bluuebunny/crossref_metadata_2025 huggingface dataset:
Multiphoton ionization of NO/CD3OH heteroclusters: Observation of [(NO)n(CD3O)x(CD3OH)m]+ cluster ions
Authors: Shin Dong Nam , DeLeon Robert L. , Garvey James F.
Published: July 2002

Ion–molecule reactions within heterogeneous NO/CD3OH cluster ions have been investigated through the use of multiphoton ionization time-of-flight mass spectrometry. For the case of the mixed cluster ions having two or more NO molecules, heterogeneous cluster ions of the form [(NO)n(CD3O)x(CD3OH)m]+, produced by multiple hydrogen atom loss, are observed. In contrast, the generation of [NO(CD3OH)m]+ is predominant in the mixed cluster ions containing one NO molecule. The hydrogen loss reaction proceeds up to x⩽n−1 for [(NO)n(CD3O)x(CD3OH)m]+ with the generation of cluster ions possessing an even number of electrons being clearly preferred. These results lead us to conclude that the generation of cluster ions containing the CD3O species is strongly dependent on the electron configuration and the number of NO molecules in the cluster. Possible mechanisms of generating cluster ions having multiple CD3O species are discussed in terms of either a prompt multiphoton ionization or photochemical process prior to ionization.
A molecular theory of the homogeneous nucleation rate. I. Formulation and fundamental issues
Authors: Senger B. , Schaaf P. , Corti D. S. , Bowles R. , Voegel J.-C. , Reiss H.
Published: July 2002

A molecular theory of the rate of homogeneous vapor phase nucleation is formulated. The ultimate goal is a theory that contains no ad hoc assumptions or arbitrary parameters having magnitudes that must be assigned in an ad hoc manner. The centerpiece of the theory is a defined cluster denoted as the n/v-Stillinger cluster, a hybrid that combines the original Stillinger cluster and the more recent n/v cluster. The Stillinger component assures that redundancy is avoided in the characterization of the cluster and the n/v component makes the Monte Carlo simulation of the free energy of the cluster relatively simple, and also allows dynamics to weight the importance of a cluster to the nucleation rate process. In the companion paper (paper II), dealing with the application of the theory to argon vapor, it is shown that the avoidance of redundancy is of primary importance to the non ad hoc nature of the theory. The theory provides a standard against which subtle inconsistencies in earlier theories, both molecular and phenomenological, are revealed, and should provide guidance for the development of necessary, useful, future phenomenological theories. Earlier theories are described in sufficient detail to allow a clear discussion of such inconsistencies. This is not just a review, since the illustration of important connections and relationships, not carefully examined in the past, forms one of the major goals of the exposition. A fairly general theory for the nucleation rate is given and some of the parameters entering the theory are discussed. This paper provides the basis for its application to argon vapor in paper II.
Modeling small hydronium–water clusters
Authors: Hodges Matthew P. , Stone Anthony J.
Published: July 2002

We have developed new potentials to model the interactions between H3O+ and H2O and used them to investigate small H3O+⋯(H2O)n clusters for n=1–7. The construction of the potentials uses monomer properties for the long-range interactions and perturbation theory for the short-range terms. We have extensively searched all the potential energy surfaces and discuss the low-energy minima that we have found. We extend the calculations for n=2, 4, and 5 by performing geometry optimizations using density functional theory, starting with minima found with the new model potential.
Structural transition in hot small clusters
Authors: Zhukhovitskii D. I.
Published: July 2002

At relatively high temperatures (higher than the melting temperature of a liquid), clusters existing in the supersaturated vapor are characterized by an intense internal motion of molecules. The virtual chains model of small “hot” clusters is proposed, which assumes that the number of bonds in small clusters is minimal, and that their structure is chainlike. Interpolation formulas for extensive thermodynamic functions of a cluster containing arbitrary number of atoms are found. Validity of model assumptions are verified by the molecular dynamics simulation for the ensemble with constant temperature and pressure. Simulation results are discussed, among which are the average potential energy of a cluster, the radial distribution function, and topological structure of clusters. Numerical results validate the basic assumption of proposed model.
Isomerization, melting, and polarity of model water clusters: (H2O)6 and (H2O)8
Authors: Rodriguez Javier , Laria Daniel , Marceca Ernesto J. , Estrin Darı́o A.
Published: July 2002

Energetics, structural features, polarity, and melting transitions in water clusters containing up to eight molecules were studied using ab initio methods and empirical force field models. Our quantum approach was based on density functional theory performed at the generalized gradient approximation level. For the specific case of (H2O)6, we selected five conformers of similar energy with different geometries and dipolar moments. For these cases, the cyclic arrangement was found to be the only nonpolar aggregate. For (H2O)8, the most stable structures corresponded to nonpolar, cubic-like, D2d and S4 conformers. Higher energy aggregates exhibit a large spectrum in their polarities. The static polarizability was found to be proportional to the size of the aggregates and presents a weak dependence with the number of hydrogen bonds. In order to examine the influence of thermal fluctuations on the aggregates, we have performed a series of classical molecular dynamics experiments from low temperature up to the melting transition using two different effective pseudopotentials: the TIP4P and MCY models. Minimum energy structures for both classical potentials were found to reproduce reasonably well the results obtained using ab initio methods. Isomerization and phase transitions were monitored by following changes in dipole moments, number of hydrogen bonds and Lindemann’s parameter. For (H2O)6 and (H2O)8, the melting transitions were found at Tm≈50 and 160 K, respectively; for both aggregates, we observed premelting transitions between well differentiated conformers as well.
Intramolecular energy transfer in highly vibrationally excited methanol. III. Rotational and torsional analysis
Authors: Boyarkin O. V. , Rizzo T. R. , Perry David S.
Published: July 2002

We report here torsional analysis of rotationally resolved spectra of the 3ν1, 5ν1, and 6ν1 (OH stretch) bands of jet-cooled methanol. The upper states are reached by a double resonance excitation scheme involving the selection of single rotational states in the ν1 fundamental band. Detection of the overtone transitions (nν1←ν1) is by infrared laser assisted photofragment spectroscopy (IRLAPS). The torsional tunneling frequency declines monotonically from 9.1 cm−1 in the vibrational ground state to 1.6 cm−1 at 6ν1. For the available rotational levels at 3ν1 (K=0–3) and 6ν1 (K=0,1), the pattern of torsional energies is approximately regular. To obtain the vibrational dependence of the torsional barrier V3, it was necessary to use the OH radical and HOOH as models for the vibrational dependence of the torsional inertial constant F. The assumed linear dependence of V3 on ν1 accounts for the torsional tunneling splittings at v1=0, 3, and 6 and for the pattern of the torsional energies. V3 increases by 40–45 cm−1 per quantum of OH excitation.
Raman study of the trans–gauche conformational equilibrium of 1,2-dichloroethane in water: Experimental evidence for the hydrophobic effect
Authors: Kato Minoru , Abe Isao , Taniguchi Yoshihiro
Published: July 2002

The effect of water on the trans–gauche conformational equilibrium of 1,2-dichloroethane has been studied by Raman spectroscopy. From the intensities of C–Cl stretching bands and their temperature dependencies, we determined the free energy and enthalpy difference between the conformers in water and organic solvents. Although the solvent effect on the free energy apparently agrees with a dielectric continuum model, the enthalpy in aqueous solutions deviates largely from the values expected from that model. The positive deviations (∼3.5 kJ/mol) in the enthalpy are compensated by an increase in the entropy term. This behavior is consistent with the picture of a hydrophobic interaction.
Exact conditions on physically realizable correlation functions of random media
Authors: Torquato S.
Published: July 2002

Algorithms have been developed recently to construct realizations of random media with specified statistical correlation functions. There is a need for the formulation of exact conditions on the correlation functions in order to ensure that hypothetical correlation functions are physically realizable. Here we obtain positivity conditions on certain integrals of the autocorrelation function of d-dimensional statistically homogeneous media and of statistically isotropic media. These integral conditions are then applied to test various classes of autocorrelation functions. Finally, we note some integral conditions on the three-point correlation function.
Theory and computer simulation of bent-core molecules
Authors: Camp Philip J. , Allen Michael P. , Masters Andrew J.
Published: July 2002

Fluids of hard bent-core molecules have been studied using theory and computer simulation. The molecules are composed of two hard spherocylinders, with length-to-breadth ratio L/D, joined by their ends at an angle 180°−γ. For L/D=2 and γ=0,10,20°, the simulations show isotropic, nematic, smectic, and solid phases. For L/D=2 and γ=30°, only isotropic, nematic, and solid phases are in evidence, which suggests that there is a nematic-smectic-solid triple point at an angle in the range 20°<γ<30°. In all of the orientationally ordered fluid phases the order is purely uniaxial. For γ=10° and 20°, at the studied densities, the solid is also uniaxially ordered, whilst for γ=30° the solid layers are biaxially ordered. For L/D=2 and γ=60° and 90° we find no spontaneous orientational ordering. This is shown to be due to the interlocking of dimer pairs which precludes alignment. We find similar results for L/D=9.5 and γ=72°, where an isotropic-biaxial nematic transition is predicted by Onsager theory. Simulations in the biaxial nematic phase show it to be at least mechanically stable with respect to the isotropic phase, however. We have compared the quasi-exact simulation results in the isotropic phase with the predicted equations of state from three theories: the virial expansion containing the second and third virial coefficients; the Parsons–Lee equation of state; an application of Wertheim’s theory of associating fluids in the limit of infinite attractive association energy. For all of the molecule elongations and geometries we have simulated, the Wertheim theory proved to be the most accurate. Interestingly, the isotropic equation of state is virtually independent of the dimer bond angle—a feature that is also reflected in the lack of variation with angle of the calculated second and third virial coefficients.
The dynamics of structural transitions in sodium chloride clusters
Authors: Doye Jonathan P. K. , Wales David J.
Published: July 2002

In recent experiments on sodium chloride clusters structural transitions between nanocrystals with different cuboidal shapes were detected. Here we present results for the thermodynamics and dynamics of one of these clusters (NaCl)35Cl−. As the time scales for the structural transitions can be much longer than those accessible by conventional dynamics simulations, we use a master equation to describe the probability flow within a large sample of potential energy minima. We characterize the processes contributing to probability flow between the different nanocrystals, and obtain rate constants and activation energies for comparison with the experimental values.
Experimental and theoretical anharmonicity for benzene using density functional theory
Authors: Miani Andrea , Cané Elisabetta , Palmieri Paolo , Trombetti Agostino , Handy Nicholas C.
Published: July 2002

The anharmonic force field of benzene has been calculated using a finite difference method by means of density functional theory (DFT) with the B3LYP functional and a TZ2P atomic orbitals basis set, and compared to the field calculated by Maslen et al. [J. Chem. Phys. 97, 4233 (1992)]. The vapor phase infrared (IR) spectra of benzene (natural isotopic mixture) and of C12-benzene have been recorded from 450 to 6000 cm−1, at resolutions varying from 0.05 to 0.008 cm−1, and at various path lengths (0.18/42 m). The parallel bands ν11, ν4+ν12, ν5+ν12, ν2+ν11, and ν7+ν16, using the Wilson numbering, with their accompanying hot bands, have been analyzed and their origins determined to test our computed anharmonic force field. The Raman spectra of gas-phase benzene have been also recorded at medium resolution (∼0.7 cm−1) using an argon laser (line at 514.5 nm) with a power of 0.8 W and a multipass cell. In this work we compare the experimental and the theoretical frequencies and band profiles of the parallel ν1, ν2, 2ν16, 2ν4, and 2ν14 and of the corresponding hot bands, taking into account the l-vibrational doubling and all Fermi resonances within 100 cm−1. By comparison with experiment, the DFT B3LYP is shown to be more accurate than the self-consistent field (SCF): the fundamentals are calculated with a mean absolute error of 10.7 cm−1 and most of the spectroscopic constants are in better agreement with the experimental values.
Microwave spectra of CuOD and AgOD: Molecular structure and harmonic force field of CuOH and AgOH
Authors: Whitham Christopher J. , Ozeki Hiroyuki , Saito Shuji
Published: July 2002

Pure rotational spectra are reported for the deuterated species of copper and silver hydroxide, 63CuOD, 107AgOD, and 109AgOD. Together with the CuOH and AgOH data previously reported, a number of harmonic force constants were determined. These constants are interpreted in terms of the balance between competing ionic and covalent interactions. The harmonic force field allowed the rz structures to be determined. Both molecules are strongly bent indicating considerable covalent character.
Semiclassical multistate Liouville dynamics in the adiabatic representation
Authors: Donoso Arnaldo , Martens Craig C.
Published: July 2002

In this paper, we describe implementation of the semiclassical Liouville method for simulating molecular dynamics on coupled electronic surfaces in the electronic adiabatic representation. We cast the formalism in terms of semiclassical motion on Born–Oppenheimer potential energy surfaces with nonadiabatic coupling arising from the coordinate dependence of the adiabatic electronic eigenstates. Using perturbation theory and asymptotic evaluation of the resulting time integrals, we derive an expression for the probability of transition between adiabatic states which agrees with the result given previously by Miller and George [W. H. Miller and T. F. George, J. Chem. Phys. 56, 5637 (1972)]. We also demonstrate numerically the equivalence of semiclassical trajectory-based calculations in the adiabatic and diabatic representations by performing molecular dynamics simulations on a model two-state system and comparing with exact quantum mechanical results. Excellent agreement between the exact and semiclassical treatments is obtained in both representations.
Translational diffusion of fluorescent probes on a sphere: Monte Carlo simulations, theory, and fluorescence anisotropy experiment
Authors: Krishna M. M. G. , Das Ranjan , Periasamy N. , Nityananda Rajaram
Published: July 2002

Translational diffusion of fluorescent molecules on curved surfaces (micelles, vesicles, and proteins) depolarizes the fluorescence. A Monte Carlo simulation method was developed to obtain the fluorescence anisotropy decays for the general case of molecular dipoles tilted at an angle α to the surface normal. The method is used to obtain fluorescence anisotropy decay due to diffusion of tilted dipoles on a spherical surface, which matched well with the exact solution for the sphere. The anisotropy decay is a single exponential for α=0°, a double exponential for α=90°, and three exponentials for intermediate angles. The slower decay component(s) for α≠0 arise due to the geometric phase factor. Although the anisotropy decay equation contains three exponentials, there are only two parameters, namely α and the rate constant, Dtr/R2, where Dtr is the translational diffusion coefficient and R is the radius of the sphere. It is therefore possible to determine the orientation angle and translational diffusion coefficient from the experimental fluorescence anisotropy data. This method was applied in interpreting the fluorescence anisotropy decay of Nile red in SDS micelles. It is necessary, however, to include two other independent mechanisms of fluorescence depolarization for molecules intercalated in micelles. These are the wobbling dynamics of the molecule about the molecular long axis, and the rotation of the spherical micelle as a whole. The fitting of the fluorescence anisotropy decay to the full equation gave the tilt angle of the molecular dipoles to be 1±2° and the translational diffusion coefficient to be 1.3±0.1×10−10 m2/s.
Relaxation time distribution from time and frequency domain dielectric spectroscopy in poly(aryl ether ether ketone)
Authors: Bello A. , Laredo E. , Grimau M. , Nogales A. , Ezquerra T. A.
Published: July 2002

A new application of the simulated annealing Monte Carlo procedure is presented and applied to the extraction of the relaxation time distribution from dielectric spectroscopy either in time or frequency domain. This decomposition method named simulated annealing direct signal analysis (SADSA), is applied to computer generated curves, ε(t), ε′(ω), and ε″(ω), by using the most widely accepted empirical distributions. The discretized distribution fits exactly the analytical expression which can be evaluated in these cases for the set of parameters used in the simulation. Also, both distribution functions are found to be identical which proves that the method is certainly converging to the right solution in both cases. Experimental results on amorphous poly(aryl ether ether ketone) for ε(t), ε′(ω), and ε″(ω) are analyzed with SADSA and the obtained relaxation time distribution is used to go from time to frequency domain and reciprocally. The results are compared to those obtained by assuming a Havriliak–Negami profile for the distribution function.
A Feynman path centroid dynamics approach for the computation of time correlation functions involving nonlinear operators
Authors: Reichman David R. , Roy Pierre-Nicholas , Jang Seogjoo , Voth Gregory A.
Published: July 2002

The centroid dynamics formalism is extended to the calculation of time correlation functions of nonlinear operators. It is shown that centroid correlation functions can be related to quantum mechanical ones via higher order Kubo-type transforms. A key step is the construction of the correlation functions from a mixed classical/semiclassical centroid representation of the operators. A general methodology is developed to relate these Kubo-type transforms to the desired quantum correlation functions. The approach is tested using a one-dimensional anharmonic potential for which the 〈x2x2(t)〉 and the 〈x3x3(t)〉 correlation functions are computed. Applications of this new approach are also outlined.
Experimental and theoretical study of the photoelectron spectra of MnOx−(x=1–3) clusters
Authors: Gutsev Gennady L. , Rao B. K. , Jena P. , Li Xi , Wang Lai-Sheng
Published: July 2002

We report a combined experimental and theoretical investigation of MnOx− and MnOx(x=1–3) clusters. Theoretically, geometrical configurations of various isomers of the clusters were optimized and vertical detachment energies for the anions were evaluated. The ground state of MnO− was predicted to be Σ+5, followed by an excited state (7Σ+) 0.14 eV higher in energy. The ground state of MnO2− is B25, with a B13 isomer 0.15 eV higher. MnO3− is predicted to be a singlet D3h cluster. Vibrationally resolved photoelectron spectra of MnOx− were measured at several photon energies and under various experimental conditions, and were interpreted based on the theoretical results. The electron affinities of MnO, MnO2, and MnO3 were determined to be 1.375 (0.010), 2.06 (0.03), and 3.335 (0.010), respectively. Five excited states of MnO were observed and assigned using the theoretical results. The Σ+7 excited state of MnO− was found to be significantly populated and was distinguished from the ground state of the anion by temperature dependent studies. We observed two isomers for MnO2− and the detachment features from both isomers were assigned. Only one vibrationally resolved band was observed for MnO3−, which corresponds to transitions from the ground state of MnO3− to that of MnO3. The combined experimental and theoretical studies allow us to elucidate the complicated electronic and geometric structures of the various manganese oxide clusters and their anions.
Fierz identities for real Clifford algebras and the number of supercharges
Authors: Baake M. , Reinicke P. , Rittenberg V.
Published: July 2002

One considers supersymmetric gauge theories in quantum mechanics with the bosons and fermions belonging to the adjoint representation of the gauge group. One shows that the supersymmetry constraints are related to the existence of certain Fierz identities for real Clifford algebras. These identities are valid when one has 2, 4, 8, and 16 supercharges.
Invariants for dissipative nonlinear systems by using rescaling
Authors: Feix Marc R. , Lewis H. Ralph
Published: July 2002

A rescaling transformation of space and time is introduced in the study of nonlinear dissipative systems that are described by a second-order differential equation with a friction term proportional to the velocity, β(t)v. The transformation is of the form (x,t)→(ξ,θ), where x=ξC(t)+α(t), dθ=dt/A2(t). This rescaling is used to find each potential for which there exists an exact invariant quadratic in the velocity and to find the invariant. The invariants are found explicitly for a power-law potential, γ(t)xm+1/(m+1), and an arbitrary coefficient of friction β(t). We show in an example how the rescaling transformation can be chosen to give an asymptotic solution of the equation in cases where the exact invariant does not exist. For certain parameters, the asymptotic solution is a self-similar solution that is an attractor for all initial conditions. The technique of applying a rescaling transformation has been useful in other problems and may have additional practical applications.
Killing tensors in spaces of constant curvature
Authors: Thompson G.
Published: July 2002

A Killing tensor is one possible way of generalizing the notion of a Killing vector on a Riemannian or pseudo-Riemannian manifold. It is explained how Killing tensors may be identified with functions that are homogeneous polynomials in the fibers on the associated cotangent bundle. As such, Killing tensors may be identified with first integrals of the Hamiltonian geodesic flow, which are homogeneous polynomials in the momenta. Again using this identification, it is shown that in flat spaces the dimension of the vector space of Killing tensors is maximal and that the Killing tensors are generated by the Killing vectors. Finally, using Riemann’s model for the metric in spaces of constant curvature, a comparison argument is used to show that similar results are valid in that more general context.
The polynomial-type analysis of SU(3) group-theoretical quantities
Authors: Castilho Alcarás J. A. , Vanagas V.
Published: July 2002

Formulas for the transformation matrix between the canonical and noncanonical SU(3) bases in both λ≥μ and λ<μ cases are derived. An expression for the isoscalar factor of the SU(3) coupling coefficient, in the noncanonical basis, with one symmetric representation is also derived. Both expressions are put in a polynomial-type form suitable for coding computer programs to obtain explicit and exact algebraic expressions.
On spherically symmetric shear-free perfect fluid configurations (neutral and charged). I
Authors: Sussman Roberto A.
Published: July 2002

A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shear-free perfect fluid configurations is derived. It is presented in the form of Jacobian elliptic functions characterized by seven free parameters: five constants and two arbitrary functions of time. This class of solutions is the most general charged version of the class derived by Kustaanheimo and Qvist [Comment. Phys. Math. Helsingf. 13, 12 (1948); Exact Solutions of Einstein’s Field Equations (Cambridge U. P., Cambridge, 1980), Chap. 12, Sec. 2]. It is found that many of the charged particular solutions expressible by elementary functions are new. Particular solutions, including neutral and uniform density solutions, are classified in detail. The physical interpretation of these solutions, including the study of their singularity structure, will be presented in a subsequent paper (Part II).
Evolution of SU(2) and SU(1,1) states: A further mathematical analysis
Authors: Dattoli G. , Richetta M. , Torre A.
Published: July 2002

The problem of the evolution of SU(2) and SU(1,1) states is analyzed from a unified point of view. A generalized Rabi matrix for a time-dependent SU(2)–SU(1,1) coherence preserving Hamiltonian is also derived.
Coexistence of symmetric periodic points in the standard map
Authors: Tanikawa Kiyotaka , Yamaguchi Yoshihiro
Published: July 2002

The problem of the coexistence of symmetric periodic points of the standard map has been investigated. First, it is shown that there is another reversibility in addition to the one already known. The dominant axis of this reversibility is the remaining coordinate axis. Using these reversibilities, simple recursion formulas that determine the positions of symmetric periodic points have been derived. Second, bifurcation structures of symmetric periodic points from the fixed point at the origin have been investigated. It is shown that periodic points bifurcate along both the dominant axes of two reversibilities every time the rotation number of the fixed point passes through a rational number. Third, the problem of the coexistence of symmetric periodic points has been numerically investigated with the aid of the recursion formulas. A devil’s staircase form of the evolution of the outermost Kolmogorov–Arnold–Moser (KAM) curve of the fixed point with the change of the perturbation parameter is observed. This indicates that bifurcated periodic points do not disappear by inverse bifurcation as long as they are in the invariant region of the fixed point.
Solution of Laplace’s equation in plane single-connected regions bounded by arbitrary single curves
Authors: Minotti F. , Moreno C.
Published: July 2002

A method is developed to solve Laplace’s equation with Dirichlet’s or Neumann’s conditions in plane, single-connected regions bounded by arbitrary single curves. It is based on the existence of a conformal transformation that reduces the original problem to another whose solution is known. The main advantage of the method is that it does not require the knowledge of the transformation itself, so it is applicable even when no transformation is available. The solution and its higher-order derivatives are expressed in terms of explicit quadratures easy to evaluate numerically or even analytically.
The Jordan–Schwinger representations of Cayley–Klein groups. II. The unitary groups
Authors: Gromov N. A. , Man’ko V. I.
Published: July 2002

The unitary Cayley–Klein groups are defined as the groups that are obtained by the contractions and analytical continuations of the special unitary groups. The Jordan–Schwinger representations of the groups under consideration are discussed based on the mixed sets of creation and annihilation operators of boson or fermion type. The matrix elements of finite group transformations are obtained in the bases of coherent states.
Real representations of finite Clifford algebras. I. Classification
Authors: Okubo Susumu
Published: July 2002

A classification of real matrix irreducible representations of finite-dimensional real Clifford algebras has been made. In contrast to the case of complex representation, three distinct types of representations can be obtained which we call normal, almost complex, and quaternionic. The dimension of the latter two cases is twice as large as that of the normal representation. A criteria for a given Clifford algebra to possess a particular type of the representations is also given with some applications.
Hamiltonian theory over noncommutative rings and integrability in multidimensions
Authors: Dorfman I. Ya. , Fokas A. S.
Published: July 2002

A generalization of the Adler–Gel’fand–Dikii scheme is used to generate bi-Hamiltonian structures in two spatial dimensions. In order to implement this scheme, a Hamiltonian theory is built over a noncommutative ring, namely the ring of formal pseudodifferential operators. Bi-Hamiltonian structures generated in this way can be used for the Kadomtsev–Petviashvili equation as well as other integrable equations in 2+1.
On integral representations of the Coulomb functions
Authors: Bera P. K. , Das U. , Bhattacharyya C. , Talukdar B.
Published: July 2002

By dealing with a new integral representation for the irregular s-wave Coulomb function, exact analytical expressions for the corresponding Jost states in momentum space are constructed, and their usefulness in studying the Coulomb half-shell scattering is demonstrated. A supersymmetry-inspired ladder-operator relation is employed to derive higher partial-wave generalization of the results presented. Some applications of the integral representation for the associated regular solution are also sought.
Spherically symmetric radiating solution with heat flow in general relativity
Authors: Kramer D.
Published: July 2002

A model describing a collapsing sphere with radial heat flow is studied. Vaidya’s pure radiation field is taken as the exterior solution. The motion of the boundary surface follows from the matching conditions. In the remote part, the evolution starts with the interior and exterior Schwarzschild solution.
Vacuum configuration for inflationary superstring
Authors: Baadhio Randy A.
Published: July 2002

The vacuum configuration for the inflationary superstring theory is established. It is argued that the basic physical contents of the inflationary universe are characterized by the Novikov higher signature. Finally it is shown, with respect to the splitting of Paper II, that the index of the Dirac operator defined in our inflated universe, and in the parallel shadow one, is indeed h-cobordant.
On global gravitational instantons in superstring theory
Authors: Baadhio Randy A.
Published: July 2002

The hypothesis is formulated that our universe and the parallel ‘‘shadow’’ one, as predicted by superstring theory, are connected by a ring of global gravitational instantons. This amounts to a favored conceptual model in which the universe would have split into two equal parts around the Planck scale. In the present formulation, the ten-dimensional space-time in which superstring theory is defined is inflated in two symmetrical directions, reaching a maximal full-fledged representation of E′8 ⊗ E8. The radius of the inflationary universe is determined and arguments are made that strongly restrict the number of interactions between our universe and the parallel one. This yields an explanation as to why the other entity is shadow to ours.
General solution to the associativity equation in the Euclidean phase space
Authors: Batalin I. A. , Tyutin I. V.
Published: July 2002

The general solution to the associativity equation in the Euclidean phase space is constructed as a formal power-series expansion in the Planck constant. The characteristic arbitrariness of this solution is also studied.
Free fields for any spin in 1+2 dimensions
Authors: Grigore D. R.
Published: July 2002

Free fields of arbitrary spin in 1+2 dimensions, i.e., free fields for which the one-particle Hilbert space carries a projective isometric irreducible representation of the Poincaré group in 1+2 dimensions have been constructed. These representations have been analyzed in detail in the fiber bundle formalism and afterwards Weinberg procedure was applied to construct the free fields. Some comments concerning axiomatic field theory in 1+2 dimensions are also made.
Affine collineations in general relativity and their fixed point structure
Authors: Hall G. S. , Low D. J. , Pulham J. R.
Published: July 2002

A general discussion of affine vector fields (collineations) in space–time is given following a previous article by Hall and da Costa. Some general remarks are presented on the zeros of affine vector fields and then the general theory of such zeros is established. Some preliminary results regarding homothetic symmetries in two- and three-dimensional space–times are also given. The impossibility of reducing an affine algebra containing proper affine vector fields to homothetic or Killing vector fields, by means of a change of compatible metric, is demonstrated.
Graded contractions and kinematical groups of space–time
Authors: de Montigny M. , Patera J. , Tolar J.
Published: July 2002

G-graded contractions of the complex Lie algebra B2 and of its real forms are considered. It is found that a particular G=Z2×Z2 is a proper choice of the grading group preserved when graded contractions leading to Lie algebras of the kinematical groups of space–time are studied.
Clock and category: Is quantum gravity algebraic?
Authors: Crane Louis
Published: July 2002

We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories. The algebraic structures are related to ideas about the reinterpretation of quantum mechanics in a general relativistic context.
Lattice properties of quantum effects
Authors: Gudder Stanley
Published: July 2002

Sufficient conditions for the existence of the infimum AΛB of two quantum effects A and B are given. The existence of AΛB is characterized for commuting A and B with pure point spectrum. Properties of a generalized infimum and supremum are studied. Some previous finite dimensional, commutative results are extended to the infinite dimensional and noncommutative case.
Simple waves and invariant solutions of quasilinear systems
Authors: Doyle P. W. , Grundland A. M.
Published: July 2002

The solutions of a system of homogeneous first-order quasilinear evolution equations for which the propagation velocity depends only on the field value are characterized by their invariance under a particular type of flow. All simple wave solutions are shown to have this property. The local images of simple wave solutions are the integral curves of a system of ordinary differential equations on the field space. The model for barotropic compressible flow is an example of a system that has invariant solutions of higher rank. A solution of this system is invariant under the flow of the convective derivative if and only if it is divergence-free. The evolution of initial data is shown to be divergence-free if and only if its differential is nilpotent.
A Rodriguez formula and integration measure for the quantum deformed Legendre functions
Authors: Schmidt Jeffrey R.
Published: July 2002

Quantum deformed analogs of the Legendre functions are constructed from shift operator representations of the quantum deformed orbital angular momentum operators. A Rodriguez formula is found as well as the measure used to orthonormalize the functions.
The limit transition q→1 of the q-Fourier transform
Authors: Fichtmüller M. , Weich W.
Published: July 2002

The behavior of the q-Fourier transformation as q→1 is investigated. It is shown that the q-Fourier transformation converges to the classical Fourier transformation in the strong operator topology.
The separability ‘‘theorem’’ in terms of distributions with discussion of electromagnetic scattering theory
Authors: Lenglart E. , Gouesbet G.
Published: July 2002

The separability theorem states that, given a linear partial differential equation and special coordinates allowing to find a family of separated solutions, all solutions of physical interest of the equations can be obtained from linear combinations of the separated solutions. In developing the theory of interaction between an infinite cylinder and a Gaussian beam, it has been recently observed that the theorem may fail in terms of functions. In this paper, it is shown that the separability theorem is recovered if solutions are expressed in terms of distributions instead of in terms of functions. Relevance to light scattering theory is discussed.
On the polynomial first integrals of the (a,b,c) Lotka–Volterra system
Authors: Labrunie Simon
Published: July 2002

Using elementary differential algebraic techniques, we prove that the 3D Lotka–Volterra dynamical system has no other nontrivial polynomial first integrals than the previously known ones.
The spectrum of the quartic oscillator
Authors: Bay Karlheinz , Lay Wolfgang
Published: July 2002

The spectrum of the quartic oscillator defined by the Hamiltonian H=−d2/dz2+az+z2+λ2z4 is calculated. The eigenvalues E(a,λ) result from a fourth-order linear difference equation by means of recurrence relations. For the symmetric oscillator (a=0) various eigenvalues have been compared with values obtained from other approaches. In addition, results for the asymmetric oscillator are presented.
Integrability and integrodifferential substitutions
Authors: Meshkov A. G.
Published: July 2002

Chen, Lee, and Liu presented in 1979 an algorithm for establishing integrability of two-dimensional partial differential systems. It is proved here that this algorithm is invariant under the point transformations, differential substitutions, and some integrodifferential substitutions. It is also proved that canonical conserved densities of linearizable systems arising in the frameworks of the method are almost all trivial. The integrability of the non-Newtonian liquid equations is investigated and it is proved that there exist two integrable systems only. A preliminary classification of the third-order integrable evolution systems is presented.
Representations of the Weyl group and Wigner functions for SU(3)
Authors: Rowe D. J. , Sanders B. C. , de Guise H.
Published: July 2002

Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl group is represented as the symmetric group of permutations of the particle coordinates of these spaces. Wigner functions for SU(3) are expressed as products of SU(2) Wigner functions and matrix elements of Weyl transformations. The constructions make explicit use of dual reductive pairs which are shown to be particularly relevant to problems in optics and quantum interferometry.
Drag effects between two-dimensional superfluid charged Bose gases separated by a rigid partition
Authors: Shevchenko S. I. , Terent’ev S. V.
Published: July 2002

The drag effect in a system of two-dimensional superfluid charged Bose gases separated by a thin insulating partition is analyzed microscopically. It is shown that in contrast to normal systems, the drag effect is observed at T=0. The temperature dependence of the entrainment current is determined. An experiment for observing the effect is proposed.
Lower critical fields of textured high-Tc superconductors
Authors: Finkel’ V. A. , Toryanik V. V.
Published: July 2002

The possibility of studying the anisotropy of lower critical fields in HTS materials during the measurements of critical currents of textured samples subjected to the action of magnetic fields applied in three different directions is explored in the theory of magnetic properties of anisotropic superconductors. The critical fields Hc1ab and Hc1c of the high-Tc materialsYBa2Cu3O7−δ and DyBa2Cu3O7−δ are determined at T=77.3 K. It is found that the dependences Hc1ab(mc/mab) and Hc1c(mc/mab) are universal for all the investigated samples.
On the mechanism of critical temperature enhancement in cuprate high-Tc superconductors under pressure
Authors: Pashitskiı̆ E. A.
Published: July 2002

The results of experiments [C. Y. Han et al., Low Temp. Phys. 24, 305 (1998)] on the influence of quasi-hydrostatic pressure P on the superconducting transition temperature Tc in polycrystalline samples of cuprate compounds Tl2Ba2Ca2Cu3Ox (Tl-2223) with the initial value of Tc=129 K and the maximum value Tc=255.4 K at P=4.3 GPa are considered. A hypothesis on the existence of two mechanisms of the effect of pressure on Tc is proposed on the basis of an analysis of the nonmonotonic dependence of Tc on P. The first mechanism operating in the pressure range P<3 GPa is connected with the anisotropic deformation of the crystal lattice of individual grains (crystallites) in the plane of cuprate layers CuO2 and with a change in the oxygen doping of layers. The second mechanism operating in the pressure range P>3 GPa is due to hydrostatic compression of the ionic lattice and an increase in the bulk concentration of charge carriers (holes) in view of the electroneutrality condition.
Screening of electrostatic potential in a composite fermion system
Authors: Fil D. V.
Published: July 2002

Screening of the electric field of a test charge by monolayer and double-layer composite fermion systems is considered taking into account the influence of the sample boundary. It is shown that the test charge field is partly screened in the system at distances much larger than the magnetic length. The value of screening as a function of distance depends considerably on the filling factor. The effect of variation of the value of screening in a double-layer system upon a transition to a state described by the Halperin wave function is determined.
Anomalous skin effect in magnetic field: dependence on the shape of the Fermi surface
Authors: Tsymbal L. T. , Cherkasov A. N. , Panchenko O. F.
Published: July 2002

A non-traditional point of view to the nature of anomalous skin effect is proposed on the basis of an analysis of the problem of coupling modes in the electron plasma of a metal. It is shown that the anomalous skin effect in an applied magnetic field is in fact the result of interaction and coupling of a number of intrinsic electromagnetic modes excited due to nonlocal effects and specific properties of doppleron modes. It is proved that the magnetic field dependence of anomalous skin effect is determined by the shape of the Fermi surface of the metal and that the classical anomalous skin effect in the model of free electrons is just a special case.
Structure and microhardness of low pressure polymerized fullerite C60
Authors: Isakina A. P. , Lubenets S. V. , Natsik V. D. , Prokhvatilov A. I. , Strzhemechny M. A. , Fomenko L. S. , Aksenova N. A. , Soldatov A. V.
Published: July 2002

We have carried out low-temperature x-ray diffraction studies on C60 fullerite polymerized by low quasi-hydrostatic pressure of 1.1 GPa at T=563 K. It is established that at room temperature in freshly prepared samples three phases mainly coexist, viz. a compressed cubic phase with the lattice parameter a=13.94 Å, an orthorhombic O′ phase with the lattice parameters a=9.12 Å, b=9.82 Å, c=14.60 Å, and a rhombohedral phase of symmetry R3m with the parameters a=9.20 Å and c=24.27 Å. Mechanical grinding or annealing at 573 K entails depolymerization of sintered samples and restoration of the fcc structure of pristine C60. During annealing in air, intercalation of fullerite lattice by oxygen molecules occurs as well as a substantial amount of some new phase is formed, most probably with tetragonal symmetry, the chemical composition and structure of which have not been determined. The microhardness of polymerized C60 is higher than that of single crystal samples roughly four-fold at room temperature and by a factor of 2.6 at liquid nitrogen temperature. Analysis shows that polymerization and grain boundaries give contributions to the microhardness of sintered samples but we did not succeed in separating these two contributions. The temperature dependence of the microhardness of polymerized samples exhibits a jump in the vicinity of 260 K, where pristine C60 fullerite undergoes the fcc-sc phase transition. We think that this jump is due to a partial destruction of the polymerized state under indentor as a result of shear straining in inhomogeneous stress fields. Annealing of polymerized C60 at a temperature of 573 K, which restores the fcc phase, leads to a considerable decrease in microhardness, the hardness “jump” near the fcc-sc transition extends in temperature and shifts to lower temperatures.
Peculiarities of the resonant phonon scattering from a plane defect in an fcc crystal
Authors: Kosevich A. M. , Savotchenko S. E. , Matsokin D. V.
Published: July 2002

Resonant peculiarities of phonon scattering from a plane defect in an fcc crystal with the central interaction between nearest neighbors are investigated. It is shown that resonance effects are associated with the interaction of phonons of two bulk branches on a plane defect. Dispersion curves for the frequencies of resonance transmission and reflection are derived. To clarify the physical nature of resonances under investigation, the dispersion relations of vibrations localized at the defect are calculated in a wide range of wavelengths. The frequency curves of localized symmetric vibrations continue in the bulk spectrum in the form of dispersion curves of the frequencies of resonant phonons transmitted through the defect.
Magnetic helix in MnO2
Authors: Kovalev O. V.
Published: July 2002

The paper pursues the following two goals: to demonstrate the principle of concordance of the basic sets of representations and to investigate possible incommensurate magnetic structures proceeding from the previously developed theory of induced representations. The methods and the results obtained differ essentially from those obtained on the basis of Lifshitz invariants. The effect of exchange energy spectrum smoothing as a result of inclusion of a nonexchange interaction is established The role of dipole interaction in the magnetic helix orientation is elucidated.
Concordance of the basis vectors of representations at symmetric points of the Brillouin zone
Authors: Kovalev O. V.
Published: July 2002

The behavior of the basis vectors of the complete representation for a nonsymmetric point in the passage to the limit to a symmetric point is studied. The structure of the limiting representation and the fact of the emergence of a linear relation between the basis vectors are established, thus eliminating a number of contradictions. The concept of a limited induced representation is introduced. The formulas for basis vectors formulated by using this concept are transformed upon the passage to the limit into the basis vectors of only one irreducible representation at a symmetric point. The principle that an irreducible representation corresponds to a single energy level is used. Two versions of the basic vectors are considered: Bloch functions (electron spectrum) and infinite sums over translations (magnetic, phonon, and exciton spectra as well as the strong coupling method). The paper is in a certain sense an extension of the well-known publication by L. P. Bouckaert, R. Smoluchowski, and E. Wigner, Phys. Rev., 50, 58 (1936).