bluuebunny/crossref_metadata_2025 huggingface dataset:
Ion–ion correlations in electrolyte solutions adsorbed in disordered electroneutral charged matrices from replica Ornstein–Zernike equations
Authors: Hribar Barbara , Pizio Orest , Trokhymchuk Andrij , Vlachy Vojko
Published: July 2002

The replica Ornstein–Zernike (ROZ) equations, supplemented by the hypernetted chain and mean spherical closures, were solved for an ionic fluid adsorbed in a disordered charged matrix. To obtain the numerical solution of the ROZ equations we performed renormalization of the initial equations. Both the matrix and adsorbed fluid were modeled as charged hard spheres in a dielectric continuum, i.e., in the so-called restricted primitive model. As a result, the pair distribution functions between fluid ions and for fluid-matrix correlations were obtained. Structural properties were studied as a function of the matrix density, the concentration of adsorbed electrolyte and for different prequenching conditions. The isothermal compressibility, excess internal energy, and the chemical potential were calculated and discussed with respect to of the model parameters. Comparison with the Monte Carlo computer simulations of Bratko and Chakraborty [J. Chem. Phys. 104, 7700 (1996)] indicates that the theory yields qualitatively correct results for the model system.
Demixing vs freezing of binary hard-sphere mixtures
Authors: Coussaert Tamara , Baus Marc
Published: July 2002

The absence of demixing in the Percus–Yevick theory of fluid mixtures of additive hard-spheres is related to the fact that this theory predicts incorrect virial coefficients Bn for n>3. Incorporation of the exact Bn for 1⩽n⩽5 into a rescaled virial expansion is shown instead to lead to demixing for any size asymmetry between the spheres. This demixing is however thermodynamically metastable relative to freezing of the mixture into a partially ordered solid phase. This conclusion is reached on the basis of a density functional estimate of the free-energy of a nonuniform phase in which the large spheres form a face-centered cubic lattice whereas the small spheres remain disordered.
Competing pathways for methoxy decomposition on oxygen-covered Mo(110)
Authors: Queeney K. T. , Friend C. M.
Published: July 2002

The reactions of methanol (CH3OH) are investigated on a range of oxygen overlayers on Mo(110), with θO from ∼0.5 to >1 ML, using a combination of vibrational spectroscopies and temperature-programmed reaction. Infrared spectroscopy identifies a common, tilted methoxy intermediate at high temperature on all overlayers studied; electron energy loss spectroscopy shows that this intermediate decomposes to deposit oxygen exclusively in high-coordination sites. While C–O bond scission to evolve gas-phase methyl radicals is the only reaction observed for methoxy on highly oxidized Mo(110), on the surface oxygen overlayers competition between dehydrogenation and methyl evolution is highly sensitive to oxygen coverage. The enhanced selectivity for hydrocarbon formation from methanol reaction on oxygen-modified Mo(110) relative to the clean surface is attributed to inhibition of dehydrogenation pathways rather than to marked changes in the C–O bond potential of methoxy.
Raman spectra and calculated vibrational frequencies of size-selected C16, C18, and C20 clusters
Authors: Ott Adina K. , Rechtsteiner Gregory A. , Felix Christian , Hampe Oliver , Jarrold Martin F. , Van Duyne Richard P. , Raghavachari Krishnan
Published: July 2002

The surface plasmon polariton-enhanced Raman spectra of size-selected C16, C18, and C20 clusters isolated in nitrogen matrices are presented along with the calculated vibrational frequencies for the ring and linear chain isomers. The Raman spectra, recorded at a range of excitation wavelengths from 457.9 to 670 nm, show strong resonance enhancement for the three clusters. The calculated vibrational frequencies for ring and linear chain isomers and the cage and bowl structures for C20 are compared to the experimental frequencies. Systematic shifts in the series of peaks in the 200 cm−1 region for C16, C18, and C20 suggest that the observed isomers have the same geometry, thereby ruling out the bowl and cage isomers for C20. The measured spectra appear to be most consistent with the linear chain isomer. This high-energy isomer may be produced during neutralization of the deposited cluster ions.
Adiabatic electron affinity and ionization potential for BrO radical
Authors: Francisco Joseph S. , Parthiban Srinivasan , Lee Timothy J.
Published: July 2002

The adiabatic electron affinity (EA) and ionization potential (IP) for the BrO radical have been computed at high levels of theory. Specifically, the singles and doubles coupled-cluster method that includes a perturbational correction for connected triple excitations, denoted CCSD(T), has been used in conjunction with several one-particle basis sets. The largest basis sets are of the atomic natural orbital (ANO) type and include up through g functions. Our best IP and EA values, 241.1±0.8 and 55.6±1.8 kcal mol−1, respectively, have been obtained by extrapolating the CCSD(T)/ANO results to the one-particle basis-set limit, and are in excellent agreement with the latest experimental values. Our best computed IP shows, definitively, that the experimental result due to Monks et al. is more reliable than the value given by Lias et al. The reliability of our CCSD(T)/ANO calculations is also demonstrated by the excellent agreement between experiment and our best calculations for the BrO and BrO− equilibrium bond distances and vibrational frequencies. Our calculations provide the most reliable equilibrium bond distance, 1.640 Å, and vibrational frequency, 854 cm−1, for BrO+ to date, since experimental data are unavailable. Based on the agreement found for BrO and BrO−, we expect the BrO+ bond distance and vibrational frequency to be accurate to within ±0.005 Å and ±20 cm−1, respectively.
Structural relaxation in Morse clusters: Energy landscapes
Authors: Miller Mark A. , Doye Jonathan P. K. , Wales David J.
Published: July 2002

We perform a comprehensive survey of the potential energy landscapes of 13-atom Morse clusters, and describe how they can be characterized and visualized. Our aim is to detail how the global features of the funnel-like surface change with the range of the potential, and to relate these changes to the dynamics of structural relaxation. We find that the landscape becomes rougher and less steep as the range of the potential decreases, and that relaxation paths to the global minimum become more complex.
Electron affinities of the oxides of aluminum, silicon, phosphorus, sulfur, and chlorine
Authors: Brinkmann Nicole R. , Tschumper Gregory S. , Schaefer Henry F.
Published: July 2002

The adiabatic electron affinities of five second row atoms (Al, Si, P, S, Cl) and their monoxides and dioxides were determined using six different density functional or hybrid Hartree–Fock/density functional methods. The 15 species selected form a convenient closed set for which reliable experimental electron affinities exist for 13 of the species. Zero-point vibrational energy corrected electron affinities are also reported. Equilibrium geometries and vibrational frequencies were determined with each density functional method. The method based on the Becke exchange functional and the Lee–Yang–Parr correlation (BLYP) functional reproduced the experimental electron affinities most accurately, having an average absolute error of 0.15 eV. Using this functional, the electron affinities were predicted for SiO and SiO2, molecules for which electron affinities are not known experimentally, as 0.11 eV and 2.03 eV, respectively. It is concluded that the accuracy observed for density functional theory methods applied to first row atoms and molecules extends to molecules containing second row atoms and that density functional theory continues to provide a computationally affordable means of producing electron affinities reliable to within a few tenths of an eV of definitive experimental values.
Photoionization of C60 by large scale one-center density functional explicit continuum wave-function
Authors: Venuti M. , Stener M. , De Alti G. , Decleva P.
Published: July 2002

The photoionization cross-section and asymmetry parameter profiles relative to the seven uppermost molecular orbitals of C60 are calculated by means of a density functional approach, based on the explicit continuum wave-function within a very large scale one center expansion in a radial B-spline basis set. The convergence with respect to the maximum angular momentum is analyzed. Strong giant resonances in the cross-section of individual states are found, their occurrence is rationalized on the ground of minimal basis set calculations. The asymmetry parameters are as well very structured, also at higher photon energy than the cross-section profiles. Good agreement between the present calculations and the available experimental data is found.
Scattering from deformed polymer networks
Authors: Müller-Nedebock Kristian K. , Edwards Sam F. , McLeish Tom C. B.
Published: July 2002

The structure factor of chains dissolved in a stretched, geometrically quenched network is computed in the framework of the replica theory for networks. A variational ansatz is used. The structure factor shows features, due to the quenched disorder, leading to “lozenge”-like and the so-called “butterfly” isointensity structure factor plots. The latter patterns increase in size in the momentum transfer vector space as the degree of affinity of the network is increased, until they disappear to be replaced by the elliptical patterns.
Anion photoelectron spectroscopy of B3N−
Authors: Asmis Knut R. , Taylor Travis R. , Neumark Daniel M.
Published: July 2002

Vibrationally resolved negative ion photoelectron spectra of B3N− at 355 and 266 nm are presented. Two intense bands are observed with adiabatic detachment energies (ADEs) of 2.923±0.008 eV and 3.063±0.008 eV and markedly different photoelectron angular distributions. Aided by electronic structure calculations, the two bands are assigned to transitions from the linear X̃ 4Σ− state of B3N− to the linear Π3 and Σ−5 electronically excited states of neutral B3N, with all three states having a B–N–B–B structure. Weak signal observed at lower electron binding energies is tentatively assigned to two additional linear-to-linear transitions from the low-lying electronically excited Π2 state of B3N− to the Σ+1 and Π3 states of neutral B3N. Based on these assignments the electron affinity of linear B–N–B–B is 2.098±0.035 eV. It remains uncertain if the Σ+1 state of linear B–N–B–B or the A13 state of cyclic B3N is the overall ground state. At the highest level of theory used here, CCSD(T)/aug-cc-pVTZ, the Σ+1 state is predicted to lie 0.09 eV below the A13 state.
Collision-induced desorption of hydrocarbons physisorbed on Au(111)
Authors: Libuda J. , Scoles G.
Published: July 2002

We have studied the collision-induced desorption (CID) of hydrocarbons physisorbed on Au(111). Adsorbed layers of benzene, toluene, deuterated toluene, and n-alkanes of various chainlengths (CnH2n+2, n=5,7,10,12) were exposed to a beam of hyperthermal Xe generated in a supersonic expansion. Adsorbate coverages and their evolution were detected using He atom reflectivity. The CID cross-sections and threshold energies were determined for Xe translational energies in the range of 1.6–5.8 eV. According to their desorption behavior the physisorbed hydrocarbons can be assigned to two categories. “Rigid” aromatic molecules, such as benzene and toluene, show large CID cross sections. The ratios between the CID threshold energies and the desorption energies as determined from TPD (temperature programmed desorption) experiments can be understood within the simple hard sphere–cube (HSC) collision model. For the “flexible” n-alkanes a strong chain-length-dependent reduction of the CID cross sections is found, whereas the desorption thresholds are shifted to higher energies and appear to be directly proportional to the corresponding desorption energies. These effects are tentatively assigned to the excitation of internal degrees of freedom for the latter group of adsorbates, for which only a fraction of the atoms composing the molecule is involved in the initial collisional energy transfer.
The interaction of gold clusters with methanol molecules: Infrared photodissociation of mass-selected Aun+(CH3OH)m
Authors: Dietrich G. , Krückeberg S. , Lützenkirchen K. , Schweikhard L. , Walther C.
Published: July 2002

Structural and energetic properties of the adducts formed by adsorbing methanol onto size-selected gold clusters are investigated by infrared photodissociation of trapped Aun+(CH3OH)m, n=1–10,15 and m=1–3. The excitation of vibrational modes of methanol leads to the desorption of neutral molecules which is monitored by time-of-flight mass spectrometry. Spectra are obtained by measuring the fragment ion intensity as a function of photon energy. The C–O stretching vibration of adsorbed methanol changes discontinuously with cluster size. By comparison with Car–Parrinello calculations this change is traced back to the dimensionality of the gold clusters. The number of photons necessary for the desorption of methanol molecules provides an estimate of the respective separation energies.
The meta-GGA functional: Thermochemistry with a kinetic energy density dependent exchange-correlation functional
Authors: Adamo Carlo , Ernzerhof Matthias , Scuseria Gustavo E.
Published: July 2002

The meta-GGA functional recently proposed by Perdew et al. [Phys. Rev. Lett. 82, 2544 (1999)] goes beyond the generalized gradient approximations (GGAs) since it employs the noninteracting kinetic energy density in addition to the local density and the gradient of the local density. In this paper, we focus on thermochemistry and present an extensive assessment of the meta-GGA functional. We find that for atomization energies meta-GGA is as accurate as the computationally more involved Perdew–Burke–Ernzerhof (PBE) hybrid scheme. However, the geometries and frequencies obtained with meta-GGA are worse than those obtained with PBE or PBE hybrid. We give a detailed analysis of our results and propose explanations for the observed differences between PBE, PBE hybrid, and meta-GGA. Furthermore, we address the question whether the parameters in the meta-GGA functional are optimal for our benchmark set.
The potassium channel: Structure, selectivity and diffusion
Authors: Allen T. W. , Bliznyuk A. , Rendell A. P. , Kuyucak S. , Chung S.-H.
Published: July 2002

We employ the entire experimentally determined protein structure for the KcsA potassium channel from Streptomyces lividans in molecular dynamics calculations to observe hydrated channel protein structure, ion solvation, selectivity, multiple ion configurations, and diffusion. Free energy perturbation calculations display a significant ion discrimination of ∼9 kT in favor of the larger K+ ion. The protein forming the channel is very flexible yet is unable to fully solvate the Na+ ion because of its smaller size and large solvation energy. There is evidence that acidic and basic sidechains may dissociate in the presence of multiple K+ ions to explain experimental ion density maps. K+ diffusion is found to vary from approximately 10%–90% of bulk, supporting the high channel currents observed experimentally.
Phase changes in 38-atom Lennard-Jones clusters. I. A parallel tempering study in the canonical ensemble
Authors: Neirotti J. P. , Calvo F. , Freeman David L. , Doll J. D.
Published: July 2002

The heat capacity and isomer distributions of the 38-atom Lennard-Jones cluster have been calculated in the canonical ensemble using parallel tempering Monte Carlo methods. A distinct region of temperature is identified that corresponds to equilibrium between the global minimum structure and the icosahedral basin of structures. This region of temperatures occurs below the melting peak of the heat capacity and is accompanied by a peak in the derivative of the heat capacity with temperature. Parallel tempering is shown to introduce correlations between results at different temperatures. A discussion is given that compares parallel tempering with other related approaches that ensure ergodic simulations.
Vibrational relaxation of CO by collisions with 11He at ultracold temperatures
Authors: Balakrishnan N. , Dalgarno A. , Forrey R. C.
Published: July 2002

Quantum mechanical coupled channel scattering calculations are performed for the ro-vibrational relaxation of CO in collisions with ultracold He atoms. The van der Waals well in the interaction potential supports a number of shape resonances which significantly influence the relaxation cross sections at energies less than the well depth. Feshbach resonances are also found to occur near channel thresholds corresponding to the j=1 rotational level in the v=0 and v=1 vibrational levels. Their existence influences dramatically the limiting values of the elastic scattering cross sections and the rotational quenching rate coefficients from the j=1 level. We present complex scattering lengths for several low lying rotational levels of CO which characterize both elastic and inelastic collisions in the limit of zero temperature. Our results for the vibrational relaxation of CO (v=1) are in good agreement with available experimental and theoretical results.
Equilibrium configurations of degenerate fluid spheres
Authors: Whitman Patrick G.
Published: July 2002

Equilibrium configurations of degenerate fluid spheres which assume a polytropic form in the ultrahigh-density regime are considered. We show that analytic solutions more general than those of Misner and Zapolsky exist which possess the asymptotic equation of state. Simple expressions are derived which indicate this nature of the fluids in the extreme relativistic limit, and the stability of these interiors is considered in the asymptotic region.
Planar factors of proper homogeneous Lorentz transformations
Authors: Fahnline Donald E.
Published: July 2002

This article discusses two constructions factoring proper homogeneous Lorentz transformations H into the product of two planar transformations. A planar transformation is a proper homogeneous Lorentz transformation changing vectors in a two-flat through the origin, called the transformation two-flat, into new vectors in the same two-flat and which leaves unchanged vectors in the orthogonal two-flat, called the pointwise invariant two-flat. The first construction provides two planar factors such that a given timelike vector lies in the transformation two-flat of one and in the pointwise invariant two-flat of the other; it leads to several basic conditions on the trace of H and to necessary and sufficient conditions for H to be planar. The second construction yields explicit formulas for the orthogonal factors of H when they exist and are unique, where two planar transformations are orthogonal if the transformation two-flat of one is the pointwise invariant two-flat of the other.
Group theoretical analysis of the Hartree–Fock–Bogoliubov equation. II.The case of the electronic system with tricrinic lattice symmetry
Authors: Ozaki Masa-aki
Published: July 2002

This paper describes a group theoretical classification of the temperature–Hartree–Fock–Bogoliubov (HFB) equation in a crystalline solid system and the electronic state of the system. It is shown that the state with a single-order parameter (charge density wave, spin density wave, etc.) is classified into 47 classes and the BCS state coexistent with other nonsuperconducting orders, such as magnetic superconductors, is classified into 26 classes. The standard HFB Hamiltonian for each class is obtained. It is found that in each of above coexistence states (except BCS+ferromagnetism) an abnormal Cooper pair occurs.
Polynomial tensors for the space groups p
m and p4m
Authors: Phaneuf D. , Sharp R. T.
Published: July 2002

Generating functions are calculated for polynomial tensors in the components of tensors of the one- and two-dimensional space groups pm and p4m. For tensors whose k vectors lie at rational points (denominator q) of the Brillouin zone, the problem is imaged by the corresponding problem for an appropriate finite group, and known methods are used for its solution. For tensors with continuous k the solution is obtained by letting q become infinite.
Generalized moments applied to Fermi-type functions
Authors: Wendel M. H. , Hilf E. R.
Published: July 2002

Generalized integral moments are defined for a general class of saturating functions [ f(0)=ρ0, f(∞)=0]. They are useful as independent variables for describing surface properties or macroscopic dynamics of finite systems. Applied especially to functions of the Fermi type, analytic solutions are given in terms of a semiconverging, and of a numerically semiunstable expansion, respectively, suitable for numerical evaluation. Results are compared to the semidivergent expansion as given by Åberg, of which some properties are exhibited here, and with the exact numerical solutions known for this special example.
Inequalities of Schwarz and Hölder type for random operators
Authors: Hegerfeldt Gerhard C.
Published: July 2002

Let A and B be random operators on a Hilbert space, and let 〈 〉 denote averages (expectations). We prove the inequality ∥〈A*B〉∥≤∥〈A*A〉∥1/2∥〈B*B 〉∥1/2. A generalized Hölder inequality involving traces is also proved.
Radially separated classical lumps in non-Abelian gauge models
Authors: Burzlaff Jürgen
Published: July 2002

We search for smooth and time-independent finite-energy solutions to Yang–Mills–Higgs theory with an arbitrary compact gauge group. Excluding the monopole solutions which have been studied before, we concentrate on configurations with no long-range fields, which include the saddle points corresponding to noncontractible (hyper-) loops. It is shown that if the radial dependence of the fields is factorized, only one solution satisfies all these conditions. This solution is the one which has been studied before by Dashen, Hasslacher, and Neveu and by Boguta, and whose existence has recently been proved rigorously. Formulas for the asymptotic behavior of this solution are given.
The Hamiltonian structures of the nonlinear Schrödinger equation in the classical limit
Authors: Verosky John
Published: July 2002

Using Madelung’s hydrodynamical variables, it is shown that the bi-Hamiltonian structure of the nonlinear Schrödinger equation goes over to a bi-Hamiltonian structure of the shallow water wave equations in the classical limit.
Finite-dimensional Lorentz covariant bifurcations
Authors: Humi Mayer
Published: July 2002

In this paper finite-dimensional Lorentz covariant bifurcation equations are constructed and their properties, solutions, and gradient structures are examined. The possible applications of these ideas and techniques to elementary particle physics are considered.
Effective potential determining one-dimensional Slater sum in independent-particle theory
Authors: March N. H.
Published: July 2002

Hilton, March, and Curtis have earlier focused on the utility of the effective potential U(r,β) in determining the Slater sum Z(r,β)=Z0(β)exp(−βU(r,β)). Here an explicit, though highly nonlinear, partial differential equation is derived for determining the effective potential U(x,β) in one-dimensional problems. Direct solution of this equation by power series expansion in β leads readily to Husimi’s results obtained from off-diagonal density matrix calculations. Perturbation theory in the potential is also developed, and thereby it is shown that an infinite subseries of the Husimi expansion is readily summed, and that a scaling property is exhibited.
Topologies for point distributions
Authors: Elizalde E.
Published: July 2002

The concepts of void and cluster for an arbitrary point distribution in a domain 𝒟 are defined and characterized by some parameters such as volume, density, number of points belonging to them, shape, etc. After assigning a weight to each void and cluster—which is a function of its characteristics—the concept of distance between two point configurations S1 and S2 in 𝒟 is introduced, both with and without the help of a lattice in the domain 𝒟. This defines a topology for the point distributions in 𝒟, which is different for the different characterizations of the voids and clusters.
A representation of SO(p+q,p+q) on SO(p,q)
Authors: Fecko Marián
Published: July 2002

A construction of a representation of SO(p+q,p+q) by operators on SO(p+q) is presented, connected with a relativistic top kinematics. In addition to a first-order differential operator part there is a multiplicative term containing a parameter λ in some of the generators. It is shown by the explicit evaluation of the corresponding Casimir invariants that the representation (λ,...,λ), λ=0, 1/2 ,1,..., is realized by this construction.
Scattering-into-cones theorem for a certain impurity scattering
Authors: Yoon Sung Hyun
Published: July 2002

The scattering-into-cones theorem for impurity scattering in a periodically stratified potential in three dimensions is given.
The unitarity relations for the four-body scattering amplitude
Authors: Matsui Yoshiko
Published: July 2002

A formal derivation of the general unitarity relation for the four-particle transition operator is given by generalizing the three-body formalism of Karlson and Zeiger to the four-body case. From this operator relation the on-shell unitarity relations for the amplitudes that describe elastic/rearrangement, partial breakup, and full breakup scattering processes are obtained.
Some unbounded commutants of a set of operators on a partial inner product space
Authors: Shabani J.
Published: July 2002

This paper continues our systematic study of unbounded commutants within the framework of operators on a partial inner product (PIP) space. The most general commutant of a set of operators on a PIP space is considered and its behavior with respect to a topology finer than the weak and quasiweak *-topologies used in previous investigations is studied. The relationship between a bicommutant introduced by Shabani and a bicommutant introduced by Araki and Jurzak for closed Op*-algebras satisfying some countability conditions is given.
Supermultiplet of particles in a Coulomb potential: States and wave functions from the representation theory of OSp(2,1)
Authors: Benoit Louis , Vinet Luc
Published: July 2002

A supermultiplet of two spin-0 and one spin- 1/2 particle in a Coulomb potential has been shown recently to possess a dynamical OSp(2,1) symmetry algebra. The canonical chain of maximal subalgebras leads to a natural choice of quantum numbers and state vectors. The relevant representations of OSp(2,1) are constructed in this adapted basis, and the wave functions subsequently obtained by going to a coordinate realization.
The quantum relativistic two-body bound state. II. The induced representation of SL(2,C)
Authors: Arshansky R. , Horwitz L. P.
Published: July 2002

It was shown in I [J. Math. Phys. 30, 66 (1989)] that the eigenfunctions for the reduced motion of the quantum relativistic bound state with O(3,1) symmetric potential have support in an O(2,1) invariant subregion of the full spacelike region. They form irreducible representations of SU(1,1) [in the double covering of O(2,1)] parametrized by the unit spacelike vector nμ, taken in I as the direction of the z axis (the spectrum is independent of this choice), for which this O(2,1) is the stabilizer. Lorentz transformations move these representations on an orbit whose range is the single-sheeted hyperboloid covered by this spacelike vector, providing a set of induced representations of SL(2,C). From linear combinations of functions from the irreducible representations of SU(1,1), the representations of the SU(2) subgroup of SL(2,C) on the orbit are extracted and the differential equations that are the eigenvalue equations for the Casimir operators of SL(2,C) are solved. It is found that these SU(2) representations form a basis for the principal series in the canonical representations of Gel’fand. There is a natural scalar product, obtained from group integration on SL(2,C), for which the canonical basis forms an orthogonal set, and the representation is unitary. Since the scalar product [over the O(2,1) invariant measure space] of SU(1,1) irreducible representations is invariant under the action of the little group, the remaining group measure [on the coset space SL(2,C)/SU(1,1)] is the volume on the hyperboloidal spacelike hypersurface dμn=d4n δ(n2−1). The family of Hilbert spaces (ℋn) that carries the representations of O(3,1) is therefore embedded in a larger Hilbert space ℋ with measure d4y dμn, where the { y} are the space-time coordinates of the restricted region associated with nμ. The representations with nonrelativistic limit coinciding with the known Schrödinger solutions for corresponding spherically symmetric potential problems are in the double covering (half-integer values for the lowest L level) of O(3,1).
Casimir force on a spherical shell when ε(ω)μ(ω)=1
Authors: Brevik Iver , Sollie Roger
Published: July 2002

The Casimir surface force on a spherical shell is calculated, assuming the material to be satisfying the condition ε(ω)μ(ω)=1, ε(ω) being the spectral permittivity and μ(ω) the spectral permeability. The basic formula for the force is given under general conditions, without any restrictive assumption on the thickness of the shell or on the specific dispersion relation. When it comes to numerical evaluations, it is assumed that the shell is of small thickness, and also that the simple form μ(ω)=μs (ω≤ω0), μ(ω)=1 (ω>ω0), for the dispersion relation. The special case when μs →∞ or 0 is given particular attention, since this case appears to be of main physical interest and also since it implies mathematical simplifications. The force ℱ may then be written as the sum of two terms: one ‘‘normal’’ term ℱ(0) containing an attractive dispersion-induced part as well as a repulsive, nondispersive finite part, and one ‘‘abnormal’’ term ℱ(1) that becomes divergent when summed over all angular momenta. This particular behavior of ℱ(1) is a consequence of the assumed small magnitude of the shell thickness. A similar analysis of the opposite extreme case of dilute media is also made, and analogous angular moment divergent results are found. The extraction of physically meaningful information from the divergent expressions is discussed. In general, numerical methods are necessary to handle the Riccati–Bessel functions, although in the special cases mentioned, useful analytic results are obtained using the Debye expansion. The numerical calculation of the Casimir force on shells of finite thickness is also commented upon, and in the Appendix the generalization of the theory to the case of finite temperatures is discussed.
Symmetries and degeneracies of a charged oscillator in the field of a magnetic monopole
Authors: Labelle Simon , Mayrand Michel , Vinet Luc
Published: July 2002

The constants of motion responsible for the level degeneracy of a charged, spin 0 particle subjected to harmonic and centrifugal forces and to the field of a magnetic monopole are obtained. Operators closing onto the SU(2)⊕SU(2) algebra are constructed in terms of these conserved quantities. The space of states decomposes into SU(2)⊕SU(2) irreducible modules whose dimensions coincide with the degree of degeneracy of the various energy levels.
Triple products and Yang–Baxter equation. I. Octonionic and quaternionic triple systems
Authors: Okubo Susumu
Published: July 2002

The Yang–Baxter equation can be recast as a triple product equation. Assuming the triple product to satisfy some algebraic relations, new solutions of the Yang–Baxter equation can be found. This program has been completed here for the simplest triple systems which are called octonionic and quaternionic. The solutions are of rational type.
A note on the unimodular theory of gravitation
Authors: Tiwari S. C.
Published: July 2002

Since the covariant divergence law for the energy tensor in general relativity does not lead to a global conservation law one has the freedom to modify it. Rather than also assuming this law in the unimodular theory, invoking only the Bianchi identity, one ends up with a theory without the cosmological constant.
Global existence and nonexistence of the solution of a forced nonlinear Schrödinger equation
Authors: Guo Bo-ling , Wu Yong-hui
Published: July 2002

In this article, we prove that the solution of the forced nonlinear Schrödinger equation (1.1) below for u0∈H1 and Q(t)∈C1 with u0(0)=Q(0) exists globally if and only if ∫T0‖Q′(t)‖2 dt<∞. This result positively answers the conjecture of Q. Y. Bu [‘‘On well-posedness of the forced NLS equation,’’ Appl. Anal. 46, 219–239 (1992)].
The squared eigenfunctions of the massive Thirring model in laboratory coordinates
Authors: Kaup D. J. , Lakoba T. I.
Published: July 2002

We demonstrate a simple procedure for finding the squared eigenfunctions of an integrable system and illustrate the method by deriving the squared eigenfunctions of the massive Thirring model. We give the formula for the inner products between the direct squared eigenfunction problem and its adjoint. We also demonstrate closure and express the variations of the potentials in terms of variations of the scattering data.
ℓP interpolation and optimized bounds on pairwise interacting fermion systems
Authors: Basdevant Jean-Louis , Martin André
Published: July 2002

We derive a set of inequalities which relate the translation invariant problem of N identical particles with pairwise interactions to an independent particle problem. These inequalities apply to attractive power law potentials V(r)=rq, 1≤q≤∞, and superpositions of such potentials; they become identities in the harmonic oscillator case q=2. We use the inequalities to derive new upper and lower bounds for the ground state energies of fermion systems, which interact through these potentials. These bounds improve all previous results in the range 1≤q≤∞; they reduce to the exact answer in the harmonic oscillator case.
Cosmological solutions in Kaluza–Klein theories of quadratic Lagrangians
Authors: Kleidis K. , Papadopoulos D. B.
Published: July 2002

We present a new class of solutions in a five-dimensional Gauss–Bonnet cosmology. The space-time consists of one time-like direction and two maximally symmetric space-like subspaces, the external space and the internal one. The universe is filled with matter in the form of a one-component perfect fluid and the analysis is carried out for various equations of state. The solutions to the field equations are based on a new approximation technique that determines the scales of the ordinary universe, in terms of the cosmological redshift parameter, at which the error between the exact and the approximate description becomes minimum, at each order of approximation. In this case, the four-dimensional Friedmann models of General Relativity result as external space solutions in the first-order approximation of the quadratic theory. Conditions for the existence of the resulting five-dimensional models are derived and discussed, together with their cosmological behavior. In this context, it is shown that under certain conditions, some of the models may be geodesically complete.
Magri–Morosi–Gel’fand–Dorfman’s bi-Hamiltonian constructions in the action-angle variables
Authors: Smirnov Roman G.
Published: July 2002

A constructive method of transforming a completely integrable in Liouville’s sense Hamiltonian system into Magri–Morosi–Gel’fand–Dorfman’s (MMGD) bi-Hamiltonian form is presented. The approach is carried out by making use of the action-angle coordinates. The classical Kepler problem is shown to be a MMGD bi-Hamiltonian system. Explicit plethoras of higher-order conserved quantities for the Kepler problem are derived by employing Oevel’s method based on the existence of the MMGD bi-Hamiltonian representation.
Geometry of the Batalin–Fradkin–Vilkovisky theorem
Authors: Bering K.
Published: July 2002

We describe gauge fixing at the level of virtual paths in the path integral as a nonsymplectic BRST-type of flow on the path phase space. As a consequence, a gauge-fixed, nonlocal symplectic structure arises. Restoring of locality is discussed. A pertinent anti-Lie-bracket and an infinite dimensional group of gauge fermions are introduced. Generalizations to Sp(2)-symmetric BLT theories are made.
An exactly soluble Schrödinger equation with smooth position-dependent mass
Authors: Dekar Liès , Chetouani Lyazid , Hammann Théophile F.
Published: July 2002

The one-dimensional generalized Schrödinger equation for a system with smooth potential and mass step is resolved exactly. The wave function depends on the Heun’s function, which is a solution of a second-order Fuchsian equation with four singularities. The behavior of the transmission coefficient as a function of energy is compared to that of the case of an abrupt potential and mass step. Two limiting cases are also studied: when the width of the mass step is vanishing, and when the smooth potential and mass step tend to an abrupt potential and mass step.
Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries
Authors: Rañada Manuel F.
Published: July 2002

The classical n-dimensional Calogero–Moser system is a maximally superintegrable system endowed with a rich variety of symmetries and constants of motion. In the first part of the article some properties related with the existence of several families of constants of motion are analyzed. In the second part, the master symmetries and the time-dependent symmetries of this system are studied.
Parallel spinors and holonomy groups
Authors: Moroianu Andrei , Semmelmann Uwe
Published: July 2002

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spinn of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.
Chaotic regimes of antiferromagnetic resonance in a quasi-two-dimensional easy-axis antiferromagnet (NH3)2(CH2)4MnCl4
Authors: Bogdan M. M. , Kobets M. I. , Khats’ko E. N.
Published: July 2002

Chaotic regimes of the microwave energy absorption are observed experimentally and analyzed for two-dimensional metallorganic antiferromagnet (NH3)2(CH2)4MnCl4 at low temperatures under the conditions of nonlinear antiferromagnetic resonance. Relaxation oscillations of energy absorption are investigated in detail. Their frequency spectra, frequency–amplitude characteristics, and dependences of absorbed power on driving power and static magnetic field are studied. It is shown that the dynamics of relaxation oscillations undergoes a transition to chaos by “irregular periods.” Peculiarities of the transition are described consistently. Among other things, the conditions for the emergence of energy absorption regimes with a spike-like and a saw-tooth signal structure are determined, and the characteristics of chaotic oscillations such as the dimensions of strange attractors are calculated. The chaotic dynamics is found to be high-dimensional with a large contribution from noise which is of deterministic origin in the antiferromagnet under investigation.
Effect of pressure on magnetic properties of the compound MnSi
Authors: Panfilov A. S.
Published: July 2002

Magnetic susceptibility of the weak itinerant-electron ferromagnet MnSi (TC≃30 K) is studied in the paramagnetic state under hydrostatic pressure up to 2 kbar in the temperature interval 78–300 K. An analysis of the experimental data using the Stoner model modified to account for the spin fluctuations leads to the estimate for the volume derivative of effective electron–electron interaction parameter d ln J/d ln V=−1.4±0.1 and of the density of electron states at the Fermi level d ln N(EF)/d ln V=2±0.5. A noticeable volume dependence of J points towards a significant role of electron correlations in the magnetism of this compound.
Commensurate–incommensurate phase transitions for multichain quantum spin models: exact results
Authors: Zvyagin A. A.
Published: July 2002

The behavior in an external magnetic field is studied exactly for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate–incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exactly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in the limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearance of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrable theories are calculated.
Heat transfer in the orientationally disordered phase of SF6
Authors: Purskiı̆ O. I. , Zholonko N. N. , Konstantinov V. A.
Published: July 2002

The isobaric thermal conductivity of solid SF6 is investigated in the high-temperature phase. The experimental results are rescaled to a constant density. The isochoric thermal conductivity initially decreases with increasing temperature, then passes through a smooth minimum and begins to grow. A modified version of the reduced coordinate method is used to calculate the phonon–phonon and phonon–rotational contributions to the total thermal resistance. The growth of the isochoric thermal conductivity is explained by a weakening of the scattering of phonons on collective rotational excitations of the molecules as the correlations of the rotation weaken.
The stability of drop shapes for translation at zero Reynolds number through a quiescent fluid
Authors: Koh C. J. , Leal L. G.
Published: July 2002

Boundary-integral calculations are used to investigate the evolution of the shape of an initially nonspherical drop that translates at zero Reynolds through a quiescent, unbounded fluid. For finite capillary numbers, it is shown that the drop reverts to a sphere, provided the initial deformation is not too large. However, drops that are initially deformed to a greater extent are shown to deform continuously, forming an elongated shape with a tail when initially prolate, and a flattened shape with a cavity at the rear when initially oblate. The critical degree of deformation decreases as the capillary number increases and appears to be consistent with the results of Kojima et al. [Phys. Fluids 27, 19 (1984)], who showed that the spherical drop is unstable to infinitesimal disturbances in the limit Ca=∞.
Turbulence spectrum of strongly conductive temperature field in a rapidly stirred fluid
Authors: Chasnov J. , Canuto V. M. , Rogallo R. S.
Published: July 2002

In an earlier paper [Phys. Fluids 31, 2065 (1988)], a numerical simulation of a passive scalar field convected by a frozen velocity field, i.e., a velocity field with an infinite correlation time, was performed. In this paper, a simulation of a passive scalar field convected by a velocity field which is rapidly stirred at all scales of motion, i.e., a velocity field with near zero correlation time, is performed. For an energy spectrum of the form E(k)∝k−5/3, the temperature spectrum G(k) is found to obey G(k)∝k−11/3 when conductive effects are dominant. A theoretical model is proposed which obtains the above result by representing the transfer of scalar variance by an eddy conductivity, whose correlation time is limited by the correlation time of the velocity field.
A row of counter-rotating vortices
Authors: Mallier R. , Maslowe S. A.
Published: July 2002

In 1967, Stuart [J. Fluid Mech. 29, 417 (1967)] found an exact nonlinear solution of the inviscid, incompressible two-dimensional Navier–Stokes equations, representing an infinite row of identical vortices which are now known as Stuart vortices. In this Brief Communication, the corresponding result for an infinite row of counter-rotating vortices, i.e., a row of vortices of alternating sign, is presented. While for Stuart’s solution, the streamfunction satisfied Liouville’s equation, the streamfunction presented here satisfies the sinh–Gordon equation [Solitons: An Introduction (Cambridge U.P., London, 1989)]. The connection with Stuart’s solution is discussed.
Elliptical instability in a stably stratified rotating fluid
Authors: Miyazaki Takeshi
Published: July 2002

The linear stability of unbounded strained vortices in a stably stratified rotating fluid is investigated theoretically. The problem is reduced to a Matrix–Floquet problem, which is solved numerically to determine the stability characteristics. The Coriolis force and the buoyancy force suppress the subharmonic elliptical instability of cyclonic and weak anticyclonic vortices, whereas enhances that of strong anticyclonic vortices. The fundamental and superharmonic instability modes occur, in addition. They are due to higher-order resonance. The growth rate of each instability shows complicated dependence on the parameters N (the normalized Brunt–Väisälä frequency) and R0 (the Rossby number: defined inversely as usual), if their values are small. It decreases as the background rotation rate becomes larger and as the stratification becomes stronger. The instability mode whose order of resonance is less than Min(N,2‖1+R0‖) is inhibited.
Theory of applied-B ion diodes
Authors: Desjarlais M. P.
Published: July 2002

A recently introduced theory of applied-B ion diodes [Phys. Rev. Lett. 59, 2295 (1987)] is developed and presented in detail. The theory incorporates the self-consistent virtual cathode motion to obtain the steady-state ion current as a function of diode voltage. The existence of a limiting voltage at which the ion current diverges is demonstrated. The voltage–current characteristics of the diode are combined with a simple circuit model of the accelerator to calculate the operating point of the diode. The theoretical results are in good agreement with experimental data at peak power. An important consequence of the theory is a relation between the limiting diode voltage and the insulating magnetic flux, suggesting a late-time voltage decay driven by flux penetration into the anode plasma.
Incompressible description of Rayleigh–Taylor instabilities in laser-ablated plasmas
Authors: Kull H. J.
Published: July 2002

An incompressible fluid model of the ablative Rayleigh–Taylor instability [Phys. Fluids 29, 2067 (1986)] is generalized to include self-consistent diffuse boundaries. With diffuse boundaries the incompressible model is found to be in excellent agreement with a number of previous stability studies of laser ablation. The present theory can predict the scaling of the instability cutoff over an extended parameter range and its dependence on the heat conduction law. It is found that more favorable stability behavior can be obtained both for weak and strong thermal diffusion. Furthermore a strong dependence of the stabilization mechanism on the functional form of the heat conductivity is indicated. Representative conditions for laser ablation are identified and discussed in detail.