bluuebunny/crossref_metadata_2025 huggingface dataset:
Conformations and dynamics of dendrimers and cascade macromolecules
Authors: La Ferla Roberto
Published: July 2002

The Rouse–Zimm discrete hydrodynamic model is extended to acyclic macromolecules of any topology, and particular attention is devoted to starlike dendrimers and other symmetric cascade structures. As a first approximation, freely rotating models are built for branched structures by means of appropriate choices of topology-dependent stiffness parameters. Relevant dynamic observables (depending on the spectrum of viscoelastic relaxation rates) are studied as functions of local stiffness, of branching topology, and of dendrimer generational growth. The present results show that a moderate increase of local stiffness accounts for the molecular dimensions of dendrimers as previously calculated by Mansfield and Klushin [J. Phys. Chem. 96, 3994 (1992)] by Monte Carlo methods, and reproduces with good precision their results for the intrinsic viscosity (upper-bound calculations). Thus omission of excluded-volume interactions within the present models can be at least partially compensated for by suitable choices of local stiffness parameters, provided that the chain portions between branching points are not very long. In addition, the inaccuracy caused by preaveraging of hydrodynamic interactions (as estimated by computing exact and preaveraged first cumulant of the structure factor) does not seem to obscure the essential conclusions.
Splitting a chemical bond with a molecular wedge via cluster-surface collisions
Authors: Yasumatsu Hisato , Terasaki Akira , Kondow Tamotsu
Published: July 2002

A cluster anion, I2−(CO2)n (n=0−30), was allowed to collide onto a silicon surface at collision energies (per I2−) of 1−80 eV in an ultrahigh vacuum surface-collision chamber equipped with a tandem time-of-flight (TOF) mass spectrometer. The product anions show that the core ion, I2−, dissociates by the collision of I2−(CO2)n on the silicon surface. The branching fraction for the I2− dissociation (fdis) was determined as functions of the collision energy and the number of the CO2 molecules, n. The marked n-dependence of fdis at a collision energy (per I2−) higher than 30 eV was explained in terms of a wedge effect in which a CO2 molecule in the vicinity of the mid point of the I2− bond splits the I2− bond as if a piece of wood is split by a hammer thrust against a wedge vs a cage effect, in which the I2− dissociation is suppressed by geminate recombination between the dissociating I and I− pair in a complete solvation shell. The wedge and cage effects in the I2− dissociation were also verified by use of the calculation based on a molecular dynamics simulation.
Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations
Authors: Millam John M. , Scuseria Gustavo E.
Published: July 2002

Advances in the computation of the Coulomb, exchange, and correlation contributions to Gaussian-based Hartree–Fock and density functional theory Hamiltonians have demonstrated near-linear scaling with molecular size for these steps. These advances leave the O(N3) diagonalization bottleneck as the rate determining step for very large systems. In this work, a conjugate gradient density matrix search (CG-DMS) method has been successfully extended and computationally implemented for use with first principles calculations. A Cholesky decomposition of the overlap matrix and its inverse is used to transform to and back from an orthonormal basis, which can be formed in near-linear time for sparse systems. Linear scaling of CPU time for the density matrix search and crossover of CPU time with diagonalization is demonstrated for polyglycine chains containing up to 493 atoms and water clusters up to 900 atoms.
Dynamics of polyelectrolyte solutions
Authors: Muthukumar M.
Published: July 2002

We have derived a theory of dynamics of dilute and semidilute polyelectrolyte solutions by explicitly considering triple screening associated with electrostatic, excluded volume, and hydrodynamic interactions. The three screening lengths corresponding to these interactions are coupled among themselves differently at different polyelectrolyte (c) and salt (cs) concentrations. We have derived expressions for the self-translational diffusion coefficient D, electrophoretic mobility μ, coupled diffusion coefficient Df, and the viscosity η of the solution by accounting for the coupling between electrostatics and hydrodynamics. In infinitely dilute solutions, we show that Zimm dynamics is applicable and D∼1/Rg, μ∼M0, and η−η0∼cRg3/M for all values of cs, where Rg and M, respectively, are the radius of gyration and molecular weight of the polyelectrolyte and η0 is the solvent viscosity. Df is derived to be M0 at low cs and to approach D at higher cs. As the polyelectrolyte concentration is increased to semidilute conditions, excluded volume and hydrodynamic interactions get progressively screened. In the Rouse regime, where hydrodynamic interaction is screened and entanglement effects are weak, we have derived expressions for the various transport coefficients. In this regime, at low cs, D∼c0M−1, Df∼c0M0, μ∼c0M0, and η−η0∼cM; at high cs, D∼c−1/2M−1, Df∼c/(c+2cs), μ∼c−1/2M0, and η−η0∼c5/4M. The crossover formulas between these asymptotic laws with numerical prefactors are derived. We have demonstrated that the Rouse law applicable to semidilute unentangled polyelectrolyte solutions at low cs is the empirical Fuoss law. The slow diffusion coefficient observed in light scattering studies of polyelectrolyte solutions is attributed to the emergence of an effective attractive interaction between similarly charged segments of topologically correlated objects such as polyelectrolytes at sufficiently high c and low cs. The consequences of entanglements at very high polyelectrolyte concentrations are briefly mentioned. The theoretical formulas derived here are in qualitative agreement with all known phenomenological results of polyelectrolyte dynamics, and some fresh predictions are made.
ESR of the BH4 molecule in solid hydrogen
Authors: Van Zee R. J. , Williams A. P. , Weltner W.
Published: July 2002

BH 4 , with isotopic substitution, has been prepared and trapped in solid H2, D2, HD by laser vaporization of boron and subsequent reaction with the matrix gas. The results confirm the C2v structure of the molecule and generally support the results of Symons et al., on γ-irradiated NaBH4. Differences from those results are discussed, and comparison is made with the CH4+ parameters of Knight et al.
Intramolecular energy transfer in highly vibrationally excited methanol. I. Ultrafast dynamics
Authors: Boyarkin O. V. , Lubich L. , Settle R. D. F. , Perry D. S. , Rizzo T. R.
Published: July 2002

Vibrational overtone excitation of jet-cooled methanol, in combination with infrared laser assisted photofragment spectroscopy (IRLAPS) detection, reveals OH stretch bands that are significantly simplified with respect to room-temperature spectra. The simplification afforded by jet-cooling permits the observation of spectral splitting on the order of 50 cm−1 in the region of the 5ν1 OH stretch overtone band. Tracking this splitting as a function of OH stretch vibrational level in combination with isotopic substitution studies allows us to identify the perturbing state as the combination level involving four quanta of OH stretch and one quantum of CH asymmetric stretch, 4ν1+ν2. Careful examination of the spectra reveals that this strong interaction arises from a fourth-order anharmonic term in the Hamiltonian that couples the OH and CH ends of the molecule. These frequency domain results indicate that subsequent to coherent excitation of the 5ν1 band, methanol would undergo energy redistribution to the methyl part of the molecule on a time scale of ∼130 fs. This work also suggests that similar strong resonances may occur more generally in molecules that possess two different high-frequency oscillators in close proximity.
Charge inversion in electric double layers and effects of different sizes for counterions and coions
Authors: Greberg Hans , Kjellander Roland
Published: July 2002

The molecular mechanisms behind the phenomena of charge inversion in the diffuse electric double layer (i.e., inversion of sign in the charge distribution profile) and attractive double-layer interactions between equally charged surfaces have been investigated with statistical mechanical methods. In aqueous systems with monovalent electrolytes these phenomena can, for example, be induced by having larger coions than counterions, while for divalent electrolytes they occur primarily for electrostatic reasons. We have identified several different mechanisms for the charge inversion. In one of the mechanisms, which only occurs at low surface charge density, the different distances of closest approach to the surface for the ions are crucial, while in some other mechanisms active in the monovalent systems the different size in the ion–ion interaction is the important factor. For divalent electrolytes the electrostatic part of the ion–ion correlations is the dominating effect and ion sizes are not as important, while in the monovalent case core–core collisions between the ions play a very important role.
Single-root multireference Brillouin-Wigner coupled-cluster theory: Applicability to the F2 molecule
Authors: Mášik Jozef , Hubač Ivan , Mach Pavel
Published: July 2002

Recently developed single-root multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory, which deals with one state at a time while employing a multiconfigurational reference wave function, is applied to the ground state of the F2 molecule using a two-determinant reference space at the level of the CCSD approximation. The method represents a brand-new coupled-cluster (CC) approach to quasidegenerate problems which combines merits of two theories: the single-reference CC method in a nondegenerate case and the Hilbert space MR CC method in quasidegenerate case. The method is able to switch itself from a nondegenerate to a fully degenerate case in a continuous manner, providing thus smooth potential energy surfaces. Moreover, in contrast to the Hilbert space MR CC approaches, it does not contain the so-called coupling terms and completely reduces to the standard single-reference CC method in a highly nondegenerate region. Using a [4s,3p,1d] and [4s,3p,2d,1f ] basis sets, the calculated potential energy curves are smooth, dissociate correctly and the results are compared with other available multireference techniques as well as experiment.
Exciton-migration and three-pulse femtosecond optical spectroscopies of photosynthetic antenna complexes
Authors: Zhang Wei Min , Meier Torsten , Chernyak Vladimir , Mukamel Shaul
Published: July 2002

A theory for four-wave-mixing signals from molecular aggregates, which includes effects of two-exciton states, static disorder, and coupling to a phonon bath with an arbitrary spectral density, is developed. The third-order polarization is rigorously partitioned into a coherent and a sequential contribution. The latter is given by a sum of an exciton-hopping and a ground state (bleaching) terms, both expressed using the doorway-window representation. Applications are made to photon-echo and pump-probe spectroscopies of the B850 system of the LH2 antenna in purple bacteria.
An efficient way to include connected quadruple contributions into the coupled cluster method
Authors: Kucharski Stanisl/aw A. , Bartlett Rodney J.
Published: July 2002

The general inclusion of the T4 operator into the coupled cluster equations requires an n10 computational procedure, and even n9 in the lowest order, as in the CCSDTQ-1 (coupled cluster singles, doubles, triples and lowest-order quadruples) method. That level of n-dependence makes it difficult to apply the method to larger systems. In this paper we circumvent this difficulty by a factorization approximation that requires only an n7 procedure, but that provides results nearly identical to those obtained with the CCSDTQ-1 method. This observation offers a practical and accurate method to go beyond the CCSDT (coupled cluster singles, doubles and triples) approach. We also consider noniterative CCSDT(Qf) (coupled cluster singles, doubles, triples and noniterative quadruples) and CCSD(TQf) (coupled cluster singles and doubles with noniterative triples and quadruples) methods.
The chemical bonding and electronic structure of RhC, RhN, and RhO by anion photoelectron spectroscopy
Authors: Li Xi , Wang Lai-Sheng
Published: July 2002

The electronic structure and chemical bonding of RhC, RhN, and RhO were experimentally investigated using anion photoelectron spectroscopy. Vibrationally resolved photoelectron spectra of RhC−, RhN−, and RhO− were obtained at two detachment photon energies, 532 (2.33 eV) and 355 nm (3.49 eV). Electron affinities, low-lying electronic states, and vibrational frequencies are reported for the neutral diatomic molecules. The adiabatic electron affinities are similar for the three molecules and increase slightly from RhC to RhO (RhC: 1.46; RhN: 1.51; RhO: 1.58 eV). The low-lying electronic states are rather simple for RhC, with its first electronic excited state occurring at 9400 cm−1 above the ground state, whereas those of RhN and RhO are more complicated, with numerous closely spaced low-lying electronic states. Excited states of the anions were also observed for RhC− and RhN−. The trend of the chemical bonding from RhC to RhO is discussed based on the experimental results.
Relation between some secondary relaxations and the α relaxations in glass-forming materials according to the coupling model
Authors: Ngai K. L.
Published: July 2002

Some secondary or β relaxations in glass-forming materials involve molecular motions that bear strong resemblance to the primitive α relaxations of the coupling model, although the two are not identical. For these β relaxations, at the glass transition temperature Tg the relaxation time τβ(Tg) is expected to be shorter than but not too different in order of magnitude from τ0(Tg), the primitive α-relaxation time at Tg. The latter can be calculated by the coupling model from the relaxation time τα(Tg), the exponent (1−n) of the Kohlrausch–Williams–Watts (KWW) correlation function exp[−(t/τα)1−n], and the experimental crossover time, tc≈2 ps, of the α relaxation. From experimental data of β and α relaxations in a variety of glass-forming materials, it is found that τβ(Tg) and τ0(Tg) are close to each other in order of magnitude as anticipated. The results indicate these β relaxations indeed bear some close relation to the corresponding primitive α relaxation, although they are not the same process. Since the relaxation times of the majority of these β relaxations have the Arrhenius temperature dependence, τβ(T)=τβ∞ exp(Eβ/RT), where τβ∞ is of the order of 10−13–10−16 s, knowing, approximately, the value of τβ(T) at one temperature Tg means the location of the β relaxation in the relaxation map can be roughly determined from the α relaxation. The findings can be restated as the empirical result: there exists a strong correlation between the value of log[τβ(Tg)] and the KWW exponent (1−n) of the α relaxation in many glass-formers. A smaller KWW exponent of the α relaxation corresponds to shorter τβ(Tg) or smaller log[τβ(Tg)]. This remarkable cross correlation between the α relaxation and the β relaxation should be of interest for any model or theory of molecular dynamics of glass formers.
Instability and dewetting of evaporating thin water films on partially and completely wettable substrates
Authors: Padmakar A. S. , Kargupta Kajari , Sharma Ashutosh
Published: July 2002

Stability, dynamics and dewetting of thin (<100 nm) evaporating water films on partially and completely wettable substrates are studied based on numerical solutions of the nonlinear thin film equation, as well as by simplified semianalytical approaches. The instability and rupture of aqueous films are engendered by the hydrophobic attraction, whereas the net van der Waals force is repulsive for aqueous films on most substrates. An evaporating aqueous film on a partially wettable surface thins uniformly to a critical thickness, and then spontaneously dewets the substrate by the formation of growing holes. Complete nonlinear simulations as well as the linear analyses are used to predict the most important, experimentally accessible characteristics of the instability such as the length scale and time scale of the instability and the mean film thickness at the instant of rupture. Curiously, in contrast to nonthinning films, the number density of holes decreases slightly with increased strength and range of hydrophobic attraction, and also with decreased strength of LW repulsion, even though both of these factors promote the macroscopic nonwettability. The rate of evaporation has the most significant influence on the length scale, λ∝Eq, where the exponent, q lies in a narrow range from −0.17 to about −0.26, depending on the rate of evaporation and the critical thickness. Thin aqueous films on completely wettable (free energy per unit area is positive) surfaces are also unstable when the free energy does not decrease monotonically with the film thickness. Simulations show that instability in such cases leads to the formation of quasiequilibrium microscopic “islands” or “pancakes” made up of largely flat thin and thick films.
A study of the molecular motion in glucose/water mixtures using deuterium nuclear magnetic resonance
Authors: Moran G. R. , Jeffrey K. R.
Published: July 2002

Using separate samples containing deuterated glucose and D2O, the motions of the glucose and the water molecules in the viscous liquid and in the amorphous glass phase of glucose/water mixtures are examined. Spin-lattice relaxation measurements and spectra obtained in the solid confirm the existence of both a crystalline ice phase and an amorphous glass phase. Diffusion measurements performed using the large gradient in the fringe field of a superconducting magnet determine the rates of translational motion of both the sugar and the water molecules over a limited range of temperature in the viscous liquid region. From the deuterium nuclear magnetic resonance spin-lattice relaxation time, T1, the spin-spin relaxation time, T2, and spin-alignment measurements, correlation times for the motion of these molecules are obtained. The correlation time for the α process increases dramatically at Tg, while the β process continues into the low temperature glass phase, following an approximately Arrhenius relationship.
The near infrared, visible, and near ultraviolet overtone spectrum of water
Authors: Carleer M. , Jenouvrier A. , Vandaele A.-C. , Bernath P. F. , Mérienne M. F. , Colin R. , Zobov N. F. , Polyansky Oleg L. , Tennyson Jonathan , Savin V. A.
Published: July 2002

New long path length, high resolution, Fourier transform spectrometer measurements for water are presented. These spectra cover the near infrared, visible, and near ultraviolet regions and contain water transitions belonging to all polyads from 3ν to 8ν. Transitions in the range 13 100–21 400 cm−1 are analyzed using line lists computed using variational first-principles calculations. 2286 new transitions are assigned to H216O. These result in the observation of transitions in 15 new overtone and combination bands of water. Energy levels for these and other newly observed levels are presented. It is suggested that local mode rather than normal mode vibrational assignments are more appropriate for the vibrational states of water in polyads 4ν and above.
The effect of carrier gas pressure on vapor phase nucleation experiments using a thermal diffusion cloud chamber
Authors: Kane D. , Fisenko S. P. , Rusyniak M. , El-Shall M. S.
Published: July 2002

Recent measurements of critical supersaturations for the vapor phase homogeneous nucleation of several substances using a diffusion cloud chamber technique exhibit a dependence on the pressure of the carrier gas used in the experiments. A model of droplet growth and motion in a diffusion cloud chamber, combined with the density and temperature profiles of the chamber is presented to explain the pressure dependent results. The model demonstrates that at higher carrier gas pressures the growth of the droplets is retarded and the optical scattering signal from the particles is reduced. It is concluded that the observed effect may not result from a pressure dependence of the nucleation rate, but from a pressure dependence of the droplet growth and motion.
Melt layer solidification of fatty acids in a rectangular cell
Authors: Fukui Keisuke , Maeda Kouji
Published: July 2002

Experiments have been performed on the impurity incorporation in the solid layer grown from a binary melt of myristic acid and palmitic acid using a rectangular cell with well-controlled temperature. The binary melt forms a simple eutectic phase diagram. Direct numerical simulations of melt solidification were carried out in order to validate the new theory of interfacial solute distribution proposed by the present authors [J. Chem. Phys. 109, 7468 (1998)]. The theoretical predictions of purity or impurity concentration profile in the solid layer agreed well with the experimental measurements. The purity profile inside the solid layer was found to be basically controlled by the flow structure of melt that essentially contributed to the transport phenomena of heat and mass near the solid layer surface.
Hydrogen adsorption and desorption on silicon revisited
Authors: Hilf M. F. , Brenig W.
Published: July 2002

Recent molecular beam data on the energy dependence of sticking coefficients for dissociative adsorption of hydrogen molecules on silicon are analyzed in terms of the five dimensional (5D) quantum reaction dynamics used before to describe data on sticking as a function of surface temperature and on state resolved desorption. The sticking coefficient of the 5D model depended strongly on the energy of surface phonons but weakly on the kinetic energy of the incoming H2 molecules. In a recent molecular beam experiment the latter dependence was measured directly and found to be substantially stronger than concluded from the earlier data. These results have important consequences for the energy and angular distribution of desorbing particles: If the parameters of the 5D model are adjusted so as to describe the new data, it predicts a mean normal kinetic energy of desorbing particles which is now about twice the thermal value. This prediction is rather model independent and can be derived almost directly from the measured data by invoking “detailed balance.” This new increased normal mean energy then is closer to ab initio generalized gradient approximation (GGA) slab calculations predicting about three times the thermal value. The increased kinetic energy also leads to a more forward-peaked angular distribution ∝(cos θ)11 to 12 instead of ∝(cos θ)3 to 4.
Convergent summation of Møller–Plesset perturbation theory
Authors: Goodson David Z.
Published: July 2002

Rational and algebraic Padé approximants are applied to Møller–Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full configuration–interaction result even when partial summation diverges. At order MP2 (the first order beyond the Hartree–Fock approximation), the best results are obtained from the rational [0/1] Padé approximant of the total energy. At MP3 rational and quadratic approximants are about equally good, and better than partial summation. At MP4, MP5, and MP6, quadratic approximants appear to be the most dependable method. The success of the quadratic approximants is attributed to their ability to model the singularity structure in the complex plane of the perturbation parameter. Two classes of systems are distinguished according to whether the dominant singularity is in the positive half plane (class A) or the negative half plane (class B). A new kind of quadratic approximant, with a constraint on one of its constituent polynomials, gives better results than conventional approximants for class B systems at MP4, MP5, and MP6. For CH3 with the C–H distance at twice the equilibrium value the quadratic approximants yield a complex value for the ground-state electronic energy. This is interpreted as a resonance eigenvalue embedded in the ionization continuum.
CASCCD: Coupled-cluster method with double excitations and the CAS reference
Authors: Ivanov Vladimir V. , Adamowicz Ludwik
Published: July 2002

A new multireference coupled-cluster method which includes double excitations and is based on the complete active space (CAS) multiconfigurational reference wave function is proposed. By partitioning the CAS orbitals into active and nonactive sets a two-component, coupled-cluster wave function involving excitations into orbitals of the different sets was constructed. The first component includes all the CAS excitations and the second component, which has the exponential form, consists of double external and semi-external excitations. The coupled-cluster equations for the energy and for the amplitudes involved in the two components of the wave function were derived and illustrated using a diagrammatic formalism. Several numerical tests were performed, and the results demonstrate a very good performance of the method as compared to the full configuration interaction results.
Noble gas–metal chemical bonding? The microwave spectra, structures, and hyperfine constants of Ar–CuX(X=F, Cl, Br)
Authors: Evans Corey J. , Gerry Michael C. L.
Published: July 2002

The rotational spectra of the complexes Ar–CuF, Ar–CuCl, and Ar–CuBr have been observed in the frequency range 5–22 GHz using a pulsed-jet cavity Fourier transform microwave spectrometer. All the complexes are linear and rather rigid in the ground vibrational state, with the Ar–Cu stretching frequency estimated as ∼200 cm−1. Isotopic data have been used to calculate an r0 structure for Ar–CuF, while for Ar–CuCl and Ar–CuBr partial substitution structures have also been obtained. To reduce zero-point vibrational effects a double substitution method (rd) has also been employed to calculate the structures of Ar–CuCl and Ar–CuBr. The Ar–Cu distance has been found to be rather short and to range from 2.22 Å in Ar–CuF to 2.30 Å in Ar–CuBr. Ab initio calculations at the MP2 level of theory model the geometries and stretching frequencies well and predict an Ar–Cu bond energy in Ar–CuF of ∼47.3 kJ mol−1. Large changes in the Cu nuclear quadrupole coupling constant on complex formation show that extensive charge rearrangement occurs upon formation of the complexes. This, in conjunction with the sizable dissociation energy, suggests that the Ar–Cu bonds in these complexes are weakly covalent. The rotational spectrum of CuF has also been reinvestigated to improve the hyperfine constants.
Molecular modeling of electron trapping in polymer insulators
Authors: Meunier M. , Quirke N.
Published: July 2002

The presence of space charge in the polymeric insulation of high-voltage cables is correlated with electric breakdown. There is a vast literature concerned with the experimental characterization of space charge and with phenomenological models of space charge formation and discharge. However, a direct link between molecular properties, space charge formation and eventual breakdown has still to be established. In this paper, we suggest a new scheme that constitutes a first step in linking microscopic defects to the formation of space charge. Although our goal is to understand the role of defects at the molecular level in electron trapping and the formation of space charge in polyethylene, we start by considering a “model” material; the wax tridecane (n-C13H28). It is clear that both physical (e.g., conformational defects) and chemical defects (e.g., broken bonds) may be present in insulating materials and may both trap electrons. In the present paper, we focus on the role of physical defects. Our analysis suggests that by defining the defect energy in terms of the molecular electron affinity, a relationship is established between the electron trap and the molecular properties of the material. The electron affinity and its variation with wax molecule conformation have been calculated using density functional theory (DFT, as implemented in the code DMol). By performing molecular-dynamics simulations of amorphous waxes, we are able to determine likely conformational defects, and by using ab initio methods estimate the trapping energies. Conformational defects in these waxy materials are predicted to produce shallow traps with energies below 0.3 eV. These results are used to estimate the energy, number, and residence times of electrons in conformational traps in polyethylene.
3+1 Regge calculus with conserved momentum and Hamiltonian constraints
Authors: Friedman John L. , Jack Ian
Published: July 2002

The Einstein action is evaluated for space-times whose three-metrics on a family of spacelike hypersurfaces are piecewise flat. The 3+1 action of Lund and Regge [F. Lund and T. Regge (private communication)], recently generalized by Piran and Williams [T. Piran and R. M. Williams, Phys. Rev. D 33, 1622 (1986)], is recovered in this way. A natural interpretation of the momentum constraint is obtained for simplicial initial data sets; and, by incorporating a nonzero shift vector and a nonconstant lapse, one finds a formalism in which the constraints are preserved by the time evolution. (In contrast to the continuum case, the constraints are not conserved if the lapse and shift are chosen a priori.) A consistent Hamiltonian formalism is readily obtained by the standard (Bergmann–Dirac) procedure or, alternatively, by algebraically solving the constraint equations for the lapse and shift on each three-simplex. Explicit solutions to the classical equations are found for spaces built from congruent simplices. In this special case, the action is that of a free relativistic particle moving in a curved space-time with indefinite metric and a conformal timelike Killing vector. For general space-times, if one a priori sets the shift vector to zero, the action has the form of a sum of such free-particle actions, but one for which the different particles interact by having coordinates in common.
Virtual power and thermodynamics for electromagnetic continua with interfaces
Authors: Daher N. , Maugin G. A.
Published: July 2002

This paper presents a systematic and rational formulation of the electromagnetic theory of deformable and fluent bodies swept out by singular surfaces that may carry their own thermodynamics (interfaces). The treatment is based on the principle of virtual power for finite velocity fields, which is so formulated that, when combined, for real velocity fields, with the first principle of thermodynamics in global form, it yields directly the so-called energy theorem both in the bulk and at the singular surface. Then the corresponding rates of entropy production are deduced after introduction of the second principle of thermodynamics. The various alternate expressions of the ponderomotive force, couple, and electromagnetic energy, obtained in the bulk from the Lorentz theory of electrons are developed across the singular surface by means of the generalized transport and Green–Gauss theorems. Finally, an extension of the constitutive theory (well established in the bulk) is given to account for surface phenomena in the case of an electromagnetic fluid. Thermodynamical restrictions are discussed, and comparisons are made with previous works.
Nonpropagating solitons of the variable coefficient and nonisospectral Korteweg–de Vries equation
Authors: Chan W. L. , Kam-Shun Li
Published: July 2002

The method of inverse scattering is extended to solve the initial value problem of a variable coefficient and nonisospectral Korteweg–de Vries equation with time varying boundary condition. One- and two-soliton solutions are examined in detail. By an appropriate decomposition, soliton interactions and asymptotic behaviors are investigated. Oscillating and asymptotically standing two-soliton solutions are discussed.
Low-density expansion for a two-state random walk in a random environment
Authors: Lawler Gregory F.
Published: July 2002

A nearest neighbor random walk on Z2 is considered where points of the lattice are labeled ‘‘good’’ or ‘‘bad.’’ A particle takes a vertical step with probability aG or aB and a horizontal step with probability 1−aG or 1−aB, depending on whether its present site is good or bad. Steps of size +1 are as probable as steps of size −1. If the good and bad sites are placed randomly, with density ρ of bad sites, it is known that there exists an ā such that for almost every placement of sites, the random walk in the long run behaves like a homogeneous walk with vertical probability ā and horizontal probability 1−ā. Here the problem of estimating ā as a function of ρ is considered; in particular when aG = 1/2 , aB fixed, the first two terms of the expansion of ā(ρ) at ρ=0 are rigorously derived.
The Burgers equation on the semiline with general boundary conditions at the origin
Authors: Calogero F. , De Lillo S.
Published: July 2002

A technique is given to solve the initial/boundary value problem for the Burgers equation ut(x,t)=uxx(x,t)+2 ux(x,t) u(x,t) on the semiline 0≤x<∞, with the general boundary condition at the origin H[u(0,t),ux(0,t);t]=0. Here ‘‘to solve’’ means ‘‘to reduce to an equation in one variable only.’’ This equation is generally nonlinear and integrodifferent ial; it comes in several (equivalent) avatars, which contain nontrivially a free parameter, whose value can be assigned arbitrarily since the solution of the equation is independent of it. In the special case when H(y,z;t)=a(t)y+b(t)(z+y2) −F(t), which is the case relevant for most applications, the equations reduce to linear integral equations of Volterra type, which can in fact be solved by quadratures if a(t)/F(t)=c1 and b(t)/F(t)=c2 are time-independent.
Hyperbolic complex structures in physics
Authors: Hucks Joseph
Published: July 2002

A brief introduction to the parabolic and hyperbolic complex number systems is given. Parabolic and hyperbolic phase transformations are shown to be equivalent to two-dimensional Galilean and Lorentzian relativity transformations, respectively. Basic properties and definitions for the hyperbolic complex numbers are given, and they are then applied to special relativistic physics and the Dirac equation in 1+1 dimensions. Turning to string theory, it is briefly shown that for Minkowski signature the string world sheet possesses an integrable almost hyperbolic complex structure, with a metric that is generalized Hermitian. Next, the hyperbolic complex numbers are applied to the formalism of Dirac spinors in 3+1 dimensions. It is shown that a four-component Dirac spinor is equivalent to a two-component hyperbolic complex spinor, that the Lorentz group is equivalent to a generalized SU(2), and that the Dirac adjoint corresponds to a generalized Hermitian adjoint. A complete formalism is presented for the hyperbolic complex two-component spinors. Lastly, it is shown that the operations of C, P, and T on Dirac spinors are closely related to the three types of complex conjugation that exist when both hyperbolic and ordinary imaginary units are present.
New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations
Authors: Clarkson Peter A. , Hood Simon
Published: July 2002

In this article symmetry reductions and exact solutions are presented for the (2+1)-dimensional Davey–Stewartson (DS) system which has the completely integrable DSI and DSII systems as special cases. These symmetry reductions are obtained using the direct method originally developed by Clarkson and Kruskal to study symmetry reductions of the Boussinesq equation which involves no group theoretic techniques. The DS system is reduced directly to ordinary differential equations, with no intermediate step. Using these reductions exact solutions of the DS system including some expressible in terms of the second and fourth Painlevé equations and elementary functions are obtained.
The stress tensor for nonlocal field equations
Authors: Percus J. K.
Published: July 2002

Construction of the stress tensor for a low differential order field theory on translation-invariant space is routine. If the underlying space is rotation, or Lorentz, invariant, an equivalent symmetric tensor can be found as well. Extension to nonlocal field equations, common, for example, in the statistical mechanical theory of fluids, is not routine and is carried out in this paper.
Imaginary parts of Stark–Wannier resonances
Authors: Buslaev Vladimir , Grigis Alain
Published: July 2002

We consider a one-dimensional Stark–Wannier Hamiltonian, H=−d2/dx2+p(x)−εx, x∈R, where p is a smooth periodic, finite-gap potential, and ε>0 is small enough. We compute rigorously the imaginary parts of the spectral resonances. For this purpose we develop some related elements of the adiabatic approach to the equations of the form −ψ″+p(x)ψ+q(εx)ψ=Eψ, ε→0.
Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of nontwisting type N solutions
Authors: Bičák Jiřı́ , Podolský Jiřı́
Published: July 2002

In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated with the cosmological constant, transverse motions corresponding to the effects of gravitational waves, longitudinal motions and Coulomb-type effects. Conditions under which the frame is parallelly transported along a geodesic are discussed. Suitable coordinates are introduced and an explicit coordinate form of the frame is determined for spacetimes admitting a nontwisting null congruence. Specific properties of all nontwisting type N vacuum solutions with cosmological constant Λ (nonexpanding Kundt class and expanding Robinson–Trautman class) are then analyzed. It is demonstrated that these spacetimes can be understood as exact transverse gravitational waves of two polarization modes “+” and “×,” shifted by π/4, which propagate “on” Minkowski, de Sitter or anti-de Sitter backgrounds. It is also shown that the solutions with Λ>0 may serve as exact demonstrations of the cosmic “no-hair” conjecture in radiative spacetimes with no symmetry.
Noncanonical quantization of gravity. I. Foundations of affine quantum gravity
Authors: Klauder John R.
Published: July 2002

The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constraints are introduced following the projection operator method, which involves no gauge fixing, no complicated moduli space, nor any auxiliary fields. The result, which is only qualitatively sketched in the present paper, involves another reproducing kernel with which inner products are defined for the physical Hilbert space and which is obtained through a reduction of the original reproducing kernel. Several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one-dimensional quantum mechanical models. These toy models help in motivating and understanding the analysis in the case of gravity.
Onset of turbulence in oscillating flow at low Womersley number
Authors: Kurzweg U. H. , Lindgren E. R. , Lothrop B.
Published: July 2002

Measurements on the onset of turbulence in oscillating flow of water in small diameter tubes are presented. Observations, based upon the streaming birefringence method, show that the heretofore observed radius independent onset criterion for turbulence fails to hold as the tube radius and oscillation frequency become small. In particular, it is found that with decreasing values of Womersley number, oscillating flows become increasingly stable.
Fractal dimensions of lines in chaotic advection
Authors: Fung J. C. H. , Vassilicos J. C.
Published: July 2002

The difference between locally self-similar fractals, called K fractals, and H fractals, which are globally self-similar fractals, is recalled . The self-similar cascade of energy [and enstrophy in the two-dimensional (2-D) case], which has been the original incentive for introducing fractals in the study of turbulence, does not seem to generate H-fractal interfaces in 2-D turbulent flows, according to the numerical evidence currently available. It only produces spiral singularities that are an example of K-fractal structures, and presumably a consequence of the structure of the turbulence that is neglected in pictures of the turbulence, based on a self-similar cascade of energy. It may be that the experimental evidence for fractal interfaces in 3-D turbulence is, in fact, evidence that these interfaces are K fractal. On the other hand, it could be that only very unsteady flows can produce H-fractal interfaces through a folding process that the unsteadiness adds to the stretching of the flow [see J. M. Ottino, The Kinematics of Mixing: Stretchings, Chaos and Transport (Cambridge U. P., Cambridge, 1989)]. That idea is investigated by releasing lines in a blinking vortex [J. Fluid Mech. 143, 1 (1984)] known to advect fluid elements ‘‘chaotically’’ in a certain range of parameters. The numerical evidence obtained supports the claim that interfaces in chaotic advection are H fractal. The length of a line in a blinking vortex grows exponentially, whereas the length of a line in a single steady vortex only grows linearly. The two ‘‘fractal’’ dimensions of the line investigated here increase with time, but they do not both asymptote to 2. The asymptotic value of the Kolmogorov capacity decreases as the time spent by the vortex in each location is decreased.
Instabilities of shallow dynamic thermocapillary liquid layers
Authors: Schwabe D. , Möller U. , Schneider J. , Scharmann A.
Published: July 2002

Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side-wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time-dependent flow states (t) was observed. Two different t-flow states have been identified by thermocouple measurements and by visualization of the dynamic-free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short-wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long-wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis [J. Fluid Mech. 132, 119, 145 (1983)] are discussed.
Electromagnetic Weibel instability in a fully relativistic bi-Maxwellian plasma
Authors: Yoon Peter H.
Published: July 2002

Detailed properties of the classical electromagnetic Weibel instability in a relativistic unmagnetized plasma are investigated for a fully relativistic bi-Maxwellian distribution. In particular, exact analytical expressions for the range of unstable wavenumbers, conditions for the instability, and the growth rate of the unstable mode for weak anisotropy are derived. The analysis shows that relativistic effects tend to stabilize the Weibel instability.
Energy redistribution in cavities by thermal radiation
Authors: Tsakiris G. D.
Published: July 2002

A method has been developed to calculate the spatial temperature distribution on the interior wall of an arbitrarily shaped cavity in which the wall elements exchange energy by means of thermal radiation. The method is based on the separation of the geometrical problem of the radiant energy exchange processes from the detailed physics of reemission from a wall element heated by thermal radiation. The reemissive properties of the interior wall are self-consistently calculated using a self-similar solution to the space- and time-dependent planar hydrodynamics equations with radiative heat conduction. As an example, the application of the method to the case of the cylindrical cavity is presented. The relevance of the model to the inertial confinement approach to fusion and its usefulness as a cavity designing tool is discussed.
Effects of sheared flows on ion-temperature-gradient-driven turbulent transport
Authors: Hamaguchi S. , Horton W.
Published: July 2002

Previous studies of the ion-temperature-gradient (ITG) driven turbulence are expanded to include the effect of sheared E×B flows in sheared magnetic fields. The radial eigenmodes are shown to substantially change character by shifting the modes off the rational surface. The new mode structure and growth rate directly affects the transport of both thermal energy and momentum in the sheared flows. The growth rate first increases with small shear flow and then decreases. The theoretical correlation of the shear flow with the thermal transport is important with respect to the transitions observed in tokamaks of a low (L mode) to a high (H mode) thermal confinement state as a function of the poloidal rotation velocity in the shear flow layer. The three-dimensional nonlinear simulations show that the anomalous ion thermal diffusivity is reduced significantly when dvE/dx≂2(cs/Ls) ((1+ηi)Ti/Te)1/2. This condition is thought to be satisfied in a boundary layer in tokamaks with shear flow.
Real group velocity in a medium with dissipation
Authors: Muschietti L. , Dum C. T.
Published: July 2002

When a medium is dissipative, the classic expression for the group velocity, dω/dk, is complex with an imaginary part often being far from negligible. To clarify the role of this imaginary term, the motion of a wave packet in a dissipative, homogeneous medium is examined. The integral representation of the packet is analyzed by means of a saddle-point method. It is shown that in a moving frame attached to its maximum the packet looks self-similar. A Gaussian packet keeps its Gaussian identity, as is familiar for the case of a nondissipative medium. However, the central wave number of the packet slowly changes because of a differential damping among the Fourier components: Im(dω/dk)=dγ/dk≠0, where ω≡ωr+iγ. The packet height can be computed self-consistently as integrated damping (or growth). The real group velocity becomes a time-dependent combination of Re(dω/dk) and Im(dω/dk). Only where the medium is both homogeneous and loss free, does the group velocity remain constant. Simple ‘‘ray-tracing equations’’ are derived to follow the packet centers in coordinate and Fourier spaces. The analysis is illustrated with a comparison to geometric optics, and by two applications: the case of a medium with some resonant damping (or growth) and the propagation of whistler waves in a collisional plasma.
Experimental observation of stabilization of an axisymmetric mirror at high beta with a nearby wall
Authors: Close R. A. , Kang B. K. , Lichtenberg A. J. , Lieberman M. A. , Meuth H.
Published: July 2002

A high β plasma is injected into an axisymmetric magnetic mirror. The β is varied principally by varying the midplane value of the magnetic field. The plasma fills most of the space inside of a conducting vacuum chamber. It is observed for a radially averaged 〈β〉>35% that the plasma is initially stable, while for 〈β〉<25% the plasma is initially unstable. The values of β required for stability are lower than those predicted from magnetohydrodynamic (MHD) theory.