bluuebunny/crossref_metadata_2025 huggingface dataset:
Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities
Authors: Tozer David J. , Handy Nicholas C.
Published: July 2002

Conventional continuum exchange-correlation functionals (e.g., local density approximation, generalized gradient approximation) offer a poor description of many response properties, such as static polarizabilities and single photon vertical excitation energies to Rydberg states. These deficiencies are related to errors in the virtual Kohn–Sham orbitals and eigenvalues, which arise due to a fundamental deficiency in the potentials of conventional continuum functionals. Namely, although these potentials approximately average over the exact integer discontinuity in energetically important regions, they fail to do so asymptotically, because they vanish. Our recent functional HCTH [J. Chem. Phys. 109, 6264 (1998)] was designed with this deficiency in mind, although its potential still fails to exhibit the appropriate asymptotic form. In this paper, we present a new procedure that explicitly corrects this asymptotic deficiency for any continuum functional. Self-consistent Kohn–Sham calculations are performed using a corrected potential, which equals the conventional potential δEXC[ρα,ρβ]/δρσ(r) in energetically important regions, but which asymptotically behaves in the required average manner −(1/r)+Iσ+εHOMO,σ. The quantity −(1/r) is determined using a nonlocal expression; Iσ is an approximate σ spin ionization potential; and εHOMO,σ is the highest occupied σ spin eigenvalue. By applying this correction to the HCTH potential, we accurately reproduce the hydrogen atom eigenvalue spectrum, without significantly changing the total energy. We determine corrected orbitals and eigenvalues for a variety of molecules, and use them to compute excitation energies and static polarizabilities. We compare the results with those from a variety of other exchange-correlation functionals. Excitations to Rydberg states are determined as accurately as those to valence states; for CO, N2, H2CO, and C2H4, mean absolute errors are less than 0.35 eV. The static isotropic polarizabilities of 14 small molecules are of MP2 quality.
Langevin modes analysis of myoglobin
Authors: Ansari Anjum
Published: July 2002

Langevin modes describe the behavior of atoms moving on a harmonic potential surface subject to viscous damping described by a classical Langevin equation. We present applications to myoglobin. The Langevin modes are obtained from the gas-phase normal modes using a perturbation expansion. The friction matrix in the Langevin description is assumed diagonal thus ignoring hydrodynamic interactions. The diagonal elements, which are the atomic friction constants on each atom, are weighted according to the surface area accessible to the solvent. Time-dependence of the position and velocity correlation functions are calculated for the Fe atom buried inside the protein for varying values of the external solvent viscosity. Even for negligibly small values of the viscosity, the time correlation functions are overdamped and suggest a substantial damping component from the neighboring protein atoms. The effective friction seen by the Fe atom has contributions from both the solvent friction as well as the internal protein friction. The internal protein friction is estimated to be about 14 ps−1 and is comparable to the friction of water. The viscosity dependence of the inverse of the effective friction on the Fe atom is found to agree qualitatively with the viscosity dependence of the experimentally measured rate of conformational changes in myoglobin.
The hexanuclear rhenium cluster ions Re6S8X64− (X=Cl, Br, I): Are these clusters luminescent?
Authors: Arratia-Pérez Ramiro , Hernández-Acevedo Lucı́a
Published: July 2002

Dirac molecular orbital calculations on the octahedral rhenium clusters Re6S8X64− (where X=Cl, Br, I) are reported. The calculated relativistic molecular orbitals indicate that the manifold of closely spaced unoccupied energy levels are mainly localized on the octahedral rhenium core with some contributions from the μ3-S ligands, while all the cluster highest occupied molecular orbitals are largely centered on the terminal halide ligands. All three hexanuclear rhenium cluster ions have singlet ground state (spanning the Γ6+ symmetry) and are therefore diamagnetic. They have the same ground state and excited state features as the intensely luminescent W6Cl142− cluster ion. The calculated charge distributions indicate that these clusters could be formulated as: Re6−0.21S8−0.16Cl6−0.24, Re6−0.23S8−0.17Br6−0.21 and Re6−0.26S8−0.26I6−0.12, respectively.
Rate constants for the reaction of O+ with NO as a function of temperature (300–1400 K)
Authors: Dotan Itzhak , Viggiano A. A.
Published: July 2002

We have measured the rate constants for the reaction of O+ ions with NO from room temperature to 1400 K. The reaction is slow (k=8×10−13 cm3 s−1) at room temperature and the rate constant increases to 2.6×10−12 cm3 s−1 at 1400 K. Comparison of the high-temperature data to drift tube data shows that rotational and translational energy are equally effective at controlling the rate constant, and that vibrational energy has at most a small effect on reactivity. Analysis of the data shows that the reaction proceeds by three different mechanisms. At the very low temperatures, we find a complex formation mechanism, and at the medium temperature range the behavior is interpreted to be a consequence of the correlation of O+(4S) and NO(2Π) with the excited states 3A1, 3B1 of NO2+, which lie slightly above the reactants in energy. At the very high energy range, a third mechanism becomes important, probably the endothermic production of NO+(3Σ+).
Structure, thermodynamics, and dynamics of the liquid/vapor interface of water/dimethylsulfoxide mixtures
Authors: Benjamin Ilan
Published: July 2002

Molecular dynamics computer simulations are used to study the structure, thermodynamics and dynamics of the liquid/vapor interface of water/DMSO (dimethylsulfoxide) mixtures. Both the infinite dilution limit (single DMSO molecule) and four different finite concentration mixtures are investigated. Considered are the potential of mean force for the adsorption of DMSO and the dependence of several surface structural properties (orientation, hydrogen bonding) and surface potential on the bulk concentration of DMSO. The adsorption dynamics are also investigated and compared with a diffusion model. In general, the results are in good agreement with recent experimental measurements.
Wet-chemical synthesis of doped nanoparticles: Blue-colored colloids of n-doped SnO2:Sb
Authors: Nütz Tanjew , Felde Ulf zum , Haase Markus
Published: July 2002

Nanocrystallites of antimony-doped tin dioxide have been prepared hydrothermally by treating colloids of tin antimony oxide in an autoclave. At a synthesis temperature of 270 °C stable colloidal solutions of blue-colored SnO2:Sb nanocrystallites have been obtained. High resolution transmission electron microscopy (TEM) images show highly crystalline particles in the 4 to 9 nm size regime. X-ray powder diffraction patterns of the nanocrystals indicate the same rutile lattice structure as known from bulk SnO2. Powders of the antimony-doped nanocrystals exhibit an up to 105 fold increase in electrical conductivity as compared to the corresponding undoped systems. The blue color of the doped colloids corresponds to a broad absorption peak in the red and the IR region. The IR-absorption spectrum of doped nanoparticles deposited onto sapphire substrates has been fit to a model based on the Drude theory of a free electron gas in SnO2:Sb and an effective medium approximation. The model indicates that the IR absorption corresponds to a plasmon polariton excitation of weakly interacting n-doped nanoparticles.
Photoionization studies of germanium and tin clusters in the energy region of 5.0–8.8 eV: Ionization potentials for Gen (n=2–57) and Snn (n=2–41)
Authors: Yoshida Shinji , Fuke Kiyokazu
Published: July 2002

Photoionization thresholds for Gen (n⩽57) and Snn (n⩽41) are examined by laser photoionization with detection by reflectron time-of-flight mass spectrometry. Stimulated Raman anti-Stokes scattering of narrow bandwidth 193, 248, and 266 nm radiation is used to produce ionization light sources in the vacuum ultraviolet region (200–141 nm). A very similar size dependence of the ionization potentials (IPs) is found for germanium and tin clusters with fewer than 12 atoms, featuring a major maximum at n=10. The rather high IP of Ge10 compared with its neighbors is consistent with the results of a photodissociation study of Gen+. We also find a rapid decrease in the IPs for Gen between n=15 and 26, which is very similar to that for silicon clusters reported in our previous paper. On the other hand, the IPs of medium size Snn (n=15–41) clusters are found to decrease slowly without such a gap. The remarkable difference in the size dependence of the IPs for the Sin, Gen, and Snn clusters is discussed in relation to the existence of a structural transition in the medium-size Sin and Gen clusters.
Dynamics of a polymer surmounting a potential barrier: The Kramers problem for polymers
Authors: Jun Park Pyeong , Sung W.
Published: July 2002

We study the dynamics of a flexible polymer under a Kramers potential using the multidimensional barrier crossing theory. The activation free energy of the polymer evaluated by a lattice statistics yields the crossing rate as a function of chain length, temperature, and potential parameters. It is found that a long chain has an enhanced crossing rate due to the extended conformation of low free energy it has at the barrier, while a short chain has the crossing dynamics of a Brownian particle. A chain of intermediate length can exhibit a minimum in the crossing rate as chain length varies. For any range of chain lengths and potential parameters, the crossing rate is larger than that of a polymer in the globular state, due to the internal degrees of freedom of the unfolded flexible chain. Our results can be applied to macromolecular separation and DNA electrophoresis.
The application of the energy landscape model to polymers
Authors: Roland C. M. , Santangelo P. G. , Ngai K. L.
Published: July 2002

The energy landscape model of the glass transition has received increasing attention, due to its potential for providing a thermodynamic interpretation of the dynamics of glass-forming liquids. Herein, the idea that the temperature-dependence of the dynamics near the glass temperature (“fragility”) can be related to thermodynamic properties is tested for polymers. Previously, for several homologous series, we found deviations from a proposed correlation between fragility and the heat capacity increment at the glass temperature. A survey of 17 polymers likewise indicates no correlation between these two quantities. More recently, the landscape approach to the dynamics of glass-formers was extended to a proposal that fragility can be determined a priori from thermodynamic information. However, for the 11 polymers for which sufficient thermodynamic and relaxation data were available, we find that thermodynamic properties bear no relationship to fragility. Thus, it appears that the status of the glass transition as an important unsolved problem in condensed matter physics remains intact.
Homogeneous nucleation rates of supercooled water measured in single levitated microdroplets
Authors: Krämer B. , Hübner O. , Vortisch H. , Wöste L. , Leisner T. , Schwell M. , Rühl E. , Baumgärtel H.
Published: July 2002

Homogeneous nucleation rates are determined for micrometer sized water droplets levitated inside an electrodynamic Paul-trap. The size of a single droplet is continuously measured by analyzing the angle-resolved light scattering pattern of the droplets with classical Mie theory. The freezing process is detected by a pronounced increase in the depolarization of the scattered light. By statistical analysis of the freezing process of some thousand individual droplets, we obtained the homogeneous nucleation rate of water between 236 and 237 K. The values are in agreement with former expansion cloud chamber measurements but could be determined with considerably higher precision. The measurements are discussed in the light of classical nucleation theory in order to obtain the size and the formation energy of the critical nucleus.
Crossed beam reaction of cyano radicals with hydrocarbon molecules. II. Chemical dynamics of 1-cyano-1-methylallene (CNCH3CCCH2; X 1A′) formation from reaction of CN(X 2Σ+) with dimethylacetylene CH3CCCH3 (X 1A1′)
Authors: Balucani N. , Asvany O. , Chang A. H. H. , Lin S. H. , Lee Y. T. , Kaiser R. I. , Bettinger H. F. , Schleyer P. v. R. , Schaefer H. F.
Published: July 2002

The reaction dynamics to form the 1-cyano-1-methylallene isomer CNCH3CCCH2 in its A′1 ground state via the radical–closed shell reaction of the cyano radical CN(X 2Σ+) with dimethylacetylene CH3CCCH3 (X 1A1′) are unraveled in a crossed molecular beam experiment at a collision energy of 20.8 kJ mol−1 together with state-of-the-art electronic structure and Rice–Ramsperger–Kassel–Marcus (RRKM) calculations. Forward convolution fitting of the laboratory angular distribution together with the time-of-flight spectra verify that the reaction is indirect and proceeds by addition of the CN radical to the π orbital to form a cis/trans CH3CNC=CCH3 radical intermediate. This decomposes via a rather lose exit transition state located only 6–7 kJ mol−1 above the products to CNCH3CCCH2 and atomic hydrogen. The best fit of the center-of-mass angular distribution is forward–backward symmetric and peaks at π/2 documenting that the fragmenting intermediate holds a lifetime longer than its rotational period. Further, the hydrogen atom leaves almost perpendicular to the C5H5N plane resulting in sideways scattering. This finding, together with low frequency bending and wagging modes, strongly support our electronic structure calculations showing a H–C–C angle of about 106.5° in the exit transition state. The experimentally determined reaction exothermicity of 90±20 kJ mol−1 is consistent with the theoretical value, 80.4 kJ mol−1. Unfavorable kinematics prevent us from observing the CN versus CH3 exchange channel, even though our RRKM calculations suggest that this pathway is more important. Since the title reaction is barrierless and exothermic, and the exit transition state is well below the energy of the reactants, this process might be involved in the formation of unsaturated nitriles even in the coldest interstellar environments such as dark, molecular clouds and the saturnian satellite Titan.
Rotational dynamics of pyrrolopyrrole derivatives in glycerol: A comparative study with alcohols
Authors: Dutt G. B. , Srivatsavoy V. J. P. , Sapre A. V.
Published: July 2002

The rotational dynamics of two structurally similar nonpolar molecules, 2,5-dimethyl-1,4dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and 1,4-dioxo-3,6-diphenylpyrrolo[3,4-c] pyrrole (DPP) has been studied in glycerol in the temperature range of 300–380 K using both time-resolved and steady-state fluorescence depolarization techniques. While the reorientation times of both the probes are varying linearly as a function of viscosity over temperature, the rotational dynamics of DMDPP is described by the Stokes–Einstein–Debye hydrodynamic theory with slip boundary condition, whereas the reorientation times of DPP are in between slip and stick limits and are about a factor of 1.5 longer than that of DMDPP. This is due to the hydrogen bonding between the two NH groups of the probe molecule and the oxygen atoms of the hydroxyl groups in glycerol. It has also been observed that the rotational dynamics of a nonpolar and noninteracting molecule like DMDPP is essentially the same, both in glycerol and in n-alcohols.
Effects of reagent rotation and the accuracy of the centrifugal sudden approximation in the H2+CN reaction
Authors: Zhang Dong H. , Lee Soo-Y.
Published: July 2002

This paper presents fully converged integral cross sections for the ground rovibrational state and some rotationally excited initial states for the title reaction on the TSH3 PES. The initial state selected time-dependent wave packet method has been employed in the calculation with all important K blocks in the body-fixed (BF) frame included. We find that CN rotational excitation up to j2=7 essentially has no effect on the integral cross section, while H2 rotational excitation substantially reduces the cross section. As a result, the thermal rate constant can be obtained accurately by only taking into account the effect of H2 rotational excitation. It is found that the resulting thermal rate constant is considerably smaller than the initial state selected rate constant for the ground rovibrational state. It is also smaller than the experimental rate constant by a factor of 3 and 30% at T=209 K and 447 K, respectively, indicating the TSH3 PES used in the calculation is not quantitatively accurate in describing the reaction. In addition, we examine in detail the accuracy of the centrifugal sudden (CS) approximation to the reaction. Comparison between this reaction and the H2+OH reaction is also carried out when possible.
Ab initio study of interactions in methylamine clusters. The significance of cooperative effects
Authors: Cabaleiro-Lago Enrique M. , Rı́os Miguel A.
Published: July 2002

Methylamine clusters consisting of up to four molecules were studied by employing Hartree–Fock, density functional theory, and Moller–Plesset calculations with the 6-31+G* basis set. The dimer was found to exhibit two minima with similar interaction energies (−13 kJ/mol) and involving a hydrogen bond. The dipole moment for the dimer differs by up to 20% from the vector addition of the dipole moments for the individual molecules by effect of the interaction; also, the N–H bond distance in the group involved in the hydrogen bond is lengthened by up to 0.006 Å as a result. The minima identified for the trimer and tetramer possess cyclic structures that differ in the position of the methyl groups with respect to the plane containing the hydrogen bonds. The contribution of nonadditivity to the interaction in these structures is quite significant (12%–18% of the overall interaction energy). N–H distances in the donor molecule are longer than in the dimer and increase with increasing cluster size. Likewise, the hydrogen bonding energy increases with cluster size. These results expose the significance of cooperative phenomena in the interactions between methylamine molecules. The computations predict slight shifts in the C–N stretching frequencies, which are consistent with their experimental counterparts. The N–H stretching and the NH2 wagging modes undergo large shifts, with a magnitude that increases as the size of the cluster grows.
Multiconfiguration molecular mechanics algorithm for potential energy surfaces of chemical reactions
Authors: Kim Yongho , Corchado José C. , Villà Jordi , Xing Jianhua , Truhlar Donald G.
Published: July 2002

We present an efficient algorithm for generating semiglobal potential energy surfaces of reactive systems. The method takes as input molecular mechanics force fields for reactants and products and a quadratic expansion of the potential energy surface around a small number of geometries whose locations are determined by an iterative process. These Hessian expansions might come, for example, from ab initio electronic structure calculations, density functional theory, or semiempirical molecular orbital theory. A 2×2 electronic diabatic Hamiltonian matrix is constructed from these data such that, by construction, the lowest eigenvalue of this matrix provides a semiglobal approximation to the lowest electronically adiabatic potential energy surface. The theory is illustrated and tested by applications to rate constant calculations for three gas-phase test reactions, namely, the isomerization of 1,3-cis-pentadiene, OH+CH4→H2O+CH3, and CH2Cl+CH3F→CH3Cl+CH2F.
On the theory of electron transfer reactions at semiconductor electrode/liquid interfaces
Authors: Gao Yi Qin , Georgievskii Yuri , Marcus R. A.
Published: July 2002

Electron transfer reaction rate constants at semiconductor/liquid interfaces are calculated using the Fermi Golden Rule and a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the electronic structures of semiconductors with surfaces and are compared. The maximum electron transfer rate constants at Si/viologen2+/+ and InP/Me2Fc+/0 interfaces are computed using the tight-binding type calculations for the solid and the extended-Hückel for the coupling to the redox agent at the interface. These results for the bulk states are compared with the experimentally measured values of Lewis and co-workers, and are in reasonable agreement, without adjusting parameters. In the case of InP/liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.
Temperature-dependent rotational relaxation of nonpolar probes in mono and diols: Size effects versus hydrogen bonding
Authors: Dutt G. B. , Krishna G. Rama
Published: July 2002

The rotational reorientation times of two nonpolar probes, 2,5-dimethyl-1,4-dioxo-3, 6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and 1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DPP) have been measured in 1-decanol and ethylene glycol as a function of temperature using steady-state fluorescence depolarization technique. Although both the probes are structurally similar and have almost identical volumes, the experimentally measured reorientation times of DMDPP are longer in ethylene glycol compared to 1-decanol whereas an exactly opposite trend has been observed for DPP. The faster rotation of DMDPP in 1-decanol has been attributed to the larger size of 1-decanol which is three times bulkier than ethylene glycol and hence offers a reduced friction. This pattern has been mimicked using the quasihydrodynamic theories of Gierer–Wirtz and Dote–Kivelson–Schwartz in a qualitative way. The slower rotation of DPP in 1-decanol compared to ethylene glycol is due to the solute–solvent hydrogen bonding which increases the effective volume of the probe more in the case of 1-decanol than ethylene glycol.
Measurements of homogeneous nucleation in normal-alkanes
Authors: Kraack H. , Sirota E. B. , Deutsch M.
Published: July 2002

The homogeneous nucleation of normal-alkanes with carbon numbers 15⩽n⩽60 is studied by scanning calorimetry, using the droplet technique. Pure, nonemulsified samples show near-zero undercoolings below the melting point, Tm, except for both ends of the n-range, where undercoolings ΔT of up to 2 °C are observed. The emulsions have much larger undercoolings. The relative undercoolings show three regimes: A fast decreasing one, up to n=17, an anomalously low constant one, ΔT/Tm≈0.04, for 17⩽n⩽30, and a gradually increasing one for 32⩽n⩽60. A value of ΔT/Tm≈0.086 is reached at n=60. The connections of these results with the bulk rotator phases and the recently discovered surface freezing effect are discussed. Strong intrinsic interrelations among these are indicated.
Adsorption and desorption processes of CO on the Pd(110) surface: Isothermal kinetics measurements
Authors: Yagi-Watanabe Kazutoshi , Fukutani Hirohito
Published: July 2002

The adsorption and desorption kinetics of carbon monoxide from a Pd(110) surface were studied under isothermal conditions using a differentially pumped line of sight mass spectrometer. A number of isothermal adsorption and desorption kinetics were taken by repeating the measurements at different surface temperatures. The sticking probability profiles are fit by the Kisliuk model with initial sticking probability of 0.95. The isothermal desorption rates show nonlinear function of coverage and the apparent desorption rate orders by means of the slope of the van’t Hoff plots show unusually high values. The temporal desorption rate curves are discussed in terms of a model which requires the presence of two CO surface phases in equilibrium.
Cooling of large molecules below 1 K and He clusters formation
Authors: Even U. , Jortner J. , Noy D. , Lavie N. , Cossart-Magos C.
Published: July 2002

We present here the design details of a high-pressure pulsed valve that generates intense supersonic jets. The measured rotational contours of Aniline indicate that temperatures lower than 0.5 K can be achieved before the formation of clusters with the He carrier gas. The spectral shifts and vibronic structure of Anthracene–Hen clusters (n=1–6) are showing some surprising features.
The fluctuation theorem and Green–Kubo relations
Authors: Searles Debra J. , Evans Denis J.
Published: July 2002

Green–Kubo and Einstein expressions for the transport coefficients of a fluid in a nonequilibrium steady state can be derived using the fluctuation theorem and by assuming the probability distribution of the time-averaged dissipative flux is Gaussian. These expressions are consistent with those obtained using linear response theory and are valid in the linear regime. It is shown that these expressions are, however, not valid in the nonlinear regime where the fluid is driven far from equilibrium. We advance an argument for why these expressions are only valid in the linear response, zero field limit.
Dynamics of the OH−+D2 isotope exchange reaction: Reactive and nonreactive decay of the collision complex
Authors: Troutman Lee Susan , Farrar James M.
Published: July 2002

Reactive and nonreactive collisions between OH− and D2 are investigated over the collision energy range from 0.27 to 0.67 eV by the method of crossed molecular beams. The angular and energy distributions measured for the isotope exchange reaction are quite similar at all collision energies, indicating that the collision dynamics are relatively insensitive to energy over this range. Although the exchange reaction involves the formation of an intermediate complex ion in which bond rearrangement takes place, the OD− products are primarily backward scattered with only low intensity scattering appearing in the forward direction. The forward scattered products do contribute proportionately more intensity to the complete differential cross section as the collision energy increases, suggesting that both direct and collision complex mechanisms are responsible for reaction. The angular distributions are interpreted in terms of the osculating model for chemical reaction occurring in a fraction of the rotational period of the intermediate complex, augmented by a small forward scattered direct component. This model suggests that the complex lifetime is approximately 150 fs at 0.27 eV. When the OD− product is backward scattered, little internal energy is found in either product. A simple impulsive model explains the lack of internal excitation based on the geometry of the transition state of the complex. More of the available energy is deposited into product internal modes when the intermediate complex lives longer and OD− is forward scattered. The collision energy can be redistributed into bending modes of the complex, which impart angular momentum to the fragments when the complex dissociates. The recoil energy distributions for the nonreactively scattered OH− show strong similarities to the reactively scattered OD− distributions and are useful in probing the origin of the product rotational excitation. Structure in the recoil energy distributions corresponding to inelastically scattered OH− indicates the preferred deposit of available energy into specific rotational modes. © 2000 American Institute of Physics.
Screening of a charged particle by multivalent counterions in salty water: Strong charge inversion
Authors: Nguyen T. T. , Grosberg A. Yu. , Shklovskii B. I.
Published: July 2002

Screening of a macroion such as a charged solid particle, a charged membrane, double helix DNA, or actin by multivalent counterions is considered. Small colloidal particles, charged micelles, short or long polyelectrolytes can play the role of multivalent counterions. Due to strong lateral repulsion at the surface of the macroion such multivalent counterions form a strongly-correlated liquid, with the short-range order resembling that of a Wigner crystal. These correlations create additional binding of multivalent counterions to the macroion surface with binding energy larger than kBT. As a result even for a moderate concentration of multivalent counterions in the solution, their total charge at the surface of the macroion exceeds the bare macroion charge in absolute value. Therefore, the net charge of the macroion inverts its sign. In the presence of a high concentration of monovalent salt the absolute value of inverted charge can be larger than the bare one. This strong inversion of charge can be observed by electrophoresis or by direct counting of multivalent counterions.
Conformal vector fields in general relativity
Authors: Hall G. S. , Steele J. D.
Published: July 2002

A general discussion of conformal vector fields in space-times is given. Amongst the topics considered are the maximum dimension of the conformal algebra for space-times that are not conformally flat, the nature of conformal isotropies and a new approach to the theorem of Bilyalov and Defrise-Carter concerning the reduction of the conformal algebra to a Killing or homothetic algebra. Some deficiencies in the original statements of this theorem are discussed (with reference to a general class of counterexamples) and corrected. The proof offered is geometrical in nature and has the advantage of displaying some of the more general features and properties of conformal vector fields and the ways in which they can differ from Killing vector fields.
Wigner function and quantum kinetic theory in curved space–time and external fields
Authors: Fonarev Oleg A.
Published: July 2002

A new definition of the Wigner function for quantum fields coupled to curved space–time and an external Yang–Mills field is studied on the example of scalar and Dirac fields. The definition uses the formalism of the tangent bundles and is explicitly covariant and gauge invariant. Derivation of collisionless quantum kinetic equations is carried out for both quantum fields by using the first order formalism of Duffin and Kemmer. The evolution of the Wigner function is governed by the quantum corrected Liouville–Vlasov equation supplemented by the generalized mass–shell constraint. The structure of the quantum corrections is perturbatively found in all adiabatic orders. The lowest order quantum–curvature corrections coincide with the ones found by Winter.
Determination of f(∞) from the asymptotic series for f(x) about x=0
Authors: Bender Carl M. , Boettcher Stefan
Published: July 2002

A difficult and long-standing problem in mathematical physics concerns the determination of the value of f(∞) from the asymptotic series for f(x) about x=0. In the past the approach has been to convert the asymptotic series to a sequence of Padé approximants {Pnn(x)} and then to evaluate these approximants at x=∞. Unfortunately, for most physical applications the sequence {Pnn(∞)} is slowly converging and does not usually give very accurate results. In this paper the results of extensive numerical studies for a large class of functions f(x) associated with strong-coupling lattice approximations are reported. It is conjectured that for large n, Pnn(∞)∼f(∞)+B/ln n. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of f(∞).
𝓟𝓣-symmetric quantum mechanics
Authors: Bender Carl M. , Boettcher Stefan , Meisinger Peter N.
Published: July 2002

This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H†=H on the Hamiltonian, where † represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement H‡=H, where ‡ represents combined parity reflection and time reversal 𝒫𝒯, one obtains new classes of complex Hamiltonians whose spectra are still real and positive. This generalization of Hermiticity is investigated using a complex deformation H=p2+x2(ix)ε of the harmonic oscillator Hamiltonian, where ε is a real parameter. The system exhibits two phases: When ε⩾0, the energy spectrum of H is real and positive as a consequence of 𝒫𝒯 symmetry. However, when −1<ε<0, the spectrum contains an infinite number of complex eigenvalues and a finite number of real, positive eigenvalues because 𝒫𝒯 symmetry is spontaneously broken. The phase transition that occurs at ε=0 manifests itself in both the quantum-mechanical system and the underlying classical system. Similar qualitative features are exhibited by complex deformations of other standard real Hamiltonians H=p2+x2N(ix)ε with N integer and ε>−N; each of these complex Hamiltonians exhibits a phase transition at ε=0. These 𝒫𝒯-symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space.
Critical Properties and Vapor Pressure Equation for Alkanes CnH2n+2: Normal Alkanes With n⩽36 and Isomers for n=4 Through n=9
Authors: Lemmon Eric W. , Goodwin A. R. H.
Published: July 2002

A correlation for estimating the vapor pressure of normal alkanes from methane through n-hexatriacontane and isomers of butane to nonane is reported. This work extends the correlation for normal alkanes (CnH2n+2), with n⩽20, reported by Ambrose, to both normal alkanes with n⩽36 and their isomers with n⩽9. This vapor pressure equation was based on the Wagner equation and is similar to that used by Ambrose. Literature vapor pressure measurements have been reviewed. Tables are given that list the type of apparatus, measurement range and precision, and chemical purity. These criteria were initially used to select measurements for inclusion in the regression analyses to determine the coefficients of the correlation. Vapor pressures estimated from the correlation were compared with all vapor pressure (p1+g) measurements reviewed in this work. At pressures greater than 1 kPa, the vapor pressure equation presented here has the following accuracies: 0.0001⋅p1+g for methane, 0.001⋅p1+g for ethane, propane, and n-butane, 0.002⋅p1+g for n-pentane through n-octane, 2-methylpropane, and 2-methylbutane, 0.005⋅p1+g for 2,2-dimethylpropane, n-nonane, n-decane, and the isomers of hexane through nonane, 0.01⋅p1+g for n-undecane to n-hexadecane, 0.02⋅p1+g for n-heptadecane to n-eicosane, 0.05⋅p1+g for n-heneicosane to n-octacosane, and 0.10⋅p1+g for n-nonacosane to n-hexatriacontane. Equations for the critical temperatures and pressures of the normal alkanes as functions of the carbon number are also reported.
The mechanism for surface wave instability in film flow down an inclined plane
Authors: Kelly R. E. , Goussis D. A. , Lin S. P. , Hsu F. K.
Published: July 2002

The equation governing the average rate of change of disturbance kinetic energy is evaluated for various wavenumbers at fixed values of Reynolds number, Weber number, and angle of inclination. The dominant energy production term is associated with the work done by the perturbation shear stress at the free surface. The mechanism of instability, however, is associated with a shift of perturbation vorticity relative to the surface displacement resulting from advection.
Nonlinear waves traveling upon a front of solitons
Authors: Pesenson M. Z.
Published: July 2002

The equation for perturbations with finite amplitude and finite wavelength traveling on a front of exponential solitons has been derived by means of an asymptotic procedure. The shock waves traveling on a front of exponentially decaying solitons, like the ‘‘shock–shocks’’ of Whitham, have been described. Stability conditions of solitons relative to the multidimensional perturbations have also been obtained. The spectrum of the soliton vibrations in the stable case, the stability threshold, and the growth rate in the unstable case have been calculated. The resulting equation is a generalization of the nonlinear quasioptics for the modulation of solitons with finite front width, in this case, the nonlinearity and diffusion of the perturbations are not independent.
Eddy-viscosity-type subgrid-scale model with a variable Smagorinsky coefficient and its relationship with the one-equation model in large eddy simulation
Authors: Yoshizawa Akira
Published: July 2002

Subgrid-scale (SGS) modeling in the large eddy simulation of incompressible turbulence is revisited with special emphasis on the equation for the SGS kinetic energy. Using this equation, the Smagorinsky model can be converted to a SGS model with the effects of advection and transport incorporated into the Smagorinsky coefficient. The relationship with the one-equation SGS model that directly uses the equation for the SGS kinetic energy is also discussed.
Unsteady spreading of thin liquid films with small surface tension
Authors: Moriarty J. A. , Schwartz L. W. , Tuck E. O.
Published: July 2002

The method of matched asymptotic expansions is used to solve for the free surface of a thin liquid drop draining down a vertical wall under gravity. The analysis is based on the smallness of the surface tension term in the lubrication equation. In a region local to the front of the drop, where the surface curvature is large, surface tension forces are significant. Everywhere else, the surface curvature is small, and surface tension plays a negligible role. A numerical time-marching scheme, which makes no small surface tension assumptions, is developed to provide a datum from which to gauge the accuracy of the small surface tension theory. Agreement between the numerical scheme and the small surface tension theory is good for small values of surface tension. Extension to the propagation of drops by spinning and by blowing with a jet of air is also discussed. It is shown that there are inherent similarities between all three spreading mechanisms.
The linear and nonlinear shear instability of a fluid sheet
Authors: Rangel R. H. , Sirignano W. A.
Published: July 2002

A theoretical and computational investigation of the inviscid Kelvin–Helmholtz instability of a two-dimensional fluid sheet is presented. Both linear and nonlinear analyses are performed. The study considers the temporal dilational (symmetric) and sinuous (antisymmetric) instability of a sheet of finite thickness, including the effect of surface tension and the density difference between the fluid in the sheet and the surrounding fluid. Previous linear-theory results are extended to include the complete range of density ratios and thickness-to-wavelength ratios. It is shown that all sinuous waves are stable when the dimensionless sheet thickness is less than a critical value that depends on the density ratio. At low density ratios, the growth rate of the sinuous waves is larger than that of the dilational waves, in agreement with previous results. At higher density ratios, it is shown that the dilational waves have a higher growth rate. The nonlinear calculations indicate the existence of sinuous oscillating modes when the density ratio is of the order of 1. Sinuous modes may result in ligaments interspaced by half of a wavelength. Dilational modes grow monotonically and may result in ligaments interspaced by one wavelength.
Nonlinear rupture of free films
Authors: Erneux Thomas , Davis Stephen H.
Published: July 2002

A free viscous film is subject to van der Waals attractions that lead to film rupture. Long-wave asymptotics is used to derive approximate equations that govern the unstable evolution of the film. The solution of the nonlinear evolution equation is then considered using bifurcation techniques leading to an estimate for the nonlinear rupture time.
Experiments on the Richtmyer–Meshkov instability: Small-scale perturbations on a plane interface
Authors: Brouillette M. , Sturtevant B.
Published: July 2002

This paper reports the results of measurements of the ‘‘visual thickness,’’ obtained from flow visualization experiments by the schlieren method, of initially plane interfaces between two gases under impulsive accelerations. It is found that when such interfaces are processed by just one incident shock wave of strength of order Ms=1.5, their thickness increases slowly and they require observation over extended times; their growth rates are found to slow down with time, in agreement with simple theoretical arguments. The observed growth rates of thin interfaces formed by plastic membranes have been found to be substantially smaller than that reported by previous investigators. Also, thick, diffusively smoothed interfaces initially grow much more slowly than the discontinuous ones do. In these experiments, it is found that wall vortices formed by shock wave/boundary-layer interaction at the interface grow much more rapidly than the shock-processed interfaces in the bulk of the fluid. These wall structures can reduce the apparent growth of interfaces by vorticity-induced strain and impair the observation of the relevant interface phenomena.
Convective heat transfer through polarized dielectric liquids
Authors: Stiles P. J. , Lin F. , Blennerhassett P. J.
Published: July 2002

An electrically insulating layer of a dielectric liquid confined between horizontal conducting electrodes, the upper of which is warmer, becomes unstable with respect to the onset of steady convection when the voltage between the plates reaches a critical value. In a rapidly varying ac field this instability is due to the Kelvin body force which depends on the polarization P and the gradient of the electric field E. Our recent linear stability analysis [Chem. Phys. Letters 179, 311 (1991)] for the critical voltage showed that as the gravitational Rayleigh number becomes increasingly negative the critical wave number at the onset of convection becomes very large. We now extend this analysis to examine how the Nusselt number depends on the extent of supercriticality in the weakly nonlinear regime. As the temperature drop between the plates increases the fraction of the heat transfer associated with convection is found to pass through a maximum value when the critical horizontal wave number is close to 4 times its value when gravity is absent.
The unsteady structure of two-dimensional steady laminar separation
Authors: Ripley Matthew D. , Pauley Laura L.
Published: July 2002

The two-dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time-step method, were used to investigate separation due to the application of an adverse pressure gradient to a low-Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP 4, 813 (1966)] was applied in the present computations to study the development of a laminar separation bubble. In all cases studied, periodic vortex shedding occurred from the primary separation region. The shed vortices initially lifted from the boundary layer and then returned towards the surface downstream. The shedding frequency nondimensionalized by the momentum thickness was found to be independent of Reynolds number. The value of the nondimensional Strouhal number, however, was found to differ from the results of Pauley et al. [J. Fluid Mech. 220, 397 (1990)], indicating that the shedding frequency varies with the nondimensional pressure distribution, Cp. The computational results were time averaged over several shedding cycles and the results were compared with Gaster. The numerical study accurately reproduced the major characteristics of the separation found in Gaster’s study such as the separation point, the pressure plateau within the upstream portion of the separation bubble, and the reattachment point. The similarity between the experimental results and the time-averaged two-dimensional computational results indicates that the low-frequency velocity fluctuations detected by Gaster are primarily due to the motion of large vortex structures. This suggests that large-scale two-dimensional structures control bubble reattachment and small-scale turbulence contributes a secondary role.
Extending the collisional fluid equations into the long mean-free-path regime in toroidal plasmas. I. Plasma viscosity
Authors: Shaing K. C. , Spong D. A.
Published: July 2002

An expression for the pressure anisotropy and thus for the viscous stress in the plateau regime is derived for arbitrary toroidal magnetic configurations without assuming incompressibility or the existence of flux surfaces, without neglecting the flow components perpendicular to the magnetic surface, and without restricting the flow velocity to be a constant on the flux surface. It can be employed to study low-frequency instabilities in the long mean-free-path regime. A smoothly connected formula for the pressure anisotropy, valid in both the collisional fluid regime and the plateau regime, is given to facilitate the numerical computation. An alternative interpretation of the neoclassical transport theory is also obtained. It is found that if the effects of the temperature gradient are neglected, neoclassical transport fluxes can be interpreted as driven by the velocity stress.
Experimental measurements on a 100 GHz frequency tunable quasioptical gyrotron
Authors: Alberti S. , Tran M. Q. , Hogge J. P. , Tran T. M. , Bondeson A. , Muggli P. , Perrenoud A. , Jödicke B. , Mathews H. G.
Published: July 2002

Experiments on a 100 GHz quasioptical (QO) gyrotron operating at the fundamental (ω=Ωce) are described. Powers larger than 90 kW at an efficiency of about 12% were achieved. Depending on the electron beam parameters, the frequency spectrum of the output can be either single moded or multimoded. One of the main advantages of the QO gyrotron over the conventional gyrotron is its continuous frequency tunability. Various techniques to tune the output frequency have been tested, such as changing the mirror separation, the beam voltage, or the main magnetic field. Within the limitations of the present setup, 5% tunability was achieved. The QO gyrotron designed for operation at the fundamental frequency exhibits simultaneous emission at 100 GHz (fundamental) and 200 GHz (second harmonic). For a beam current of 4 A, 20% of the total rf power is emitted at the second harmonic.
Hyperresistivity due to densely packed tearing mode turbulence
Authors: Craddock G. G.
Published: July 2002

A theory for tearing turbulence in the limit of overlapping islands is developed. A resulting hyperresistivity is found by consistent inclusion of resistivity which differs from that of Strauss [Phys. Fluids 29, 3668 (1986)]. Further, a saturated magnetic fluctuation level is found in a reversed-field pinch (RFP) by balancing anomalous vorticity damping (not hyperresistivity) with current gradient free energy. The role of hyperresistivity is to participate in energy equipartitioning and a cascade of energy to small scales. The effects of magnetic curvature on hyperresistivity are also considered.
The plasma–sheath transition in an asymmetric collisionless plasma
Authors: van den Berg H.-P. , Riemann K.-U. , Ecker G.
Published: July 2002

The plasma–sheath problem (λD → 0) for an asymmetric warm collision-free plasma is solved in plane parallel geometry. To this end Emmert’s model source term [Phys. Fluids 23, 803 (1980)] is generalized to account for a superimposed plasma drift. The quasineutral plasma approximation results in a system of coupled integral equations that can be solved analytically. In contrast to Emmert’s symmetric model the upstream facing sheath edge shows the usual field singularity. At the downstream facing sheath edge, a finite field strength and an oversatisfied Bohm criterion are found. These results are in full agreement with general considerations on the Bohm criterion and on the sheath edge field singularity [Phys. Fluids B 1, 961 (1989)].