bluuebunny/crossref_metadata_2025 huggingface dataset:
Reaction diffusion patterns in the catalytic CO-oxidation on Pt(110): Front propagation and spiral waves
Authors: Nettesheim S. , von Oertzen A. , Rotermund H. H. , Ertl G.
Published: July 2002

The dynamic behavior of elliptical front propagation and spiral-shaped excitation concentration waves associated with the catalytic oxidation of CO on a Pt(110)-surface was investigated by means of photoemission electron microscopy (PEEM). The properties of these patterns can be tuned through the control parameters, viz., the partial pressures of CO and O2 and the sample temperature. Over a wide range of control parameters the transition between two metastable states (COad and Oad covered surface) proceeds via nucleation and growth of elliptical reaction-diffusion (RD)-fronts. Front velocities and critical radii for nucleation are determined by the diffusion of adsorbed CO under reaction conditions. If at constant pO2, T the CO partial pressure is increased beyond a critical value a transition to qualitatively different dynamic behavior takes place. The elliptical fronts give way to oxygen spiral waves of excitation spreading across the CO-covered areas. For fixed experimental conditions a broad distribution of spatial wavelengths and temporal rotation periods was found. This effect has to be attributed to the existence of surface defects of μm-size to which the spiral tip is pinned. These data lead to a dispersion relation between the front propagation velocity and the wavelength, respectively, period. In addition, the dynamics of free spiral-shaped excitation waves was investigated under the influence of externally modulated temperature. Now the spiral starts to drift, resulting in distortion of the Archimedian shape and a pronounced Doppler effect.
Dipolar interactions in model Langmuir–Blodgett films
Authors: Munn R. W. , Shabat M. M.
Published: July 2002

Planewise dipole sums give the electric field at a point due to an array of electric dipole moments in a plane. Calculations are reported for model lattice structures of Langmuir–Blodgett films with elongated molecules represented by a string of spherical ‘‘beads’’ or submolecules; interactions are averaged over submolecules. Results are given for parent hexagonal and tetragonal lattices, with molecules allowed to tilt away from the vertical and with the in-layer cell parameters allowed to distort from equality. Beyond about five submolecules, molecular length makes little difference. Interactions within a layer dominate, with those between adjacent layers much smaller and those between remoter layers negligible. Tilt affects the interactions more than the detailed lattice structure does. The results provide a key ingredient for theories of the optical and electrical properties of Langmuir–Blodgett films.
Thermal maximum in the size of short polyelectrolyte chains. A Monte Carlo study
Authors: Severin Mattias
Published: July 2002

We present Monte Carlo simulation results for the temperature dependence of the conformation characteristics for an isolated polyelectrolyte chain with counterions immersed in a continuum dielectric. The polyion consists of an ordered set of N identical charged hard spheres with fixed separation. All interactions between the ions are taken to be Coulombic. An interesting temperature dependence is found; for high temperatures the polymer conformation approaches the random coil on increasing the temperature in contrast to the behavior at low temperatures, where we find that the polymer tends to swell with increasing temperature. It is argued that this phenomenon can be understood in terms of the screening effect introduced by Manning condensation of the counterions.
Molecular dynamics with electronic frictions
Authors: Head-Gordon Martin , Tully John C.
Published: July 2002

A generalization of classical adiabatic molecular dynamics, which we term molecular dynamics with electronic frictions, is described for nuclear motion on a continuum of potential-energy surfaces, such as for adsorbate dynamics at a metal surface. In this situation, the Born–Oppenheimer approximation fails, since for any molecular motion—such as vibrations, rotations, or translations—there are resonant electronic excitations of the metal. However, such excitations are often highly delocalized, so that the continuum of electronic potential-energy surfaces on which nuclear motion occurs are all of similar shape, and can be replaced by a single, effective potential. Nonadiabatic energy exchange between nuclear and electronic degrees of freedom is then represented by frictional and fluctuating forces on the nuclei, and no explicit electronic dynamics are required. The friction in general involves memory, although it is shown that the Markov limit in which memory vanishes is likely to be quite broadly applicable. Expressions for the electronic friction in the Markov limit are obtained in terms of the electronic structure of the gas-surface system, which opens the way for direct calculation of these quantities. There is exact agreement between the frictions and previous time-dependent perturbation theory results for the lifetime of excited adsorbate vibrations at metal surfaces.
Surface properties of diluted aqueous solutions of normal propyl alcohol
Authors: Glinski Jacek , Chavepeyer Guy , Platten Jean-Karl
Published: July 2002

Surface tension σ of aqueous solutions of n-propyl alcohol was measured in the temperature range between 278 and 303 K using Wilhelmy plate method. The surface entropies and enthalpies are calculated. The results are interpreted in terms of specific interactions of the hydrophobic parts of the molecules adsorbed at the interface and possible interaction of these molecules with the bulk. The results are compared to those obtained previously for water+tert-butanol solutions.
Computational study of many-dimensional quantum vibrational energy redistribution. I. Statistics of the survival probability
Authors: Schofield Sarah A. , Wyatt Robert E. , Wolynes Peter G.
Published: July 2002

We statistically analyze the dynamics of vibrational energy flow in a model system of anharmonic oscillators which are nonlinearly coupled, with a local topology. The spectra of many basis states of similar energy are computed, for different values of the magnitude of the coupling in the Hamiltonian between these states. From individual spectra of zero order basis states at each coupling strength the individual survival probabilities are determined, which are then used in computing statistical averages. When the average fluctuation of the survival probability is small, in the strongly coupled limit, the average survival probability closely follows a semiclassical diffusion prediction and reflects a predicted linear dependence of the rate of energy flow on coupling strength. When the average fluctuation is large, in the weakly coupled limit, the average survival probability closely follows a power law decay of t−1, in agreement with a quantum extension of the diffusion picture. In this regime, individual survival probabilities show strong quantum beats. We conclude that these large variations reflect a strong influence of quantum interference in the weakly coupled limit.
Thermodynamics of the curvature effect on ice surface tension and nucleation theory
Authors: Bogdan Anatoli
Published: July 2002

The Gibbs model of surface tension, together with the approach by Defay and Prigogine [Surface Tension and Adsorption (Longmans, New York/London, 1966)] and Dufour and Defay12 [Thermodynamic of Clouds (Academic, New York/London, 1963)] for calculation of the Gibbs adsorption Γ, is used to estimate the curvature effect on ice surface tension. For the case of the ice-water interfaces a new model for calculation of the Gibbs adsorption Γi/w is proposed. Ice surface tension decreases with the curvature which in turn reduces the equilibrium radius of an ice embryo thus making the nucleation event more probable. The comparison of the calculated transitional region between ice and supercooled water with that obtained from experiments and theoretical calculations showed that the proposed new model gives the correct sign and correct order of magnitude for Γi/w.
On the electronic states and photochemistry of simple alkyl amines
Authors: Taylor D. P. , Dion C. F. , Bernstein E. R.
Published: July 2002

This paper extends recent work on the excited states of methyl amine to some other simple amines. Jet-cooled mass-resolved multiphoton ionization spectroscopy is reported for methyl amine, dimethyl amine, trimethyl amine, ethyl amine, diethyl amine, and triethyl amine. A set of high-level calculations for methyl amine supports the assignment of S1 as a 3s Rydberg state by predicting the experimental transition energy to within about 1000 cm−1 after including vibrational zero-point energies for each potential energy surface. Perturbations observed in the experimental S1←S0 spectrum prompt a series of calculations which implicate a dissociative 3s Rydberg state in both the perturbation in the spectrum and in the photodissociation of methyl amine at these energies. A series of excited state calculations performed at the ground state geometry for methyl amine, dimethyl amine and trimethyl amine indicates the relative energies of the bound 3s and 3p Rydberg states as well as the first dissociative 3s Rydberg state. Taken together, this work presents a picture of the S1 and S2 excited states in which dissociative low-lying Rydberg states play a significant role in both the spectroscopy and photochemistry of the simple amines.
The absolute absorption strength and vibrational coupling of CH stretching on diamond C(111)
Authors: Cheng C.-L. , Lin J.-C. , Chang H.-C.
Published: July 2002

This research investigates the infrared absorption intensity and isotope-dependent frequency shifts of CH stretching on diamond C(111) single-crystal surfaces by Fourier transform infrared spectroscopy (IRS). By employing single-pass direct absorption and in situ surface oxidation methods, a single sharp feature at νm=2832.2±0.9 cm−1 with a FWHM of Γ≈6 cm−1 is observed at 800 K. Systematic measuring of how band intensity depends on hydrogen etching time indicates that a well hydrogen-terminated C(111)-1×1 can be prepared only after prolonged exposure of the surface to H, generated by hot W filaments, at 1100 K. A study of the band intensity at saturation, and assuming an electronic polarizability of αe=0.65 Å3 for the CH bond as that in CH4, yields an integrated cross section σ̄z=5.5×10−18 cm for the CH stretching motion along the internuclear axis. Additional measurements of band position as a function of mixed isotope concentrations afford a stretching frequency of νi=2816.2±0.9 cm−1 for a single CH isolated in a monolayer of CD oscillators at 800 K. The frequency shift of νm−νi=16.0 cm−1 is too large for dipole coupling theories to explain. The implications of the present findings with regard to applying IRS for quantitatively characterizing CVD diamondlike carbon films are discussed.
Semiclassical study on multidimensional effects in tunneling chemical reactions: Tunneling paths and tunneling tubes
Authors: Ushiyama Hiroshi , Takatsuka Kazuo
Published: July 2002

The effects of multidimensionality in the quantum mechanical tunneling of chemical reactions are investigated. The aim of the present report is twofold. In the first place, we construct a new semiclassical theory to describe the tunneling by incorporating nonclassical solutions of the time-dependent Hamilton–Jacobi equation into the Feynman kernel. A systematic class of complex-valued (nonclassical) solutions for the time-independent Hamilton–Jacobi equation has been found that are generated along non-Newtonian paths in real-valued configuration space [K. Takatsuka and H. Ushiyama, Phys. Rev. A 51, 4353 (1995)]. In the present paper, the straightforward extension is applied to the time-dependent Hamilton–Jacobi equation, the solutions of which describe the tunneling in chemical reactions. It is shown that no damping factor due to the tunneling arises from the preexponential factor in the thus obtained nonclassical kernel, since it is still real valued, aside from the complex phase due to the Maslov index, and moreover its functional form is essentially the same as in the nontunneling case. Thus only the imaginary part of the action integral is responsible for the damping. A quasiclassical treatment of the semiclassical mechanics is developed to characterize the real-valued tunneling paths. In the second-half of this paper, some typical tunneling reactions in collinear three atomic systems on the LEPS (London–Eyring–Polanyi–Sato) potential surface are investigated in terms of our semiclassical theory. The effect of the initial energy distribution among the vibrational and translational modes is investigated asking which is preferable for tunneling and what is the resultant distribution of the energy in the product molecules. The following two factors to control the tunneling reactions are mainly examined as our first case study: (a) the mass effects featuring heavy–light–heavy and light–heavy–light patterns and (b) the anisotropy of the potential surface, namely, the early or late barrier. Tunneling paths of the types of Marcus–Coltrin and Miller–George are both generated spontaneously. A path of Marcus–Coltrin type takes a major role when the translational energy dominates in tunneling, while that of Miller–George type is dominant in a case where the vibrational excitation is important. As a distinguished feature of the multidimensionality in tunneling, we have identified what we call a tunneling tube, in which a bunch of the tunneling paths are involved emanating from the so-called caustic line. It turns out that the width of the tunneling tube determines in part the final energy distribution among the product vibrational modes.
The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data
Authors: Partridge Harry , Schwenke David W.
Published: July 2002

We report on the determination of a high quality ab initio potential energy surface (PES) and dipole moment function for water. This PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J⩽5 for H216O. The changes in the PES are small, nonetheless including an estimate of core (oxygen 1s) electron correlation greatly improves the agreement with the experiment. Using this adjusted PES, we can match 30 092 of the 30 117 transitions in the HITRAN 96 data base for H216O with theoretical lines. The 10, 25, 50, 75, and 90 percentiles of the difference between the calculated and tabulated line positions are −0.11, −0.04, −0.01, 0.02, and 0.07 cm−1. Nonadiabatic effects are not explicitly included. About 3% of the tabulated line positions appear to be incorrect. Similar agreement using this adjusted PES is obtained for the 17O and 18O isotopes. For HD16O, the agreement is not as good, with a root-mean-square error of 0.25 cm−1 for lines with J⩽5. This error is reduced to 0.02 cm−1 by including a small asymmetric correction to the PES, which is parameterized by simultaneously fitting to HD16O and D216O data. Scaling this correction by mass factors yields good results for T2O and HTO. The intensities summed over vibrational bands are usually in good agreement between the calculations and the tabulated results, but individual line strengths can differ greatly. A high-temperature list consisting of 307 721 352 lines is generated for H216O using our PES and dipole moment function.
Orientational ordering of two-dimensional ice on Pt(111)
Authors: Glebov A. , Graham A. P. , Menzel A. , Toennies J. P.
Published: July 2002

Two highly ordered, epitaxially rotated phases of bilayer ice are observed on Pt(111) in high resolution helium atom diffraction. Analysis of helium diffraction patterns shows that the two phases differ slightly in their density and alignment with respect to the surface. The lack of any isotope effect for both phases indicates that the ice bilayers have structures and hydrogen bond lengths very similar to bulk ice.
Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem
Authors: Ben-Nun M. , Martı́nez Todd J.
Published: July 2002

The recently introduced full multiple spawning (FMS) method for molecular dynamics beyond the Born–Oppenheimer approximation is tested against exact numerical solution of the coupled nuclear Schrödinger equation for a two-dimensional model problem with two electronic states. The method uses a multiconfigurational frozen Gaussian ansatz for the wave function and the key idea is to expand the size of the basis set only during nonadiabatic events, using available information to predict the regions of phase space where population will be created. This is accomplished via the spawning procedure which keeps the basis size manageable while ensuring that it provides a reasonable approximation to the exact wave function. The parameters that govern the numerical accuracy of the method are discussed in detail. Expectation values and branching ratios are predicted quantitatively over a broad range of energies.
Molecular simulation of the intercrystalline phase of chain molecules
Authors: Balijepalli Sudhakar , Rutledge Gregory C.
Published: July 2002

Off-lattice Monte Carlo simulations of the interphase between crystals for freely rotating chains are reported. Both conformational and topological spaces are sampled during a single simulation. The transition region between the crystal and the amorphous phase is characterized in terms of density, bond orientation order, and interfacial energy. The topology of the interphase is quantified in terms of loop and bridge chain populations, and the position of loop re-entry sites.
Atomic structure of solid and liquid polyethylene oxide
Authors: Johnson J. A. , Saboungi M.-L. , Price D. L. , Ansell S. , Russell T. P. , Halley J. W. , Nielsen B.
Published: July 2002

The structure of polyethylene oxide (PEO) was investigated by neutron scattering in both semicrystalline and liquid states. Deuterated samples were studied in addition to the protonated ones in order to avoid the large incoherent scattering of hydrogen and identify features in the pair correlation functions attributable to C–H pairs. Analysis of the deuterated sample gave additional information on the C–O and C–C pairs. The results are compared with molecular-dynamics simulations of liquid PEO.
Quasisemiclassical trajectory approach to tunneling chemical reactions
Authors: Ushiyama Hiroshi , Takatsuka Kazuo
Published: July 2002

A quasisemiclassical trajectory method (QSCT) is proposed, which provides a practical procedure to study tunneling chemical reaction dynamics in multidimensional systems. QSCT incorporates the semiclassical tunneling paths that are generated by our previously proposed method [K. Takatsuka and H. Ushiyama, Phys. Rev. A 51, 4353 (1995)] into the so-called quasiclassical trajectory method, whereby the chemical reactions in a wide energy range are calculated in a systematic way. The accuracy of this approach is tested with the system of collinear H+H–H reaction on the so-called LSTH (Liu–Siegbahn–Truhlar–Horowitz) potential surface. The thermal rate constants at 1–3000 K are calculated. The resultant reaction rates are compared with the quantum mechanical values [Bondi et al., J. Chem. Phys. 76, 4986 (1982)], showing that they are in a systematically good agreement in this wide temperature range. We have also examined the dependence of the reaction probability on the initial sampling of the quasiclassical method. The contribution of the paths of dynamical tunneling to chemical reaction above the reaction threshold is estimated for the first time.
Simulation of polymer melt intercalation in layered nanocomposites
Authors: Lee Jae Youn , Baljon Arlette R. C. , Loring Roger F. , Panagiotopoulos Athanassios Z.
Published: July 2002

Polymer layered silicates form an important class of nanocomposite materials. These structures may be formed by annealing layered silicate particles, whose surfaces have been chemically modified to render them organophilic, with a polymer melt. During intercalation, polymer molecules leave the bulk melt and enter the galleries between the silicate layers. An essential feature of this process is the flow of macromolecules from a bulk fluid to a confined environment. To model this phenomenon, we have performed molecular-dynamics simulations of the flow of polymer molecules from a bulk melt into a rectangular slit. The simulations are consistent with a diffusive description of the transport, and show qualitative agreement with time-dependent x-ray diffraction measurements of intercalation kinetics in layered nanocomposites.
The ultrasonic relaxation in aqueous solutions of N-ethylacetamide
Authors: Miecznik Piotr
Published: July 2002

Measurements are reported of the ultrasonic absorption in the frequency range 10–100 MHz in aqueous solutions of N-ethylacetamide (NEAA). The occurrence of a relaxation process due to forming and to breaking of molecular complexes is demonstrated. Relaxation parameters of the discovered process have been calculated. The value of the activation enthalpy of the process indicates that molecular complexes composed of H2O–NEAA are formed through the hydrogen bond. The theoretical model of ultrasonic absorption in aqueous solutions of nonelectrolytes developed by Andreae, Edmonds, and McKellar, is applied.
Concept of interbasin mixing and extension of the Lyapunov exponent in multiple potential-basin dynamics as in structural isomerization of clusters
Authors: Takatsuka Kazuo , Seko Chihiro
Published: July 2002

For Hamilton dynamics on a potential that has multiple local basins as in structural isomerization reaction of clusters, a notion of interbasin mixing is introduced that is responsible for Markov-type stochastic appearance of molecular structures. An extension of the Lyapunov exponent to quantify the time scale to reach interbasin mixing is proposed. The present dynamics also serves as a prototype of multichannel chemical reactions.
The vibrational spectrum and molecular constants of silicon dihydride SiH2 in the ground electronic state
Authors: Hirota Eizi , Ishikawa Haruki
Published: July 2002

The infrared spectrum of SiH2 was observed in the 5 μm region by using diode laser spectroscopy, and the three bands ν1, 2ν2, and ν3 were recorded and assigned. A separate analysis of the three bands yielded the band origins, 1995.9280, 1987.6938, and 1992.816 cm−1, respectively, thereby establishing that ν1 is higher than 2ν2, contrary to the result of a previous matrix study. The anharmonic resonances, both ν1/2ν2 Fermi and 2ν1/2ν3 Darling–Dennison, which were observed in the laser induced fluorescence spectra previously reported, were reanalyzed by removing the condition ν1<2ν2, leading to a much improved set of vibrational parameters. The harmonic frequencies of SiH2 were then obtained to be ω1=2076.55, ω2=1020.49, and ω3=2065.65 cm−1. Molecular constants of SiH2 in the ground vibronic state were reexamined in light of the present as well as other spectroscopic results recently obtained on the molecule.
Thermal coarsening of uniaxial and biaxial field-structured composites
Authors: Martin James E. , Anderson Robert A. , Tigges Chris P.
Published: July 2002

When a suspension of colloidal particles is subjected to a strong electric or magnetic field, the induced dipolar interactions will cause the particles to form organized structures, provided a sufficient permittivity or permeability mismatch exists, respectively, between the particles and the suspending liquid. A uniaxial field will produce uniaxial structures, and a biaxial field, such as a rotating field, will produce biaxial structures, and either of these structures can be pinned by polymerizing the continuous phase to produce field-structured composites. We have previously reported on the coarsening of field-structured composites in the absence of thermal effects, i.e., Brownian motion. Athermal simulations are primarily valid in describing the deep quenches that occur when the induced dipolar interactions between particles greatly exceed kBT. However, deep quenches can lead to kinetic structures that are far from equilibrium. By introducing Brownian motion we have shown that structures with significantly greater anisotropy and crystallinity can form. These structures have enhanced material properties, such as the conductivity, permittivity, and optical attenuation. Careful anneals at certain fixed fields, or at continuously increasing fields, should produce more anisotropic structures than the deep quenches we have used to synthesize real materials.
Permanent electric dipole moment and polarizability in Stark modulation spectra of the ICl B–X transition
Authors: Takei Taka-aki , Watanabe Akiyoshi , Amako Yoshito
Published: July 2002

Because the induced dipole moment due to polarizability in a moderate electric field is thought to be small, the Stark effect due to polarizability has generally been ignored for molecules that have a permanent electric dipole moment. However, by observation of the Stark modulation spectra (SMS), we have confirmed that the effects of polarizability and of the permanent dipole moment are sometimes comparable. Based on this observation, we have sought an estimate of the polarizability. It was also found that the effect of the polarizability on the SMS depends mainly on its isotropic part. Thus, for the B–X electric transition of the ICl molecule, the differences in isotropic polarizabilities were estimated to be Δᾱ=3.4–3.8 Å3 at the 3–1 transition, and Δᾱ=3.6–4.3 Å3 at the 1–0 transition, assuming that the differences of anisotropic polarizability Δαan are within the range 2–9 Å3 for both transitions. Thus, obtained values of Δᾱ were confirmed to be in a reasonable range, in spite of a wide range uncertainty in Δαan.
Femtosecond time-resolved photoelectron imaging on ultrafast electronic dephasing in an isolated molecule
Authors: Suzuki Toshinori , Wang Li , Kohguchi Hiroshi
Published: July 2002

Ultrafast dephasing in an intermediate case of molecular radiationless transition has been visualized for the first time by femtosecond time-resolved photoelectron imaging. The decay of photoexcited S1(n,π*) state of pyrazine in 100 ps and the corresponding build-up of triplet states were clearly observed.
Molecular view of polymer flow into a strongly attractive slit
Authors: Baljon Arlette R.C. , Lee Jae Youn , Loring Roger F.
Published: July 2002

We present molecular dynamics simulations of the flow of macromolecules from a bulk melt into a slit of nanometer dimension with strongly attracting walls. Such flow is central to the formation of polymer-layered silicate nanocomposites by direct melt intercalation. In this process, polymer molecules flow from a melt into the galleries between the sheets that compose a mica-type layered silicate. We present a systematic study of the effects of polymer molecular weight and polymer-surface interactions on the flow dynamics.
Behaviors of an excess proton in solute-containing water clusters: A case study of H+(CH3OH)(H2O)1–6
Authors: Wu C.-C. , Jiang J. C. , Boo D. W. , Lin S. H. , Lee Y. T. , Chang H.-C.
Published: July 2002

Behaviors of an excess proton in solute-containing water clusters were investigated using infrared spectroscopy and ab initio calculations. This investigation characterized the structures of protonated methanol-water clusters, H+(CH3OH)(H2O)n with n=2–6, according to their nonhydrogen-bonded and hydrogen-bonded OH stretches in the frequency range of 2700–3900 cm−1. Ab initio calculations indicated that the excess proton in these clusters can be either localized at a site closer to methanol, forming a methyloxonium ion core (CH3OH2+), or at a site closer to water, forming a hydronium ion core (H3O+). Infrared spectroscopic measurements verified the calculations and provided compelling evidence for the coexistence of two distinct structural isomers, CH3OH2+(H2O)3 and H3O+(CH3OH)(H2O)2, in a supersonic expansion. The spectral signatures of them (either CH3OH2+ or H3O+ centered) are the free-OH stretching absorption band at 3706 cm−1 of a single-acceptor-single-donor H2O, and the band at 3673 cm−1 of a single-acceptor CH3OH. At n=4–6, the clusters adopt structures similar to their pure water analogs with five-membered rings starting to form at n=5. The position of the excess proton in them varies sensitively with the number of solvent water molecules as well as the geometry of the clusters. To further elucidate the behaviors of the excess proton in these clusters, we analyze in detail the potential energy surface along the proton transfer coordinate for two specific isomers of n=2 and 4: MW2II and MW4I. It is found that the proton can be nearly equally shared by methanol and the water dimer subunit in the form of CH3OH–H+–(H2O)2, as substantiated by hydrogen bond cooperativity and zero-point vibrational effects.
Exponential convergence for nonlinear diffusion problems with positive lateral boundary conditions
Authors: Holland Charles J. , Berryman James G.
Published: July 2002

It is established that the solution u of ut=Δ(um)>0, with positive initial data, positive lateral boundary data, and positive exponent m, converges exponentially to the solution v of the corresponding stationary equation Δ(vm)=0. The analysis also provides the form of the leading contribution to the difference (u−v).
Kerr–Newman metric endowed with magnetic dipole moment
Authors: Manko V. S. , Sibgatullin N. R.
Published: July 2002

The full metric representing the nonlinear superposition of the Kerr–Newman solution with a massless magnetic dipole is obtained. This metric is asymptotically flat and describes correctly the exterior gravitational field of a charged, magnetized, spinning mass.
On the definition of the center of mass for a system of relativistic particles
Authors: Lehner Luis R. , Moreschi Osvaldo M.
Published: July 2002

The notion of center of mass is reviewed and three natural definitions for the relativistic regime are proposed. This construction can be explicitly calculated by means of an algorithm which is described below.
A non-commutative central limit theorem
Authors: Dorlas T. C.
Published: July 2002

We prove a non-commutative version of the Central Limit Theorem for spin-1/2 variables. The non-commutative spins satisfy Bose–Einstein statistics. The proof involves the Feynman–Kac formula for a hopping process and an explicit calculation of the Fourier transform of the corresponding measure. The limit process is a modification of the Ornstein–Uhlenbeck process, the Fourier transform of which was essentially already calculated by Feynman. However, his derivation is not rigorous and we therefore present an alternative derivation here.
A geometrical method towards first integrals for dynamical systems
Authors: Labrunie Simon , Conte Robert
Published: July 2002

We develop a method, based on Darboux’s and Liouville’s works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements’ forms. We apply it to three dynamical systems: Lotka–Volterra, Lorenz and Rikitake.
Hypergeometric states and their nonclassical properties
Authors: Fu Hong-Chen , Sasaki Ryu
Published: July 2002

“Hypergeometric states,” which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to the coherent and number states are studied. The ladder operator formulation of the hypergeometric states is found and the algebra involved turns out to be a one-parameter deformation of su(2) algebra. These states exhibit highly nonclassical properties, like sub-Poissonian character, antibunching, and squeezing effects. The quasiprobability distributions in phase space, namely the Q and the Wigner functions are studied in detail. These remarkable properties seem to suggest that the hypergeometric states deserve further attention from theoretical and applicational sides of quantum optics.
New finite-dimensional integrable systems and explicit solutions of Hirota–Satsuma coupled Kortweg–de Vries equation
Authors: Geng Xianguo , Wu Yongtang
Published: July 2002

The nonlinearization approach is extended to the Hirota–Satsuma coupled Kortweg–de Vries (KdV) equation associated with a 4×4 matrix spectral problem, from which two new finite-dimensional integrable Hamiltonian systems are obtained in the Liouville sense. It is shown that the solutions of this coupled KdV equation are reduced to solving a compatible system of ordinary differential equations. The reductions of the two Hamiltonian systems and their separability are discussed. An interesting connection between the two reduced Hamiltonian systems in the case of one-parameter and known two-dimensional integrable systems is revealed. As application, some explicit solutions of the Hirota–Satsuma coupled KdV equation are derived.
Hyperfinite-dimensional representations of canonical commutation relation
Authors: Yamashita Hideyasu
Published: July 2002

This paper presents some methods of representing canonical commutation relations in terms of hyperfinite-dimensional matrices, which are constructed by nonstandard analysis. The first method uses representations of a nonstandard extension of the finite Heisenberg group, called hyperfinite Heisenberg group. The second is based on hyperfinite-dimensional representations of so(3). Then, the cases of infinite degree of freedom are argued in terms of the algebra of hyperfinite para-Fermi oscillators, which is mathematically equivalent to a hyperfinite-dimensional representation of so(n).
Magnetooptical effects in ferroelectric materials
Authors: Chupis I. E.
Published: July 2002

An expression for high-frequency susceptibility of a ferroelectric material in a constant magnetic field H0 parallel to the direction of spontaneous polarization P0 has been derived. The reflection and transmission of light through the ferroelectric is considered for the normal incidence at the surface (along the normal ν⃗ to the surface). It is shown that the polarization plane in reflected light should be rotated through an angle proportional to the product P0H0. For H0⊥ν⃗, the angle of rotation of the polarization plane of transmitted light is a periodic function of the optical path, its amplitude being proportional to P0H0. In the H0‖ν⃗ geometry, a weak gyration effect proportional to P0H0 is observed in transmitted light, in addition to the Faraday effect. This effect does not depend on the optical path, and is canceled during backward transmission, in contrast with the Faraday effect. The effect is apparently similar to “magnetopolarization gyration,” but the estimates give a much smaller magnitude of the effect. The above magnetooptical effects can be observed not only in ferroelectric crystals of any symmetry, but also in insulators in constant electric and magnetic fields.
Effect of local defects on vibrational characteristics of infinite and semi-infinite one-dimensional structures in an external periodic field
Authors: Mamalui M. A. , Syrkin E. S. , Feodosyev S. B.
Published: July 2002

Exact analytic expressions for Green’s functions of the chain type structures with defects in an external periodic field are obtained by the method of Jacobi matrices. A diatomic impurity molecule in a monatomic chain as well as adsorbed chains with a monatomic and a diatomic unit cell are considered. The conditions for the formation and the characteristics of local and gap vibrations are investigated. The evolution of the threshold values of mass of the defect required for the formation of localized vibrations by two isotopic impurities upon a change in the separation between them is analyzed.
Surface spin waves near a ferromagnet–antiferromagnet interface
Authors: Grechnev A. G. , Kovalev A. S.
Published: July 2002

The existence of surface spin waves near a compensated ferromagnet–antiferromagnet interface is predicted on the basis of the classical Heisenberg model. The frequencies of these spin waves lie outside the continuous spectra of the magnets. In the case of a noncollinear configuration of the interface there exists a Goldstone mode of surface spin waves, while for a collinear configuration there are activational modes.
Three-equation modeling of inhomogeneous compressible turbulence based on a two-scale direct-interaction approximation
Authors: Yoshizawa Akira
Published: July 2002

Mathematical functional forms of important correlation functions in inhomogeneous compressible turbulence are investigated, with the focus on the turbulence modeling based on bulk turbulence quantities. A two-scale direct-interaction approximation (TSDIA) is applied using three fundamental variables, that is, the density, momentum, and internal energy per unit volume. This choice of variables under the ensemble-mean procedure retains the simplicity of the mean-field equations under the Favre-mean procedure. Using these theoretical results, a three-equation turbulence model is constructed, where the turbulence equations consist of the equations for the intensity of momentum fluctuation, its viscous dissipation rate, and the intensity of density fluctuation. Direct effects of compressibility on the Reynolds stress and other important correlation functions are related to the intensity of density fluctuation. These results give a clue for explaining the virtual decrease of the eddy-viscosity effect near a shock wave.
Kelvin–Helmholtz instability of Couette flow between vertical walls with a free surface
Authors: Walker John S. , Talmage Gita , Brown Samuel H. , Sondergaard Neal A.
Published: July 2002

A novel type of Kelvin–Helmholtz instability model is developed from hydrodynamic theory. The classical Kelvin–Helmholtz instability involves a horizontal interface between two fluids with different parallel, uniform, horizontal velocities. If the upper fluid is a gas with a much smaller density than the lower fluid which is a liquid, then the phase velocity of the critical disturbance equals the liquid’s velocity, so that the liquid sees a standing interfacial wave. The inertial force driving the interfacial instability involves only the gas, no matter how small its density is. In a much more realistic flow model, the liquid velocity at the free surface is not uniform, but varies across the free surface. The disturbance phase velocity can only equal the liquid velocity at one point, while liquid on either side of this point moves faster or slower than the wave. The inertial forces in the liquid then dominate and the gas plays a negligible role. The concept is developed from a Couette flow hydrodynamic model where the fluid flows between two parallel vertical walls with a free surface. The importance of a nonuniform liquid velocity is demonstrated. This modified theory will be applied in future work to study the ejection instability at the interface of the liquid metal and inert cover gas in sliding electrical contacts.
Unsteady natural coordinates for a viscous compressible flow
Authors: Emanuel G.
Published: July 2002

Natural, or intrinsic, coordinates are examined for an unsteady, compressible, viscous, Newtonian fluid in two-dimensional or axisymmetric flow. The corresponding Navier–Stokes equations are obtained along with Crocco’s equation, an entropy production equation, and an equation for the rate of change of vorticity following a fluid particle. The extension to a three-dimensional flow is discussed.
Induced Mach wave–flame interactions in laminar supersonic fuel jets
Authors: Hu F. Q. , Jackson T. L. , Lasseigne D. G. , Grosch C. E.
Published: July 2002

A model problem is proposed to investigate the steady response of a reacting, compressible laminar jet to Mach waves generated by wavy walls in a channel of finite width. The model consists of a two-dimensional jet of fuel emerging into a stream of oxidizer which are allowed to mix and react in the presence of the Mach waves. The governing equations are taken to be the steady parabolized Navier–Stokes equations which are solved numerically. The kinetics is assumed to be a one-step, irreversible reaction of the Arrhenius type. Two important questions on the Mach wave–flame interactions are discussed: (i) how is the flame structure altered by the presence of the Mach waves, and (ii) can the presence of the Mach waves change the efficiency of the combustion processes?
Compatibility of the turbulent dynamo concept with reversed field pinches
Authors: Yoshizawa Akira
Published: July 2002

The sustainment phase of reversed field pinches (RFP’s) is investigated with the concept of the turbulent dynamo. In the case of a finite toroidal voltage, the familiar alpha–beta dynamo, which is equivalent to Taylor’s and modified Bessel function models, cannot satisfy the condition of vanishing currents at the plasma edge. The importance of another alpha term is stressed, and the deep reversal resulting from a large toroidal voltage, the enhanced dynamo effect in ramped discharges, and the F-Θ pumping are discussed in light of the characteristics of the edge region that have a great influence on the global structure of the RFP.
Relaxation time of potential formation across the magnetic field in a collisionless plasma
Authors: Okuno Yoshihiro , Yagura Shinya , Fujita Hiroharu
Published: July 2002

The relaxation time of potential formation across the magnetic field in a collisionless plasma is experimentally studied. The time variation of the local potential is directly measured with a high time resolution technique when a pulsed potential is applied between magnetized coaxial cylindrical double plasmas. It is found that the relaxation times of the potential and density decrease with the applied voltage and the density of the target plasma, and increase with the magnetic field strength and the density of the driver plasma. These results could be understood consistently by the diffusion of ions in the driver plasma to the target plasma.
Stability of stationary three-wave interactions in homogeneous and infinite systems
Authors: Pietsch H. , Blaha R. , Laedke E. W. , Spatschek K. H.
Published: July 2002

One-dimensional three-wave models, known for stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS), are investigated. It is shown that in homogeneous systems of infinite extent the steady-state three-wave solution for SBS with a reflectivity less than 100% is intrinsically unstable. From a numerical solution it is concluded that nearly all stationary states decay in time and result in a state with reflectivity coefficient R=1; only the latter is linearly stable in a homogeneous plasma of infinite length. The asymptotic solutions for SBS in plasmas are calculated and the similarity in the dynamics between SBS and SRS is discussed.
Experimental investigation of magnetic compression of a spheromak plasma
Authors: Yamada M. , Chu T. K. , Ellis R. A. , Janos A. C. , Levinton F. M. , Mayo R. M. , Motley R. W. , Nagata M. , Ono Y. , Satomi N. , Ueda Y.
Published: July 2002

Magnetic compression of S-1 spheromak plasmas [Nucl. Fusion 22, 1407 (1982)] was performed to extend the investigation of confinement properties of the spheromak to plasmas with larger current density and higher plasma pressure than obtained before. Evolution of the magnetic configuration was mapped using internal-probe-based flux plots, and it was found that the plasma compression was approximately self-similar. The Taylor equilibrium state was maintained without flux conversion or relaxation phenomena. With a compression factor of up to 1.6, a significant increase of plasma pressure was observed. The peak electron temperature rose from approximately 40 eV before compression to about 100 eV, and the peak density increased somewhat less than the adiabaticity based scaling, which suggests the presence of an enhanced particle loss mechanism. In general, the electron’s beta value was approximately constant during the compression; that is, ne0Te0∝B20. This result is consistent with the S-1 scaling obtained earlier without compression. The ion temperature measured by Doppler broadening of low Z impurity line radiation was observed to rise as high as 0.5 keV.
Macroclump model of the nonlinear evolution of the sideband instability in a helical wiggler free-electron laser
Authors: Yang T.-Y. Brian , Davidson Ronald C.
Published: July 2002

The nonlinear evolution of a helical wiggler, free-electron laser is investigated within the framework of a macroclump model for the trapped electrons. The model describes the nonlinear evolution of a right-circularly polarized electromagnetic wave with frequency ωs and wave number ks, and slowly varying amplitude âs(z,t) and phase δs(z,t) (eikonal approximation). The model further assumes that the trapped electrons can be treated as tightly bunched macroclumps that interact coherently with the radiation field. The analysis is carried out in the ponderomotive frame, which leads to a substantial simplification in both the analytical and numerical studies. As a first application, the nonlinear evolution of the primary signal is examined when ∂/∂l′=0 (no spatial variation of the wave amplitude and phase). The evolution equations are reduced to quadrature, and the maximum excursion of the wave amplitude âs,max is calculated analytically. Subsequently, the nonlinear evolution of the sideband instability is investigated, making use of the equations describing the self-consistent evolution of the wave amplitude âs and phase δs, which vary slowly with both space and time, together with the macroclump orbit equation.

In the present analysis, the sideband signals are treated as perturbations (not necessarily small) about a constant-amplitude (â0s =const) primary electromagnetic wave with slowly varying phase δ0s(z′). The coupled orbit and field equations are investigated analytically and numerically over a wide range of system parameters to determine detailed scaling properties of the sideband instability. The results of the present analysis suggest that free-electron lasers operating with system parameters corresponding to the strong-pump regime [(Ω′B/Γ0)6/4≫1] are least vulnerable to the sideband instability. Moreover, the nonlinear evolution of the sideband instability is investigated numerically for system parameters corresponding to the Los Alamos free-electron laser experiment [Warren et al., IEEE J. Quantum Electron. QE-21, 882 (1985)]. In several aspects, the numerical results are found to be in good qualitative agreement with the experimental results.
Mode competition in the quasioptical gyrotron
Authors: Riyopoulos S. , Fliflet A. W.
Published: July 2002

A set of equations describing the nonlinear multimode dynamics in the quasioptical gyrotron is derived. These equations, involving the slow amplitude and phase variation for each mode, result from an expansion of the nonlinear induced current up to fifth order in the wave amplitude. The interaction among various modes is mediated by coupling coefficients, of known analytic dependence on the normalized current I, the interaction length μ, and the frequency detunings Δi corresponding to the competing frequencies ωi. The particular case when the modes form triads with frequencies ω1+ω3−2ω2≂0 is examined in more detail. The equations are quite general and can be used to study mode competition, the existence of a final steady state, its stability, as well as its accessibility from given initial conditions. It is shown that when μ/β⊥≫1, μ can be eliminated as an independent parameter. The control space is then reduced to a new normalized current Î and the desynchronism parameters νi=Δiμ for the interacting frequencies. Each coupling coefficient Gij is written as Gij=ÎSijĜij (νi,νj), where the nonlinear filling factor Sij, carrying the information of the beam current spatial profile, can be computed independently. Therefore, it suffices to compute tables of Ĝij as functions of ν1, ν2, and ν3 once to cover the parameter space. Results for a cold beam are presented here.