bluuebunny/crossref_metadata_2025 huggingface dataset:
Kinetics of wollastonite nucleation in CaO⋅SiO2 glass
Authors: Gránásy László , Wang Tianhe , James Peter F.
Published: July 2002

The nucleation and growth of wollastonite crystals have been investigated in stoichiometric CaO⋅SiO2 glass. In the temperature range of 1043 to 1073 K, the nucleation rate was evaluated from crystallite densities, determined by optical microscopy on samples subjected to double-stage heat treatment. Turnbull’s method was used to analyze the nucleation rates in terms of various theoretical models: the classical theory (CNT), a semiempirical density functional approach (SDFA) based on the model of Bagdassarian and Oxtoby, and the phenomenological diffuse interface theory (DIT). When either the viscosity or the transient time of nucleation is used in determining the rate constants, a strongly temperature dependent interfacial free energy is obtained that approaches a linear behavior at high temperatures. Accordingly, Turnbull’s plot is curved; however, the high-temperature asymptotic behavior is well described by both the SDFA and the DIT. The DIT analysis indicates a homogeneous process, as opposed to the heterogeneous mechanism suggested by the SDFA. The melting point values of the dimensionless interfacial free energy (Turnbull’s α) deduced from the slope of Turnbull’s plot are 0.79–0.85 (DIT) and >1.06–1.14 (SDFA). The somewhat too high values in the latter case originate from a broad (∼200 Å) interfacial region predicted by the SDFA that exceeds considerably the interface width from computer simulations. Attempts to remove this problem by adjusting the parameters of the SDFA failed, suggesting that a more accurate free energy functional needs to be introduced into the model. Possible origins of the nonlinear Turnbull plot are discussed.
Efficient transition path sampling: Application to Lennard-Jones cluster rearrangements
Authors: Dellago Christoph , Bolhuis Peter G. , Chandler David
Published: July 2002

We develop an efficient Monte-Carlo algorithm to sample an ensemble of stochastic transition paths between stable states. In our description, paths are represented by chains of states linked by Markovian transition probabilities. Rate constants and mechanisms characterizing the transition may be determined from the path ensemble. We have previously devised several algorithms for sampling the path ensemble. For these algorithms, the numerical effort scales with the square of the path length. In the new simulation scheme, the required computation scales linearly with the length of the transition path. This improved efficiency allows the calculation of rate constants in complex molecular systems. As an example, we study rearrangement processes in a cluster consisting of seven Lennard-Jones particles in two dimensions. Using a quenching technique we are able to identify the relevant transition mechanisms and to locate the related transition states. We furthermore calculate transition rate constants for various isomerization processes.
Fragility under pressure: Diamond anvil cell viscometry of ortho-terphenyl and salol
Authors: Schug K. U. , King H. E. , Böhmer R.
Published: July 2002

Viscosities of the fragile glass-forming liquids ortho-terphenyl and salol have been measured in a diamond anvil cell for pressures up to 1 GPa and for temperatures 300 K<T<425 K. Utilizing a rolling ball technique viscosities up to 108 mPas could be determined. From these data the pressure dependence of the fragility index, corresponding to a reference viscosity of about 108 mPas, has been calculated. For ortho-terphenyl it is found that this “low-viscosity” fragility index is pressure invariant within experimental error. Salol exhibits a more complicated behavior.
Dynamics of alkane chains included in an organic matrix: Molecular dynamics simulation and comparison with neutron scattering experiment
Authors: Morelon Nhan-Duc , Kneller Gerald R. , Ferrand Michel , Grand André , Smith Jeremy C. , Bée Marc
Published: July 2002

An 800 ps molecular dynamics simulation is used to characterize a variety of 290 K rigid-molecule and intramolecular motions in an inclusion compound consisting of heptane guest molecules in channels formed by a matrix of TANO (C9H16NO2) molecules. The heptane molecules undergo highly anisotropic rigid-molecule motion, consisting of fast (characteristic time, τ=3 ps) rotationally isotropic and slower translational diffusion. Internal conformational transitions in the heptane molecules are also present (τ=28 ps). The methyl rotational (τ=80 ps) and ring puckering (τ=160 ps) conformational transitions in the TANO molecules are examined in detail; the former reach equilibrium during the simulation whereas the latter do not. The vibrational density of states, dynamical structure factor, and elastic incoherent structure factors (EISFs) are computed from the simulation and found to be in good agreement with experiment, indicating that the small-amplitude vibrations, the characteristic times, and geometries of the large-amplitude diffusive motions are well represented. The main peaks in the density of states are assigned to methyl librations and rigid-molecule translational vibrations. The rigid-molecule diffusion of the heptane molecules is found to dominate the EISF decay.
Low-temperature excess specific heat and fragility in polymers: Crystallinity dependence
Authors: D’Angelo G. , Tripodo G. , Carini G. , Bartolotta A. , Di Marco G. , Salvato G.
Published: July 2002

A study of the mechanical characteristics and the low-temperature specific heat has been performed on a class of polymers whose crystallinity degree varies in a wide range, from a wholly amorphous to a highly crystalline structure. Typical features of the amorphous phase have been analyzed in order to shed further light on their correlations: the deviation from the exponentiality and the “fragility” obtained by modeling the mechanical αa-relaxation and the excess specific heat over the predictions of the Debye theory. It has been found that increasing crystallinity enhances the nonexponentiality of the αa-relaxation, and decreases both the fragility and the excess specific heat. This behavior is intrinsic to semicrystalline polymers. Consequently, the recently suggested correlation between the degree of fragility and the additional low-energy vibrations causing the low-temperature excess specific heat in glasses fails in semicrystalline polymers.
Fluorescence from molecules and aggregates in polycrystalline thin films of α-oligothiophenes
Authors: Yang Aiping , Kuroda Masami , Shiraishi Yotaro , Kobayashi Takayoshi
Published: July 2002

We report stationary fluorescence, fluorescence excitation spectra, site-selective fluorescence spectra, and femtosecond time-resolved fluorescence spectra of vacuum-evaporated α- quaterthiophene (T4) and α-quinquethiophene (T5) polycrystalline thin films at various temperatures. It is found that the fluorescence spectrum of each compound studied is a superposition of emission spectra originated from energetically and spatially separated fluorescent species or sites, which are suggested to be disordered-molecules, pre-aggregates, aggregates, and physical defects. The disordered molecules lying at grain boundaries display a solutionlike fluorescence decay feature. Multiple fluorescence spectra with identical vibrational developments from pre-aggregate species are observed in the T5 film. A long-lived fluorescence decay component observed in the T4 film is attributed to the dipole-allowed transition in the aggregates. A slow rise observed in the time-resolved fluorescence of the T4 film is interpreted in terms of energy transfer from the energetically high-lying species to the physical defects in crystal.
Interchain interaction in a prototypical conjugated oligomer from polarized absorption at 4.2 K: α-sexithienyl single crystal
Authors: Muccini M. , Lunedei E. , Taliani C. , Beljonne D. , Cornil J. , Brédas J. L.
Published: July 2002

The polarized absorption spectra in the bc face of an α-sexithienyl (T6) single crystal have been measured at 4.2 K. The origin of the lowest electronic transition is at 18 360 cm−1 and has been assigned to the lowest b-polarized au Davydov component of the 1 1Bu molecular level. The second optically allowed Davydov component (bu) is polarized in the ac crystal plane and is located at 20 945 cm−1. Therefore, the interchain interaction leads to a Davydov splitting of about 2600 cm−1. A quantum chemical model, which considers the total molecular wavefunctions for each transition, shows good agreement with the experimental findings for the energy and polarization of the optically allowed crystal levels. The vibronic manifold in the absorption spectra has been interpreted in terms of the Herzberg–Teller and Franck–Condon vibronic coupling. In particular, two false origins due to the coupling of the molecular electronic levels 1 1Bu and 2 1Bu have been identified at 18 486 and 18 657 cm−1. Consistently, the emission counterpart of the two false orgins has been identified in the polarized fluorescence spectra. The totally symmetric modes involved in the coupling are in excellent agreement with the Raman scattering data of the single crystal.
Assessment of dynamical and nondynamical correlation energy components for the beryllium-atom isoelectronic sequence
Authors: Valderrama E. , Ludeña E. V. , Hinze J.
Published: July 2002

The partitioning of electron correlation energy into dynamical and nondynamical components is examined in the context of the local-scaling transformation version of density-functional theory. An assessment is made of the relative importance of these components for the beryllium atom and its isoelectronic sequence. In particular, the problem of finding a multiconfiguration reference wave function differing only in dynamical correlation from the exact wave function is considered. It is shown that to a good approximation this reference wave function is given by Ψ=C11s22s2+C21s22p2. The concepts of “long-range” and “short-range” correlation are re-examined from a perspective based on the reference wave function.
Modification of the bubble model for positronium atoms in high surface tension liquids
Authors: Mukherjee Tapas , Gangopadhyay Debarshi , Das Subir K. , Ganguly Bichitra N. , Dutta-Roy Binayak
Published: July 2002

The bubble model is widely used for the analysis of the decay characteristics of the positronium atom in liquids. However, according to some authors this description is inappropriate in the case of polar liquids with high surface tension. It has been advocated that for such media, rather than employing the value of the bulk surface tension (which appears as a parameter in the model), one should incorporate the notion of a transition layer between the liquid phase and the cavity that encloses the positronium. Accordingly, the usual bubble model with sharp boundaries is modified in the present work through the introduction of a diffusivity in the bubble surface, thus developing the proper setting (without involving any extra free parameters) such that liquids with high surface tension may also be meaningfully discussed in this context and confronted with experimental data.
Spectroscopy, resolution, and ab initio calculation of vibronic fine structure in the optical absorption of Rh(III) doped in NaCl
Authors: Ribbing Carl , Gilliams Ben , Ceulemans Arnout , Pierloot Kristine , Vandenbroucke Dirk , Roos Björn O.
Published: July 2002

A combined spectroscopic and theoretical investigation is devoted to the vibrational fine structure in the broad band spectrum at 4.2 K of the 1T1g and 1T2g states of Rh(III) d6 doped in NaCl. The vibrational structure is resolved with a noise reduction technique using quadrature mirror filters. A weak signal at 16805 cm−1 is identified as the zero phonon line of the 1T1g←1A1g transition, 194 cm−1 below a false origin of a progression in a single 264 cm−1 mode. The observed spectrum can be reproduced quantitatively by ab initio calculations involving identification of the Jahn-Teller active distortions, derivation of the shapes of excited state potential energy surfaces, and calculation of the Franck–Condon factors. The dominant mode of the progression is identified as a combination of the a1g and eg(a) modes with a calculated frequency of 279 cm−1. The calculations further reveal the existence of a conical intersection between the 1T1g and 1T2g states, situated in the optical window between the two absorption bands and expected to play an important role in the deactivation of the 1T2g state.
Electron spin echo envelope modulation spectroscopy in mixed alkali silicate glasses
Authors: Astrakas Loukas , Kordas George
Published: July 2002

Lithium and sodium silicate glasses of the x mole % Li2O y mole % Na2O (100-x-y) mole % SiO2 composition with x, y between 10–50 were γ-irradiated at room temperature and subsequently studied by electron spin echo envelope modulation (ESEEM) spectroscopy at the X-band and 20 K temperature. Evaluation of the ESEEM spectra revealed weak magnetic coupling between the nonbridging oxygen (NBO) and the neighboring alkali metal. The covalent character between NBO and alkali metal is negligible, though it depends upon the kind weakly. The alkali metal occupies sites forming an angle of 60° with respect to the z-axis of the g-tensor. The magnetic couplings remain unchanged with the variation of the concentration of the alkali or the doping with another alkali.
Diffusive and oscillatory dynamics of liquid iodobenzene measured by femtosecond optical Kerr effect
Authors: Bartolini Paolo , Ricci Marilena , Torre Renato , Righini Roberto , Sánta Imre
Published: July 2002

The dynamics of liquid iodobenzene are studied by means of time resolved heterodyne detected optical Kerr effect in a wide temperature range (263–371 K). In the picosecond regime the relaxation is characterized by a biexponential decay, attributed to the rotational diffusion of an anisotropic rotator. The temperature dependence of the two relaxation times agrees only in part with the prediction of the hydrodynamic theory. The subpicosecond dynamics is essentially oscillatory in nature; the Raman spectra obtained by Fourier transform of the time domain data show the contribution of two intramolecular low-frequency vibrations, and that of the intermolecular dynamics. The intermolecular spectra at different temperatures are interpreted on the basis of the Brownian oscillator model, and consist of the superposition of overdamped and underdamped modes. The intermolecular spectrum of the liquid shows a close resemblance with the low-frequency Raman spectrum of crystalline iodobenzene, and suggests an interpretation in terms of collective dynamics with coupling of librational and translational oscillations. The evolution with temperature of the spectra indicates that at high temperature the time-independent picture of the intermolecular modes is not adequate.
Molecular dynamics simulation of structure formation of short chain molecules
Authors: Fujiwara Susumu , Sato Tetsuya
Published: July 2002

Molecular dynamics simulations are carried out to study the structure formation of 100 short chain molecules, each of which consists of 20 CH2 groups. Our simulations show that the orientationally ordered structure is formed from a random configuration by quenching. The global orientational order starts to increase suddenly after a certain duration and grow in a stepwise fashion afterwards. This behavior is also found in the growth process of the local orientationally-ordered domains. It is found from the microscopic analysis of the structure formation process, that parallel ordering of chain molecules starts to occur after the chain molecules stretch to some extent. From the analysis of the obtained orientationally ordered structure and the molecular mobility, we also find the following characteristic features: (i) The chain molecules are packed hexagonally at 400 K and the transition from the hexagonal phase toward the orthorhombic phase takes place as the temperature decreases. (ii) The gauche bonds in the same chain molecule tend to form gauche pairs. The gauche pairs with the same sign form the double gauche defects and those with the opposite sign form the kink defects. (iii) In the hexagonal phase, the chain molecules become longitudinally mobile. This result, which is obtained by the microscopic analysis of the chain motion, is the microscopic evidence to confirm the existence of the chain sliding diffusion in the hexagonal phase which underlies the sliding diffusion theory of polymer crystallization proposed by Hikosaka [Polymer 28, 1257 (1987); 31, 458 (1990)].
Ultra-small-angle x-ray scattering studies on order-disorder transition in diblock copolymers
Authors: Koga Tadanori , Koga Tsuyoshi , Hashimoto Takeji
Published: July 2002

The phase behavior near the order-disorder transition (ODT) in diblock copolymers was characterized by ultra-small-angle x-ray scattering (USAXS) method for two polystyrene-block-polyisoprene (PS-b-PI) copolymers having about equal block volume fraction f=0.45 (f is the volume fraction of PS) but different molecular weights. By using USAXS method, the peak width and peak intensity were found to change by about 2 orders of magnitude across the ODT temperature for both PS-b-PI. Furthermore, in a narrow temperature region very close to the ODT, it is revealed that the coexistence of the ordered and the disordered phases occurs at thermal equilibrium for both PS-b-PI. The systematic results in the present study clearly show the thermal fluctuation effects on the phase diagram in the low molecular weight diblock copolymer systems.
Interpretation of x-ray emission spectra: NO adsorbed on Ru(001)
Authors: Staufer M. , Birkenheuer U. , Belling T. , Nörtemann F. , Rösch N. , Stichler M. , Keller C. , Wurth W. , Menzel D. , Pettersson L. G. M. , Föhlisch A. , Nilsson A.
Published: July 2002

A density functional investigation of the x-ray emission spectrum of NO adsorbed on Ru(001) has been carried out using model cluster calculations. The dipole matrix elements governing the emission probability were evaluated in the frozen ground-state approximation. The resulting simulated spectra exhibit all characteristic features of the experimental data. A detailed analysis of the electronic structure of the model clusters permits a complete rationalization of all observed trends. Furthermore, a picture of the surface chemical bond results in which the classical Blyholder frontier orbital model is extended to a three-orbital description for both the π and σ interactions. Comparison of different adsorption sites reveals that threefold coordinated NO features a stronger orbital interaction with the substrate than NO adsorbed in an on-top position.
A coupled-cluster study of the mechanism for the CHF+H reaction
Authors: Francisco Joseph S.
Published: July 2002

The reaction of atomic hydrogen with the CHF radical has been examined using coupled-cluster ab initio methods. The heats of formation for both CHF and CH2F radicals have been examined using isodesmic reaction schemes. The best estimate of the heats of formation are 36.5±3 and −4.5±3 kcal mol−1, respectively. For the CHF+H reaction, there are two pathways for the formation of each of the products (CH+HF and CF+H2). The lowest energetic pathway appears to proceed by an association–elimination mechanism, which is consistent with results from experiments. The reaction channels leading to the products (CH+HF and CF+H2) via the CH2F intermediate proceed without a barrier relative to the CHF+H reactants.
An extreme problem revisited: The hyperpolarizability of the open and cyclic forms of ozone
Authors: Maroulis George
Published: July 2002

Single and double excitation coupled-cluster [CCSD(T)] theory including an estimate of connected triple excitations by a perturbational treatment, calculations with a specially optimized [7s5p4d2 f] basis set, consisting of 168 contracted Gaussian-type functions, yield mean values β̄=−14.0 e3a03Eh−2 and γ̄=2642 e4a04Eh−3 for the first and second dipole hyperpolarizability of the open (C2v) form of ozone. Due to the higher predictive capability of the CCSD(T) method and the improved completeness of the basis set, we expect these values to be more accurate than those obtained with the CCD+ST(CCD) method and a smaller [6s4p3d1f] basis set [G. Maroulis, J. Chem. Phys. 101, 4949 (1994)]. The hyperpolarizability of the cyclic (D3h) form of ozone, calculated with a [7s5p4d2 f] basis set optimized for the ring structure, is β=−6.5 e3a03Eh−2 and γ̄=1549 e4a04Eh−3. In both symmetries, electron correlation changes drastically the self-consistent field picture of the hyperpolarizability tensor. Fourth-order Møller–Plesset perturbation theory is seen to predict very reliable values for the hyperpolarizability of the cyclic form. This is in marked contrast to the state of things brought forth by the study of the open form.
On the application of Flory–Huggins and integral equation theories to asymmetric hard sphere mixtures
Authors: Björling Mikael , Pellicane Giuseppe , Caccamo Carlo
Published: July 2002

Flory–Huggins (FH) and integral equation theories (IETs) are used to describe the equation of state and the relevant mixing properties of hard sphere binary mixtures in the limit of high size-asymmetry. The results are compared with those obtained from the heuristic equation of state of Mansoori et al. (BMCSL) [J. Chem. Phys. 54, 1523 (1971)] and with the Flory–Huggins scheme of other authors. By choosing a physical recipe for the volume fractions of the two species in the mixture FH theory is shown to be a good approximation to the entropy and the Gibbs free energy of mixing, which shows improvement at high size-asymmetry. In addition, the results of the IETs are found to be in overall quantitative agreement with BMCSL. The implications of our study concerning colloidal systems are discussed.
An atomistic mechanism for the production of two- and three-dimensional etch hillocks on Si(111) surfaces
Authors: Flidr Jaroslav , Huang Yi-Chiau , Hines Melissa A.
Published: July 2002

The formation of stable and unstable two-dimensional etch hillocks during the NH4F etching of Si(111) surfaces was observed by scanning tunneling microscopy and explained using atomistic, kinetic Monte Carlo simulations. These hillocks are kinetic, self-propagating features on the etching steps. The hillocks have a characteristic shape and size which is governed by the relative rates of site-specific etching. In simulations of highly miscut surfaces, step–step collisions lead to the coalescence and self-organization of 2D (two dimensional) hillocks into 3D (three-dimensional) hillocks. This coalescence was driven by step–step collisions which promote a “step broaching” behavior. As a result, the terrace width distribution of the 3D hillocked surfaces is exponential in form. The formation of 2D and 3D hillocks is controlled by the reactivity of a single minority species on the etching surface. Unlike previous models of hillock formation, chemical heterogeneities, such as contamination or reactant depletion, are not required for hillock formation.
Dielectric spectroscopy of cosurfactant facilitated percolation in reverse microemulsions
Authors: Alexandrov Yuriy , Kozlovich Nick , Feldman Yuri , Texter John
Published: July 2002

Percolation in reverse microemulsion systems can be driven by various field variables, including temperature and cosurfactant concentration. We use dielectric spectroscopy and a macroscopic dipole correlation function (DCF) derived therefrom to examine mesoscale structural aspects of charge transport in a water, AOT, toluene reverse microemulsion that is driven into percolation by cosurfactant (acrylamide). A multiexponential fitting of the DCF data gives firm support to the importance of a parameter marking the onset of percolation, as distinguished from the percolation threshold. A stretched exponential fitting of the DCF data reveals microstructural and mesoscale similarities and differences between this case of cosurfactant-induced percolation and a previously examined case of temperature-induced percolation. This cosurfactant-driven system appears to exhibit a critical slowing down on approach to the percolation threshold, as does the temperature-driven case, but a much shorter relaxation time suggests the development of much less fractal structure in this cosurfactant case. The effective fractal dimensionality and number of self-similarity stages of the fractal structure are only weak functions of the reduced field variable in the case of cosurfactant-driven percolation, and contrast sharply with the temperature case.
Calculation of nuclear spin–spin couplings. X. Analytical derivative method of perturbation energy
Authors: Fukui H. , Baba T. , Kurogi Y.
Published: July 2002

The expression for the analytical derivatives of the second-order correlation energy was derived for a system under the spin-dependent perturbations, and it was applied to the correlated calculation of the 3JHH's in ethane, methanol, and methylamine. The calculation showed that the addition of tight s-type functions to the basis set considerably affects the Fermi contact (FC) contribution. Furthermore, the third- and fourth-order correlations were also evaluated for the FC contribution with the finite perturbation theory. The three noncontact contributions were computed at the Hartree–Fock (HF) level. The total contribution to the 3JHH in ethane was significantly lower than the experimental value. The calculated 3JHH's in methanol and methylamine were nearer to the experimental couplings than in ethane.
The exponential dielectric relaxation dynamics in a secondary alcohol’s supercooled liquid and glassy states
Authors: Kalinovskaya O. E. , Vij J. K.
Published: July 2002

To gain insight into a recent observation that the prominent, Debye-type relaxation process observed for a primary alcohol may not be the α-relaxation process associated with molecular diffusion of a liquid [Europhys. Lett. 40, 549 (1997), J. Chem. Phys. 107, 1086 (1997)], the dielectric spectra of an uncrystallizable secondary alcohol, 5-methyl-2-hexanol, has been investigated by broadband spectroscopy. Measurements made over a temperature range from 110 to 298 K showed that three relaxation processes occur. Processes I and II have a non-Arrhenius variation of the relaxation rate with temperature, and process III an Arrhenius. Only process I, the slowest of the three, has a single relaxation rate, the other two, a broad distribution. The contribution to permittivity from process II was 0.8, i.e., ∼3% of the static permittivity, and from process III, the fastest was 0.1, i.e., ∼0.3%. It is argued that the mechanism of process I is the breaking followed by dipolar reorientation and reforming of the H-bonds in the intermolecularly H-bonded structure, and process II is that of the orientation of the other dipolar groups, such as the -OR group. Process III is the usual Johari–Goldstein process. For 5-methyl-2-hexanol, the mode-coupling and another theory by Souletie and Bertrand [J. Phys. I 1, 1627 (1991)] seem to agree with the relaxation rate of processes I and II, and predict temperatures for 10−4 Hz relaxation rate, within a few degrees of that expected.
Polymer crystallization in quasi-two dimensions. II. Kinetic models and computer simulations
Authors: Sommer Jens-Uwe , Reiter Günter
Published: July 2002

A novel simulation model for crystallization of polymer mono-layers is presented and compared with experiments on short PEO chains. We assume that crystallized chains can exist in states of different degrees of order. The resulting morphologies are nonequilibrium intermediate structures which can further relax on increasingly long time scales. The parameters of the model are the maximum stretching length of the chains M, the energy of the crystal–crystal interaction in terms of the Metropolis rate p0 and the barrier for increasing the degree of chain order pS. Since flatly adsorbed chains in a mono-layer must be oriented upright in order to crystallize, diffusion controlled growth patterns emerge which change their morphology depending on the model parameters. Different morphologies can be used to compare the model phase diagram with experiments. For large values of M, the interplay of the ordering barrier pS and the unbinding barrier p0 controls the growth morphologies as well as internal structures such as the average stem length L. We find the variation of L with temperature in agreement with empirical relations proposed from experimental observations. When the free chains of the reservoir are exhausted, the edges of the crystal start to relax into energetically favored states which stabilize the growth patterns at long time scales. Such patterns are frequently observed in experiments. For high barrier factors the chains are poorly ordered and relax into a pronounced hole-rim morphology as observed experimentally at low temperatures. At higher temperatures secondary relaxation processes result in a destruction of the growth morphology into dropletlike structures having a higher degree of internal chain order.
Polarizabilities of azabenzenes
Authors: Calaminici Patrizia , Jug Karl , Köster Andreas M. , Ingamells Victoria E. , Papadopoulos Manthos G.
Published: July 2002

This paper presents static polarizabilities, polarizability anisotropies, second hyperpolarizabilities, and an analysis of the vibrational effects for these polarizabilities of azabenzenes calculated in the framework of density functional theory. All molecular geometries were fully optimized. The calculations of the polarizabilities and second hyperpolarizabilities have been performed using a finite field approach implemented in the density functional program ALLCHEM. The calculations were of all-electron type using a local exchange-correlation functional. The calculated polarizabilities are in excellent quantitative agreement with available experimental data. The effect of the replacement of CH groups by N atoms is discussed.
Electrophoresis of concentrated spherical particles with a charge-regulated surface
Authors: Hsu Jyh-Ping , Lee Eric , Yen Fong-Yuh
Published: July 2002

The electrophoretic behavior of spherical colloidal particles is modeled theoretically. The classic analysis is extended to the case of a concentrated dispersion in which the double layer surrounding a particle can assume an arbitrary thickness, and the effect of double-layer polarization is taken into account. Also, the surface of a particle is charge regulated, which leads to a general mixed-type boundary condition, and simulates entities bearing dissociable functional groups such as biological cells and particles with a membrane layer. We show that the absolute surface potential decreases with the increase in κa, κ and a are, respectively, the reciprocal Debye length and the radius of a particle. The variation of the absolute electrophoretic mobility as a function of κa is found to have a local maximum. The higher the surface potential the more significant the effect of double-layer polarization, and it becomes insignificant if κa approaches infinity.
Differential geometric aspects of the Cartan form: Symmetry theory
Authors: Betounes David
Published: July 2002

This paper demonstrates that the classical Cartan form θ1L is not adequate for the determination of all the natural symmetries and conservation laws for a Lagrangian L. It is shown that the various extensions θ2L,..., θrL of the classical Cartan form, introduced in recent papers, give larger symmetry groups: G1⊆G2⊆⋅⋅⋅⊆Gr. This paper also introduces the notion of contact equivalent Lagrangians, which serves to clarify the idea that different Lagrangians can give rise to the same variational and symmetry theories.
Phase space localization theorem for ondelettes
Authors: Battle Guy
Published: July 2002

It is proven that an orthonormal basis of ondelettes can never have exponential localization in both position space and momentum space.
Derivation of the real form of Schrödinger’s equation for a nonconservative system and the unique relation between Re(ψ) and Im(ψ)
Authors: Chen Robert L. W.
Published: July 2002

A unique relationship between the real part and the imaginary part of a wave function that obeys the time-dependent Schrödinger equation is derived. Thence the real form of the Schrödinger equation for the case of a nonconservative time-dependent potential V=V(x,t) is obtained. Earlier work on this subject is found to be inadequate, applicable only to the conservative system. The results obtained here were first sought by Schrödinger but can be used in ways other than his original intention and purposes. Some unresolved issues relating to the nature of the dependency of Im(ψ) and Re(ψ) are also discussed.
Classical scattering of a charged particle on an extended magnetic monopole
Authors: Bowlin James B. , Goldhaber Alfred S.
Published: July 2002

The classical equations of motion for a charged particle scattering on an extended magnetic monopole are found in a model that includes the possibility of charge exchange between the particle and the pole. The special case of a spherical shell of monopole density is examined in detail. Deviations from point monopole scattering are analyzed.
The Yang–Baxter equations and differential identities
Authors: Pu Fu-Cho , Sattinger D. H.
Published: July 2002

The solution of the Yang–Baxter equation for integrable systems is shown to be equivalent to the existence of a differential identity. Quantum integration formulas for the calculation of commutators of monodromy matrices are given. Based on the integration formulas and the systematic use of differential identities, the Yang–Baxter equations for the nonlinear Schrödinger model for the quantum case of both bosons and fermions are derived. The case for discrete models is also included. The parallelism between the classical and quantum case and the classical limiting process from the latter to the former are discussed.
On Chandrasekhar’s perturbation analysis. I. The superfluity of the N.P. system
Authors: Edgar S. B.
Published: July 2002

Chandrasekhar has developed a method of analyzing first-order perturbations about some known metrics using the N.P. system of equations. In this paper it is shown that some of the intriguing aspects that have been noted in his method—the superfluity of the N.P. system, and the existence of very complicated integral identities—are not peculiar to this particular type of perturbation analysis; rather the underlying principles are fundamental properties associated with the differential structure of the N.P. system. Specifically the three different subsystems used in the three space-times where Chandrasekhar’s method has been applied, are confirmed directly as sufficient subsystems for extracting all information from the complete N.P. system, for the respective situations in which they have been used.
A Marderlike solution in higher dimensions
Authors: Krori K. D. , Borgohain P. , Das Kanika
Published: July 2002

A vacuum solution in higher dimensions that corresponds to the exterior Marder solution in four-dimensional general relativity is presented.
Applications of the new scattering formalism: The Dirichlet boundary condition
Authors: Dashen Roger , Wurmser Daniel
Published: July 2002

This is the third in a series of articles concerning the theory of scattering from a rough surface. Consideration of the scattering problem for a scalar wave obeying Dirichlet boundary conditions enables one to investigate the formalism developed in the previous work. The advantages of this new representation of the scattering amplitude is discussed. This result is supplemented with an improved integral equation for the desired solutions on the surface. This new equation not only allows one to reproduce the approximations for the scattering amplitude obtained previously, but it can also be used to extend those results to higher orders. This is illustrated with a derivation of the second-Born approximation. The correction to the scattering amplitude due to a distribution of point scatters is also obtained. To the order under consideration, this phenomenon is shown to be equivalent to a perturbation of the surface. A similar result is found when the index of refraction is allowed to vary near the scattering surface.
Algebraic treatment of a general noncentral potential
Authors: Chetouani L. , Guechi L. , Hammann T. F.
Published: July 2002

It is shown that the problem of a particle moving in a noncentral potential generalizing the Coulomb potential and the Hartmann ring-shaped potential accepts SO(2,1)⊗SO(2,1) as a dynamical group, within the framework of the Kustaanheimo–Stiefel transformation. The Green’s function relative to this compound potential is calculated through the algebraic approach so(2,1) and with the help of the Baker–Campbell–Hausdorff formulas. The energy spectrum and the normalized wave functions of the bound states can then be deduced. Eventually, the Coulomb potential, the Hartmann ring-shaped potential and also, due to its close link with the latter, the compound Coulomb plus Aharonov–Bohm potential may all be considered as particular cases.
Parastatistics as Lie-supertriple systems
Authors: Okubo Susumu
Published: July 2002

Parastatistics are reformulated herein in terms of Lie-supertriple systems. In this way, various new kinds of parastatistics discovered recently by Palev in addition to the standard one are reproduced. Also, bosonic and fermionic operators may not necessarily commute with each other.
Functional integration and the theory of knots
Authors: Kauffman Louis H.
Published: July 2002

This paper examines the role of functional integration in the theory of knots and links. It is shown how it is possible to find many properties and conjectures about link invariants via this point of view and how these considerations lead to ideas about the mathematical status of such forms of integration.
Quasi-exactly solvable systems and orthogonal polynomials
Authors: Bender Carl M. , Dunne Gerald V.
Published: July 2002

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials {Pn}. The quantum-mechanical wave function is the generating function for the Pn(E), which are polynomials in the energy E. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index n exceeds a critical value J. The zeros of the critical polynomial PJ(E) are the quasi-exact energy eigenvalues of the system.
A relation between the Kauffman and the HOMFLY polynomials for torus knots
Authors: Labastida J. M. F. , Pérez E.
Published: July 2002

Polynomial invariants corresponding to the fundamental representation of the gauge group SO(N) are computed for arbitrary torus knots in the framework of Chern–Simons gauge theory making use of knot operators. As a result, a formula that relates the Kauffman and the HOMFLY polynomials for torus knots is presented.
Gravitational energy of rotating black holes
Authors: Maluf J. W. , Martins E. F. , Kneip A.
Published: July 2002

In the teleparallel equivalent of general relativity the energy density of asymptotically flat gravitational fields can be naturally defined as a scalar density restricted to a three-dimensional spacelike hypersurface Σ. Integration over the whole Σ yields the standard ADM energy. Here we obtain the formal expression of the localized energy for a Kerr black hole. The expression of the energy inside a surface of constant radius can be explicitly calculated in the limit of small a, the specific angular momentum. Such expression turns out to be exactly the same as the one obtained by means of the method proposed recently by Brown and York [Phys. Rev. D 47, 1407 (1993)]. We also calculate the energy contained within the outer horizon of the black hole, for any value of a. The result is practically indistinguishable from E=2Mir, where Mir is the irreducible mass of the black hole.
Massless fields in plane wave geometry
Authors: Metsaev R. R.
Published: July 2002

Conformal isometry algebras of plane wave geometry are studied. Then, based on the requirement of conformal invariance, a definition of masslessness is introduced and gauge invariant equations of motion, subsidiary conditions, and corresponding gauge transformations for all plane wave geometry massless spin fields are constructed. Light cone representation for elements of conformal algebra acting as differential operators on wavefunctions of massless higher spin fields is also evaluated. Interrelation of plane wave geometry massless higher spin fields with ladder representation of u(2,2) algebra is investigated.
Elliptic fibrations associated with the Einstein space–times
Authors: Nurowski Paweł
Published: July 2002

Given a conformally nonflat Einstein space–time we define a fibration P̃ over it. The fibers of this fibration are elliptic curves (two-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the Weyl tensor of the Einstein metric. The fibration P̃ is a double branched cover of the bundle 𝒫 of null direction over the space–time and is equipped with six linearly independent one-forms which satisfy a certain relatively simple system of equations.
Perturbations in inflationary cosmologies with smooth exit
Authors: Tilley Daniel , Maartens Roy
Published: July 2002

We give a comprehensive analysis of how scalar and tensor perturbations evolve in cosmologies with a smooth transition from power-law-like and de Sitter-like inflation to a radiation era. Analytic forms for the superhorizon and subhorizon perturbations in the inflationary and radiation dominated eras are found.
Quantum coordinates of an event in local quantum physics
Authors: Giannitrapani R.
Published: July 2002

Recently Toller [quant-ph/9702060 (1997)] has proposed, using the formalism of positive-operator-valued measures, a possible definition of quantum coordinates for events in the context of quantum mechanics. In this short note we analyze this definition from the point of view of local algebras in the framework of local quantum theories.
Vertex operator representation of the soliton tau functions in the An(1) Toda models by dressing transformations
Authors: Belich H. , Cuba G. , Paunov R.
Published: July 2002

We study the relation between the group-algebraic approach and the dressing symmetry one to the soliton solutions of the An(1) Toda field theory in 1+1 dimensions. Originally, solitons in the affine Toda models were found by Olive, Turok, and Underwood. Single solitons are created by exponentials of elements which ad-diagonalize the principal Heisenberg subalgebra. Alternatively, Babelon and Bernard exploited the dressing symmetry to reproduce the known expressions for the fundamental tau functions in the sine-Gordon model. In this paper we show the equivalence between these two methods to construct solitons in the An(1) Toda models.
Slater sum for central field problems characterized by its s-wave component alone
Authors: March N. H. , Nieto L. M. , Amovilli C. , Balbás L. C. , Glasser M. L.
Published: July 2002

For the hydrogenlike atom, with central potential −Z/r, partial differential equations exist for the Slater sum Z(r,β) [β=(kBT)−1] and for its s-wave (l=0) component Z0(r,β). It is shown that Z can be eliminated, to lead to a result in which Z(r,β) is solely characterized by Z0(r,β). A similar situation is exhibited for the three-dimensional isotropic harmonic oscillator, for which closed forms of both Z(r,β,ω) and Z0(r,β,ω) can be obtained explicitly. Finally, a third central field problem is considered in which independent electrons are confined within a sphere of radius R, but are otherwise free. We are able to derive explicitly for this model the s-wave component Z0(r,β,R). The full Slater sum Z(r,β,R) then is also analyzed in some detail.
An exact solution for several charges in classical electrodynamics
Authors: Rivera R. , Villarroel D.
Published: July 2002

An exact solution for an arbitrary number of identical charges that are equally spaced along a circumference and that rotate at constant angular velocity is presented. The solution is valid for any velocity of the charges less than the speed of light and considers the radiation reaction effects as well as the retarded interaction between the charges. The external field that allows this motion consists of a time-independent electric field tangent to the charges’ orbit and a homogeneous time-independent magnetic field that points orthogonally to the orbit plane. A detailed analytical study of the total power of radiation associated with this system of charges is carried out, and it is shown that it is in perfect agreement with the energy that the external electric field supplies to the charges. In particular, in the limit when N goes to infinity only static fields remain.
Random walk with memory
Authors: Rudnicki Ryszard , Wolf Marek
Published: July 2002

A reinforced random walk on the d-dimensional lattice is considered. It is shown that this walk is equivalent to an iterated function system (IFS). Criteria for the existence of limit cycles are given. Numerical results and conjectures about the quantitative behavior of the walk are stated.
Nonlinear superposition formulas based on imprimitive group action
Authors: Havlı́ček M. , Pošta S. , Winternitz P.
Published: July 2002

Systems of nonlinear ordinary differential equations are constructed for which the general solution is expressed algebraically in terms of a finite number of particular solutions. The equations and the corresponding nonlinear superposition formula are based on a nonlinear action of the Lie group SL(N,C) on a homogeneous space M. The isotropy group of the origin of this space is a nonmaximal parabolic subgroup of SL(N,C). Such equations can occur as Bäcklund transformations for soliton equations on flag manifolds.
Unitary representations of the quantum algebra suq(2) on a real two-dimensional sphere for q∈R+ or generic q∈S1
Authors: Irac-Astaud M. , Quesne C.
Published: July 2002

Some time ago, Rideau and Winternitz introduced a realization of the quantum algebra suq(2) on a real two-dimensional sphere, or a real plane, and constructed a basis for its representations in terms of q-special functions, which can be expressed in terms of q-Vilenkin functions, and are related to little q-Jacobi functions, q-spherical functions, and q-Legendre polynomials. In their study, the values of q were implicitly restricted to q∈R+. In the present paper, we extend their work to the case of generic values of q∈S1 (i.e., q values different from a root of unity). In addition, we unitarize the representations for both types of q values, q∈R+ and generic q∈S1, by determining some appropriate scalar products. From the latter, we deduce the orthonormality relations satisfied by the q-Vilenkin functions.
Propagation of short nonlinear second-sound pulses through He-II in one- and three-dimensional geometry
Authors: Efimov V. B. , Kolmakov G. V. , Kuliev A. S. , Mezhov-Deglin L. P.
Published: July 2002

The results of an experimental study of the evolution of the shape of nonlinear second-sound pulses in superfluid He-II are reported. The pulses propagate in the bulk (3D geometry) and along a cryoacoustic waveguide filled with liquid helium (quasi-1D geometry) at temperatures corresponding to the negative, positive, or zero nonlinearity coefficient. A strong dependence of the shape of the propagating pulse on the dimensionality of the wave was observed. The finite size of the heater (generator of a sound) affects the profile of a short 3D pulse even at distances many times greater than the heater size, which restricts the minimal width of the excited pulse. The experimental data are compared with the results of numerical simulations.