The energy of interaction between two hydrogen atoms by the Gaussian-type functions
Energy of interaction between two hydrogen atoms in their ground states described by Gauss-type functions
MOLECULAR ENERGY↗
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A class of nonlinear functions and the convergence of Gauss-Seidel and Newton-Gauss-Seidel iterations
Class on nonlinear functions and convergence of Gauss-Seidel and Newton-Gauss-Seidel iterations
More, J. J.↗
Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality
We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine{sub 2},Airy{sub 2},Bessel{sub 2}, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Kinetic theory of quasi-stationary collisionless axisymmetric plasmas in the presence of strong rotation phenomena
The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Advection of passive magnetic field by the Gaussian velocity field with finite correlations in time and spatial parity violation
Using the field theoretic renormalization group technique the model of passively advected weak magnetic field by an incompressible isotropic helical turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation) in the framework of an extended Kazantsev-Kraichnan model of kinematic magnetohydrodynamics. Statistical fluctuations of the velocity field are taken in the form of a Gaussian distribution with zero mean and defined noise with finite correlations in time. The two-loop analysis of all possible scaling regimes is done and the influence of helicity on the stability of scaling regimes is discussed and shown in the plane of exponents ɛ − η, where ɛ characterizes the energy spectrum of the velocity field in the inertial range E ∞ k{sup 1−2ε}, and η is related to the correlation time at the wave number k which is scaled as k {sup −2+η}. It is shown that in non-helical case the scaling regimes of the present vector model are completely identical and have also the same properties as those obtained in the corresponding model of passively advected scalar field. Besides, it is also shown that when the turbulent environment under consideration is helical then the properties of the scaling regimes in models of passively advected scalar and vector (magnetic) fields are essentially different. The results demonstrate the importance of the presence of a symmetry breaking in a given turbulent environment for investigation of the influence of an internal tensor structure of the advected field on the inertial range scaling properties of the model under consideration and will be used in the analysis of the influence of helicity on the anomalous scaling of correlation functions of passively advected magnetic field.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Twisted Landau damping rates in multi-component dusty plasmas
Keeping in view the kinetic treatment for plasma particles, the electrostatic twisted dust-acoustic (DA) and dust-ion-acoustic (DIA) waves are investigated in a collisionless unmagnetized multi-component dusty plasma, whose constituents are the electrons, singly ionized positive ions, and negatively charged massive dust particulates. With this background, the Vlasov–Poisson equations are coupled together to derive a generalized dielectric constant by utilizing the Laguerre-Gaussian perturbed distribution function and electrostatic potential in the paraxial limit. The dispersion and damping rates of twisted DA and DIA waves are analyzed with finite orbital angular momentum states in a multi-component dusty plasma. Significant modifications concerning the real wave frequencies and damping rates appeared with varying twisted dimensionless parameter and dust concentration. In particular, it is shown that dust concentration enhances the phase speed of the DIA waves in contrary to DA waves, whereas the impact of twisted parameter reduces the frequencies of both DA and DIA waves. The results should be useful for the understanding of particle transport and trapping phenomena caused by wave excitation in laboratory dusty plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Kinetic study of ion acoustic twisted waves with kappa distributed electrons
The kinetic theory of Landau damping of ion acoustic twisted modes is developed in the presence of orbital angular momentum of the helical (twisted) electric field in plasmas with kappa distributed electrons and Maxwellian ions. The perturbed distribution function and helical electric field are considered to be decomposed by Laguerre-Gaussian mode function defined in cylindrical geometry. The Vlasov-Poisson equation is obtained and solved analytically to obtain the weak damping rates of the ion acoustic twisted waves in a non-thermal plasma. The strong damping effects of ion acoustic twisted waves at low values of temperature ratio of electrons and ions are also obtained by using exact numerical method and illustrated graphically, where the weak damping wave theory fails to explain the phenomenon properly. The obtained results of Landau damping rates of the twisted ion acoustic wave are discussed at different values of azimuthal wave number and non-thermal parameter kappa for electrons.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Size Distribution of Graphite Nodules in Hypereutectic Cast Irons of Varying Nodularity
An SGI was machined into 400 g cylindrical pieces and remelted in an electrical resistance furnace protected by Ar gas to produce materials ranging from SGI to CGI. The graphite morphology was controlled by varying the holding time at 1723 K (1450 °C) between 10 and 60 minutes. The discrete sectional size distribution of nodules by number density was measured on cross sections of the specimens and translated to volumetric distribution by volume fraction. Subpopulations of nodules were distinguished by fitting Gaussian distribution functions to the measured distribution. Primary and eutectic graphite, were found to account for most of the volume of nodular graphite in all cases. For holding times of 40 minutes and greater, corresponding to nodularity roughly below 40 pct, the primary subpopulation was very small and difficult to distinguish, leaving eutectic nodules as the dominant subpopulation. The mode and standard deviation of the two subpopulations were roughly independent of nodularity. Moreover, the nodular and vermicular graphite were segregated in the microstructure. In conclusion, the results suggest that the parallel development of the vermicular eutectic had small influence on the size distribution of eutectic graphite nodules.
36 MATERIALS SCIENCE↗
Cluster truncated Wigner approximation in strongly interacting systems
We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean-field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids
Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
PROBABILISTIC MODEL OF BEAM–PLASMA INTERACTION IN RANDOMLY INHOMOGENEOUS PLASMA
We propose a new model that describes beam–plasma interaction in the presence of random density fluctuations with a known probability distribution. We use the property that, for the given frequency, the probability distribution of the density fluctuations uniquely determines the probability distribution of the phase velocity of waves. We present the system as discrete and consisting of small, equal spatial intervals with a linear density profile. This approach allows one to estimate variations in wave energy density and particle velocity, depending on the density gradient on any small spatial interval. Because the characteristic time for the evolution of the electron distribution function and the wave energy is much longer than the time required for a single wave–particle resonant interaction over a small interval, we determine the description for the relaxation process in terms of averaged quantities. We derive a system of equations, similar to the quasi-linear approximation, with the conventional velocity diffusion coefficient D and the wave growth rate γ replaced by the average in phase space, by making use of the probability distribution for phase velocities and by assuming that the interaction in each interval is independent of previous interactions. Functions D and γ are completely determined by the distribution function for the amplitudes of the fluctuations. For the Gaussian distribution of the density fluctuations, we show that the relaxation process is determined by the ratio of beam velocity to plasma thermal velocity, the dispersion of the fluctuations, and the width of the beam in the velocity space.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Dispersion-correcting potentials can significantly improve the bond dissociation enthalpies and noncovalent binding energies predicted by density-functional theory
Dispersion-correcting potentials (DCPs) are atom-centered Gaussian functions that are applied in a manner that is similar to effective core potentials. Previous work on DCPs has focussed on their use as a simple means of improving the ability of conventional density-functional theory methods to predict the binding energies of noncovalently bonded molecular dimers. We show in this work that DCPs developed for use with the LC-ωPBE functional along with 6-31+G(2d,2p) basis sets are capable of simultaneously improving predicted noncovalent binding energies of van der Waals dimer complexes and covalent bond dissociation enthalpies in molecules. Specifically, the DCPs developed herein for the C, H, N, and O atoms provide binding energies for a set of 66 noncovalently bonded molecular dimers (the “S66” set) with a mean absolute error (MAE) of 0.21 kcal/mol, which represents an improvement of more than a factor of 10 over unadorned LC-ωPBE/6-31+G(2d,2p) and almost a factor of two improvement over LC-ωPBE/6-31+G(2d,2p) used in conjunction with the “D3” pairwise dispersion energy corrections. In addition, the DCPs reduce the MAE of calculated X-H and X-Y (X,Y = C, H, N, O) bond dissociation enthalpies for a set of 40 species from 3.2 kcal/mol obtained with unadorned LC-ωPBE/6-31+G(2d,2p) to 1.6 kcal/mol. Our findings demonstrate that broad improvements to the performance of DFT methods may be achievable through the use of DCPs.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Modeling solvation effects in real-space and real-time within density functional approaches
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the OCTOPUS code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Charge transport properties of poly(dA)-poly(dT) DNA in variation of backbone disorder and amplitude of base-pair twisting motion
By using tight binding Hamiltonian model, charge transport properties of poly(dA)-poly(dT) DNA in variation of backbone disorder and amplitude of base-pair twisting motion is studied. The DNA chain used is 32 base pairs long poly(dA)-poly(dT) molecule. The molecule is contacted to electrode at both ends. The influence of environment on charge transport in DNA is modeled as variation of backbone disorder. The twisting motion amplitude is taking into account by assuming that the twisting angle distributes following Gaussian distribution function with zero average and standard deviation proportional to square root of temperature and inversely proportional to the twisting motion frequency. The base-pair twisting motion influences both the onsite energy of the bases and electron hopping constant between bases. The charge transport properties are studied by calculating current using Landauer-Buttiker formula from transmission probabilities which is calculated by transfer matrix methods. The result shows that as the backbone disorder increases, the maximum current decreases. By decreasing the twisting motion frequency, the current increases rapidly at low voltage, but the current increases slower at higher voltage. The threshold voltage can increase or decrease with increasing backbone disorder and increasing twisting frequency.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
PREDOMINANTLY LOW METALLICITIES MEASURED IN A STRATIFIED SAMPLE OF LYMAN LIMIT SYSTEMS AT Z = 3.7
We measured metallicities for 33 z = 3.4–4.2 absorption line systems drawn from a sample of H i-selected-Lyman limit systems (LLSs) identified in Sloan Digital Sky Survey (SDSS) quasar spectra and stratified based on metal line features. We obtained higher-resolution spectra with the Keck Echellette Spectrograph and Imager, selecting targets according to our stratification scheme in an effort to fully sample the LLS population metallicity distribution. We established a plausible range of H i column densities and measured column densities (or limits) for ions of carbon, silicon, and aluminum, finding ionization-corrected metallicities or upper limits. Interestingly, our ionization models were better constrained with enhanced α -to-aluminum abundances, with a median abundance ratio of [ α /Al] = 0.3. Measured metallicities were generally low, ranging from [M/H] = −3 to −1.68, with even lower metallicities likely for some systems with upper limits. Using survival statistics to incorporate limits, we constructed the cumulative distribution function (CDF) for LLS metallicities. Recent models of galaxy evolution propose that galaxies replenish their gas from the low-metallicity intergalactic medium (IGM) via high-density H i “flows” and eject enriched interstellar gas via outflows. Thus, there has been some expectation that LLSs at the peak of cosmic star formation ( z ≈ 3) might have a bimodal metallicity distribution. We modeled our CDF as a mix of two Gaussian distributions, one reflecting the metallicity of the IGM and the other representative of the interstellar medium of star-forming galaxies. This bimodal distribution yielded a poor fit. A single Gaussian distribution better represented the sample with a low mean metallicity of [M/H] ≈ −2.5.
79 ASTRONOMY AND ASTROPHYSICS↗
Vibrationally resolved NEXAFS at C and N K-edges of pyridine, 2-fluoropyridine and 2,6-difluoropyridine: A combined experimental and theoretical assessment
In the present work, the near edge X-ray absorption spectroscopy (NEXAFS) spectra at both C and N K-edges of pyridine, 2-fluoropyridine, and 2,6-difluoropyridine have been studied both experimentally and theoretically. From an electronic point of view, both transition potential density functional theory and time-dependent density functional theory approaches lead to reliable results provided that suitable basis sets and density functionals are employed. In this connection, the global hybrid B3LYP functional in conjunction with the EPR-III basis set appears particularly suitable after constant scaling of the band positions. For the N K-edge, vertical energies obtained at these levels and broadened by symmetric Gaussian distributions provide spectra in reasonable agreement with the experiment. Vibronic contributions further modulate the band-shapes leading to a better agreement with the experimental results, but are not strictly necessary for semi-quantitative investigations. On the other hand, vibronic contributions are responsible for strong intensity redistribution in the NEXAFS C K-edge spectra, and their inclusion is thus mandatory for a proper description of experiments. In this connection, the simple vertical gradient model is particularly appealing in view of its sufficient reliability and low computational cost. For more quantitative results, the more refined vertical Hessian approach can be employed, and its effectiveness has been improved thanks to a new least-squares fitting approach.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Plasma Dispersion Function for the Kappa Distribution
The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.
Podesta, John J.↗
On electron bunching and stratification of glow discharges
Plasma stratification and excitation of ionization waves is one of the fundamental problems in gas discharge physics. Significant progress in this field is associated with the name of Lev Tsendin. He advocated the need for the kinetic approach to this problem contrary to the traditional hydrodynamic approach, introduced the idea of electron bunching in spatially periodic electric fields, and developed a theory of kinetic resonances for analysis of moving striations in rare gases. The present paper shows how Tsendin's ideas have been further developed and applied for understanding the nature of the well-known S-, P-, and R-striations observed in glow discharges of inert gases at low pressures and currents. We review numerical solutions of a Fokker-Planck kinetic equation in spatially periodic electric fields under the effects of elastic and inelastic collisions of electrons with atoms. We illustrate the formation of kinetic resonances at specific field periods for different shapes of injected Electron Distribution Functions (EDF). Computer simulations illustrate how self-organization of the EDFs occurs under nonlocal conditions and how Gaussian-like peaks moving along resonance trajectories are formed in a certain range of discharge conditions. The calculated EDFs agree well with the experimentally measured EDFs for the S, P, and R striations in noble gases. We discuss how kinetic resonances affect dispersion characteristics of moving striations and mention some non-linear effects associated with glow discharge stratification. We propose further studies of stratification phenomena combining physical kinetics and non-linear physics.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗