Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c^3∑g^＋ and B^1-Пu states of dimer 7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.     

Comparison study of the charge density distribution induced by heavy ions and pulsed lasers in silicon

Heavy ions and pulsed lasers are important means to simulate the ionization damage effects on semiconductor materials. The analytic solution of high-energy heavy ion energy loss in silicon has been obtained using the Bethe-Bloch formula and the Kobetich-Katz theory, and some ionization damage parameters of Fe ions in silicon, such as the track structure and ionized charge density distribution, have been calculated and analyzed according to the theoretical calculation results. Using the Gaussian function and Beer＇s law, the parameters of the track structure and charge density distribution induced by a pulsed laser in silicon have also been calculated and compared with those of Fe ions in silicon, which provides a theoretical basis for ionization damage effect modeling.     

Thermodynamic study of fluid in terms of equation of state containing physical parameters

We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster.Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy.The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied.Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity(radial distribution function).From the thermodynamic profile of the fluid,the model results are discussed in terms of the cavity due to the closed surface along with suitable energy.The present calculation is based upon the sample thermodynamic data for n-hexanol,such as the ultrasonic wave,density,volume expansion coefficient,and ratio of specific heat in the liquid state,and it is consistent with the thermodynamic relations containing physical parameters such as size and energy.Since the data is restricted to n-hexanol,we avoid giving the physical meaning of f,which is the key parameter studied in the present work.     

A methodology to achieve the basis function for the expansion of sound speed profile

In order to evaluate the reliability and applicability of the Empirical Orthogonal Functions（EOFs）in the acoustic inversion of sound speed profile（SSP）and reduce EOF＇s dependence on the sample data,a methodology is proposed for the achievement of the basis functions for SSP＇s expansion.By analyzing the oceanographic dynamics which is the main cause of the SSP＇s variation,the basis functions are obtained naming the Hydrodynamic Normal Modes（HNMs）.The HNM basis functions are almost the same as those derived from the EOF method,while HNMs has less dependence on the amount of the sample data.HNMs method has a physically meaningful interpretation,and it could give out the physical parameters which determine the basis functions for the expansion of SSP,and this makes it possible to analyze and evaluate the trustiness and applicability of EOFs.     

Axial distribution of Gaussian beam limited by a hard-edged aperture

In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraun-hofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam, the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given. The theoretical results conform to the numerical analysis.     

Numerical Simulations on the Formation of Speckles in Nanofluids Illuminated by a TEM00 Laser Beam

On the basis of a Rayleigh scattering model for a single nanoparticle illuminated by a TEMoo laser beam, we theoretically and numerically study the speckle formation when nanofluids are illuminated by a TEMoo laser beam. The results show that the laser speckles possess a Gaussian distribution, which are in agreement with the experimental results. The results may be useful for using a laser speckle velocimetry to determine the velocitiies of nanoparticles in nanofluids.     

Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate are investigated by using the Hartree–Fock–Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements.According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.     

Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution

The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type （KT） distribution. Numerical calculations are performed for a direct comparison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency （e.g.,ω 〈~0.1Ω） due to a larger fractional number of the resonant electrons ηrel （which controls the wave growth）, while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Are1 by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.     

A Simple Calculation Approach for the Second－Harmonic Sound Beam Generated by an Arbitrary Distribution Source

We present a simple calculation approach for the fundamental and second-harmonic sound beams with an arbitrary distribution source in the quasilinear approximation. The analysis is based on the assumption that the source function with an arbitrary geometry and distribution is expanded into the sum of a set of two-dimensional Gaussian functions. The two- and five-dimensional integral solutions for the fundamental and second-harmonic fields are, respectively, reduced in terms of Gaussian functions and simple one-dimensional integrals. The numerical evaluation of field distributions is then greatly simplified.     

Optimal design of magnetic systems

The methods and the algorithms of the magnetic system design, producing the fields with a required distribution (the inverse problem of magnetostatics), are considered. The mathematical statement of the problem is reduced to the expansion of a given function into Fourier series on a non-orthonormal basis. The basis functions are the fields of the sections of a magnetic system, and the coefficients of the expansion are the components of the magnetization vector of the sections (the vector synthesis). The algorithms proposed to solve the problem take into account the physical constraints on the magnetization distribution of the assembly sections.     

Simulations of counterions at charged plates

Using Monte Carlo simulations, we study the counterion distribution close to planar charged walls in two geometries: i) when only one charged wall is present and the counterions are confined to one half-space, and ii) when the counterions are confined between two equally charged walls. In both cases the surface charge is smeared out and the dielectric constant is the same everywhere. We obtain the counterion density profile and compare it with both the Poisson-Boltzmann theory (asymptotically exact in the limit of weak coupling, i.e. low surface charge, high temperature and low counterion valence) and the strong-coupling theory (valid in the opposite limit of high surface charge, low temperature and high counterion valence) and with previously calculated correction terms to both theories for different values of the coupling parameter, thereby establishing the domain of validity of the asymptotic limits. Gaussian corrections to the leading Poisson-Boltzmann behavior (obtained via a systematic loop expansion) in general perform quite poorly: At coupling strengths low enough so that the Gaussian (or one-loop) correction does describe the numerical deviations from the Poisson-Boltzmann result correctly, the leading Poisson-Boltzmann term by itself matches the data within high accuracy. This reflects the slow convergence of the loop expansion. For a single charged plane, the counterion pair correlation function indicates a behavioral change from a three-dimensional, weakly correlated counterion distribution (at low coupling) to a two-dimensional, strongly correlated counterion distribution (at high coupling), which is paralleled by the specific-heat capacity which displays a rounded hump at intermediate coupling strengths. For the case of counterions confined between two equally charged walls, we analyze the inter-wall pressure and establish the complete phase diagram, featuring attraction between the walls for large enough coupling strength and at intermediate wall separation. Depending on the thermodynamic ensemble, the phase diagram exhibits a discontinuous transition where the inter-wall distance jumps to infinity (in the absence of a chemical potential coupling to the inter-wall distance, as for charged lamellae in excess solvent) or a critical point where two coexisting states with different inter-wall distance become indistinguishable (in the presence of a chemical potential, as for charged lamellae with a finite fixed solvent fraction). The attractive pressure decays with the inter-wall distance as an inverse cube, similar to analytic predictions, although the amplitude differs by an order of magnitude from previous theoretical results. Finally, we discuss in detail our simulation methods and compare the finite-size scaling behavior of different boundary conditions (periodic, minimal image and open). Received 6 November 2001     

Research on temperature field characteristics of optical films under 1064 nm short-pulse laser radiation

The 3-D temperature field distribution (TFD) equation of optical films (OFs) was analyzed, based on the film temperature field distribution (FTFD) model irradiated by Gaussian short-pulse laser, and short-pulse laser-induced temperature field distribution of TiO₂/SiO₂ composite membranes on K9 glasses was obtained by means of numerical simulation. The results show that the thermal effect of optical films is very obvious under the Gaussian short-pulse laser. Temperature at the center of the spot rises faster than in other areas, and it decreases along the radius rapidly. It provides theoretical basis for progress analysis of short-pulse laser acting on optical films.     

Polyakov loop distributions near deconfinement inSU(2) lattice gauge theory

The distribution function of the Polyakov loop is investigated on a 16³×3 lattice in the neighbourhood of the deconfinement transition ofSU(2) gauge theory. We find, that well above the transition the distribution is a Gaussian; when the coupling approaches the critical point it is modified due to phase flip attempts of the system. Corresponding distributions for the plaquettes remain, however, Gaussian. For one coupling close to the transition we study the distributions on 8³, 12³ and 18³×4 lattices and show that strong finite size effects are present. Using the maximum values of the Gaussian parts of the distributions we construct a more physical (and therefore scaling) order parameter whose critical exponent is in excellent agreement with the universality hypothesis.     

Simulation of random packing of spherical particles with different size distributions

A numerical model for a loose packing process of spherical particles is presented. The simulation model starts with randomly choosing a sphere according to a pregenerated continuous particle-size distribution, and then dropping the sphere into a dimension-specified box, and obtaining its final position by using dropping and rolling rules which are derived from a similar physical process of spheres dropping in the gravitational field to minimize its gravity potential. Effects of three different particle-size distributions on the packing structure were investigated. Analysis on the physical background of the powder-based manufacturing process is additionally applied to produce optimal packing parameters of bimodal and Gaussian distributions to improve the quality of the fabricated parts. The results showed that higher packing density can be obtained using bimodal size distribution with a particle-size ratio from 1.5 to 2.0 and the mixture composition around n ₂:n ₁=6:4. For particle size with a Gaussian distribution, the particle radii should be limited in a narrow range around 0.67 to 1.5.     

Focusing and phase compensation of paraxial beams by a left-handed material slab

On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase compensation by LHM slab. Because of the negative refractive index of LHM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. It is shown that the phase difference caused by the Gouy phase shift in right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at the image plane.     

On a study of the superposition effect of diffracted X-rays by a liquid column and the optimum thickness for X-ray diffraction

A measure of intensity due to the superposition of diffracted X-rays from elementary regions in the line of X-ray path has been calculated on the basis of Gaussian distribution of intensity from every element. This gives the optimum thickness for maximum intensity implicitly by the relation. Μt₀=α?′(αt₀)/?(αt₀) where ? is the error integral and α is a characteristic of the liquid which determines the Gaussian distribution form for the particular liquid. Good agreement between the theoretical relations and the experimental values have been observed.     

Scarring and the Statistics of Tunnelling

We show that the statistics of tunnelling can be dramatically affected by scarring and derive distributions quantifying this effect. Strong deviations from the prediction of random matrix theory can be explained quantitatively by modifying the Gaussian distribution which describes wavefunction statistics. The modified distribution depends on classical parameters which are determined completely by linearised dynamics around a periodic orbit. This distribution generalises the scarring theory of L. Kaplan (1998, Phys. Rev. Lett.80, 2582) to describe the statistics of the components of the wavefunction in a complete basis, rather than the overlaps with single Gaussian wavepackets. In particular it is shown that correlations in the components of the wavefunction are present, which can strongly influence tunnelling-rate statistics. The resulting distribution for tunnelling rates is tested successfully on a two-dimensional double-well potential.     

Inverse method for determining the depth of nonhomogeneous surface layers in elastic solids from the measurements of the dispersion curves of group velocity of surface SH Waves

In this paper, the variational inverse method for determining the depth of nonhomogeneous surface layers in elastic materials, from the measurements of the group velocity of surface shear horizontal (SH) waves, is developed. The direct problem for a given a priori type of profile of the coefficientc44in(x) (e.g. linear, Gaussian, etc.) is solved. The dispersion curves of phase and group velocity of surface SH waves in nonhomogeneous solids are calculated. Experimental verification of the inverse method has been performed for step profiles (structure of Cu on steel). It is stated that the inverse method based on the measurements of group velocity (for step profile) gives a smaller error in the unknown depth of the surface layer than that resulting from the inverse method based on the measurements of phase velocity of surface SH waves.