Mean spherical approximation for a model liquid metal potential

The solution of the Ornstein-Zernike equation for a direct correlation function c(x) with damped oscillations and a hard core condition imposed upon the total correlation function h(x) has been proposed by Cummings as a means of treating a simple model potential for liquid metals in the mean spherical approximation [1]. Here some numerical results are given for this model and their significance is discussed. The solution of the Ornstein-Zernike equation is also extended; the hard core condition is generalized to a soft core condition, and Yukawa terms are added to the oscillatory c(x). Ways in which these extensions can be incorporated into more accurate liquid metal models, as well as into more accurate approximations for these models, are discussed. Finally, it is shown that our solution of the Ornstein-Zernike equation, after a change in the core condition, yields the structure of a spin glass model considered by Høye and Stell in the MSA-like approximation they propose [22].     

Network topology and subgap resonances observed by Fourier transform scanning tunnelling microscopy of cuprate high-temperature superconductors

Fourier transform scanning tunnelling microscopy (STM) on Bi₂Sr₂CaCu₂O_{8+ δ} (BSCCO) subgap resonances has deciphered an octet of ‘quasiparticle’ states that are consistent with the Fermi surface and energy gap observed by angle-resolved photoemission spectroscopy (ARPES), but the origin of the high-intensity k-space octets and the sharply defined r-space chequerboard is unexplained. The filamentary ferroelastic nanodomain model that predicted the r-space chequerboard also explains the k-space octets and the origin of the apparent anisotropic surface d-wave gap by using strong electron–phonon interactions outside the CuO₂ planes. The topological model identifies the factors that stabilize high-intensity k-space octets in the presence of a very high level of irregular r-space chequerboard noise.     

Centric scan SPRITE magnetic resonance imaging

Two rapid, pure phase encode, centric scan, Single Point Ramped Imaging with T₁-Enhancement (SPRITE) MRI methods are described. Each retains the benefits of the standard SPRITE method, most notably the ability to image short T₂^* systems, while increasing the sensitivity and generality of the technique. The Spiral-SPRITE method utilizes a modified Archimedean spiral k-space trajectory. The Conical-SPRITE method utilizes a system of spirals mapped to conical surfaces to sample the k-space cube. The sampled k-space points are naturally Cartesian grid points, eliminating the requirement of a re-gridding procedure prior to image reconstruction. The effects of transient state behaviour on image resolution and signal/noise are explored.     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

The Fisher-Widom line for systems with low melting temperature

We present Monte Carlo results for the pair distribution function of three simple fluid models, with pairwise interactions, which have low triple point temperatures and mimic some aspects of Na and Hg liquid metals. The results are then used to get the direct correlation function, by numerical solution of the Ornstein-Zernike equation, and to characterize the decay modes of any density distribution towards the bulk fluid. The Fisher-Widom line is obtained from the crossing of the two lowest inverse decay lengths, associated to monotonic and to oscillatory decay modes. For the pair potential models with a soft repulsive core, the Fisher-Widom line appears well below the critical temperature and has positive slope of the temperature with respect to the density, contrary to previous results for the Lennard-Jones and square-well potentials which had located that line quite close to T _c and with negative slope.     

基于布里渊区谱的二维光子晶格线性缺陷模式分析

结合均匀光子晶格的衍射关系和晶格中正负缺陷的布里渊区谱特性,探讨了光诱导二维光子晶格中线性缺陷模式的形成条件,对布里渊区中各点的缺陷模式进行了模拟分析,并得到了光子带隙结构中“嵌入点”X₁点的正、负缺陷模式.结果表明：对于二维缺陷,只有当衍射关系曲面中沿两个正交的横向波矢方向同时为正常（反常）衍射的区域才能存在正（负）缺陷模式;而对于一维缺陷,只要在一个横向波矢方向上存在正常（反常）衍射的区域就可以支持正（负）缺陷模式,因此在某些特殊点处,正和负的缺陷模式可以同时存在.X₁点正缺陷模式的存在预示着自聚焦非线性同样可以支持带内孤子.研究结果有助于对光子晶格中晶格孤子（特别是带内孤子）的理解和进一步研究. 关键词： 光诱导光子晶格 光子带隙 线性缺陷态     

A relation between X-ray diffraction based liquid structure and packing coefficient

A relation between the liquid structure and the molecules packing coefficient has been derived on the grounds of the experimental results of X-ray diffraction studies. The packing coefficientk was assumed to be a criterion of correctness of the structural models of 2-methyl-1-propanol and 2-methyl-2-propanol based on experimental results. This coefficient was estimated from the specific volumes of moleculesV ₀, volumes of elementary pseudocellsV and the number of molecules comprised into these pseudocells. The volumesV of pseudocells were estimated from the same X-ray diffraction pattern as was used for determination of the liquid structure. The determined values of the packing coefficient support the chain-like structure of associates of liquid 2-methyl-1-propanol and reject the chain-like structure for liquid 2-methyl-2-propanol.     

Development of interatomic potentials appropriate for simulation of liquid and glass properties of NiZr2 alloy

A new interatomic potential for the Ni–Zr system is presented. This potential was developed specifically to match experimental scattering data from Ni, Zr and NiZr₂ liquids. Both ab initio and published thermodynamic data were used to optimise the potential to study the liquid and amorphous structure of the NiZr₂ alloy. This potential has the C ₁₆ phase, being more stable than C _11b phase in the NiZr₂ alloy, consistent with experiments. The potential leads to the correct glass structure in the molecular dynamics simulation and, therefore, can be used to study the liquid–glass transformation in the NiZr₂ alloy.     

Vibrational relaxation in liquids

A new theory is presented for vibrational energy relaxation in a liquid. It is shown that a vibrationally excited probe molecule relaxes through interaction with the density fluctuations in the surrounding solvent fluid. This interaction occurs through a potential V(k), which is expressed in terms of the intermolecular force between the excited probe molecule and the surrounding fluid molecules. By assuming spherically symmetric solvent particles the T ₁ energy relaxation time for direct V-T processes is related to the translational dynamic structure factor for the fluid S(k, ω_v), evaluated at the vibrational resonance frequency. It is shown that this is described by gas-like particle motions on a very short distance scale corresponding to k vectors lying well beyond the first or second peaks of the fluid structure factor S(k). Such motions can be pictured as high-frequency, short-distance distortions of the local equilibrium configuration of the solvent particles around the probe. T ₁ ^-1 is found to be proportional to ρ_e T ^1/2 ω_v ^-3. The V-V energy exchange relaxation time is also calculated. This is found to be proportional to S(k, ω′) evaluated at a frequency ω′, corresponding to the vibrational energy missmatch. An energy gap law for the V-V process is derived.     

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ _k has two degenerate minima at finite wave-vectors ± q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.     

An iterative reconstruction technique for geometric distortion-corrected segmented echo-planar imaging

In this article, we present a modified interleaved segmented echo-planar imaging (SEPI) sequence with a center-out k-space trajectory that is especially designed for susceptibility-weighted imaging applications. We introduce a simple and efficient technique to phase correct the acquired SEPI data in the presence of moderate field inhomogeneities. This phase correction reduces the distortion in the phase-encoding direction without requiring an extra reference scan. With the use of a center-out k-space trajectory and a low-spatial-frequency phase map, phase discontinuities between segments can be eliminated, in principle, iteratively using a fast Fourier transform from the center segment to the outermost segment in k-space. With an extra echo added in front of the echo train, neither phase unwrapping nor an extra reference scan is required to obtain a low-spatial-frequency phase map. The method is shown to remove blurring and reduce geometric distortion caused by phase changes from echo to echo in both phantom and human data. The method is most useful for high-resolution imaging applications and moderate factors of speed improvement.     

On self-diffusion and surface energy upon compression or tension of an iron crystal

The dependences of the activation parameters (formation of vacancies and self-diffusion) and specific surface energy on the volume fraction (V/V ₀) are calculated in terms of the Mie-Lenard-Jones pair potential of interatomic interaction for bcc-Fe along the 300-K and 3000-K isotherms. It is shown that under strong compressions (V/V ₀ < 1) or tensions (V/V ₀ > 1), the surface energy has a negative value, which must lead to the crystal structure fragmentation.     

Electron-phonon interaction in LaAg

Magnetoacoustic de Haas-van Alphen data on LaAg are compared with a new relativistic band structure calculation including La-4f states. We find convincing agreement of the measured and calculated dHvA frequencies. The deformation of the Fermi surface under strain is determined from the magnetoacoustic dHvA amplitude. The strongest deformation potential coupling is found for three equivalent pockets which become inequivalent under orthorhombic strain. The lifting of their degeneracy leads to the softening of theT ₃ elastic constant. This is different from the useual band Jahn-Teller effect which is based on the lifting of subband degeneracy at a single point ink-space.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Liquids in equilibrium: Beyond the hypernetted chain

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature T_c is predicted from the structure route. This T_c scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.     

Influence of crystal dimensions on interatomic distances in dispersed carbon

The relationship between the interatomic distances and crystal dimensions in dispersed carbon is studied by x-ray structure analysis and by performing model calculations. It is established that the interatomic distances in dispersed carbon are determined by the dimensions of the crystals along the crystallographic a axis (L _a). Small crystal dimensions dictate smaller interatomic distances than in graphite; an increase in the crystal dimensions leads to a corresponding increase in this parameter. The interatomic distances in dispersed carbon depend on the degree in covalency of the bonding, which is a function of L _a. Fiz. Tverd. Tela (St. Petersburg) 41, 744–747 (April 1999)     

Influence of interatomic repulsion on the structure of liquids at melting

Radial distribution functions and liquid structure factors for fluids of particles interacting through 1/rⁿ repulsive potentials are computed ‘exactly’ and systematically compared at crystallization for several values of n ranging between the two extremes of hard spheres (n = ∞) and Coulomb forces (n = 1). Striking similarities are pointed out in the large r behaviour (beyond the first peak) of the various radial distribution functions, and in the small k behaviour (including the first peak) of the various structure factors. Some information about the steepness of the repulsive potential in liquid rare gases and in liquid alkalis is gained from a comparison of the damping of successive peaks of the structure factors with experimental data.     

Geometrical relationship between the classical and quantum descriptions of arbitrary force interactions

The paper is a continuation of a series papers by the author in which it is shown that the equations of contemporary quantum theory (the Klein-Gordon equation and the Dirac integral equation) can be interpreted as conditions of harmonicity of linear form in the manifold^sV₄. In this paper, geometrization of classical and quantum interactions of a physical object is performed for the case of an arbitrary external force field in the manifold^kV₄. This manifold is constructed on the same set of surfaces as the manifold^sV₄. The equation representing conditions of harmonicity of linear form in^kV₄ is derived and is analogous to the KleinGordon equation.     

Integral equation theory of the exchange potential,HOMO–LUMO properties,and sum rules for the exchange-correlation force

Recently, a formally exact integral equation for the exchange potential V _x(r) has been presented by the authors. In the admittedly simplistic limit in which Slater–Kohn–Sham and Hartree–Fock determinants become equal, this integral equation reduces to that given by Della Sala and Görling. Here, a proposal is made to relate, but now approximately, the formally exact equation for V _x(r) to HOMO–LUMO properties. The addition of a correlation contribution V _c(r) to V _x(r), the sum being the exchange-correlation potential V _xc(r), is finally considered, some exact properties and especially sum rules for the force ??V _xc/?r being the focus.     

Distribution function for large velocities of a two-dimensional gas under shear flow

The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degreek⩾4 diverge for shear rates larger than a critical valuea _c ^(k) , which behaves for largek asa _c ^(k) ∼k ⁻¹. This divergence is consistent with an algebraic tail of the formf(V) ∼V ^−4-σ(a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann equation far from equilibrium.     

Bond lengths and location of the inner-ring protons in the corrole molecule

Ps IR laser pulse induced dissociation of vibrationally excited ABA* molecular resonances is simulated by simple model calculations. The stretching vibrations of ABA are represented by the Rosen-Thiele-Wilson coupled Morse oscillator hamiltonian with time dependent potential V(t) describing the interaction with a gaussian laser pulse in the semiclassical dipole approximation. The Schrödinger-equation is solved by Fast-Fourier-Transform propagation. The resulting wavefunctions ψ_t yield mode selective effects, e.g. the decays of hyperspherical and local modes with natural life times 5·92 ps and 0·07 ps are accelerated by the laser by factors 40 and 2, respectively. The mechanisms of photodissociation are analysed in detail, including laser-induced oscillations of the potential V(t) which transform dissociative frontier lobes of the wavefunction ψ_t of a slowly decaying hyperspherical mode into those of a rapidly dissociating local resonance.