bluuebunny/crossref_metadata_2025 huggingface dataset:
Langmuir monolayers of C17, C19, and C21 fatty acids: Textures, phase transitions, and localized oscillations
Authors: Ramos Salvador , Castillo Rolando
Published: July 2002

The phase diagrams of Langmuir monolayers of heptadecanoic (C17), nonadecanoic (C19), and heneicosanoic (C21) acids have been determined from pressure-area isotherms, and from direct observations of the monolayers using Brewster angle microscopy. In this paper, we describe the observed domains, textures and phase boundaries for all mesophases presented by these fatty acids between 2° and 45 °C. The phase diagrams of the three fatty acids can be superposed moving the temperature scale according to the number of carbons in the tail of the fatty acids. The L2/Ov phase transition, which is not detected through isotherms, was observed in all the fatty acids under study. At low temperatures, CS,L2′, and L2″ phases of C21 were observed, as well as, the transitions among them. Also, we observed in C21 a new phase located among the phases L2,L2′, and L2″. This phase was found recently, in the relative same place, in the fatty acid C20 with a tilting azimuth between the nearest-neighbor and the next nearest-neighbor directions. In the crystalline phases of the monolayer of C21, L2″ and CS, we observed localized oscillations. These localized oscillations can be observed by long periods of time. The number of localized oscillations in the monolayer can be modified by long periods of relaxation or by heat treatment. Our results seem to indicate that these localized oscillations are areas with high density of defects, expelling material out of the monolayer. Therefore, they could be important in the events previous to the collapse.
Accurate dipole moments from Hartree–Fock calculations by means of class IV charges
Authors: Li Jiabo , Xing Jianhua , Cramer Christopher J. , Truhlar Donald G.
Published: July 2002

Charge Model 2 (CM2) is parameterized for Hartree–Fock calculations with the correlation-consistent polarized valence double zeta (cc-pVDZ) basis set. The resulting charge model has an RMS error of 0.18 D over a training set of 198 polar molecules. The charge model is additionally applied to 8 nucleic acid bases and methyl azide to test its performance for nitrogen-containing compounds not found in the training set. The results demonstrate that this new CM2 model based on ab initio Hartree–Fock calculations is robust in predicting the charge distributions of such molecules. Comparison of CM2 results for the nitrogen-containing test set with those from a previous charge model, charge model 1 (CM1) based on AM1 (Austin model 1) and PM3 (parameterized model 3) wave functions, indicate that the CM2 charges are more accurate than those from the previous model.
The conical intersection effects and adiabatic single-surface approximations on scattering processes: A time-dependent wave packet approach
Authors: Adhikari Satrajit , Billing Gert D.
Published: July 2002

Using a quasi-Jahn-Teller model and an extended version of the approximate Born-Oppenheimer (BO) single surface equations, Baer, Charutz, Kosloff, and Baer [J. Chem. Phys. 105, 9141 (1996)] have performed time-independent scattering calculations to study a direct effect on the symmetry of the nuclear wave function due to conical intersections between BO potential energy surfaces. In this article, we have addressed the same problem using the same model by introducing either a vector potential in the nuclear Hamiltonian or by incorporating a phase factor in the nuclear wave function. The scattering calculations have been carried out by using a time-dependent wave packet approach.
Recursion representation of gradient expansion for free fermion ground state in one dimension
Authors: Šamaj L. , Percus J. K.
Published: July 2002

We consider noninteracting Fermion system in an external field, confined to one-dimensional space. Our main objective is to take advantage of low dimension to find explicitly potential-density profile as well as kinetic energy functional in the ground state. This is accomplished by deriving the complete x-space linear response and a simple recursion representation of the gradient expansion for the kinetic energy. The results can serve as a potential test for higher dimensions, e.g., in exploring convergence properties of the gradient expansion in various regions of the energy spectrum.
Vibrational spectrum of B2C in argon at 10 K
Authors: Larson C. William , Domingo Presilla-Márquez José
Published: July 2002

The vibrational spectrum of B2C has been observed for the first time in solid argon by Fourier-transform infrared spectroscopy. Absorption frequencies of the three boron isotopomers of cyclic symmetric B2C, previously deduced by ab initio theory, are in accord with measured frequencies, which enables assignment of an absorption at 1392.8 cm−1 to the ν1(a1) fundamental of B2C(1A1).
Inner shell excitation spectroscopy of transient molecules: HBS, HBO, and H3B3O3
Authors: Ennis L. E. , Hitchcock A. P.
Published: July 2002

Inner shell electron energy spectroscopy (ISEELS) was used to study HBS, HBO, and H3B3O3, reactive, transient species generated in situ. The reaction of H2S with crystalline boron in a quartz tube was used to produce thioborine (HBS) at ∼1100 °C, and borine (HBO) at ∼1200 °C. The reaction of H2O vapor with crystalline boron in a quartz tube at ∼1200 °C was used to produce boroxine (H3B3O3). These species were identified from their inner shell excitation spectra and mass spectrometry. The B 1s, S 2s, and S 2p ISEEL spectra of HBS, and the B 1s and O 1s spectra of HBO and H3B3O3 are reported and analyzed with the help of GSCF3 ab initio calculations. A reaction scheme is proposed for the generation of HBO from the reaction of H2S and boron in a heated quartz tube.
Feynman path centroid dynamics for Fermi–Dirac statistics
Authors: Roy Pierre-Nicholas , Jang Seogjoo , Voth Gregory A.
Published: July 2002

In this communication the centroid molecular dynamics (CMD) method is tested for systems of fermions using a modified version of the expression for the fermion Feynman path centroid density derived in a recent publication [J. Chem. Phys. 110, 3647 (1999)]. The method is applied to a model system consisting of two noninteracting fermions in an anharmonic potential well and the position autocorrelation function is computed. The exact fermion position autocorrelation function exhibits a longer period of oscillation when compared to the bosonic case. This shift is due to the anharmonic nature of the given potential function where the level spacing decreases with the increase of energy. The CMD results agree very well with the exact quantum mechanical results for this example. This indicates, along with the previous results on a boson system, that quantum statistics can in principle be incorporated into the CMD method without any degradation of the accuracy of the approximation.
Surface color centers as novel hydrogen bond acceptors
Authors: Diwald O. , Knözinger E. , Martra G.
Published: July 2002

In recent combined electron paramagnetic resonance and infrared spectroscopic studies a very specific interaction between surface OH groups and surface color centers was observed on nanometer-sized MgO particles. The positions of the respective OH stretching bands point to hydrogen bond-like interactions. On the other hand, the bandwidths indicate that the color center electron as proton acceptor is strongly localized.
The relationship between molecular symmetry and second-rank orientational order parameters for molecules in chiral liquid crystalline solvents
Authors: Merlet Denis , Emsley James W. , Lesot Philippe , Courtieu Jacques
Published: July 2002

From group theoretical arguments, we demonstrate that the effective molecular symmetry is reduced in a chiral liquid crystalline phase. This reduction changes the location of the principal axes of the orientational order matrices for four molecular point groups, namely Cs, C2v, S4, and D2d. These symmetries correspond to compounds which have prochiral faces, groups, or directions. The change in effective molecular symmetry can be detected by NMR spectroscopy, and this is illustrated by the example of acenaphthene dissolved in a chiral nematic solvent.
Thermodynamics of cavity formation in water and n-hexane using the Widom particle insertion method
Authors: Tomás-Oliveira Isabel , Wodak Shoshana J.
Published: July 2002

The Widom particle insertion (WPI) method is used to compute the free energy, enthalpy, and entropy associated with the creation of empty cavities of different sizes in water and n-hexane. These thermodynamic parameters are computed from the likelihood of encountering such cavities in thermally equilibrated configurations from 4 ns (1 ns=10−9 s) molecular dynamics trajectories of the neat liquids. The obtained free energy values are in excellent agreement with those computed previously, using the same or other methods. We find that the entropy term is large and unfavorable in both liquids, but more so in water than in hexane. The change in internal energy is, on the other hand, virtually zero in hexane and slightly favorable in water. Comparison with scaled particle theory (SPT) predictions shows good agreement for the free energy values for small cavities, but the theory systematically underestimates these values for large cavities. In contrast, the free energy components obtained by the two methods show several significant differences. With WPI, the entropy of cavity formation is unfavorable in both liquids for all cavity sizes. SPT yields an unfavorable entropy only for water. In hexane, however, the predicted entropy is negative for small cavities, but changes sign for cavity radii >1.1 Å. In addition, SPT yields an unfavorable enthalpy of cavity formation in water, whereas with WPI this term is small but favorable. Taking n-hexane as a model for organic solvents, our calculations thus suggest that the process of cavity formation is similar in water and these solvents, a conclusion which seems to make good physical sense. SPT reaches an opposite conclusion, which seems harder to rationalize, and probably arises from the highly simplified solvent model used by this theory.
Comment on “Hindered rotor density-of-states interpolation function” [J. Chem. Phys. 106, 6675 (1997)] and “The hindered rotor density-of-states” [J. Chem. Phys. 108, 1748 (1998)]
Authors: Knyazev Vadim D.
Published: July 2002

It is demonstrated that an approximation to the partition function of a hindered rotor derived by McClurg, Flagan, and Goddard III is an equivalent of a formula published by Pitzer and Gwinn in 1942. Error in analytical expression for internal energy is pointed out. Classical density-of-states function derived by McClurg in a subsequent article has also been published before.
Photoelectron spectroscopy of pyridine cluster anions, (Py)n−(n=4–13)
Authors: Han Sang Yun , Song Jae Kyu , Kim Jeong Hyun , Oh Han Bin , Kim Seong Keun
Published: July 2002

Photoelectron spectroscopy was carried out for mass-selected anion clusters of pyridine (C5H5N=Py) up to (Py)13−. The smallest anion cluster observed was (Py)4−, which exhibited two distinctly different photoelectron bands arising from dipole-bound and valence electron states. A mixed cluster of [(Py)3(H2O)1]− displayed similar features. No dipole-bound state was observed in the larger clusters of neat pyridine, (Py)5–13−, which were interpreted as solvated clusters of pyridine molecular anion, Py−(Py)4–12. Threshold electron binding energies were measured as the upper limit value of adiabatic electron affinities. They increased monotonically from 0.33 eV for the cluster size of n=4 to 1.02 eV for n=13. But their incremental change showed a large drop at n=8, as did the incremental change in vertical detachment energy, which was viewed as due to the completion of the first solvation shell at n=7. The energetics of anion solvation suggested nearly pure electrostatic interactions at play. A boundary was drawn on the adiabatic electron affinity of the pyridine molecule between −0.67 and −0.15 eV. Under a very high laser fluence condition, multiphoton processes were found to occur that lead to photofragmentation followed by photodetachment. Photofragmentation of (Py)5,6− yielded photofragments which revealed the same features as the dipole-bound state of (Py)4−. This was taken as evidence for the existence of dipole-bound excited states of diffuse orbital character in these larger clusters.
The diffusion of simple penetrants in tangent site polymer melts
Authors: Rottach Dana R. , Tillman Patrick A. , McCoy John D. , Plimpton Steven J. , Curro John G.
Published: July 2002

The diffuse behavior of penetrants in simple polymer melts was investigated by molecular dynamics simulation. For the case where the polymer melt consisted of pearl-necklace chains, the diffusive behavior of the loose pearl penetrants was seen to be qualitatively different than would be expected in realistic models of polymer melts. In particular, there was little or no “non-Fickian” region; the variation of the diffusion coefficient with the penetrant diameter was what one would expect for diffusion through small molecular liquids; and, finally, the long time tail of the velocity autocorrelation displayed a “−3/2” power law form, also as in the small molecular liquid case. When the chains’ backbone motion was further constrained by the introduction of a bond angle potential, the qualitative nature of the penetrant diffusion became more “polymer-like.” A non-Fickian region developed; the diffusion coefficient varied more rapidly with penetrant diameter; and the velocity autocorrelation function developed a “−5/2” power law tail.
Dissociation of diatomic molecules by elliptically polarized chirped pulses
Authors: Kim Jung-Hoon , Liu Wing-Ki , McCourt Frederick R. W. , Yuan Jian-Min
Published: July 2002

The effects of the rotational degrees of freedom in the photodissociation dynamics of diatomic molecules by a chirped laser pulse is studied. In general, the inclusion of rotational degrees of freedom reduces the efficiency of the chirping excitations relative to that found for nonrotating molecules. However, using classical 2D and 3D rotating Morse oscillator models we demonstrate that field polarization can cause dramatic enhancements of the dissociation probabilities, with circularly polarized chirped pulses inducing dissociation in rotating molecules almost as efficiently as that previously seen for nonrotating Morse oscillators. We suggest reasons for such improvement in efficiency and discuss the validity of the bucket dynamics model for rotating Morse oscillators.
Molecular dynamics study of diffusion in bidisperse polymer melts
Authors: Barsky Sandra
Published: July 2002

Molecular dynamics simulations of the diffusion coefficient of systems of polydisperse chains are presented. Each system consists of two lengths of chain of chemically identical flexible polymers. The mean square displacement of the center of mass of each species is measured as a function its length and volume fraction in the blend. The polymer lengths range from N=10 monomers per chain to N=90, about three times the entanglement length. The polymer species that comprises the bulk of the melt shows little change in behavior regardless of the length of polymer which makes up the remainder. By contrast, when a species is the minority component, its motion is significantly affected by the length of the matrix chains. When a chain is immersed in a matrix of longer chains, its diffusion coefficient is smaller than its monodisperse value; conversely when a chain is in a blend of shorter chain its diffusion coefficient increases compared to a monodisperse melt. For chains shorter than the entanglement length, the diffusion coefficient compares well to theoretical predictions. The scaling exponent of the mean square displacement of the longest polymer is found to be sublinear, unless blended with very short polymers. The scaling exponent seems to be a measurement of the entanglements that the long polymers experience.
A selected ion flow tube study of the reactions of small CmHn+ ions with O atoms
Authors: Scott Graham B. I. , Milligan Daniel B. , Fairley David A. , Freeman Colin G. , McEwan Murray J.
Published: July 2002

The reactions of thirteen CmHn+ ions (m⩽6) with atomic and molecular oxygen and nitric oxide have been measured using a selected ion flow tube operating at room temperature. Rate coefficients and product distributions are reported for each reaction. Most of the hydrocarbon ions studied exhibit relatively rapid reactions with O atoms and proceed at substantial fractions of the collision rate. All O atom reactions showed multiple product channels and the formation of a –C–O bond, either in the ion product or the neutral product of reaction.
Effect of H-bond active sites on transport properties of poly(ethylene oxide) dissolved in its monomers: Shear viscosity and diffusion coefficient studies
Authors: Crupi V. , Faraone A. , Maisano G. , Majolino D. , Migliardo P. , Venuti V. , Villari V.
Published: July 2002

The possibility of dissolving poly(ethylene oxide) [PEO:H–(O–CH2–CH2)n–OH] in its monomeric liquid ethylene glycol [EG:H–(O–CH2–CH2)–OH] represents the only way to verify the complex polymer–monomer interactions, through the OH end groups, resulting in the scaling law R∝Nν. We report viscosity results, in conjunction with photon correlation spectroscopy data, on different molecular weight PEO samples, in a wide range of concentrations, dissolved in EG. In order to distinguish among various interaction mechanisms, we also studied PEO dissolved in EG monomethyl ether [EGmE:CH3–(O–CH2–CH2)–OH] and EG dimethyl ether [EGdE:CH3–(O–CH2–CH2)OCH3], the latter not having in its chemical structure OH hydroxylic groups available to give rise to hydrogen bond interactions. In particular, the quality (good-theta-poor) of the solvents has been analyzed by verifying the well-known Mark–Houwink–Sakurada scaling law and the effects of the polymer–solvent interactions on the coils diffusive properties.
The nonplanarity of the peptide group: Molecular dynamics simulations with a polarizable two-state model for the peptide bond
Authors: Rick Steven W. , Cachau R. E.
Published: July 2002

The general properties of the peptide bond can be described from a linear combination of two states: a single bond neutral form and a double bond zwitterionic form. However, environmental effects can shift the balance of the linear combination. This would cause the rigidity of torsional rotations of the peptide bond to be environmentally dependent and, in fact, an analysis of protein structures in the protein data bank reveals a different degree of nonplanarity for different secondary structure elements. A potential is presented in which the peptide bond is treated as a linear combination of two states; the coefficients of the two states are updated as the simulation progresses using an extended Lagrangian formalism. The model is applied to the helix/coil transition of polyalanine. Fluctuations in the planarity of the peptide dihedral angle are found to increase the rate constant for the coil to helix transition by a factor of two.
Photodissociation of H2O and D2O below 132 nm
Authors: Zanganeh A. H. , Fillion J. H. , Ruiz J. , Castillejo M. , Lemaire J. L. , Shafizadeh N. , Rostas F.
Published: July 2002

A complete determination of the rotational and vibrational distributions in the OH/OD(A 2Σ+) fragments which result from the VUV photodissociation of H2O/D2O as a function of excitation energy is presented. VUV excitation was performed at eight different wavelengths (eleven for D2O) in the range between 132 and 124 nm. The vibrational branching ratios show a relatively fast rise of the vibrational excitation at threshold followed by a plateau. The general trend of the experimental results is well reproduced by a phase space theory calculation and by ab initio calculations reported by van Hemert and van Harrevelt. Rotational distributions seem to depend only on the available excess energy and, for a given excess energy appear to be similar for all vibrational levels in OH and OD.
The C 3Π, d 1Π, and e 1Π states of SO
Authors: Archer Christopher P. , Elks John M. F. , Western Colin M.
Published: July 2002

The energy region just above the first dissociation limit in SO is investigated by a combination of jet cooled 1+1 multiphoton ionization spectroscopy and ab initio calculations. Two electronic states, the C 3Π and d 1Π states, are found to give sharp, rotationally resolved spectra, and a complete analysis of these is presented for the first time. The potential energy curve for the d 1Π is found to be unusual, with only four bound levels and a maximum that does not correspond to a conventional avoided crossing. Our assignments are supported by ab initio calculations, which also predict the interactions between electronic states from spin–orbit coupling. Experimental evidence for these, in the form of perturbations in the observed spectra and predissociation is discussed. Based on our ab initio calculations we also reassign some previous observations to the e 1Π state.
Near-field optics: The nightmare of the photon
Authors: Keller Ole
Published: July 2002

A first-quantized theory describing the birth process of a single photon in the near-field zone of a pointlike particle (atom, molecule, etc.) is established. The space-time description of the photon energy wave function embryo is shown to be useful for the understanding of the role played by (unborn) photons in near-field interactions where the spatial confinement of light plays a crucial role.
Frequency-dependent second hyperpolarizabilities in the time-dependent restricted open-shell Hartree–Fock theory: Application to the Li, Na, K, and N atoms
Authors: Kobayashi Takao , Sasagane Kotoku , Yamaguchi Kizashi
Published: July 2002

The implementation of frequency-dependent second hyperpolarizabilities is presented using the time-dependent (spin-)restricted open-shell Hartree–Fock (TDROHF) theory (ROHF cubic response theory). The expression for the ROHF cubic response function (frequency-dependent second hyperpolarizability) is derived based on the quasienergy derivative (QED) method. We present an application of the ROHF cubic response theory to the frequency-dependent second hyperpolarizabilities of ground states of open-shell atoms (which are in S states) [Li(2S), Na(2S), K(2S), and N(4So)] for various third-order optical processes.
Dynamics of DNA electrophoresis in dilute and entangled polymer solutions
Authors: Noguchi Hiroshi
Published: July 2002

We studied the electrophoresis of polyelectrolyte chains, such as DNA, in linear polymer solutions using Brownian dynamics simulation with anisotropic friction tensor. We show anisotropic friction is an effective method to describe dynamics of polyelectrolyte chains under an electric field in dilute polymer solution as well as in entangled polymer solution or gel. With a low anisotropy of friction, a chain fluctuates between elongated and compact states with no periodicity under a steady electric field and in field-inversion electrophoresis, its mobility shows an abrupt change at a certain chain length without antiresonance. With a high anisotropy of friction, a chain oscillates periodically and in field-inversion electrophoresis its mobility shows antiresonance. The above results agree well with experiments on DNA electrophoresis.
A numerical study on the performance of the multiconfiguration time-dependent Hartree method for density operators
Authors: Raab A. , Meyer H.-D.
Published: July 2002

A numerical study based on the multiconfiguration time-dependent Hartree (MCTDH) method for the propagation of density operators is presented. Within the MCTDH framework, there exist two types of expansions of the density operator which employ different kinds of so-called single-particle density operators. The latter may either represent Hermitian operators (type I), or else ket-bra products of so-called single-particle functions (type II). The performance of these two types of representations is tested on three models for closed and open system dynamics. The open dynamics is induced for each system by Lindblad-type dissipation operators. We find that the MCTDH representation of type I is most efficient if the coupling between the degrees of freedom is weak, but if the temperature of the initial state and/or the strength of the dissipation is moderate. On the other hand, for strong coupling between the degrees of freedom, but for lower temperatures and for weak dissipation type II is more efficient. Furthermore, considering the open dynamics of the systems both types of MCTDH density operators can be very efficiently used to calculate absorption spectra. The Lindblad-type dissipation operator is shown, however, to capture only partially the effects of a real environment.
A reduction relation for an n-body trace of an operator product consisting of coupled C+’s and C’s
Authors: Nomura Masao
Published: July 2002

A reduction relation for the trace of an operator product consisting of C+’s and C’s is derived in the truncated space of n fermions or n bosons being distributed over definite orbits. The state operator formalism (derived in a preceding paper) is fully used so as to perform normal ordering (or contraction) of coupled C+’s and C’s in the operator string with the least destruction of the preexisting coupling.
Generalized Green’s functions and spectral densities in the complex energy plane
Authors: Engdahl Erik , Brändas Erkki , Rittby Magnus , Elander Nils
Published: July 2002

The Titchmarsh–Weyl theory is applied to the Schrödinger equation in the case when the asymptotic form of the solution is not known. It is assumed that the potential belongs to the Weyl’s limit-point classification. A rigorous analytical continuation of the Green’s function, obtained from the solution regular at the origin and the square integrable Weyl’s solution (regular at infinity), to the ‘‘unphysical’’ Riemann energy sheet is carried out. It is demonstrated how the Green’s function can be uniquely constructed from the Titchmarsh–Weyl m-function and its Nevanlinna representation. The behavior of the m-function in the neighborhood of poles is investigated. The m-function is decomposed in a, so called, generalized real part (Reg) and a generalized imaginary part (Img). Reg(m) is found to have a significant argument change upon pole passages. Img(m) is found to be a generalized spectral density. From the generalized spectral density, a spectral resolution of the differential operator and its resolvent is derived. In the expansion contributions are obtained from bound states, resonance states (Gamow states), and the ‘‘deformed continuum’’ given by the generalized spectral density.

The present expansion theorem is applicable to the general partial differential operator via a decomposition into partial waves. The numerical procedure involves all quantum numbers l and m, but for convenience, and with the inverse problem in mind, this study is focused on the case when the rotational quantum number equals zero. The theory is tested numerically and analyzed for an analytic model potential exhibiting a barrier and decreasing exponentially at infinity. The potential is Weyl’s limit point at infinity and allows for an analytical continuation into a sector in the complex plane. An attractive feature of the generalized spectral density of the present potential is that the poles close to the real axis seem to exhaust or deflate the above-mentioned density inside the pole string. Outside this string the density rapidly approaches that of a free particle. This information is used to derive an approximate representation of the m-function in terms of poles and residues as well as free-particle background. In order to display the features mentioned above, the present study is accompanied with several plots of analytically continued quantities related to the Green’s function.
Physical relations and the Weyl group
Authors: Cieciura Grzegorz , Szczyrba Igor
Published: July 2002

Let a given particle symmetry be described by a reductive Lie group G. It is proved that the corresponding Weyl group W(R) acts canonically in all zero-weight spaces of G and hence, in particular, on observables. Moreover, it is shown how this W(R) action provides many physical relations, including those believed to be implied by G-transformation properties of observables. The results simplify a testing of symmetries based on various Lie groups (algebras). Their use extends beyond particle physics, e.g., to nuclear physics.
Superinvariant chiral and vector fields
Authors: Panagopoulos Haralambos , Vinet Luc
Published: July 2002

This work is concerned with the characterization of field supermultiplets on four-dimensional Minkowski space that are stable under the action of subgroups of the superconformal group SU(2,2/1). The most general scalar and vector superfields whose Lie derivative with respect to a fermionic tangent vector vanishes are determined. Invariance under subgroups of SU(2,2/1) with more than one odd generator is also discussed.
Composite systems in quaternionic quantum mechanics
Authors: Nash C. G. , Joshi G. C.
Published: July 2002

The natural composition of systems in quaternionic quantum mechanics is examined via their lattices of propositions and it is shown that the criticisms that have been made of such a composition are unconvincing.
The nonlinear desingularization phenomenon in the Abelian Higgs model for isotropic solutions
Authors: Chen Y. Y.
Published: July 2002

In this paper, the occurrence of a linearization phenomenon in the Abelian Higgs model for isotropic solutions will be proved. In this linearizing process, as the parameter λ→∞, the smooth solutions of the nonlinear differential equations will degenerate to the Green’s function of the related linearized equation, which is an inhomogeneous linear elliptic equation.
Special relativity with Clifford algebras and 2×2 matrices, and the exact product of two boosts
Authors: Baylis W. E. , Jones George
Published: July 2002

Formulations of the special theory of relativity in the Dirac or ‘‘space-time’’ algebra are compared with those in the simpler algebra of 2×2 matrices (‘‘Pauli algebra’’). The Dirac algebra separates elements into odd and even multivectors, but this feature is not needed in most practical calculations. As a result, Pauli-algebra formulations are just as powerful in most cases. Furthermore, the new correction angle φ, which Salingaros found with the Dirac algebra to be required to describe the product of two boosts, is shown to be identically zero, and new results for special boost combinations are derived.
A solution to the one-dimensional missing moment problem
Authors: Handy Carlos R.
Published: July 2002

The one-dimensional ‘‘missing moment problem’’ is solved using Padé analysis. The realization of this affords the most efficient framework within which to apply a Hankel–Hadamard analysis for generating rapidly convergent bounds to quantum eigenvalues. The method is applied to the quartic potential problem.
Nonsymmetric vortices for the Ginzberg–Landau equations on the bounded domain
Authors: Chen Y. Y.
Published: July 2002

It is shown by means of the Cronström gauge condition [Phys. Lett. B 90, 267 (1980)] and the constrained variational principle that there exist nonsymmetric solutions to the steady-state Ginzburg–Landau equations with arbitrary parameter λ>0 in bounded domain Ω contained in two-dimensional Euclidean space.
Diagonalization and Hamiltonian structures of hyperbolic systems
Authors: Neyzi Fahrünisa
Published: July 2002

A simple algorithm for casting two-dimensional hyperbolic systems into the Hamiltonian form is given. First-order conserved quantities are found and expressed in terms of eigenvalues. It is shown that for some systems the dependence of the eigenvalues on the field variables can be used for classification.
Generalized Fourier transforms for nonlinear systems
Authors: Díaz Bejarano J. , Martín Sánchez A.
Published: July 2002

A simple generalization is presented of the usual Fourier transforms using generalized exponential and Fourier series developed previously for nonlinear systems. The expressions are given in terms of Jacobi elliptic functions in a form as close as possible to the Fourier transform. There is a pair of transforms for each value of the Jacobi parameter m. Simple applications are presented, one of which gives the generalized Yukawa potential and another that gives the generalized Breit–Wigner potential: Both correspond to the generalized Klein–Gordon equation.
Reduction of the Einstein equations in 2+1 dimensions to a Hamiltonian system over Teichmüller space
Authors: Moncrief Vincent
Published: July 2002

In this paper the ADM (Arnowitt, Deser, and Misner) reduction of Einstein’s equations for three-dimensional ‘‘space-times’’ defined on manifolds of the form Σ×R, where Σ is a compact orientable surface, is discussed. When the genus g of Σ is greater than unity it is shown how the Einstein constraint equations can be solved and certain coordinate conditions imposed so as to reduce the dynamics to that of a (time-dependent) Hamiltonian system defined on the 12g−12-dimensional cotangent bundle, T*𝒯(Σ), of the Teichmüller space, 𝒯(Σ), of Σ. The Hamiltonian is only implicitly defined (in terms of the solution of an associated Lichnerowicz equation), but its existence, uniqueness, and smoothness are established by standard analytical methods. Similar results are obtained for the case of genus g=1, where, in fact, the Hamiltonian can be computed explicitly and Hamilton’s equations integrated exactly (as was found previously by Martinec). The results are relevant to the problem of the reduction of the 3+1-dimensional Einstein equations (formulated on circle bundles over Σ×R and with a spacelike Killing field tangent to the fibers of the chosen bundle) and to the recent discussion by Witten of the possible exact solvability of the ‘‘topological dynamics’’ associated with Einstein’s equations in 2+1 dimensions.
Noether’s theorem and gauge transformations: Application to the bosonic string and C
P n−12 model
Authors: Batlle C. , Gomis J. , Gràcia X. , Pons J. M.
Published: July 2002

New results on the theory of constrained systems are applied to characterize the generators of Noether’s symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples.
Classical, linear, electromagnetic impedance theory with infinite integrable discontinuities
Authors: DeFacio Brian
Published: July 2002

The impedance theory is formulated for classical, linear electromagnetic scattering from a compact obstacle with a finite number of nonintersecting boundaries. The boundaries are allowed to support infinite, integrable discontinuities in electromagnetic response and the compact regions can depend on space and time. The direct scattering problem is discussed, generalizing recent results by Sabatier and collaborators for the scalar impedance acoustic problem to classical electromagnetism. A chain of Maxwell scattering equations are derived for the direct scattering problem. Two kinds of ambiguities of electromagnetism at a fixed angle of incidence are found to arise, one from discontinuities in electromagnetic material properties, and the other is from time dispersion. Cases are mentioned when parts of the scattering medium are allowed to have time-dependent motions. This is in contrast to the case of scalar acoustics where ambiguities are intrinsic to certain infinite families of values of Young’s modulii.
Second-order equations and quadratic Lagrangians
Authors: Hammond Richard T.
Published: July 2002

From a general Lagrangian that is quadratic in the Ricci tensor, independent variations of the metric and torsion tensors produce gravitational field equations that are of second differential order in the metric tensor. This reduction in order from four results from the use of the torsional field equations. Also, the equation of motion is derived and several special cases are considered.
Noether’s theorem in nonlinear σ models with a Wess–Zumino term
Authors: Zainuddin Hishamuddin
Published: July 2002

The σ model with a Wess–Zumino term is treated as a system of a particle in a magnetic field on an infinite-dimensional configuration space. Noether’s theorem has to be modified to take account of this background gauge field in the configuration space. The questions of possible ‘‘anomalous’’ constants of motion and an ‘‘Aharonov–Bohm effect’’ for nonsimply connected configuration spaces are also addressed.
Balance laws and centro velocity in dissipative systems
Authors: van Groesen E. , Mainardi F.
Published: July 2002

Starting with a density that is conserved for a dynamical system when dissipation is ignored, a local conservation law is derived for which the total flux (integrated over the spatial domain) is unique. When dissipation is incorporated, the conservation law becomes a balance law. The contribution due to dissipation in this balance law is split in a unique way in a part that is proportional to the density and in a divergence expression that adds to the original (conservative) flux density; the total additional flux is uniquely defined. It is shown that these total fluxes appear in the expression for the centro velocity, i.e., in the velocity of the center of gravity of the density, which shows that this velocity can be defined in a unique way (in contrast to a local velocity). Applications to the Korteweg–de Vries–Burgers equations and to the incompressible Navier–Stokes equations are given.
Ricci collineation vectors in fluid space-times
Authors: Tsamparlis M. , Mason D. P.
Published: July 2002

The properties of fluid space-times that admit a Ricci collineation vector (RCV) parallel to the fluid unit four-velocity vector ua are briefly reviewed. These properties are expressed in terms of the kinematic quantities of the timelike congruence generated by ua. The cubic equation derived by Oliver and Davis [Ann. Inst. Henri Poincaré 30, 339 (1979)] for the equation of state p=p(μ) of a perfect fluid space-time that admits an RCV, which does not degenerate to a Killing vector, is solved for physically realistic fluids. Necessary and sufficient conditions for a fluid space-time to admit a spacelike RCV parallel to a unit vector na orthogonal to ua are derived in terms of the expansion, shear, and rotation of the spacelike congruence generated by na. Perfect fluid space-times are studied in detail and analogues of the results for timelike RCVs parallel to ua are obtained. Properties of imperfect fluid space-times for which the energy flux vector qa vanishes and na is a spacelike eigenvector of the anisotropic stress tensor πab are derived. Fluid space-times with anisotropic pressure are discussed as a special case of imperfect fluid space-times for which na is an eigenvector of πab.
The group theoretic analysis of hyperheavenly equations
Authors: Przanowski M.
Published: July 2002

Contact symmetries of generalized hyperheavenly and hyperheavenly equations are investigated. It is shown that the groups of contact transformations admitted by these equations are the first prolongations of appropriate point transformation groups.
The wetted solid—A generalization of the Plateau problem and its implications for sintered materials
Authors: Salamon Peter , Bernholc J. , Berry R. Stephen , Carrera-Patiño Martin E. , Andresen Bjarne
Published: July 2002

A new generalization of the Plateau problem that includes the constraint of enclosing a given region is introduced. Physically, the problem is important insofar as it bears on sintering processes and the structure of wetted porous media. Some primal and dual characterizations of the solutions are offered and aspects of the problem are illustrated in one and two dimensions in order to clarify the combinatorial elements and demonstrate the importance of numerous local minima.
Biorthogonal sets for energy bands in solids
Authors: Zak J.
Published: July 2002

A biorthogonal set is constructed for a basis of a band representation. A simple fact is used that any band representation can be induced from a one-dimensional representation of a point group (the latter is not necessarily an isotropy group of a Wyckoff position). It is shown that the biorthogonal set has the same symmetry structure as the original basis of the band representation. Symmetry relations are established for the matrix connecting the biorthogonal set with the functions of the original basis.
Representations of the SL(2,C) Kac–Moody current algebra in the Fock space
Authors: Haba Z.
Published: July 2002

A representation of the SL(2,C) current algebra in terms of Hermitian currents constructed from free fields is obtained. The representation is not of the highest weight type. The restriction k≥4 on the Kac–Moody central charge k is obtained. If k=4, then the Sugawara construction defines the energy-momentum tensor equal to the energy-momentum tensor of the free-field theory.
Study of some dual solutions in 2+1 dimensions
Authors: Keszthelyi B. , Piard E. , Ramond P.
Published: July 2002

Some consequences of duality in three dimensions is studied. In the case of pure gravity, a dual Ansatz is shown to lead to pure gauge configurations, and in a Weyl invariant gravitational theory, duality arises as an equation of motion. Its solutions obey the Liouville equation, and describe a rotating Chern–Simons fluid in a gravitational field.
Quantum logic as a consequence of realistic measurements on deterministic systems
Authors: Doebner H. D. , Lücke W.
Published: July 2002

It is shown why, from the deterministic point of view, quantum logic and not classical logic is the appropriate language for describing realistic measurements.
Three-body quantum system on a line: Wave function asymptotics for increasing interactions
Authors: Kuperin Yu. A. , Merkuriev S. P. , Yarevsky E. A.
Published: July 2002

The asymptotical analysis for the wave function of a three-body quantum system on a line with increasing interactions is given within the framework of the eikonal method in configuration space. For the linear increasing interactions, an explicit solution of the eikonal equation is constructed.
On large coupling operator norm convergences of resolvent differences
Authors: Demuth M.
Published: July 2002

Schrödinger operators with Kato’s class potentials are perturbed by positive potentials with compact supports and increasing heights. The convergences of the corresponding resolvent differences are investigated in different operator norms. Necessary and sufficient conditions are given for Hilbert–Schmidt and trace class convergences. The usefulness of the results is explained by some spectral theoretical examples.
Generalization of the Glansdorff–Prigogine stability criterion
Authors: Sicardi Schifino A. C. , Costa A. , Ferro Fontán C.
Published: July 2002

It will be shown that a mathematical reformulation of the Glansdorff–Prigogine local equilibrium hypothesis makes it possible to associate the Glansdorff–Prigogine stability criterion to the sign of a quadratic form. A comparison with other known results of literature is presented. Moreover, the equivalence between the local potential method of Glansdorff–Prigogine and the Keizer–Lavenda’s generalization of the Onsage–Machlup Lagrangian formulation will be proven.
Electromagnetic momenta for systems of charged particles
Authors: Willis Barton L.
Published: July 2002

The electromagnetic linear and angular momenta are defined as an integral of the appropriate density over a forward lightcone. It will be shown how to relate the electromagnetic momenta, for a system of charged point particles, as an integral over finite segments of each world line. Other treatments of this problem, where the momenta is defined as the integral over a spacelike hyperplane, require the integral over infinite segments of the world lines. In general, these integrals diverge for point particles. However, the integrals over the forward lightcones are finite. Several examples are worked.
The interacting Boson model with the exceptional groups G2 and E6
Authors: Morrison I. , Pieruschka P. W. , Wybourne B. G.
Published: July 2002

The extension of the interacting Boson model of (IBM) nuclei to sdgi bosons leads naturally to the group structure U28→SU3→SO3. There exist alternative group structures involving the exceptional Lie groups G2 and E6, namely, U28→SU7→SO7→G2→SO3 and U28→SU27×U1→E6→G2→SO3. This represents a different use of G2 to that used in the atomic and nuclear spectroscopy of the f shell. In this paper, details of the explicit construction of the group generators, the calculation of the relevant isoscalar factors, and branching rules will be shown and specific application to the nuclear levels of the A=200 isotope of Hg will be made. The analysis of the foregoing example encourages the more general application of these group structures.
Wave interactions in the singular Zakharov system
Authors: Newton Paul K.
Published: July 2002

A multiscale perturbation method is used to derive solutions to the singular Zakharov equations governing the interaction of an acoustic wave with a plasma envelope. The method is described in general terms and then used to study two specific interactions. The first is that of a plasma standing wave with a monochromatic acoustic plane wave, the second is that of plasma soliton with a monochromatic plane wave. Systems of modulation equations governing the leading-order interactions and higher-order interactions are derived and solved. The higher-order interaction equations ultimately reduce to solving a Schrödinger eigenvalue problem that can be solved using hypergeometric functions. The solutions are examined for fixed time as ε is increased and for fixed ε as time evolves.
About the existence of recursion operators for completely integrable Hamiltonian systems near a Liouville torus
Authors: Brouzet R.
Published: July 2002

It is shown that the existence of a recursion operator near a Liouville torus of a completely integrable Hamiltonian system is not always satisfied and that such an existence implies very strong conditions on the Hamiltonian and on the actions.
Variational derivation of the equations of motion for a perfect fluid in a rotating cylinder
Authors: Nahmad-Achar E.
Published: July 2002

The relativistic Euler equations for a compressible perfect fluid are derived from a variational principle based on angular momentum flux. Both the stationary and time-dependent cases are considered, and the variational principle is satisfactory in the sense that it is based on Eulerian variables. A comment is made for dissipative fluids.
On convergence of normal forms for complex frequencies
Authors: Ottolenghi A.
Published: July 2002

Convergence of the normal form for the Hamiltonian system is proven ẋi=−∂Hε/∂yi, ẏi=−∂Hε/∂xi, 1≤i≤n, where Hε has the form Hε(x,y) =H0(x)+εH1(x,y), (x,y)∈Rn×Tn and is holomorphic with respect to (x,y,ε), provided n≤2 and the ratio (∂H0/∂x1)/(∂H0/∂x2) is not real.
The conformal geometry of complex quadrics and the fractional-linear form of Möbius transformations
Authors: Robinson Ivor , Trautman Andrzej
Published: July 2002

A new derivation is given of the Vahlen (1902) form of the local conformal transformations of Cn, v ■ (av+b)(cv+d)−1, where v∈Cn and a, b, c, d are suitable elements of the complex Clifford algebra Cl(n). The derivation is based on the homomorphism of groups Spin(n+2)→SO(n+2), the isomorphism of algebras Cl(n+2)≂C(2)⊗Cl(n), and the action of the Möbius group SO(n+2) on the quadric Qn, the conformal compactification of Cn. It is shown how the conformal geometry of Qn lifts, for every n=1,2,..., to a unique conformal spin structure. The Hermite–Sylvester interpolation method is used to represent the map exp: spin(n)→Spin(n) in such a manner that exp a becomes a Clifford polynomial in a∈Λ2Cn.
Quantum theory of anharmonic oscillator: Energy levels of a three-dimensional oscillator with quartic anisotropic perturbation
Authors: Witwit M. R. M.
Published: July 2002

The energy levels of the Schrödinger equation for a three-dimensional oscillator with quartic perturbation, V(x,y,z)= 1/2[x2+y2+z2]+λ[axxx4+ayyy4 +azz z4 +2axyx2y2+2axzx2z2+2ayz y2z2], are calculated using matrix diagonalization for various values of the perturbation parameters and state numbers (nx,ny,nz).