bluuebunny/crossref_metadata_2025 huggingface dataset:
Spectroscopic characterization of the AsF2 radical
Authors: Brum Jeffrey L. , Hudgens Jeffrey W.
Published: July 2002

The electronic spectrum of the AsF2 radical was observed between 330 and 380 nm using one-color, mass-resolved, 2+1 resonance enhanced multiphoton ionization (REMPI) spectroscopy. The spectrum arises from two-photon resonances with the F̃ (T0=54 355±15 cm−1, ν1′=813±6 cm−1, and ν2′=308±5 cm−1)  and  H̃ (T0=57 480±15 cm−1, ν1′=810±10 cm−1, and ν2′=310±20 cm−1), Rydberg states. A third photon ionized the radicals. The REMPI spectrum exhibits vibrational hot bands that give spectroscopic constants for AsF2 (X̃ 2B1) of ν1″=705±10 cm−1 and ν2″=285±10 cm−1. Solutions of the Rydberg equation indicate that plausible assignments for the F̃ and H̃ states are limited to the set of 4d and 5p Rydberg states.
Doppler-free spectroscopy of KLi
Authors: Bednarska V. , Ekers A. , Kowalczyk P. , Jastrzȩbski W.
Published: July 2002

The B 1∏–X 1∑+ band system of the 39K7Li molecule was investigated by Doppler-free polarization spectroscopy in a heat-pipe oven. Precise molecular constants for levels v=0–3 in the ground X 1∑+ state and levels v=0–2 in the excited B 1∏ state were determined. The e-parity components in all three vibrational levels of the B state were found to be subject to rotational perturbations, assigned to interaction with the C 1∑+ state. The deperturbation analysis provided preliminary constants of the perturbing C state and values of the coupling matrix elements.
The growth mechanism of (–Cu–O–) strings on a Ag(110) surface studied by scanning tunneling microscopy, x-ray photoelectron spectroscopy, and high resolution electron energy loss spectroscopy
Authors: Matsumoto Yuji , Sakamoto Kazuyuki , Okawa Yuji , Suto Shozo , Tanaka Ken-ichi
Published: July 2002

A (–Cu–O–) string on a Ag(110) surface defined by scanning tunneling microscopy (STM) was studied using the x-ray photoelectron spectroscopy (XPS), high resolution electron energy loss spectroscopy (HREELS). These data give the information about bonding properties which cannot be derived from the STM images. The combinative studies could show the structure as well as the growth mechanism of (–Cu–O–) strings on the Ag(110) surface. Deposition of Cu atoms on a p(2×1)-O Ag(110) surface resulted in a new O(1s) peak at 529.9 eV in the XPS and a new electron energy loss peak at 35 meV in the HREELS. These new peaks are assignable to the (Cu–O) bonding state on Ag(110), which is corresponding to the growth of new (–Cu–O–) strings in the [11̄0] direction shown by the STM. These results suggest a stoichiometric reaction producing (–Cu–O–) strings according to an equation of (–Ag–O–)+Cu→(–Cu–O–)+Ag on the Ag(110) surface. The fact that the Ag atoms released by the chemical reaction make layered Ag islands and the (–Cu–O–) strings also grow on the Ag islands in the [11̄0] direction is indicative that the reaction proceeds perfectly in stoichiometric manner over the terrace.
Short-range effects in resonant electron–molecule scattering from van der Waals clusters
Authors: Lucchese R. R. , Gianturco F. A.
Published: July 2002

A theoretical study is presented of the dynamics of resonant electron scattering from N2–Ar and N2–Ar2 van der Waals clusters. Using the results of quantum electron-molecule scattering calculations we analyze the effects of adjacent Ar atoms on the width and position of the low-energy Πg2 electron-scattering resonance of N2. The results indicate that the presence of the Ar atoms leads to positive energy shifts and an increase in the width of the resonance. The magnitude of these changes depended on the orientation of N2 relative to the Ar atoms and on the number of Ar atoms. Additionally, in some arrangements, the degenerate Πg2 resonance was split into two distinct resonances. Implications for electron scattering from N2 adsorbed on solid Ar surfaces are also discussed.
Quantum theory of four-atom reactions using arrangement channel hyperspherical coordinates: Formulation and application to OH+H2↔H2O+H
Authors: Pogrebnya Sergei K. , Echave Julian , Clary David C.
Published: July 2002

An arrangement channel hyperspherical coordinate method for performing quantum scattering calculations on four-atom reactions is formulated. This method treats the vibrational and rotational states in different arrangement channels by a close-coupling expansion in nonorthogonal functions. The method is applied to the calculation of state-to-state probabilities for the OH+H2→H2O+H reaction. Good agreement is found with cumulative and state-selected reaction probabilities previously calculated by other methods. The major advantage of this general approach is that the whole S matrix can be obtained in a single calculation.
Structure and vibrational spectra of methanol clusters from a new potential model
Authors: Buck Udo , Siebers Jörg-Gerald , Wheatley Richard J.
Published: July 2002

The structures and vibrational spectra of small methanol clusters from dimer to decamer have been calculated using a newly developed intermolecular potential which is essentially based on monomer wave functions. Special care has been taken for the description of the electrostatic interaction using a distributed multipole representation and including a penetration term. In addition, the potential model consists of repulsion, dispersion, and induction terms. Based on this potential model cluster structures have been calculated. The lowest energy dimer configuration is linear, while from trimer to decamer for the most stable structures ring configurations were found. Tetramer, hexamer, and octamer have S4-, S6-, and S8-symmetry, respectively. Vibrational spectra of the CO stretch and the OH stretch mode have been determined in the harmonic and in the anharmonic approximation using perturbation theory and variational calculations. Up to the tetramer the experimental spectra of the CO stretch mode are well reproduced, for larger clusters an increasing blueshift with respect to the experimental evidence is found. The experimental data for the OH stretch mode of the dimer are fairly well reproduced in all approximations, however, the spectrum of the trimer can only be reproduced using the variational calculation which includes Darling–Dennison resonance terms.
Parallel and vertical morphologies in block copolymers of cylindrical domain
Authors: Suh K. Y. , Kim Y. S. , Lee Hong H.
Published: July 2002

We present a theoretical result on the ordering of cylindrical morphology in diblock and triblock copolymers. The equilibrium morphology of A–B diblock and A–B–A triblock copolymer films is shown to have the cylinders oriented parallel or vertical to the surface, depending on the film thickness and surface tensions. A criterion is derived that can be used to determine the conditions under which the orientation is parallel or vertical.
A field theory study of the effect of specific interactions in ionic systems: A simple model
Authors: di Caprio D. , Stafiej J. , Badiali J. P.
Published: July 2002

The effect of specific ionic interactions on the Debye length has been studied using a simple model Hamiltonian for a binary mixture of anions and cations in the framework of the field theory. The Hamiltonian contains the Coulombic interaction and an independent non-Coulombic part describing a binary mixture of equivalent uncharged particles. We use a local and quadratic approximation to calculate the partition function via a functional integral. The Debye limiting law is obtained with a renormalized screening length. The screening is enhanced when the specific interactions favor demixion. This is illustrated on the example of an asymmetric hard sphere mixture.
The inner-hydrogen migration and ground-state structure of porphycene
Authors: Kozlowski Pawel M. , Zgierski Marek Z. , Baker Jon
Published: July 2002

Following on from previous work on free-base porphyrin, we present the results of a comprehensive study on the structure and inner-hydrogen migration in porphycene, a structural isomer of porphyrin. We used density functional theory with the hybrid B3-LYP exchange-correlation functional, and both the 6-31G(d) and a triple-zeta double-polarization (TZ2P) basis set (the latter containing 726 contracted basis functions). Full geometry optimizations were carried out and all stationary points were characterized by vibrational analysis. A scaled quantum mechanical (SQM) treatment of the theoretical force constants shows convincingly that the trans-isomer is the ground state, with trans–trans inner-hydrogen migration taking place—as is the case with porphyrin—in a two-step process via a (highly unstable) cis intermediate. With the TZ2P basis, excluding zero-point effects, the trans–cis barrier height is 4.9 kcal/mol, the cis–trans energy difference is 2.4 kcal/mol and the reverse cis–trans barrier height is only 2.5 kcal/mol. We also map out and fully characterize an alternative, high-energy migration path involving a second, nonplanar cis isomer.
The structure of Ni39
Authors: Parks E. K. , Kerns K. P. , Riley S. J.
Published: July 2002

The geometrical structure of Ni39 is probed via molecular adsorption of nitrogen on its surface. Nitrogen uptake patterns are determined at various reaction temperatures, and the results are interpreted in terms of the number and nature of nitrogen binding sites on possible structures. It is found that an adsorbate-induced isomerization occurs at partial nitrogen coverage, but that at saturation a reverse isomerization returns the cluster to its initial structure. The two lowest energy structures calculated by Wetzel and DePristo [T. L. Wetzel and A. E. DePristo, J. Chem. Phys. 105, 572 (1996)] are completely consistent with the observed saturation and isomerization behavior. The structures consist of atom caps packed around a central pentagonal bipyramid, and reflect a marked change from the octahedral structure determined earlier for Ni38.
Designability, thermodynamic stability, and dynamics in protein folding: A lattice model study
Authors: Mélin Régis , Li Hao , Wingreen Ned S. , Tang Chao
Published: July 2002

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be “protein-like,” heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We find two criteria which, together, guarantee that a sequence will be “protein like:” (i) the ground state is a highly designable structure, i.e., the native structure is the ground state of a large number of sequences, and (ii) the sequence has a large Δ/Γ ratio, Δ being the average energy separation between the ground state and the excited compact conformations, and Γ the dispersion in energy of excited compact conformations. These two criteria are not incompatible since, on average, sequences whose ground states are highly designable structures have large Δ/Γ values. These two criteria require knowledge only of the compact-state spectrum. These claims are substantiated by the study of 45 sequences, with various values of Δ/Γ and various degrees of designability, by means of a Borst–Kalos–Lebowitz algorithm, and the Ferrenberg–Swendsen histogram optimization method. Finally, we report on the reasons for slow folding. A comparison between a very slow folding sequence, an average folding one, and a fast folding one, suggests that slow folding originates from a proliferation of nearly compact low-energy conformations, not present for fast folders.
Dielectric constant of water at high electric fields: Molecular dynamics study
Authors: Yeh In-Chul , Berkowitz Max L.
Published: July 2002

Molecular dynamics computer simulations have been carried out for water enclosed between Pt(111) surfaces at high external electric fields. The dielectric constant of water as a function of electric fields has been calculated. Two-dimensional Ewald summation technique has been used for the calculation of long-range Coulombic forces. Simulations with a larger distance between walls, different surfaces, and bulk water have been done to confirm the macroscopic nature of the dielectric constant. Calculated dielectric constants have been compared with those obtained by a theoretical prediction and a recent simulation study.
Rotationally inelastic scattering of jet cooled H2O with Ar: State-to-state cross sections and rotational alignment effects
Authors: Chapman William B. , Kulcke Axel , Blackmon Bradley W. , Nesbitt David J.
Published: July 2002

State-to-state rotationally inelastic scattering cross sections of H2O with Ar are measured under single-collision conditions in crossed supersonic jets at a collision energy of 480(90) cm−1. The H2O is initially prepared in its lowest ortho (101) and para (000) rotational levels by supersonic cooling in a Ne expansion, and then excited in the intersection region by single collisions with a second pulsed jet of Ar atoms. Column-integrated densities of H2O in both initial and final scattering states are monitored via direct absorption of narrow bandwidth (Δν≈0.0001 cm−1) infrared light from a continuous wave (cw) F-center laser. Absolute inelastic cross sections for state-to-state collisional energy transfer out of para and ortho initial states are determined from the dependence of infrared absorption signals on collider gas densities. Overall, the results can be approximately characterized by an exponential decrease in cross section with the magnitude of rotational energy transferred, i.e., as suggested by exponential energy gap models. However, at the state-to-state level, a highly structured, nonmonotonic dependence on energy is observed, which indicates a propensity for rotational excitation around the A (in-plane, perpendicular to C2) and C (out-of-plane) principal axes. This preferential state-to-state scattering dynamics reflects an intramolecular alignment of J in the body-fixed frame and is in good qualitative agreement with theoretical classical trajectory predictions. A rigorous comparison is made via full quantum close-coupling scattering calculations on empirical and ab initio Ar-H2O potential energy surfaces, which successfully reproduce all the state-to-state trends observed, but at the more quantitative level appear to overestimate the intramolecular alignment effects experimentally observed.
Direct multiquantum relaxation of highly vibrationally excited NO in collisions with O/Cu(111)
Authors: Hou H. , Huang Y. , Gulding S. J. , Rettner C. T. , Auerbach D. J. , Wodtke A. M.
Published: July 2002

We present a new experimental approach to the study of vibrational relaxation of highly vibrationally excited molecules at solid surfaces. We observe NO in v=13 and 15 losing up to five vibrational quanta in collisions with an O-covered copper surface. The data indicate this vibrational relaxation occurs via a direct scattering mechanism.
Infrared spectroscopy of the phenol-N2 cluster in S and D: Direct evidence of the in-plane structure of the cluster
Authors: Fujii Asuka , Miyazaki Mitsuhiko , Ebata Takayuki , Mikami Naohiko
Published: July 2002

The OH stretching vibration of jet-cooled phenol-N2 in the neural and cationic ground states was observed by using infrared–ultraviolet double resonance spectroscopy and infrared photodissociation spectroscopy, respectively. The OH vibration showed a small but significant low-frequency shift of 5 cm−1 upon the cluster formation in the neutral, while the shift drastically increased up to 159 cm−1 in the cation. These results represent the direct evidence of the in-plane cluster structure, in which phenolic OH is hydrogen bonded to N2, as was proposed in the zero kinetic energy photoelectron study [S. R. Haines et al., J. Chem. Phys. 109, 9244 (1998)].
The induction period of the CaCl2–Na2CO3 system: Theory and experiment
Authors: Chien Wen-Chen , Tai Clifford Y. , Hsu Jyh-Ping
Published: July 2002

The induction period, tind, of CaCO3 precipitated from an aqueous CaCl2–Na2CO3 solution is investigated both experimentally and theoretically. The tind of primary nucleation is measured by applying a conductivity method and estimated by using the rapid coagulation theory. By using a novel data acquisition system in the experiment, tind can be easily estimated from the desupersaturation curve, which is a plot of solution conductivity against time. The desupersaturation curves obtained at various levels of supersaturation reveal the important features at different desupersaturation stages, including clusters coagulation, formation of critical nuclei, growth of critical nuclei, detection of visible crystals and equilibrium stage. These individual stages are affected greatly by the initial supersaturation of solution. An oscillation in conductivity, which arises from the fluctuation of solution concentration, is observed between tind and tv, tv being the instant that visible crystals are detected. A comparison between theoretical and experimental results, which include the data obtained in this study and those reported in the literature, shows that the present model is satisfactory for a wide range of supersaturation, and unifies the homogeneous and heterogeneous mechanisms of nucleation. The results also imply that the interparticle forces between clusters are important for the formation of critical nuclei in the primary nucleation regime.
Infrared spectra of (NO)2− and (NO)2+ isomers trapped in solid neon
Authors: Andrews Lester , Zhou Mingfei
Published: July 2002

Laser-ablation of six different metal targets with concurrent deposition of neon/nitric oxide samples at 4 K produces metal independent absorptions that can be assigned to charged (NO)2 species. The sharp 1227.3 cm−1 band and weaker 1225.1 cm−1 absorption show the different isotopic frequency ratios observed for the argon matrix counterparts at 1221.0 and 1222.7 cm−1 for trans-(NO)2− and cis-(NO)2−, respectively. Strong 1619.0 and weaker 1424.1 cm−1 absorptions, also observed in previous experiments with discharged neon, are enhanced with CCl4 doping while the (NO)2− bands are diminished, which supports cation identifications. These cation bands reverse absorbance with yellow and near-infrared photolysis. We suggested that the 1619.0 cm−1 band corresponds to the (NO)2+ isomer made by direct photoionization of cis-(NO)2. The 1424.1 cm−1 absorption shares the extreme red photosensitivity found for thermal (NO)2+ ions. Accordingly, the 1424.1 cm−1 absorption is probably due to the trans isomer, more stable in the gas phase, based on high level calculations, and the 1619.0 cm−1 band arises from the more stable matrix-isolated cis isomer with a dipole moment, which is produced by the more favorable Franck–Condon photoionization of the cis-(NO)2 precursor.
Permanent dipole moment and charges in colloidal semiconductor quantum dots
Authors: Shim Moonsub , Guyot-Sionnest Philippe
Published: July 2002

The presence of a large permanent dipole moment has important implications on our understanding of nanocrystalline materials. We report the results of dielectric dispersion studies of CdSe, ZnSe, and metal nanocrystals. Due to the polar nature of the wurtzite lattice, a permanent dipole moment may be expected for CdSe nanocrystals. However, dielectric dispersion studies reveal a similar magnitude of the dipole moment, as well as its dependence on size, in zinc-blende ZnSe nanocrystals. These dipole moments may be intrinsic attributes to all nonmetal nanoparticles with surface localized charges. We show evidence for thermally induced charging of both semiconductor and metal nanocrystals and present a simple picture to describe the linear dependence of dipole moment on the size in semiconductor nanocrystals.
Density functional theory with fractionally occupied frontier orbitals and the instabilities of the Kohn–Sham solutions for defining diradical transition states: Ring-opening reactions
Authors: Goddard John D. , Orlova Galina
Published: July 2002

Density functional theory with fractionally occupied frontier orbitals was combined with an analysis of the instability of the Kohn–Sham solutions and applied to the study of the ring-opening reactions of 1,2-dioxetene, 1,2-dithiete, 1,2-diselenete, and 1,2-ditellurete. These molecules possess transition structures and reactive intermediates for the ring-opening reactions which exhibit strong nondynamical electron correlation. All restricted density functional theory (DFT) solutions for the closed shell transition state structures for all these species are unstable. The solutions with the hybrid Hartree–Fock DFT functionals, B3LYP and B3PW91, are triplet unstable, while for the pure DFT functional BLYP the instability is due to a violation of the Aufbau principle. The same types of instabilities were found for the 1,2-diselenete and 1,2-ditellurete intermediates. Lower energy stable solutions for the diradical transition structures were found with unrestricted DFT methods allowing fractionally occupied orbitals. This DFT approach indicates a decrease in the active orbital space from four fractionally occupied natural orbitals in earlier multireference predictions to two fractionally occupied Kohn–Sham orbitals.
Surveying determinants of protein structure designability across different energy models and amino-acid alphabets: A consensus
Authors: Buchler Nicolas E. G. , Goldstein Richard A.
Published: July 2002

A variety of analytical and computational models have been proposed to answer the question of why some protein structures are more “designable” (i.e., have more sequences folding into them) than others. One class of analytical and statistical-mechanical models has approached the designability problem from a thermodynamic viewpoint. These models highlighted specific structural features important for increased designability. Furthermore, designability was shown to be inherently related to thermodynamically relevant energetic measures of protein folding, such as the foldability ℱ and energy gap Δ10. However, many of these models have been done within a very narrow focus: Namely, pair–contact interactions and two-letter amino-acid alphabets. Recently, two-letter amino-acid alphabets for pair–contact models have been shown to contain designability artifacts which disappear for larger-letter amino-acid alphabets. In addition, a solvation model was demonstrated to give identical designability results to previous two-letter amino-acid alphabet pair–contact models. In light of these discordant results, this report synthesizes a broad consensus regarding the relationship between specific structural features, foldability ℱ, energy gap Δ10, and structure designability for different energy models (pair–contact vs solvation) across a wide range of amino-acid alphabets. We also propose a novel measure Zdk which is shown to be well correlated to designability. Finally, we conclusively demonstrate that two-letter amino-acid alphabets for pair–contact models appear to be solvation models in disguise.
Simulation of delocalized exchange by local density functionals
Authors: Becke Axel D.
Published: July 2002

Exchange holes in molecules can be delocalized over several centers, thus throwing into question their approximation by local density functionals. This work introduces a simple model which detects delocalization in molecules through a local variable related to kinetic energy density. A local exchange functional is derived that reproduces exact-exchange atomization energies of molecules with relatively low error. This has important implications for the simplification of “hybrid” density-functional theories which contain an exactly computed exchange term.
Molecular dynamics simulations of polarizable water at different boundary conditions
Authors: Nymand Thomas M. , Linse Per
Published: July 2002

Simulations of liquid water using a model with atomic charges, dipoles, and anisotropic polarizabilities (NEMO) have been carried out by employing spherical cutoff, Ewald summation (ES), and reaction field (RF) boundary conditions. From trajectories of several ns, information on both structural, dynamical, as well as dielectric properties of polarizable water have been obtained. The sensitivity of these properties towards the applied boundary conditions along with finite system size effects have been examined and discussed. These results have been compared with simulations using an unpolarizable water model (SPC/E) conducted under the exact same conditions. For the polarizable model, it was found that an ordinary spherical cutoff tends to overestimate the induced polarization, resulting in an overestimation of the interaction energy, a sharper liquid structure, and slower dynamics, as compared with the Ewald summation and reaction field methods. The reaction field method displayed a larger system size sensitivity, and a system of at least 512 water molecules is needed to reach the thermodynamic limit, whereas 216 is sufficient for the ES. The computational effort required to simulate a polarizable system using ES was found to increase by a factor of 9 in comparison with the unpolarizable water model with the same boundary conditions.
Integrals of three Bessel functions and Legendre functions. I
Authors: Gervois A. , Navelet H.
Published: July 2002

Integrals of products of three Bessel functions of the form ∫∞0 tλ−1Jμ(at)Jν ×(bt)H(1)ρ(ct)dt are calculated when some relations exist between the indices λ, μ, ν, ρ: in these cases, the Appell function F4 factorizes into two hypergeometric functions of one variable, so that analytical continuation is possible. New results are given, mainly when a, b, and c are real and positive and ‖a−b‖<c<a+b, which correspond to most physical situations.
Symmetry algebras of third-order ordinary differential equations
Authors: Gat Omri
Published: July 2002

The main result of this paper is the complete classification of the third-order ordinary differential equations according to their symmetries. The same classification was done for second order by Tresse [‘‘Détermination des invariants ponctuels de l’équation différentielle ordinaire du second ordre y″=ω(x,y,y′),’’ Gekrönte Preisschrift, Hirzel, Leipzig (1896)], and recently for arbitrary order linear ordinary differential equations. The sections preceding the classification consist of a brief description of the concepts and methods along the lines of Krause and Michel [Lecture Notes Phys. 382, 251 (1991)]. These sections also contain some definitions and a table listing the prolongations of a few vector fields. Finally, two appendices give additional information relevant to equations in real variables and describe how some of the results can be easily generalized to higher orders.
Exact scalar and spinor solutions in the field of a stationary cosmic string
Authors: Krori K. D. , Borgohain P. , Das (Kar) Dipali
Published: July 2002

In this article exact solutions of the Klein–Gordon and Weyl equations in the field of a stationary cosmic string are presented.
Transport properties in resonant tunneling heterostructures
Authors: Presilla Carlo , Sjöstrand Johannes
Published: July 2002

An adiabatic approximation in terms of instantaneous resonances to study the steady-state and time-dependent transport properties of interacting electrons in biased resonant tunneling heterostructures is used. This approach leads, in a natural way, to a transport model of large applicability consisting of reservoirs coupled to regions where the system is described by a nonlinear Schrödinger equation. From the mathematical point of view, this work is nonrigorous but may offer some fresh and interesting problems involving semiclassical approximation, adiabatic theory, nonlinear Schrödinger equations, and dynamical systems.
Lie algebraic structures of (1+1)-dimensional Lax integrable systems
Authors: Chen Deng-yuan , Zhang Da-jun
Published: July 2002

An approach of constructing isospectral flows Kl, nonisospectral flows σk and their implicit representations of a general Lax integrable system is proposed. By introducing product function matrices, it is shown that the two sets of flows and of related symmetries both constitute infinite-dimensional Lie algebras with respect to the commutator ⟦⋅,⋅⟧ given in this paper. Algebraic properties for some well-known integrable systems such as the AKNS system, the generalized Harry Dym system, and the n-wave interaction system are obtained as particular examples.
On the root mean square quantitative chirality and quantitative symmetry measures
Authors: Petitjean Michel
Published: July 2002

The properties of the root mean square chiral index of a d-dimensional set of n points, previously investigated for planar sets, are examined for spatial sets. The properties of the root mean squares direct symmetry index, defined as the normalized minimized sum of the n squared distances between the vertices of the d-set and the permuted d-set, are compared to the properties of the chiral index. Some most dissymetric figures are analytically computed. They differ from the most chiral figures, but the most dissymetric 3-tuples and the most chiral 3-tuples have a common remarkable geometric property: the squared lengths of the sides are each equal to three times a squared distance vertex to the mean point.
From unsharp to sharp quantum observables: The general Hilbert space case
Authors: Cattaneo G. , Nisticò G.
Published: July 2002

An unsharp quantum observable can be considered a realization of a sharp observable if and only if it is commutative. In this paper we describe an explicit procedure for reconstructing such a sharp observable and for establishing the probabilistic correlations between the sharp reconstruction and the given unsharp observable.
Nonlinear second sound in He-II under pressure
Authors: Efimov V. B. , Kolmakov G. V. , Mezhov-Deglin L. P. , Trusov A. B.
Published: July 2002

The dependence of the nonlinearity coefficient α for the roton second sound in superfluid He-II on pressure P is studied for the first time. It is found that as the value of P increases from saturated vapor pressure to 25 atm, the temperature Tα at which the coefficient α reverses its sign decreases from 1.88 to 1.58 K, i.e., there exists a wide temperature interval below Tλ in He-II at all pressures, in which the nonlinearity coefficient α is negative, and a temperature discontinuity (shock wave) is formed at the trailing edge of the second sound compression wave.
Stability of a compressed gas bubble in a viscous fluid
Authors: Iooss G. , Laure P. , Rossi M.
Published: July 2002

The stability of the spherical shape of the free surface of a gas bubble compressed by an incompressible fluid as it appears in the inertial confinement fusion problem is considered. (i) The equations derived by Prosperetti [Accad. Naz. Lincei 62, 196 (1977)] generalizing the Plesset equation are recovered in cases when the outer fluid is nonviscous, the flow being not potential, and it is shown that vorticity may change drastically the results of the potential case. (ii) In the case of viscous external fluid, the equations derived by Prosperetti [Q. Appl. Math. 1, 399 (1977)] and other external conditions on a sphere of finite radius are derived. (iii) Assuming that the time scale of the dynamics of the spherical bubble is large with respect to the time scale of the perturbation (frozen assumption), the linear stability of the collapsing bubble is studied numerically. The parameters are here (a) an inertia force (related with acceleration R̈ of the radius of the bubble), (b) the Reynolds number built with the decaying rate of the bubble, (c) surface tension, and (d) the aspect ratio (ratio between the gap width of the viscous fluid and the radius of the bubble). It is shown that the spherical shape is always linearly unstable in the absence of surface tension. In the presence of surface tension, there is a critical inertia parameter value and the most dangerous mode is always stationary. For the case of a large surface tension, the spherical wavenumber l of the most dangerous mode, is low. Finally, it is shown that the Rayleigh–Taylor instability might only be observed for both small aspect ratio and Reynolds number, depending on the surface tension.
On the interaction between a strong vortex pair and a free surface
Authors: Tyvand Peder A.
Published: July 2002

The initial motion of a pair of strong vortices suddenly created close to a free surface is calculated analytically by means of a Taylor expansion in time. While weak vortices moving toward a free surface repel each other [see Hydrodynamics (Cambridge U.P., Cambridge, 1932)], strong vortices attract each other to the leading order. But, they cannot merge and annihilate each other because of nonlinear free-surface effects. Several features of the solution depend on whether or not the vortices are below a critical depth. At the critical depth the two vortex points span an angle of 120° with respect to the surface center. The dominating gravitational effects are investigated.
A numerical study on the formation of a thermocline in shear-free turbulence
Authors: Noh Y. , Fernando H. J. S.
Published: July 2002

The formation of a thermocline generated by the interaction between a stabilizing buoyancy flux and shear-free turbulence was studied using a numerical model. The time evolutions of the vertical distributions of the buoyancy and turbulent kinetic energy were calculated and were used to evaluate the depth of the thermocline and the time required for its formation. The numerical results are compared with the results of previous laboratory experiments. The mechanisms responsible for the formation of the thermocline are discussed in view of the numerical results.
A comparison of intermittency models in turbulence
Authors: Borgas M. S.
Published: July 2002

A variety of turbulent intermittency models from the literature is listed and directly contrasted. The multifractal notation [J. Feder, Fractals (Plenum, New York, 1988)] is used to present these results. Two of the models in particular, Yamazaki’s [J. Fluid Mech. 219, 181 (1990)] B-model and a prediction from renormalization-group analysis (Yakhot et al.22 [Phys. Fluids A 1, 289 (1989)]), are closely examined and inherent flaws are pointed out.
The efficiency of symmetric vortex merger
Authors: Waugh Darryn W.
Published: July 2002

The coalescence of two identical vortices with uniform vorticity is investigated using the numerical method of ‘‘contour surgery,’’ for two-dimensional inviscid, incompressible vortex dynamics (2VD), and quasigeostrophic shallow-water dynamics (QGSW), to quantify the differences and similarities between the two models. High-resolution calculations show that the evolution of the vortices may fall into three different regimes depending on the initial intercentroid separation. The efficiency of the merger of two vortices into a single elliptical-like vortex is determined by calculating the loss of globally conserved quantities to filaments and small-scale structures. In the 2VD model, it is found that the resultant central vortex always has at least 56% more circulation than either of the initial vortices, showing that the merger process indeed forms larger scales. From energetics, the initial separation for an inviscid transition from two elliptical vortices to a single elliptical vortex is determined, and is shown to be close to the critical merger separation obtained from full numerical calculations. Confirming the results of Polvani et al. [J. Fluid Mech. 205, 215 (1989)], the calculations in the QGSW model show that as the radius of deformation LR decreases, the critical merger separations decrease, the resultant vortex is nonelliptical, fewer filaments are shed, and those filaments shed show an increased propensity to roll up into small vortices (consistent with previous analysis of the stability of strips of potential vorticity with imposed shear). Furthermore, the efficiency of the merger process increases as LR decreases (to perfect efficiency in the limit of small LR).
An exploration of the wake three dimensionalities caused by a local discontinuity in cylinder diameter
Authors: Lewis C. G. , Gharib M.
Published: July 2002

The wake three-dimensionality caused by a local discontinuity in cylinder diameter (a stepped cylinder) was studied. Changes in vortex shedding frequency caused by the discontinuity took place in either a direct or an indirect mode, depending on the diameter ratio and the Reynolds number. The roles of oblique shedding and frequency modulation of vortex shedding were studied. The physical change in vortex shedding frequency occurred differently for each mode. A wavelet analysis is used to explore frequency modulations in the wake. The relationship between vortex linkages, frequency changes, secondary instability, and these two modes is discussed.
Ballooning modes in an axisymmetric mirror machine
Authors: Close R. A. , Lichtenberg A. J.
Published: July 2002

High-beta ballooning modes are studied in an axisymmetric multiple mirror which is made average-minimum B with end cusps. Electric and magnetic field measurements in the plasma characterize the predominant azimuthal mode number as m=1. The ballooning character of the mode is determined by measuring the ratio of the mode amplitude near the device center to that near the cusp, and confirmed by measurement of perturbed perpendicular magnetic fields. Theoretical growth rates are calculated numerically using ideal and resistive magnetohydrodynamic (MHD) equations for the rigid m=1 ballooning mode. Within experimental error it is found that the m=1 resistive ballooning growth rate scales with radially averaged beta 〈 β〉 approximately as 〈 β〉1/2 for 〈 β〉≲0.10 (on axis β0≲0.20), in agreement with theory. The observed growth rates increase with mirror ratio as expected. The resistive growth rates calculated numerically agree reasonably well with experimental observations.
Nonlinear evolution of the unmagnetized ion Rayleigh–Taylor instability
Authors: Hassam A. B. , Huba J. D.
Published: July 2002

The nonlinear evolution of the unmagnetized ion Rayleigh–Taylor instability is investigated. A nonlinear state corresponding to localized clumps of high-density plasma is obtained analytically. The characteristic scale size of the clumps is given by Δ∼D(gLn)−1/2, where g is the gravitational acceleration, Ln is the density gradient scale length, and D is a diffusion coefficient associated with the short-scale dissipation processes in the system. It is shown numerically that this nonlinear state may be both accessible and stable.
Preferential positron heating and acceleration by synchrotron maser instabilities in relativistic positron–electron–proton plasmas
Authors: Hoshino Masahiro , Arons Jonathan
Published: July 2002

In this paper, a new process of the preferential strong heating of positrons through the ion synchrotron maser instability in positron–electron–proton (e+–e−–p+) magnetized plasmas is studied, using particle-in-cell simulations. It is found that the positrons form a nonthermal power-law-like energy distribution through their gyroresonant interaction with the extraordinary modes emitted by the ions. This process may be important for the shock excitation of the nonthermal synchrotron radiation observed from astrophysical systems powered by relativistic outflows from compact central objects (e.g., supernova remnants powered by pulsars and jets from active galactic nuclei). When the initial particle distributions are cold rings in momentum space for all three species, there are two stages of instability. The electrons and positrons first thermalize through the emission of collective extraordinary modes. This phase is followed by the emission of collective proton synchrotron radiation, a process with a slower growth rate than the maser in the e− and e+. When the gyrational energy density of the protons exceeds that of the e+, a significant amount of energy can be transferred to the positrons through resonant interaction between the e+, which gyrate in the same sense as the p+, and the elliptically polarized proton synchrotron modes whose frequency is at high harmonics of the fundamental proton gyrofrequency and whose electric field vector has the same sense of rotation as the protons and positrons. The final spectrum of the positrons has a power-law distribution in energy space: The number of positrons with relativistic energy between E and E+dE is N(E)dE∝E−2. The electrons, which have the opposite sense of gyromotion to the protons, are not accelerated and retain the relativistic Maxwellian distribution that results from the synchrotron maser instability in the pairs alone. A brief discussion of the relevance of these results to the structure of collisionless relativistic shock waves in astrophysical sources of synchrotron radiation is presented.
Stochastic diffusion and Kolmogorov entropy in regular and random Hamiltonians
Authors: Isichenko M. B. , Horton W. , Kim D. E. , Heo E. G. , Choi D.-I.
Published: July 2002

The scalings of the E×B turbulent diffusion coefficient D and the Kolmogorov entropy K with the potential amplitude φ̃ of the fluctuation are studied using the geometrical analysis of closed and extended particle orbits for several types of drift Hamiltonians. The high-amplitude scalings, D∝φ̃2 or φ̃0 and K∝log φ̃, are shown to arise from different forms of a periodic (four-wave) Hamiltonian φ̃(x,y,t), thereby explaining the controversy in earlier numerical results. For a quasirandom (six-wave) Hamiltonian numerical data for the diffusion D∝φ̃0.92±0.04 and the Kolmogorov entropy K∝φ̃0.56±0.17 are presented and compared with the percolation theory predictions Dp∝φ̃0.7, Kp∝φ̃0.5.
Secondary instability in three-dimensional magnetic reconnection
Authors: Dahlburg R. B. , Antiochos S. K. , Zang T. A.
Published: July 2002

The transition to turbulence in three-dimensional reconnection of a magnetic neutral sheet is investigated. The transition can occur via a three-step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two-dimensional quasisteady state. Third, this secondary equilibrium is itself ideally unstable when it is perturbed by three-dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three-dimensional linear stability properties of the two-dimensional saturated tearing layer. The numerical simulations are performed with a semi-implicit, pseudospectral-Fourier collocation algorithm. A three-dimensional secondary linear instability that grows on the ideal time scale is identified. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three-dimensional field, with the two-dimensional field acting as a catalyst. Results of some high-resolution, fully nonlinear calculations that provide insight into the complete evolution of the system are then presented. During the nonlinear phase, the modes with structure in the third dimension are, in general, more energetic than the purely two-dimensional modes. The evolution is interpreted as being due to a kinking of flux tubes formed during the initial two-dimensional tearing stage. The system reorganizes itself turbulently into a new three-dimensional quasisteady state, which, however, dissipates much more energy than the two-dimensional saturated state. The present work has important implications for a wide range of astrophysical processes that are believed to involve rapid magnetic energy release.
The realizable Markovian closure. I. General theory, with application to three-wave dynamics
Authors: Bowman John C. , Krommes John A. , Ottaviani Maurizio
Published: July 2002

A type of eddy-damped quasinormal Markovian (EDQNM) closure is shown to be potentially nonrealizable in the presence of linear wave phenomena. This statistical closure results from the application of a fluctuation–dissipation (FD) ansatz to the direct-interaction approximation (DIA); unlike in phenomenological formulations of the EDQNM, both the frequency and the damping rate are renormalized. A violation of realizability can have serious physical consequences, including the prediction of negative or even divergent energies. A new statistical approximation, the realizable Markovian closure (RMC), is proposed as a remedy. An underlying Langevin equation that makes no assumption of white-noise statistics is exhibited. Even in the wave-free case the RMC, which is based on a nonstationary version of the FD ansatz, provides a better representation of the true dynamics than does the EDQNM closure. The closure solutions are compared numerically against the exact ensemble dynamics of three interacting waves.
Coulomb collision rates for self-similar and kappa distributions
Authors: Marsch E. , Livi S.
Published: July 2002

The Coulomb collision operator for two nonthermal particle distributions, the self-similar and kappa distribution, is investigated theoretically. Associated friction and diffusion rates are evaluated and calculated numerically as a function of velocity. It is shown that the full collision term can be cast into a relaxation time form with an effective collision rate that differs drastically from the smooth overall diffusion rates and is very sensitive to the shape of the distribution. Numerical results for the effective rates are presented and the relevance of our analysis with respect to observed distributions in space plasmas and for quasilinear turbulence is discussed.
A study of high-beta ballooning modes
Authors: Price H. D. , Benjamin N. M. P. , Kang B. K. , Lichtenberg A. J. , Lieberman M. A.
Published: July 2002

Ballooning instabilities are studied in the Berkeley multiple mirror experiment. Counterstreaming theta pinch and Marshall gun source hydrogen plasmas are used to achieve a high beta ( β>25%), where β is the ratio of plasma to magnetic pressure at temperatures Te=Ti≊15 eV. Four magnetic field configurations are investigated, each at varying mirror ratios, to explore a range of drive and connection length parameters. In two of these the magnetic field is pulsed from a stable to a locally unstable configuration for initiation of ballooning activity. The other two (static) configurations are a weakly unstable local field region, and the standard linked quadrupole multiple-mirror configuration. Depending on the configuration, critical β’s are found for the onset of ballooning that vary from 5% for the most unstable configuration to greater than 25% for the standard multiple-mirror configuration. The m=1 azimuthal mode is predominant, with some admixture of m=2. The experimental results are compared with predictions from a magnetohydrodynamic theory. In the model the pressure is taken to be isotropic and constant along the axis, except in the diverging field regions at the device ends where the pressure falls to maintain beta constant, consistent with experimental observations. The theoretical results generally predict somewhat higher critical betas for the m=1 mode than those observed. Estimates of the effect of finite Larmor radii, nearby conducting walls, axially nonuniform pressure profiles and resistivity, are also given.
Observation of a curvature-driven, trapped particle mode created by a potential barrier
Authors: Fernandez J. C. , Chang C. P. , Lichtenberg A. J. , Lieberman M. A. , Meuth H.
Published: July 2002

A mirror-confined hot-electron distribution is created using high-power, short-pulse electron-cyclotron resonance heating (ECRH) in a single, good curvature (magnetically stable) cell of a plasma-filled multiple mirror device. The hot electrons are observed to decouple good and bad curvature regions on the two sides of the hot-electron cell. An unstable magnetohydrodynamic (MHD)-like, rigid plasma motion to the walls occurs in the bad curvature region, with velocity comparable to that of a mode driven by the bad curvature alone. In some magnetic configurations the plasma restabilizes later in time. The hot-electron distribution decays stably, independent of the other processes. The initiation of the instability is correlated with the appearance in the hot-electron cell of a negative potential barrier. For the configurations in which plasma is restabilized, the restabilization is correlated with the decay of the potential barrier caused by ion trapping in the hot-electron cell. An electron beam time-of-flight probe has been used to measure the potential barrier and its decay. The experimental results are compared to a curvature-driven, trapped particle theory, including the effects of finite collisionality.