bluuebunny/crossref_metadata_2025 huggingface dataset:
Spectroscopic investigation of the generation of “isomerization” states: Eigenvector analysis of the bend-CP stretch polyad
Authors: Ishikawa Haruki , Nagao Chioko , Mikami Naohiko , Field Robert W.
Published: July 2002

The highly excited vibrational levels of HCP exhibit a regular energy level and intensity pattern characteristic of 2:1 bend-CP stretch polyads. Stimulated by the experimental observation of vibrational levels with rotational constants (B-values) 5%–10% larger than other observed levels, Schinke and co-workers noticed that these large-B levels were characterized by atypical nodal structures indicative of large amplitude motion along the minimum energy HCP↔CPH isomerization path [J. Chem. Phys. 107, 9818 (1997)]. In this paper, we show that the transition from “normal-mode-type” to “isomerization” vibrational states arises naturally out of a traditional spectroscopic (algebraic) effective Hamiltonian polyad model. A global least squares fit, based on this polyad Heff model, shows that all of the observed “isomerization” states belong to polyads and that the eigenvectors of this Heff model have the qualitatively distinct nodal structure first noticed by Schinke and co-workers. The “isomerization” states are not indicative of a breakdown of the polyad model; rather they are a natural consequence of this traditional spectroscopic model.
Density functional approach to study the elastic constants of biaxial nematic liquid crystals
Authors: Longa Lech , Stelzer Joachim , Dunmur David
Published: July 2002

A density functional theory for bulk and surface elastic constants of biaxial nematic liquid crystals is developed. It is based on a functional Taylor expansion of the free energy of a distorted biaxial nematic with respect to the one-particle distribution function. Detailed microscopic expressions for the biaxial elastic constants of bulk and surface deformations are derived by expanding further the distribution functions into symmetry-adapted Wigner matrices. The final expressions depend on generalized orientational order parameters characterizing the biaxial nematic and on expansion coefficients of the direct pair correlation function. The case where the expansions are truncated at the lowest nontrivial order with respect to the momentum index of the Wigner matrices is analyzed in detail. It gives only six distinct, nonzero bulk elastic constants. The mixed elastic constants, which measure distortions of more than one director, vanish within this approximation. As in the uniaxial case, a splay-bend degeneracy for all directors is apparent. The theory is next applied to the biaxial nematic phase recently studied by Biscarini et al. [Phys. Rev. Lett. 75, 1803 (1995)] providing numerical estimates of biaxial elastic constants for the case of thermodynamically stable biaxial ordering. It is shown that the values of the elastic constants connected with secondary directors are much lower than those associated with the primary one.
The critical hydration reactions of NO+ and NO2+
Authors: Angel L. , Stace A. J.
Published: July 2002

The reactions of NO+ and NO2+ with water are considered to make an important contribution to the formation of proton hydrates in the upper atmosphere. There have been several recent studies of the relevant reactions, with the result that discrepancies have arisen in each case over the critical number of water molecules required to promote the appearance of a proton hydrate. Presented here are new results based on the collision-induced reactions of NO+⋅(H2O)n and NO2+⋅(H2O)n cluster ions, which we believe clarify the situation.
Reaction of S2 and H2S with Sn/Pt(111) surface alloys: Effects of metal–metal bonding on reactivity towards sulfur
Authors: Rodriguez José A. , Chaturvedi Sanjay , Jirsak Tomas , Hrbek Jan
Published: July 2002

The surface chemistry of S2 and H2S on polycrystalline Sn, Pt(111), and a (∛×∛)R30°-Sn/Pt(111) surface alloy has been investigated using synchrotron-based high-resolution photoemission and ab initio self-consistent-field calculations. At 100–300 K, S2 chemisorbs and reacts on polycrystalline tin to form metal sulfides. The reactivity of pure tin toward sulfur is large even at a temperature as low as 100 K. In contrast, tin atoms in contact with Pt(111) interact weakly with S2 or H2S. Tin does not prevent the bonding of S to Pt in a (∛×∛)R30°-Sn/Pt(111) surface alloy, but the alloy is less reactive toward H2S than polycrystalline Sn or pure Pt(111). At room temperature, S2 and H2S adsorb dissociatively on Pt sites of (∛×∛)R30°-Sn/Pt(111). Upon the dosing of S2 and H2S to (∛×∛)R30°-Sn/Pt(111), one sees the formation of only a chemisorbed layer of sulfur (i.e., no sulfides of tin or platinum are formed). The Pt–Sn bond is complex, involving a Sn(5s,5p)→Pt(6s,6p) charge transfer and a Pt(5d)→Pt(6s,6p) rehybridization that localize electrons in the region between the metal centers. These phenomena reduce the electron donor ability of Pt and Sn, and the metals are not able to respond in an effective way to the presence of species that are strong electron acceptors like S2, HS, and S. The redistribution of charge produces surfaces that have a remarkable low reactivity toward sulfur. When compared to other admetals (Cu, Zn, Ag, Au), tin is the best choice as a site blocker that can enhance the tolerance of Pt reforming catalysts to sulfur poisoning. The Sn/Pt system illustrates how a redistribution of electrons that occurs in bimetallic bonding can be useful for the design of catalysts that are less sensitive to the presence of S-containing molecules.
The application of complex absorbing potentials to an invariant embedding scattering method: I. Theory and computational details
Authors: Huarte-Larrañaga Fermı́n , Giménez Xavier , Aguilar Antonio
Published: July 2002

In this article, an extension of quantum scattering methods based on propagative R-matrix techniques to deal with negative imaginary potentials is presented. Reactive probabilities can be then obtained, considering only the reactants arrangement channel and Jacobi coordinates. It has been necessary to generalize the R-matrix propagation method, in order to consider the complex-valued nature of the interaction matrix. The new formulation has been particularized, in the present case, to the Infinite-Order Sudden Approximation, for which several results, focusing on the reliability and numerical performances of the method, will be shown.
Computer simulation study of the structure and dynamics of ring polymers
Authors: Brown Scott , Szamel Grzegorz
Published: July 2002

We study the equilibrium structure and dynamics of unconcatenated, unknotted polymer rings in the melt. In agreement with earlier studies we find that rings in the melt are more compact than linear chains. In addition, we show that the “correlation hole” in the equilibrium correlation functions is deeper and wider for rings than for linear chains. This suggests that there is less interpenetration in the melt of rings compared to the melt of linear chains. We also find that rings diffuse faster than linear chains. For smaller rings this result agrees with the earlier work of Müller, Wittmer, and Cates [Phys. Rev. E 53, 5063 (1996)]. The main result of this study is that faster ring diffusion persists up to ring size at least ten times greater than the entanglement crossover of linear chains. Furthermore, we show that, for all ring sizes studied, the dependence of the single-chain relaxation time on ring size is weaker than for linear chains. Finally, we find that both faster diffusion and faster relaxation can be rationalized by the smaller size of rings: The dependence of self-diffusion coefficient and relaxation time on radius of gyration of rings and linear chains is remarkably similar.
Molecular dynamics of homogeneous nucleation in the vapor phase. I. Lennard-Jones fluid
Authors: Yasuoka Kenji , Matsumoto Mitsuhiro
Published: July 2002

Molecular dynamics computer simulation was carried out to investigate the dynamics of vapor phase homogeneous nucleation at the triple point temperature under supersaturation ratio 6.8 for a Lennard-Jones fluid. To control the system temperature, the 5000 target particles were mixed with 5000 soft-core carrier gas particles. The observed nucleation rate is seven orders of magnitude larger than prediction of a classical nucleation theory. The kinetically defined critical nucleus size, at which the growth and decay rates are balanced, is 30–40, as large as the thermodynamically defined value of 25.4 estimated with the classical theory. From the cluster size distribution in the steady state region, the free energy of cluster formation is estimated, which diminishes the difference between the theoretical prediction and the simulational result concerning the nucleation rate.
Potential energy surface and spectroscopy of clusters of rare-gas atoms with cyclopropane
Authors: Roncero Octavio , Villarreal Pablo , Delgado-Barrio Gerardo , González-Platas Javier , Bretón José
Published: July 2002

Analytical empirical potential energy surfaces describing the van der Waals interaction between rare-gas atoms and cyclopropane are presented. The functional form is based on pairwise Lennard-Jones-type potentials which have been widely used to describe rare-gas-benzene complexes, also studied in this work in order to check our theoretical method and for comparison. The parameters have been chosen in order to accurately fit the high resolution microwave spectra recently reported by Xu and Jäger [J. Chem. Phys. 106, 7968 (1997)]. The observed splitting in the microwave spectra of Ne-cyclopropane, associated with rotational tunneling, is well reproduced. Moreover, such tunneling is also important for complexes of Ar and Kr in excited van der Waals states. These phenomena involve a high delocalization of the wave functions and, therefore, intermolecular spectroscopy techniques would provide a good check of the potential energy surface over a broad region of the configuration space.
Wall slip in the molecular dynamics simulation of thin films of hexadecane
Authors: Jabbarzadeh A. , Atkinson J. D. , Tanner R. I.
Published: July 2002

A molecular dynamics simulation of a thin liquid film as it is sheared between two planar walls is reported. The model liquid is composed of linear chain molecules of hexadecane (C16H34) with intramolecular architecture such as bond stretching, angle bending and dihedral potentials included in the model. Designing a model that can mimic the planar shear flow enables us to study important questions on the effects of the wall properties on the slip between the liquid film and the wall. Different properties of the wall such as wall density, wall stiffness and wall–fluid interaction strength have been studied to determine the slip between the wall and fluid. The slip has been investigated for strong and weak adsorbing surfaces at various shear rates. The results emphasize the importance of adsorption on the degree of slip. The dependence of slip on the film thickness is also demonstrated.
Density functional study of the Fe–CO bond dissociation energies of Fe(CO)5
Authors: González-Blanco Oscar , Branchadell Vicenç
Published: July 2002

Fe(CO) n (n=1–5) complexes have been studied using density functional theory (DFT) methods. Several functionals have been used in the geometry optimizations, harmonic frequencies computation and calculation of the iron–carbonyl bond dissociation energies. Coupled-cluster single double (triple) bond dissociation energies have also been computed for the smaller systems. The obtained results show that DFT methods yield reasonable geometries and vibrational frequencies. Regarding the bond dissociation energies, it is shown that the validity of the results depends on whether there is a change in the atomic state of the metal during the dissociation. When the atomic state is the same for both complexes, the bond dissociation energy computed using gradient corrected functionals is within the range of the experimental values, while when the atomic state changes, DFT methods overestimate the bond dissociation energy due to a poor description of the atomic multiplets.
Time-dependent quantum mechanical calculations on H+O2 for total angular momentum J>0 II: On the importance of Coriolis coupling
Authors: Meijer Anthony J. H. M. , Goldfield Evelyn M.
Published: July 2002

The H+O2→OH+O reaction has been studied for total angular momentum J>0 with a time-dependent wave packet method using the Coriolis coupled method of Goldfield and Gray [E. M. Goldfield and S. K. Gray, Comp. Phys. Commun. 98, 1 (1996)] on parallel computers. Helicity conserving (HC) and coupled channel (CC) calculations were performed for J=1, J=2, J=5, and J=10 using two different embeddings for the body fixed coordinate system to investigate the importance of Coriolis coupling for this reactive system. If the H–O2 distance is taken to be the z axis of the coordinate system, we find poor agreement between the HC and the CC calculations for J>2. When the O2 bond is taken to be the z axis, we find good agreement between the CC and HC calculations at low J. For higher J the agreement gets progressively worse, especially at higher energies. We can explain these results using a classical model from a previous paper on H+O2 [A. J. H. M. Meijer and E. M. Goldfield, J. Chem. Phys. 108, 5404 (1998)].
Rotational dynamics of methyl groups in durene: A crystallographic, spectroscopic, and molecular mechanics investigation
Authors: Neumann M. A. , Johnson M. R. , Radaelli P. G. , Trommsdorff H. P. , Parker S. F.
Published: July 2002

Neutron powder diffraction measurements of perdeutero durene in the temperature range from 1.5 K to 290 K have been performed. The lowest temperature structure is the starting point for calculations of the methyl group tunneling and librational dynamics. Ab initio methods and atom–atom potentials are used to determine rotational single particle and coupling potentials. Tunneling splittings and librational bands are calculated by numerical solution of Schrödinger’s equation for a system of many coupled methyl groups. High-resolution inelastic neutron scattering measurements of methyl tunneling and molecular vibrations have been repeated, the tunneling results resolving an inconsistency with earlier NMR work. Quantum molecular dynamics provide a stringent test of the numerical methods and the data are ultimately well reproduced. These results are also discussed in the context of optical measurements of dye molecules in a host lattice of durene.
Macroscopic and mesoscopic characterization of a bistable reaction system: CO oxidation on Pt(111) surface
Authors: Berdau Martin , Yelenin Georgii G. , Karpowicz Andrzej , Ehsasi Mohammad , Christmann Klaus , Block Jochen H.
Published: July 2002

The catalytic oxidation of CO by oxygen on a platinum (111) single-crystal surface in a gas-flow reactor follows the Langmuir–Hinshelwood reaction mechanism. It exhibits two macroscopic stable steady states (low reactivity: CO-covered surface; high reactivity: O-covered surface), as determined by mass spectrometry. Unlike other Pt and Pd surface orientations no temporal and spatiotemporal oscillations are formed. Accordingly, CO+O/Pt(111) can be considered as one of the least complicated heterogeneous reaction systems. We measured both the macroscopic and mesoscopic reaction behavior by mass spectrometry and photoelectron emission microscopy (PEEM), respectively, and explored especially the region of the phase transition between low and high reactivity. We followed the rate-dependent width of an observed hysteresis in the reactivity and the kinetics of nucleation and growth of individual oxygen and CO islands using the PEEM technique. We were able to adjust conditions of the external control parameters which totally inhibited the motion of the reaction/diffusion front. By systematic variation of these conditions we could pinpoint a whole region of external control parameters in which the reaction/diffusion front does not move. Parallel model calculations suggest that the front is actually pinned by surface defects. In summary, our experiments and simulation reveal the existence of an “experimental” bistable region inside the “computed” bistable region of the reactivity diagram (S-shaped curve) leading to a novel dollar ($)-shaped curve.
The application of complex absorbing potentials to an invariant embedding scattering method. II. Applications
Authors: Huarte-Larrañaga Fermı́n , Giménez Xavier , Lucas Josep M. , Aguilar Antonio
Published: July 2002

The application to several triatomic reactions of a novel implementation of absorbing potentials on a generalized R-matrix propagation method [Chem. Phys. Lett. 291, 346 (1998) and J. Chem. Phys. 109, 5761 (1998)] is presented. Specific systems chosen have been Li+FH, Mg+FH and H+F2, so that an extensive application covering a wide range of potential energy surfaces (PESs) has been performed: it includes moderately and largely exoergic and endoergic processes, simple and involved PES, moderate to large skew angles, and direct and complex-forming collisions. In all cases, it is shown that the use of the absorbing potential is simple and robust, yielding correct values at a fraction of the computer’s resources consumption. The best effectiveness is obtained for exothermic, direct reactions, for which up to one order of magnitude in CPU time saving is obtained. This efficiency opened the possibility for a very detailed exploration of the reactive process, in particular on those quantities strongly dependent on the collision energy. In addition, it is shown that, as previously known from a totally different numerical approach, the cumulative reaction probability can be efficiently and accurately calculated propagating the scattering solution along a very short range of the scattering coordinate.
Phase behavior of colloidal rod-sphere mixtures
Authors: Vliegenthart G. A. , Lekkerkerker H. N. W.
Published: July 2002

We investigate the depletion induced phase separation in mixed suspensions of colloidal spheres with diameter σ and colloidal rods with length L and diameter D. Using an extension of the free volume method developed by one of us [H.N.W. Lekkerkerker and A. Stroobants, Physica A 195, 387 (1993)], we calculate the phase diagrams for L⩽σ and various L/D ratios. For long thin rods, the volume fractions of rods needed to induce phase separation scale as D2/Lσ. Good agreement with recent experimental results is obtained.
Four-dimensional quantum and two-dimensional classical mechanical study of molecule–surface interactions
Authors: Adhikari Satrajit , Billing Gert D.
Published: July 2002

The collision of a hydrogen molecule with a copper surface has been studied using a semiclassical theory. The four molecular coordinates, the distance from the surface, the vibrational coordinate, and the polar angles, are treated quantum mechanically using a grid method. The kinetic energy is evaluated by a fast Fourier transformation (FFT) technique and the wave function propagated by a Lanczos iterative method. Two translational degrees of freedom for motion at the lattice are treated classically, whereas the normal modes of the solid are quantized using a quantum boson approach. The present calculation indicates that rotational state distributions of the scattered molecule and dissociative chemisorption of the diatom on the metal surface are significantly affected by the phonon coupling.
An excitonic mechanism of detonation initiation in explosives
Authors: Kuklja Maija M. , Stefanovich Eugene V. , Kunz A. Barry
Published: July 2002

A novel mechanism for detonation initiation in solid explosives is proposed. This is based on electronic excitations induced by an impact wave propagating through the crystal. We illustrate the model by using the RDX (C3H6N6O6) crystal as an example. In our model, a key role belongs to lattice defects, in particular edge dislocations, which promote dramatic changes in the electronic structure, primarily a reduction of the optical gap due to the splitting off of local electronic states from both valence and conduction bands. The pressure inside the impact wavefront further reduces the band gap, making it close to zero. This promotes highest occupied molecular orbital–lowest unoccupied molecular orbital HOMO–LUMO transitions resulting in N–NO2 bond breaking and the creation of favorable conditions for the initiation of a chain reaction. Experimental facts supporting the suggested mechanism are discussed.
Radio-frequency-mediated dipolar recoupling among half-integer quadrupolar spins
Authors: Baldus Marc , Rovnyak David , Griffin Robert G.
Published: July 2002

It is demonstrated that through-space recoupling can be achieved in dipolar coupled quadrupolar spins in the presence of an appropriate radio-frequency field. Experimental and theoretical results for 23Na–23Na pairs are presented that elucidate the experimental conditions leading to homonuclear dipolar transfer. The effect of adiabatic amplitude modulation on spin-3/2 systems is compared to spin-1/2 cases and applications of this approach in the context of high resolution multiquantum magic angle spinning for dipolar filtering and correlation are discussed.
Electric-field-dependent empirical potentials for molecules and crystals: A first application to flexible water molecule adsorbed in zeolites
Authors: Cicu P. , Demontis P. , Spanu S. , Suffritti G. B. , Tilocca A.
Published: July 2002

A general method to include electric-field-dependent terms in empirical potential functions representing interatomic interactions is proposed. It is applied to derive an intramolecular potential model for the water molecule able to reproduce the effects of an electric field on its geometry and dynamics: to enlarge the HOH angle, to increase slightly the OH bond lengths, to red-shift the stretching vibrational frequencies, and to blue-shift slightly the bending mode frequency. These effects have been detected experimentally for water adsorbed in zeolites and have been confirmed by quantum mechanical calculations. The electric-field-dependent intramolecular potential model for water has been combined with a newly refined intermolecular potential for bulk water and with new potentials representing cation–water and aluminosilicate–water interactions in order to simulate, by classical molecular dynamics (MD) technique, the behavior of water adsorbed in zeolites. The performances of the model have been checked by a MD simulation of liquid water at room temperature, by the structural and vibrational properties of the water dimer, and by test MD calculations on a hydrated natural zeolite (natrolite). The results are encouraging, and the simulations will be extended to study the behavior of water adsorbed in other zeolites, including diffusion and some aspects of ion exchange processes.
High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60
Authors: Hendrickx E. , Kippelen B. , Thayumanavan S. , Marder S. R. , Persoons A. , Peyghambarian N.
Published: July 2002

Photogeneration of carriers was measured at 633 nm in a series of polymer composites based on polystyrene, doped with a triphenyldiamine derivative as hole transport molecule and C60 as sensitizer. Light absorption and generation of mobile carriers was achieved through the charge-transfer (CT) complex formed between the hole transport molecule and the sensitizer. We discuss the influence of the ionization potential of the hole-transport molecule on the photogeneration efficiency of the CT complex it forms with the sensitizer C60. Photogeneration efficiency of unity at an applied electric field of 55 V/μm is found in one composite.
Kinetics of the reactions of N2+ with CO2 and SO2 from 300–1400 K
Authors: Dotan Itzhak , Midey Anthony J. , Viggiano A. A.
Published: July 2002

Rate constants and branching ratios have been measured for the reactions of N2+ with CO2 and SO2 in a high-temperature flowing afterglow from 300–1400 K. The rate constants have also been measured as a function of kinetic energy in a selected ion flow drift tube at 298 K for the reaction of N2+ with CO2. The rate constants for the reaction of N2+ with CO2 in the selected ion flow drift tube (SIFDT) and high temperature flowing afterglow (HTFA) both decrease monotonically with increasing energy. The rate constants at high temperatures have a large fraction of the available energy in internal energy (rotational and vibrational). Compared to the SIFDT rate constants with most of the energy in translation, internal energy hinders the reactivity more than translational energy. The rate constants for the reaction of N2+ with SO2 also decrease with increasing energy up to around 0.4 eV. The rate constants increase above 0.4 eV when an endothermic dissociative charge-transfer channel forming SO+ becomes important. Comparing the HTFA results with previous flow drift tube measurements shows that translational, rotational, and vibrational energy affect the reactivity identically at low energy where the SO2+ channel dominates. It appears that N2+ vibrational excitation is mainly responsible for the SO+ channel, consistent with a previous study. The results for the N2+ reactions are compared to the energetically similar reactions of Ar+ with CO2 and SO2.
A uniqueness theorem for an inverse Sturm–Liouville problem
Authors: McLaughlin Joyce R. , Rundell William
Published: July 2002

A new uniqueness theorem is established for the inverse Sturm–Liouville problem. It is shown that the measurement of a particular eigenvalue for an infinite set of different boundary conditions is sufficient to determine the unknown potential.
Conformally Ricci-flat viscous fluids
Authors: Tupper B. O. J.
Published: July 2002

It is shown that if the gradient of the conformal scalar in a conformally Ricci-flat space-time is parallel to an eigenvector (timelike, spacelike, or null) of the stress-energy tensor, then acceptable solutions, without restrictions on the physical and kinematical quantities, of the Einstein field equations for a viscous fluid with heat conduction may be found.
Onsager’s algebra and the Dolan–Grady condition in the non-self-dual case
Authors: Davies Brian
Published: July 2002

In this paper, it is shown that a pair of operators that satisfy the Dolan–Grady conditions generate an Onsager algebra even in the case that they are not self-dual. Briefly considered will be the implications for the spectra of superintegrable spin chains, in various sectors.
Preliminary group classification of equations v
t
t=f (x,v
x)v
x
x+g(x,v
x)
Authors: Ibragimov N. H. , Torrisi M. , Valenti A.
Published: July 2002

A classification is given of equations vtt=f(v,vx)vxx+g(x,vx) admitting an extension by one of the principal Lie algebra of the equation under consideration. The paper is one of few applications of a new algebraic approach to the problem of group classification: the method of preliminary group classification. The result of the work is a wide class of equations summarized in Table II.
A new N=2 supersymmetric Korteweg–de Vries equation
Authors: Labelle P. , Mathieu P.
Published: July 2002

There are two known integrable N=2 space supersymmetric extensions of the KdV equation. Both can be written as Hamiltonian systems with a common Poisson structure which corresponds to the N=2 supersymmetric form of the second KdV structure. By analyzing the conservation laws of the one parameter family of equations that share this Hamiltonian structure, one finds that a third system is singled out by the existence of nontrivial conservation laws. It is conjectured to be integrable.
A supergroup based supersigma model
Authors: de Azcárraga J. A. , Izquierdo J. M. , Zakrzewski W. J.
Published: July 2002

The supergroup UOSp(1,2) is used to construct geometrically a twice graded supersymmetric supersigma model. In an appropriate contraction limit, the model reduces to the conventional supersymmetric sigma model.
The gravitational sector in the Connes–Lott formulation of the standard model
Authors: Chamseddine A. H. , Fröhlich J. , Grandjean O.
Published: July 2002

We studied the Riemannian aspect and the Hilbert–Einstein gravitational action of the noncommutative geometry underlying the Connes–Lott construction of the action functional of the standard model. This geometry involves a two-sheeted, Euclidian space–time. We show that if we require the space of forms to be locally isotropic and the Higgs scalar to be dynamical, then the Riemannian metrics on the two sheets of Euclidian space–time must be identical. We also show that the distance function between the two sheets is determined by a single, real scalar field whose vacuum expectation value (VEV) sets the weak scale.
Inhibition of chaotic escape from a potential well using small parametric modulations
Authors: Chacón Ricardo , Balibrea F. , López M. A.
Published: July 2002

It is shown theoretically for the first time that, depending on its period, amplitude, and initial phase, a periodic parametric modulation can suppress a chaotic escape from a potential well. The instance of the Helmholtz oscillator is used to demonstrate, by means of Melnikov’s method, that parametric modulations of the linear or quadratic potential terms inhibit chaotic escape when certain resonance conditions are met.
On a certain renormalization group method
Authors: Ziane M.
Published: July 2002

In this paper, a mathematical study of the renormalization group method, recently introduced by Chen, Goldenfeld, and Oono [Phys. Rev. E 54, 376 (1997); Phys. Rev. Lett. 73, 1311 (1994), NATO Adv. Study Inst. Ser., Ser. B 284, 375 (1991)] is given for the case of autonomous nonlinear systems of differential equations. We also observe that the approximation results obtained by this method by Chen, Goldenfeld, and Ono [NATO Adv. Study Inst. Ser., Ser. B 284, 375 (1991)] are valid over long time intervals. Moreover, a connection between this method and the classical Poincaré–Dulac normal forms and the averaging method is briefly discussed.
On the theory of superfluid Fermi liquid with spin-triplet pairing in a magnetic field
Authors: Tarasov A. N.
Published: July 2002

The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.
Numerical solution and analysis of asymmetric convention in a vertical cylinder: An effect of Prandtl number
Authors: Crespo del Arco E. , Bontoux P.
Published: July 2002

Three-dimensional steady flows are simulated with a finite-difference technique in a cylinder of height-to-radius ratio A=4 heated from below. Basic axisymmetric (m=0) and asymmetric (m=1,2) modes are identified in the solutions. The relative contributions of these modes to the supercritical flow are assessed for Rayleigh numbers up to Ra≅10 Rac at Prandtl number Pr=6.7 and Ra≅2.5 Rac at Pr=0.02. At low Rayleigh number the core flow exhibits characteristic features of the m=1 dominant mode. At elevated Rayleigh numbers secondary vortices corresponding to the m=0 mode appear and develop differently in both size and magnitude for the two Prandtl numbers. The Ra dependence of important characteristic variables is analyzed in light of available nonlinear theories and laboratory measurements.
Waves on a viscous fluid film down a vertical wall
Authors: Nakaya C.
Published: July 2002

Waves on a viscous fluid film flowing down a vertical plane wall are studied theoretically. Stationary solutions are sought for a nonlinear equation that describes the variation of the free surface, and a solitary wave is found as an exact solution. The corrugation of the surface concentrates in a small portion comparable with the film thickness and propagates with a constant speed. There exist various kinds of solitary waves characterized by the number of their humps. To compare these solitary waves with the so-called single waves, solitary waves of the same kind are arranged at regular intervals on the laminar flow. When the nonlinearity is comparatively weak, individual solitary waves are so close to one another that this procedure of finding the periodic solution has to be replaced by the method of expanding the free surface as a Fourier sum and determining its coefficients. The periodic solution of arbitrary wavelength is obtained from these two procedures. There are as many kinds of periodic solutions as those of solitary waves, and a selection rule is proposed as to the problem of which kind of periodic solutions actually appears. Each kind of our periodic solutions is compared with the nearly sinusoidal wave as well as the single wave. It is seen that the wave that was observed experimentally is nothing but a superposition of solitary waves that are mistaken for the solitary waves with only one principal hump. Further, it is expected that solitary waves are still excited, even though there are no artificial perturbations.
The effect of Mach number on the stability of a plane supersonic wake
Authors: Chen Jacqueline H. , Cantwell Brian J. , Mansour Nagi N.
Published: July 2002

Recent interest in supersonic combustion and problems of transatmospheric flight has prompted renewed research efforts in laminar–turbulent free-shear flow transition. In the present work, the influence of Mach number on the stability of supersonic planar wake flows is investigated to gain insight into the physics of linear, nonlinear, and three-dimensional (3-D) stages of transition. The effect of varying the relative phase difference between a fundamental instability mode and its subharmonic is investigated as a possible means of controlling the evolution of a wake. From a linear stability analysis, it is found that the influence of increasing Mach number is stabilizing, resulting in a growth rate at a Mach number of 3 which is 60% that of an incompressible wake. Direct numerical simulations of the time-dependent compressible Navier–Stokes equations in two and three dimensions are performed for a forced time-developing wake using a spectral collocation method. The results of the two-dimensional (2-D) simulations show the slow rollup of spanwise vortices at high Mach numbers that is attributed to the influence of baroclinic and dilatational effects. Finally, the results of three-dimensional simulations forced with the most unstable Kelvin–Helmholtz wave and a pair of oblique three-dimensional waves show that, depending on the initial phasing between the 2-D and 3-D waves, vortex loops may or may not form as a result of the interaction between the streamwise and spanwise vorticity.
Numerical study of discrete-velocity gases
Authors: Inamuro Takaji , Sturtevant Bradford
Published: July 2002

A finite-difference method for solving the discrete Boltzmann equations, which are the governing equations for a model gas in which molecules have many discrete velocities, is developed. The method is applied to three fundamental problems in rarefied gas flow to study the features of discrete-velocity gases: normal shock wave structure, heat transfer between two parallel plates, and two-dimensional vapor deposition. Two different discrete-velocity gas models are used.
A route to chaos in an oscillatory flow: Feigenbaum scenario
Authors: Blondeaux Paolo , Vittori Giovanna
Published: July 2002

The transition process which leads the oscillatory flow over a wavy wall from a periodic behavior to chaos is studied by means of the numerical algorithm described by Blondeaux and Vittori [J. Fluid Mech. 226, 257 (1991)]. By increasing the Reynolds number, it has been found that the flow experiences an infinite sequence of period doublings (pitchfork bifurcations) which take place at successive critical values. These critical values of the Reynolds number accumulate to a finite limit with the Feigenbaum rate of convergence. For Reynolds numbers larger than the above limit a chaotic flow is detected.
Stability of miscible displacements in porous media with nonmonotonic viscosity profiles
Authors: Manickam O. , Homsy G. M.
Published: July 2002

The effect of a nonmonotonic viscosity profile on the stability of miscible displacements in porous medium is studied. A linear theory using the quasi-steady-state approximation is employed to find the growth rate of the perturbations in the flow. The resulting eigenvalue problem has both a discrete and continuous spectrum. It is possible to obtain an analytical solution for a step base state concentration profile. The step profile result indicates that a nonmonotonic viscosity profile can be stable even when the viscosity contrast, measured by the end-point viscosities, is unfavorable, and vice versa. Asymptotic expansions of the growth rate for short times and for small wave numbers of the disturbances are obtained. The short-time expansion shows that the diffusion of the base state does not always mitigate the instabilities and the small wave-number expansion gives a sufficient condition for the flow to be unstable. Finally, the eigenvalue problem is solved numerically for diffused concentration profiles using finite difference methods. A model viscosity profile is chosen to parametrically study the stability of nonmonotonic profiles. The parametric study shows that the diffusion of the base state can have a destabilizing effect, with the surprising result that the nonmonotonic profiles that are predicted to be stable by the step profile analysis eventually become unstable by the destabilizing effect of diffusion. The ‘‘critical’’ time at which a stable flow turns unstable is obtained as a function of the parameters of the problem. A physical mechanism is proposed to explain the effects of diffusion on the stability of the flow.
Temporal scaling behavior of decaying two-dimensional turbulence
Authors: Weiss Jeffrey B. , McWilliams James C.
Published: July 2002

Decaying two-dimensional turbulence is characterized by the emergence of coherent vortices, which subsequently dominate the evolution. The temporal scaling behavior of the flow is analyzed using a scaling theory, a long-time integration of the fluid equations, and a dissipative, modified point-vortex model that represents the turbulence as a system of interacting coherent structures. Good agreement is found in the behavior of average vortex properties, low-order moments of the flow fields, and the form of self-similar evolution.
Predicting equilibrium states with Reynolds stress closures in channel flow and homogeneous shear flow
Authors: Abid R. , Speziale C. G.
Published: July 2002

Turbulent channel flow and homogeneous shear flow have served as basic building block flows for the testing and calibration of Reynolds stress models. In this paper, a direct theoretical connection is made between homogeneous shear flow in equilibrium and the log layer of fully developed turbulent channel flow. It is shown that if a second-order closure model of the standard type is calibrated to yield good equilibrium values for homogeneous shear flow, it will also yield good results for the log layer of channel flow provided that the Rotta coefficient is not too far removed from one. Most of the commonly used second-order closure models introduce an ad hoc wall reflection term in order to mask deficient predictions for the log layer of channel flow that arise either from an inaccurate calibration of homogeneous shear flow or from the use of a Rotta coefficient that is too large. Illustrative model calculations are presented to demonstrate this point which has important implications for turbulence modeling.
Gyrokinetic energy conservation and Poisson-bracket formulation
Authors: Brizard A.
Published: July 2002

An integral expression for the gyrokinetic total energy of a magnetized plasma, with general magnetic field configuration perturbed by fully electromagnetic fields, was recently derived through the use of a gyrocenter Lie transformation. It is shown that the gyrokinetic energy is conserved by the gyrokinetic Hamiltonian flow to all orders in perturbed fields. An explicit demonstration that a gyrokinetic Hamiltonian containing quadratic nonlinearities preserves the gyrokinetic energy up to third order is given. The Poisson-bracket formulation greatly facilitates this demonstration with the help of the Jacobi identity and other properties of the Poisson brackets.
Stabilization of collisionless trapped particle modes in tokamaks
Authors: Dominguez R. R.
Published: July 2002

A quadratic form is derived to study the stability of collisionless trapped particle modes in tokamaks. Marginal stability criteria show that stability can be obtained by controlling the electron temperature profile. In a low aspect ratio equilibrium (such as the recently proposed Comet [Comments Plasma Phys. XII, 125 (1989)]), the stability requirement is ηe≂O(1) (ηe=∂ ln Te/∂ ln ne); in a standard large aspect ratio tokamak with a broad density profile, the requirement is LTe/R≂O(1) (L−1Te=−∂ln Te/∂r). Possible application of the second scenario to H-mode plasmas is noted.
Competition among nonlinear effects in tearing instability saturation
Authors: Malara Francesco , Veltri Pierluigi , Carbone Vincenzo
Published: July 2002

The nonlinear evolution of a tearing instability in a sheet pinch in a slab geometry is numerically studied. It is found that, when the whole unstable spectrum is excited, to a small but finite level, a new nonlinear effect, an inverse energy cascade, occurs. The inverse cascade corresponds, in the physical space, to a coalescence process. The nonlinear development of the instability is then considerably modified with respect to the case in which only one unstable mode is present. In particular, the inverse cascade is responsible for the saturation of the single tearing-unstable modes. However, the nonlinear effects associated to the coalescence do not slow the growth of the instability, as a whole. On the contrary, the perturbation energy exponentially also grows during the nonlinear stage, up to the saturation of the instability. Moreover, a recurrent behavior is found after the saturation, corresponding to the creation of localized current sheets, where new tearing instabilities develop. The competition among the different nonlinear effects is discussed.
Weak double layers in ion-acoustic turbulence
Authors: Barnes C. , Hudson M. K. , Lotko W.
Published: July 2002

The evolution of weak double layers in ion-acoustic turbulence in one and two-dimensional particle simulations is examined. Weak double layers (eφ≲Te) evolve in simulations when a subthermal electron drift is imposed on a long or nonperiodic system with Te/Ti≫1. Their growth rate increases with the electron drift, and they decay because of ion trapping. They do not form in weakly magnetized or unmagnetized two-dimensional (2-D) systems unless a nonuniformity is introduced in the initial or boundary conditions. When the plasma is strongly magnetized (ωce>ωpe), they emerge from 2-D ion-acoustic turbulence as coherent structures localized transversely to the magnetic field.
Evidence in the second-harmonic emission for self-focusing of a laser pulse in a plasma
Authors: Stamper J. A. , Lehmberg R. H. , Schmitt A. , Herbst M. J. , Young F. C. , Gardner J. H. , Obenschain S. P.
Published: July 2002

Short-pulse (300 psec), high-intensity (1014−1015 W/cm2) Nd-laser light was propagated into variable scale length plasmas (Ln≡n/∇n=200–400 μm at 0.1 critical density) preformed by long-pulse (4 nsec), low-intensity (≂6×1012 W/cm2) irradiation of planar targets. For high short-pulse intensities (≥5×1014 W/cm2), time-integrated images show filament-shaped regions of second-harmonic (2ω0) emission from the low density (0.01≤ne/nc≤0.2) region of the ablation plasma. Two-dimensional computer calculations of the hyrodynamics and laser beam propagation indicate that these filaments are consistent with ponderomotive self-focusing of the short pulse. A theoretical model that explains the 2ω0 generation mechanism within low-density filaments is also presented.
Inverse energy cascade in two-dimensional turbulence
Authors: Qian J.
Published: July 2002

The closure method developed in earlier papers [J. Qian, Phys. Fluids 26, 2098 (1983); 27, 2412 (1984)] is applied to the study of the inverse energy cascade in two-dimensional turbulence. The resultant inertial-range energy spectrum is E(k)=2.58g0.244ε2/3k−5/3. Here g is a localization factor and ε is the rate of energy cascade. This result is compatible with the numerical experiments by Lilly [D. K. Lilly, Phys. Fluids Suppl. II 12, 24 (1969)], Siggia and Aref [E. D. Siggia and H. Aref, Phys. Fluids 24, 171 (1981)], and Frisch and Sulem [U. Frisch and P. L. Sulem, Phys. Fluids 27, 1921 (1984)].
Direct drag measurements for a flat plate with passive boundary layer manipulators
Authors: Sahlin Alexander , Alfredsson P. Henrik , Johansson Arne V.
Published: July 2002

Drag measurements for a flat plate equipped with passive boundary layer turbulence manipulators, the so-called Large Eddy Break Up (LEBU) devices, have been carried out in a towing tank at plate length Reynolds numbers of 5–20 million. The towing tank facility allowed direct drag measurements as opposed to indirect methods based on, e.g., measurement of momentum loss thickness of the boundary layer. The LEBU devices consisted of two hydrofoils arranged in tandem, with a spacing of five to eight boundary layer thicknesses at the manipulator position (δm) and a height in the boundary layer of 0.5δm–0.9δm. Four different manipulator configurations were tested, with and without a trip wire on the test plate. The LEBU foil section was 10% thick and symmetric. The ratio between the LEBU chord and δm ranged from 0.8 to 1.1, and the chord Reynolds number ranged from 25 000 to 100 000. Only for the lowest Reynolds number was a 2% drag reduction obtained. However, the main body of the experiments showed no drag reduction in contrast to previously reported experiments.
Analytic theory for the linear stability of the Saffman–Taylor finger
Authors: Tanveer S.
Published: July 2002

An analytic theory is presented for the linear stability of the Saffman–Taylor finger in a Hele–Shaw cell. Eigenvalues of the stability operator are determined in the limit of zero surface tension and it is found that all modes for the McLean–Saffman branch of solutions [J. Fluid Mech. 102, 455 (1980)] are neutrally stable, whereas other branches first calculated by Romero (Ph.D. thesis, California Institute of Technology, 1982) and Vanden-Broeck [Phys. Fluids 26, 2033 (1983)] are unstable to arbitrary infinitesimal disturbances. It is also shown that the Saffman–Taylor discrete set of eigenvalues is a special case of a continuous unstable spectrum for zero surface tension. The introduction of any amount of surface tension perturbs the corresponding eigenmodes such that the finger boundary is a nonanalytic curve in general. Only transcendentally small terms in surface tension are responsible for the nonanalyticity of the finger boundary as in the case of Saffman–Taylor steady finger solutions of arbitrary finger width.