Landau level quantization and possible superconducting instabilities in highly oriented pyrolitic graphite

Measurements of the basal-plane resistivity ρ _a(T,H) performed on highly oriented pyrolitic graphite, with magnetic field H∥c-axis in the temperature interval 2–300K and fields up to 8 T, provide evidence for the occurrence of both field-induced and zero-field superconducting instabilities. Additionally, magnetization M(T,H) measurements suggest the occurrence of Fermi surface instabilities which compete with the superconducting correlations. Fiz. Tverd. Tela (St. Petersburg) 41, 2135–2138 (December 1999)     

基于复杂网络研究中国温度变化的区域特征

为分析中国温度变化复杂性的区域特征,利用中国地区435个台站1961—2002年逐日平均温度序列,分别构建温度波动网络,并计算网络拓扑统计性质,给出全国的空间分布图像.顶点RRD,RDD,DRR,DDR,DdR的顶点度异常高,以这些顶点为代表的温度波动模态发生概率较大,对温度变化的趋势预测有一定的指导意义;根据5种顶点的顶点度在全国435个台站中的排行分布,将它们的主要作用区域依次定义为：全国型、次全国型、东部型、西南混合型及混合型.各 关键词： 气候变化 气候复杂网络 拓扑结构 复杂性     

Investigation of the axisymmetric buckling of round plates

The stress-strain behavior of a round plate during thermal cycling through the range for martensitic phase transformations is investigated. It is shown that the plate loses stability and recovers its original shape with a clap when a certain temperature A _in<T _ls⩽A _fin is reached. The results of measurements of the impact and reactive forces are presented. The conditions for the occurrence of a clap are determined. Zh. Tekh. Fiz. 67, 118–120 (June 1997)     

Conformational analysis of <Emphasis Type="Italic">o</Emphasis>-allylphenol by density functional and IR spectroscopy methods

The two-dimensional cyclic potential energy surfaces for internal rotation of the allyl substituent and its vinyl fragment in o-allylphenol (o-APh) depending on the OH group orientation relative to the allyl substituent were constructed by a B3LYP/6-31G method. It is shown that o-APh exists in the gas phase as a mixture of eight non-planar rotamers (A, B, C, D, E, F, G, and H) and their eight optical isomers (A ₁, B ₁, C ₁, D ₁, E ₁, F ₁, G ₁, and H ₁). An intramolecular H-bond (IHB) O–H...π occurs only in four rotamers (A, B, A ₁, and B ₁). The content of such rotamers in the gas phase is 47.2% (as calculated by the B3LYP/cc-pVTZ method). Taking into account the solvation effect in the polarizable continuum model (PCM) for a solution of o-APh in cyclohexane decreases the total content of rotamers with an IHB (A and B) to 37.7%. The ratio of rotamers with OH groups bonded by an IHB and with free OH groups that is predicted theoretically agrees with the value measured experimentally from IR spectra of o-APH in CCl₄ solution.     

The influence of climate on the oxygen isotopes in tree rings

Natural variations in the oxygen isotope ratio ¹⁸O/¹⁶O are occurring in the hydrological cycle as a result of isotope fractionations during evaporation and condensation. These processes imprint a valuable climatic signal in the precipitation, which is stored in ice caps as well as in the cellulose of trees. Recent developments in the continuous-flow analysis of ¹⁸O/¹⁶O of organic matter now enable a systematic application of this method in tree rings. It becomes possible to build maps of the past oxygen isotope distribution in continental areas, yielding important information on regional climate changes. In this paper, the factors influencing the isotope composition of tree rings are discussed with an example from trees in northern Eurasia. Oxygen isotope values of Larix, Picea and Pinus trees were measured over a large climatic gradient extending from Norway to Siberia. The spatial isotope variations were highly correlated to the annual mean temperature (r ² =0.84), whereby the slope of the corresponding regression line was 0.35/°C. When considering the changes in ¹⁸O/¹⁶O during the 20th century, not only the temperature, but also changes in the precipitation patterns have to be considered, in particular the observed increase in the amount of winter precipitation.     

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G _D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G _D(r,r′, N) = G ₀(r,r′, N) - G ₀(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Spherical harmonics and Cartesian tensor scalar product expansion in the Fokker-Planck equation

On the basis of the expansion of the distribution functionf(v, r,t) in a sum of spherical harmonics, which is equivalent to a Cartesian tensor scalar product expansion of the distribution function, i.e.,f(v, r, t)=f ₀(v,r,t)+v. f ₁(v,r,t)+vvf ₂(v,r,t)+vvvf ₃(v,r,t)+ wheref _k (k=2, 3) arek-th order irreducible tensors, the Rosenbluth potential functions and the Fokker-Planck collision term are expanded in a similar sum. Collisions termsJ _Fk (k=0, 1, 2) and the equations forf _k (k=0, 1, 2) for the case of the Coulomb interactions are also determined.Technická 2, Praha 6, Czechoslovakia.The autor wishes to express his thanks to Prof. J. Kracík, DrSc. for valuable advice and suggestion.     

Transport Equation Evaluation of Coupled Continuous Time Random Walks

The transport behavior of a migrating particle in a disordered medium is exhibited in the solution of a transport equation derived from a coupled continuous time random walk (CTRW). A core aspect of CTRW is the spectrum of transitions in displacement s and time t, ψ(s,t), that characterizes the disordered system, which determine the transport. In many applications the CTRW approach has successfully accounted for the anomalous or non-Fickian nature of the particle plume propagation based on a power-law dependence ψ(t) in a decoupled p(s)ψ(t) approximation to ψ(s,t). For example, this power-law dependence in t derives from the complex Darcy flow fields in geological formations. Recently, the fully coupled CTRW was analyzed using a particle tracking approach, demonstrating that the decoupled approximation is valid only for a compact distribution of s. In this paper we solve the nonlocal-in-time transport equation with a ψ(s,t) containing a power-law dependence in both s (a Lévy-like distribution) and t, which necessitates the strong s,t coupling. We show enhanced transport behavior (relative to the plume propagation behavior reported in the literature) that derives from the rare large displacements in s (limited by the transition t). The interplay between the two coupled power laws is clearly shown in the changes in the breakthrough curves in the arrival times, dispersion and dependence on the velocity (v=s/t) distribution. Similar enhancements are exhibited in the particle tracking results.     

From macroscopic to atomic motions in liquid metals

Summary In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andF _s(Q,t), as well as the longitudinal and transversal current correlation functionsJ ₁(Q,t) andJ _T(Q,t). The MD simulation ?calibrated? via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ ₁(Q,t) andJ _T(Q,t), the generalized viscosity functions ν₁(Q,t), ν₁(Q) and ν_s(Q). Information regarding bulk viscosity ν_B(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) ? for the cases studied. The spatial properties of the viscosity functions ν₁(r), ν_s(r) and ν_B(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties. The authors have agreed not to receive proofs for correction.     

Large-scale amplification of a magnetic field by turbulent helicity fluctuations

In this paper the procedure of large-scale averaging of the magnetic-field diffusion equation with the α-term curlα(r,t)B(r,t) is used to show that a nonuniform distribution of the turbulent helicity fluctuations (more precisely, the fluctuations of the coefficient α) with a zero average value gives rise to large-scale amplification of the initial magnetic field. A detailed study is carried out of the dependence of the resulting large-scale α effect on the characteristics of the correlator 〈〈α(r, t)α(r″,t″)〉〉 in a rotating medium with a nonuniform distribution of the angular velocity ω=ω(ρ,z) (ρ is the distance for the rotation axis z). The effect of helicity fluctuations and the diffusion coefficient on the turbulent diffusion process is also investigated. Zh. éksp. Teor. Fiz. 116, 85–104 (July 1999)     

Two-Particle Irreducible Effective Action in Gauge Theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) (G. Baym (1962). Physical Review 127, 1391; H. D. Dahmen and G. Jona Lasino (1962). Nuovo Cimento A 52, 807; C. de Dominicis and P. Martin (1964). Journal of Mathematical Physics 5, 14; J. Luttinger and J. Ward (1960). Physical Review 118, 1417; B. Vanderheyden and G. Baym (1998). Journal of Statistical Physics 98, 843; B. Vanderheyden and G. Baym (2000). In Progress in Nonequilibrium Green's Functions, World Scientific, Singapore). (or Cornwall–Jackiw–Tomboulis (CJT) (J. Cornwall, R. Jackiw, and E. Tomboulis (1974). Physical Review D 10, 2428; U. Kraemmer and A. Rebhan (2004). Reports on Progress in Physics 67, 351; R. Norton and J. Cornwall (1975). Annals of Physics 91, 106) effective action (EA) in a way appropiate to its application to nonequilibrium gauge theories. We hope this review article will stimulate new work into this field.     

The magnetic structure of neodymium crystal below the néel temperature

The phase transition in neodymium crystal from the paramagnetic to the magnetically ordered phase at the temperature T _N = 19.9 K is discussed in the terms of Landau's theory. It is shown that the calculated six-dimensional active representations at the point q = vb ₁, with—0.5 < v < 0.5, v ≠ 0, induce transitions to “single-q”, “double-q” and “triple-q” spin structures. A general formula for the spin vector S(r) for T < T _N is derived, from which a variety of spin structures can be obtained depending on the choice of the free parameters. The spin structure calculated by Bak and Lebech (1978) is obtained from that formula as a particular solution which is compatible with Landau's theory. An antiferromagnetic spin structure which represents a modification of that given by Bak and Lebech (1978) is calculated. The corresponding cross-section for neutron elastic magnetic scattering fulfils the experimental conditions listed by Lebech (1981). It is shown that the magnetic satellites of the type (h ± v, 0, 0) cannot appear for any type of structure following from our general formula for S(r). These satellites therefore can be connected only with representations at the point q = μ₁ b ₁ + μ₂ b ₂,—0.5 < μ₁, μ₂ < 0.5, μ₁, μ₂ ≠ 0, μ₁ ≠ μ₂.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.     

Coexistence and Joint Measurability in Quantum Mechanics

This talk is a survey of the question of joint measurability of coexistent observables and it is based on the monograph Operational Quantum Physics (Busch et al., Springer-Verlag, Berlin, 1997) and on the papers (Lahti et al., Journal of Mathematical Physics 39, 6364–6371, 1998; Lahti and Pulmannova, Reports on Mathematical Physics 39, 339–351, 1997; 47, 199–212, 2001).     

Interplay between elastic fields due to gravity and a partial dislocation for a hard-sphere crystal coherently grown under gravity: driving force for defect disappearance

We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in ?001? by Monte Carlo simulations [Mori et al., Molec. Phys. 105, 1377 (2007)]; it was an answer to a one-decade long standing question why the stacking disorder in colloidal crystals reduced under gravity [Zhu et al., Nature 387, 883 (1997)]. Here, we present an elastic energy calculation; in addition to the self-energy of the partial dislocation [Mori et al., Prog. Theor. Phys. Suppl. 178, 33 (2009)] we calculate the cross-coupling term between elastic field due to gravity and that due to a Shockley partial dislocation. The cross-term is an increasing function of the linear dimension R over which the elastic field expands, showing that a driving force arises for the partial dislocation moving toward the upper boundary of a grain.     

Molecular simulation of chemical reaction equilibria by Kinetic Monte Carlo

ABSTRACT

We describe a new algorithm for the molecular simulation of chemical reaction equilibria, which we call the Reactive Kinetic Monte Carlo (ReKMC) algorithm. It is based on the use of the equilibrium Kinetic Monte Carlo (eKMC) method (Ustinov et al., J. Colloid Interface Sci., 2012, 366, 216–223) to generate configurations in the underlying nonreacting system and to calculate the species chemical potentials at essentially zero marginal computational cost. We consider in detail the typical case of specified temperature, T and pressure, P, but extensions to other thermodynamic constraints are straightforward in principle. In the course of this work, we also demonstrate an alternative method for calculating simulation box volume changes in NPT ensemble simulations to achieve the specified P. We consider two sets of example reacting systems previously considered in the literature, and compare the ReKMC results and computational efficiencies with those of different implementations of the REMC algorithm (Turner et al., Molec. Simulation, 2008, 34, 119–146).     

Stable potentials I

We discuss a conjecture of Ruelle concerningstable potentials on a group. For the groupsZ ₂,Z ₃, ₄, andZ ₆ any stable potential can be written as the sum of a non-negative function and a function of non-negative type. This is not true for the groupsZ _k (k odd, 5). For the Euclidean groupR ^v the question is open.Supported by NSF GP 7946.