison of the energy levels for negatively charged and uncharged quantum dots is used as an alternative explanation of the observed reversible blue shift in the absorption spectrum of semiconductor colloids under illumination.
Comparison study of the prediction of Raman intensities using electronic structure methods
Authors: Halls Mathew D. , Schlegel H. Bernhard
Published: July 2002

Raman intensities have been computed for a series of test molecules (N2, H2S, H2O, H2CO, CH4, C2H2, C2H4, C2H6, SiO2, NH3, CH2F2, and CH2Cl2) using Hartree–Fock, second-order Mo/ller–Plesset perturbation theory (MP2), and density functional theory, including local, gradient-corrected, and hybrid methods (S-VWN, B-LYP and B3-LYP, and MPW1-PW91) to evaluate their relative performance. Comparisons were made with three different basis sets: 6-31G(d), Sadlej, and aug-cc-pVTZ. The quality of basis set used was found to be the most important factor in achieving quantitative results. The medium sized Sadlej basis provided excellent quantitative Raman intensities, comparable to those obtained with the much larger aug-cc-pVTZ basis set. Harmonic vibrational frequencies computed with the Sadlej basis set were in good agreement with experimental fundamentals. For the quantitative prediction of vibrational Raman spectra, the Sadlej basis set is an excellent compromise between computational cost and quality of results.
Time-dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids
Authors: Glotzer Sharon C. , Novikov Vladimir N. , Schrøder Thomas B.
Published: July 2002

Dynamical heterogeneity and the decoupling of diffusion and relaxation in a supercooled liquid is investigated via a time-dependent, four-point density correlation function. We show that the main contribution to the corresponding generalized susceptibility χ4(t) in a molecular dynamics simulation of a Lennard-Jones liquid arises from spatial correlations between temporarily localized (“caged”) particles. By comparing χ4(t) with a generalized susceptibility χM(t) related to a correlation function for the squared particle displacements, we demonstrate a connection between dynamical heterogeneity and the decoupling of relaxation and diffusion.
Simulation of adsorption kinetics of lipid vesicles
Authors: Zhdanov V. P. , Keller C. A. , Glasmästar K. , Kasemo B.
Published: July 2002

Employing the Monte Carlo technique, we study the kinetics of vesicle adsorption at a solid–liquid interface. The proposed model combines a treatment of the surface kinetics, including spontaneous, adsorption- and lipid-membrane-induced decomposition of adsorbed vesicles, and limitations of the adsorption rate by vesicle diffusion in the solution. With this model, we demonstrate different kinetic cases, corresponding to various scenarios of vesicle adsorption and decomposition. The general results are employed to simulate recent experimental kinetic data for adsorption of small phospholipid vesicles at a SiO2 surface.
Period adding and broken Farey tree sequence of bifurcations for mixed-mode oscillations and chaos in the simplest three-variable nonlinear system
Authors: Kawczyński Andrzej L. , Strizhak Peter E.
Published: July 2002

A detailed study of the simplest three-variable model exhibiting mixed-mode oscillations and chaos is presented. We show that mixed-mode oscillations appear due to a sequence of bifurcations which is characterized by a combination of the Farey tree that is broken by chaotic windows and period adding. This scenario is supported by a family of one-dimensional return maps. The model also exhibits hysteresis between stable steady state and mixed modes.
Polarization transfer dynamics in Lee–Goldburg cross polarization nuclear magnetic resonance experiments on rotating solids
Authors: Ladizhansky Vladimir , Vega Shimon
Published: July 2002

This paper presents a theoretical description of continuous wave (CW) high frequency Lee–Goldburg cross polarization magic angle spinning (LG–CPMAS) nuclear magnetic resonance experiments. The full time-dependent LG–CPMAS Hamiltonian is replaced by its zero order time-independent Hamiltonian in the interaction representation. Carbon signal enhancements of LG–CPMAS experiments are calculated for spin systems consisting of six H1 nuclei coupled to one C13 nucleus. These simulations are based on Floquet theory calculations, explicitly taking into account the time dependence because of magic angle spinning, and calculations based on the zero-order Hamiltonian. The good agreement between these calculations justifies the use of the zero-order Hamiltonian. The time-dependent intensities of the cross peaks in heteronuclear C13–1H correlation spectra, extracted from 3D LG–CPMAS experiments on a natural abundant DL–alanine sample with increasing CP mixing times, are in good agreement with the theoretical intensities simulated by using the zero-order Hamiltonian. The approximated LG–CPMAS Hamiltonian can be used to obtain structural information about a proton coupled to a single carbon. The simulated intensities of the carbon signals of an isolated C13–1H group and a C13–1H group that is coupled to additional protons, measured by LG–CPMAS experiments with increasing CP mixing times, are compared. This study suggests that the buildup curve of each LG–CPMAS carbon signal and its Fourier transformed CP spectrum can be interpreted in terms of a single distance between the observed C13 and its nearest proton, if the additional protons are removed from this carbon by at least 1.2 times this distance.
Structural relaxation of the fragile glass-former propylene carbonate studied by nuclear magnetic resonance
Authors: Qi F. , Schug K. U. , Dupont S. , Döß A. , Böhmer R. , Sillescu H. , Kolshorn H. , Zimmermann H.
Published: July 2002

Proton, deuteron, and carbon NMR methods were applied to study various isotopic species of supercooled and glassy propylene carbonate. The molecular diffusion was investigated via static field gradient diffusometry and yielded evidence for a particularly pronounced enhancement of the translational over the reorientational dynamics. The latter was monitored using measurements of spin-lattice relaxation times and of two-time stimulated echoes. The sin–sin correlation functions exhibited a pronounced dependence on the evolution times. From these results it is concluded that the geometry of molecular reorientation can be described as a superposition of moderately small jump angles (about 30°) and a quasi-diffusive component which is responsible for about one-third of the total angular displacement. Finally, four-time stimulated echoes confirmed that the nonexponential relaxation in propylene carbonate is dynamically heterogeneous in nature.
Molecular π pulses: Population inversion with positively chirped short pulses
Authors: Cao Jianshu , Bardeen Christopher J. , Wilson Kent R.
Published: July 2002

Detailed theoretical analysis and numerical simulation indicate that nearly complete electronic population inversion of molecular systems can be achieved with intense positively chirped broadband laser pulses. To provide a simple physical picture, a two-level model is used to examine the condition for the so-called π pulses and a four-level model is designed to demonstrate for molecular systems the correlation between the sign of the chirp and the excited state population. The proposed molecular π pulse is the combined result of vibrational coherence in the femtosecond regime and adiabatic inversion in the picosecond regime. Numerical results for a displaced oscillator, for LiH and for I2, show that the proposed molecular π pulse scheme is robust with respect to changes in field parameters such as the linear positive chirp rate, field intensity, bandwidth, and carrier frequency, and is stable with respect to thermal and condensed phase conditions including molecular rotation, rovibronic coupling, and electronic dephasing.
On the Poisson brackets of differentiable generators in classical field theory
Authors: Brown J. David , Henneaux Marc
Published: July 2002

The canonical formulation of field theory on open spaces is considered. It is proved, under appropriate assumptions, that the Poisson bracket of two differentiable generators is also a differentiable generator.
A simplified variational characterization of Schrödinger processes
Authors: Wakolbinger A.
Published: July 2002

The variational problem E[1/2 ∫T0(βt−A(t,Xt))2 dt −∫T0c(t,Xt)dt]=min, where βt is the drift process of a diffusion process with unit diffusion coefficient and given initial and final distributions, A is a given vector field, and c is a given scalar field, is considered. It is shown that the solution is given by a certain Markovian diffusion process, which (in the case A=0, c=0) first was investigated by Schrödinger (Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 1931, 144).
Phase operators via group contraction
Authors: Ellinas D.
Published: July 2002

The problem of quantization of the classical phase of a harmonic oscillator (HO) is solved here in two steps. First, polar decomposition of the step operators of the u(2) algebra is performed. Second, the method of group contraction is used through which, in the limit j→∞, â,â° is passed to for the quantized HO and its Hermitian phase operators. Also, phase states, i.e., states with sharply defined phase, are constructed and the dynamical aspects of the contraction limit between the Jaynes–Cummings model (JCM) and a finite-dimensional counterpart with increasing j parameter are studied. Finally, the old problem of the phase operators is discussed in the wider frame of rank-1 algebras and classify the previous works in this frame.
Theory of two-index Bessel functions and applications to physical problems
Authors: Dattoli G. , Lorenzutta S. , Maino G. , Torre A. , Voykov G. , Chiccoli C.
Published: July 2002

In this article the theory of two-index Bessel functions is presented. Their generating function, series expansion, and integral representations are discussed. Their usefulness in physical problems is also discussed in the context of analysis of radiation emitted by relativistic electrons in two-frequency undulators. Finally, the theoretical analysis proving addition and multiplication theorems for two-index Bessel functions are completed and their modified forms are introduced.
Infinite products, partition functions, and the Meinardus theorem
Authors: Actor Alfred Arthur
Published: July 2002

The Meinardus theorem provides an asymptotic value for the infinite-product generating functions of many different partition functions, and thereby asymptotic values for these partition functions themselves. Under assumptions somewhat stronger than those of Meinardus a more specific version of the theorem is derived, then this is generalized from the spectrum of integers considered by Meinardus to infinite products constructed from an arbitrary spectrum. Included are infinite products that generate partition functions able to count states in the quantum theory of extended objects. There emerges a quite general and explicit method (of which only limited details are given here) for deriving the asymptotic growth of the state density function of multidimensional quantum objects. One finds a universal geometry-independent leading behavior, with nonleading geometry-dependent corrections that the method is capable of providing explicitly.
A class of exact, periodic solutions of nonlinear envelope equations
Authors: Chow Kwok W.
Published: July 2002

A class of periodic solutions of nonlinear envelope equations, e.g., the nonlinear Schrödinger equation (NLS), is expressed in terms of rational functions of elliptic functions. The Hirota bilinear transformation and theta functions are used to extend and generalize this class of solutions first reported for NLS earlier in the literature. In particular a higher order NLS and the Davey–Stewartson (DS) equations are treated. Doubly periodic standing waves solutions are obtained for both the DSI and DSII equations. A symbolic manipulation software is used to confirm the validity of the solutions independently.
Euclidean random fields obtained by convolution from generalized white noise
Authors: Albeverio Sergio , Wu Jiang-Lun
Published: July 2002

We study Euclidean random fields X over Rd of the form X=G*F, where F is a generalized white noise over Rd and G is an integral kernel. We give conditions for the existence of the characteristic functional and moment functions and we construct a convergent lattice approximation of X. Finally, we perform the analytic continuation of the moment functions and the characteristic functional of X, obtaining the corresponding relativistic functions on Minkowski space.
Group theoretical foundations of fractional supersymmetry
Authors: de Azcárraga J. A. , Macfarlane A. J.
Published: July 2002

Fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized Grassmann variable, θ=θ̄,θn=0, for arbitrary integer n=2,3,.... An explicit formula is given in the case of general n for the transformations that leave the theory invariant, and it is shown that these transformations possess interesting group properties. It is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group. Careful attention is paid to some technically important issues, including differentiation, that arise as a result of the peculiar nature of quantities such as θ.
On a hierarchy of macroscopic models for semiconductors
Authors: Abdallah N. Ben , Degond P.
Published: July 2002

This paper shows that various models of electron transport in semiconductors that have been previously proposed in the literature can be connected one with each other by the diffusion approximation methodology. We first investigate the diffusion limit of the semiconductor Boltzmann equation towards the so-called ‘‘spherical harmonic expansion model,’’ under the assumption of dominant elastic scattering. Then, this model is again connected, either to the energy-transport model or to a ‘‘periodic spherical harmonic expansion model’’ through a diffusion approximation, respectively making electron–electron or phonon scattering large. We provide the mathematical background which makes the Hilbert expansions associated with these various diffusion limits rigorous.
Multivector fields and connections: Setting Lagrangian equations in field theories
Authors: Echeverrı́a-Enrı́quez Arturo , Muñoz-Lecanda Miguel C. , Román-Roy Narciso
Published: July 2002

The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle J1E→E→M, it is shown that integrable multivector fields in E are equivalent to integrable connections in the bundle E→M (that is, integrable jet fields in J1E). This result is applied to the particular case of multivector fields in the manifold J1E and connections in the bundle J1E→M (that is, jet fields in the repeated jet bundle J1J1E), in order to characterize integrable multivector fields and connections whose integral manifolds are canonical lifting of sections. These results allow us to set the Lagrangian evolution equations for first-order classical field theories in three equivalent geometrical ways (in a form similar to that in which the Lagrangian dynamical equations of nonautonomous mechanical systems are usually given). Then, using multivector fields, we discuss several aspects of these evolution equations (both for the regular and singular cases); namely, the existence and nonuniqueness of solutions, the integrability problem and Noether’s theorem, giving insights into the differences between mechanics and field theories.
Phase-integral formulas for Coulomb wave functions with complex values of the variable and the parameters
Authors: Dzieciol Aleksander , Yngve Staffan , Fröman Per Olof
Published: July 2002

Phase-integral formulas for the Coulomb wave functions FL(η,ρ) and GL(η,ρ) and certain linear combinations of these functions, with complex values of the variable ρ and the parameters L and η, are obtained explicitly up to the fifth order of the phase-integral approximation for two different choices of the base function.
Adjoint symmetries, separability, and volume forms
Authors: Sarlet W. , Ramos A.
Published: July 2002

Two results of a preceding paper are generalized. The first is about characterizing to what extent preservation of the energy function of a Lagrangian of mechanical type turns dynamical symmetries into Noether symmetries. The generalization here is twofold: polynomial integrals of arbitrary degree are considered and the kinetic energy can have an arbitrary metric. The second result (here again for arbitrary metrics) is about the way separation variables for the Hamilton–Jacobi equation, when they are ensured to exist by Eisenhart’s theorem, can be computed, in principle, from a factorization property of a certain volume form. The main novelty in the way the generalizations are discussed is that the emphasis is shifted from symmetries to the dual concept of adjoint symmetries.
Bifurcations and a chaos strip in states of long Josephson junctions
Authors: Yugay K. N. , Blinov N. V. , Shirokov I. V.
Published: July 2002

Stationary and nonstationary, in particular, chaotic states in long Josephson junctions are investigated. Bifurcation lines on the parametric bias current-external magnetic field plane are calculated. The chaos strip along the bifurcation line is observed. It is shown that transitions between stationary states are the transitions from metastable to stable states and that the thermodynamical Gibbs potential of these stable states may be larger than for some metastable states. The definition of a dynamical critical magnetic field characterizing the stability of the stationary states is given.
Shock wave driven by a phased implosion
Authors: Menikoff R. , Lackner K. S. , Johnson N. L. , Colgate S. A. , Hyman J. M. , Miranda G. A.
Published: July 2002

In this paper the theory of an axially phased radial implosion of a channel is developed. When the phase velocity of the implosion exceeds the sound velocity inside the channel, a planar shock wave traveling along the channel axis can develop. For the energy of the implosion system in the appropriate range, the theory predicts a stable steady-state flow configuration. The effect of the phased implosion is for the channel wall to form a nozzle that travels along the channel axis. The flow behind the axial shock is well described by the equations for nozzle flow with an additional dynamical degree of freedom for the shape of the wall. Experiments presented here verify the theoretical predictions. The numerical simulations show the formation of the axial shock during start-up and the approach to steady state to be in good agreement with experiment and theory. A potential application of the axially phased implosion is the design of a super shock tube.
Kinetic energy of Rayleigh–Taylor and Richtmyer–Meshkov instabilities
Authors: Mikaelian Karnig O.
Published: July 2002

General expressions for the kinetic energy associated with Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities in incompressible fluids are derived. The results are valid for small perturbations in continuous as well as discontinuous density profiles. It was found that KERT /KERM=ge2γτ /(ΔvΓ)2=(geγτ/Δvγ)2, where τ=time, g=acceleration, Δv=velocity jump, and γ is the exponential growth rate of the RT amplitude. The linear growth rate of the RM amplitude is ΔvΓ2=Δvγ2/g, and is found by solving an eigenvalue equation for a given density profile subject to appropriate boundary conditions. In general, KERT asymptotes to a constant value at large k (k=2π/λ, λ=wavelength), while KERM continues to grow with k. Several analytic examples are illustrated and the k dependence of the kinetic energies is displayed.
On the collision of rigid spheres in a weakly compressible fluid
Authors: Kytömaa H. K. , Schmid P. J.
Published: July 2002

Reliable representations for the interparticular collision laws for inertially dominated particulate flows remain elusive due to the complexity of this interaction. In this study, compressibility of both the solid and the containing fluid are considered in the context of pairwise collisions, and the conditions under which these are important are identified in terms of a regime map. To identify the suspension flow conditions under which compressibility effects are important, the map is presented in terms of granular flow quantities, which are derived from the parameters associated with the pairwise collision problem. After demonstrating that there exists a flow regime where the compressibility of the fluid is important, the collision of two rigid spherical particles in a weakly compressible fluid is investigated. Lubrication theory and a perturbation approach for the fluid density are applied to analytically determine the pressure correction due to weak fluid compressibility. It is shown that the first-order dynamical equation describing the collision process does not support rebounding particle trajectories, therefore characterizing rebound as an inherently nonlinear compressibility effect.
Low Mach number two-dimensional hydrodynamic turbulence: Energy budgets and density fluctuations in a polytropic fluid
Authors: Ghosh S. , Matthaeus W. H.
Published: July 2002

Theory suggests that three distinct types of turbulence can occur in the low Mach number limit of polytropic flow: nearly incompressible flows dominated by vorticity, nearly pure acoustic turbulence dominated by compression, and flows characterized by near statistical equipartition of vorticity and compressions. Distinctions between these kinds of turbulence are investigated here by direct numerical simulation of two-dimensional compressible hydrodynamic turbulence. Dynamical scalings of density fluctuations, examination of the ratio of transverse to longitudinal velocity fluctuations, and spectral decomposition of the fluctuations are employed to distinguish the nature of these low Mach number solutions. A strong dependence on the initial data is observed, as well as a tendency for enhanced effects of compressibility at later times and at higher wave numbers, as suggested by theories of nearly incompressible flows.
Maximum values of gas-dynamic flux densities
Authors: Roshko A.
Published: July 2002

A general result valid for any compressible fluid is noted. It gives the maximum values of the flux densities of mass, momentum, and kinetic energy in steady and unsteady flows which are expanding isentropically from a reservoir.
An experimental study of evaporating small diameter jets
Authors: Kowalewski T. A. , Hiller W. J. , Behnia M.
Published: July 2002

The behavior of evaporating small diameter jets in a low-pressure environment is studied experimentally. Charged coupled device (CCD) cameras connected to a computerized data logging system are employed for high-speed imaging. Experiments at different jet velocities and environmental pressures have been performed with pure ether and ethanol, and also the mixtures of the two. Complex instability structures during the evaporation of the jet were observed. The recorded experimental evidences of these structures are presented and discussed.
Reply to the comments of Hirose
Authors: Andersson P. , Weiland J.
Published: July 2002

The questions raised in the comment by Hirose are answered.
Plasma distribution models in a rotating magnetic dipole and refilling of plasmaspheric flux tubes
Authors: Lemaire J.
Published: July 2002

Rotating stars or planets like Earth are sometimes surrounded by a dipolar magnetic field distribution. The thermal plasma forming a corona or an ionosphere around these astrophysical objects diffuses upward along the magnetic field lines and forms a toroidal region filled with this thermal plasma, like the terrestrial plasmasphere. The field-aligned distribution of this thermal ionospheric plasma is controlled by the gravitational and pseudocentrifugal potential distribution. One can distinguish two extreme types of plasma distribution in this field-aligned potential: the diffusive equilibrium distribution and the exospheric equilibrium distribution corresponding, respectively, (i) to a saturated, and (ii) to an almost depleted, magnetic flux tube. As a result of pitch angle scattering by Coulomb collisions, an increasing number of ions escaping from the ionosphere are stored in trapped orbits. These trapped particles have magnetic mirror points at high altitudes, i.e., in the low-density exospheric region. Also as a result of collisions, the field-aligned density distributions irreversibly evolve from exospheric equilibrium with a highly anisotropic pitch angle (cigarlike) distribution to a diffusive equilibrium distribution characterized by an isotropic pitch angle distribution. It is shown that the suprathermal ions become anisotropic much more slowly than ions of energies smaller than 1 eV.
Comments on ‘‘Linear waves and stability in ideal magnetohydrodynamics’’ [Phys. Fluids 3
, 3673 (1987)]
Authors: González Alejandro G. , Gratton Julio
Published: July 2002

It is shown that the most dangerous modes for stability of the slab geometry case considered by Eckhoff are not flute modes but quasi-interchange perturbations.
Stability of elongated cross-section tokamaks to axisymmetric even poloidal mode number deformations
Authors: Weiner R. , Jardin S. C. , Pomphrey N.
Published: July 2002

In a recent paper, Nakayama, Sato, and Matsuoka [Phys. Fluids 31, 630 (1988)] suggested that elliptical cross-section tokamaks with aspect ratio R/a=3.2 and with elongation κ=2.6 are unstable to a splitting (m=2, n=0) instability for plasma β>5%, and that κ≥4.0 plasmas are unstable to a splitting for β≥1%. The magnetohydrodynamic evolution code tsc [J. Comput. Phys. 66, 481 (1986)] indicates, however, that such plasmas are robustly stable with respect to this splitting. In fact, a κ=3.7 plasma with β=23.0% shows no tendency to split. However, the addition of pinching coils at the waist will cause the plasma to split if the current in these coils exceeds a critical value Ic, which decreases with increasing beta.
Linear analysis of a free-electron laser coupled to betatron oscillations
Authors: Latham P. E.
Published: July 2002

The dispersion relation is derived for the interaction of a sheet beam propagating between parallel plates in a planar wiggler magnetic field. Instead of the usual free electron laser (FEL) mode, one is considered in which the radiation field is perpendicular to the quiver velocity and couples either to betatron or plasma oscillations. In the cold beam limit, coupling to betatron oscillations leads to an absolute instability. This mode competes with the conventional FEL and can disrupt the beam unless suppressed. The effects of energy spread are investigated, and a critical energy spread is found that suppresses the instability. For ultrarelativistic beams, this energy spread is an exponentially decreasing function of the beam energy. For moderately relativistic high current beams, it is proportional to the square root of the beam current. In this regime, there is a limit to the current that can propagate stably in the FEL circuit. Coupling to plasma oscillations also leads to an instability. However, the instability associated with this mode can be made convective with a suitable choice of parameters, and thus is not particularly dangerous to the conventional FEL. It is, however, interesting because the dispersion relation is characteristic of a second harmonic FEL, even though the wiggler is planar.
Atom–atom inelastic collisions and three-body atomic recombination in weakly ionized argon plasmas
Authors: Braun C. G. , Kunc J. A.
Published: July 2002

A stationary collisional-radiative model including both inelastic electron–atom and atom–atom collisions is used to examine nonequilibrium weakly ionized argon plasmas with atomic densities 1016–1020 cm−3, temperatures below 6000 K, and with different degrees of radiation trapping. It is shown that three-body atomic recombination (e+A++A→A+A) becomes important at high particle densities. Comparison is made between the present approach and Thomson’s theory for atomic recombination.