A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

Studies of porosity and diffusion coefficient in porous matrices by computer simulations

We present a series of molecular dynamics simulations to study the porosity on different matrix configurations. The matrices were prepared using two different processes. In the fist method we used direct simulations of a fluid at a fixed density and the matrix was taken from the last configuration of its particles. In the second method we simulated a binary mixture where one of the components served as a template material and the final porous matrix configuration was obtained by removing template particles from the mixture. Matrices were prepared at different densities and at different matrix particle interactions. The results showed that the matrix structure and the matrix porosity were affected by the way the porous matrices were prepared. Finally, we also investigated the diffusion of a fluid inside the matrices. The diffusion coefficient was measured by mean square displacements of the particles in the fluid. It was observed that this quantity was also affected by the kind of porous matrix employed. The calculations were performed for several fluids at different densities in the different porous matrices. From these studies we observed that the highest porosity and diffusion coefficient were found in matrices prepared with attractive particle interactions and without any template.     

Blue phase liquid crystal phase transition for cyano compound chiral nematic liquid crystal mixtures with three two-ring core structures and chiral dopant concentrations

Blue phase (BP) temperature range of a chiral nematic liquid crystal (LC) mixture is dependent upon the host nematic LC chemical structure and chiral dopant concentration. In this study, we investigated BP phase transition behaviour and helical twisting power (HTP) using three chiral dopant concentrations of cyano compound chiral nematic LC mixtures incorporating three two-ring core structures in the host nematic LCs. The effect of the host nematic LC core structure, HTP and chiral dopant concentrations were considered on BP temperature ranges, for two types of complete BPI and BPII without isotropic phase (Iso) and two types of coexistence state of BPI+Iso and BPII+Iso.     

CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART II: ELEMENTARY STRUCTURE-PRESERVING TRANSFORMATIONS

It has been shown in a previous paper that there is a real-valued transformation from the generalN -degree-of-freedom second order system to a second order system characterized by diagonal matrices. An immediate extension of this fact is that for any second order system, there is a set of real-valued transformations (thestructure-preserving transformations) which transform this system to a different second order system having identical characteristic behaviour. There are several possible reasons why it may be very useful to achieve a particular structure in the transformed system. It is obvious that a diagonal structure is extremely useful and a method has been devised for determining the diagonalizing transformation from the solution of the usual (complex) eigenvalue-eigenvector problem.This paper begins by outlining the usefulness of some other structures. Then it defines a class of elementary structure-preserving co-ordinate transformations that transform from one N -degree-of-freedom second order system to another. The termelementary is applied because any one of these transformations is the minimum-rank modification of the identity transformation. The changes occurring in the system matrices as a result of the application of one such elementary transformation transpire to be very simple in form, they are low rank, and they can be computed very efficiently.This paper provides the fundamental tools to enable the design of structure-preserving co-ordinate transformations which transform a second order system originally characterized by three general matrices in stages into a mathematically similar second order system characterized by three diagonal matrices. The procedure by which the individual elementary transformations are obtained is still under development and it is not discussed in this paper. However, an illustration is given of a five-degree-of-freedom self-adjoint system being transformed into tridiagonal form.     

Loop-Erased Walks and Random Matrices

Journal of Statistical Physics - It is well known that there are close connections between non-intersecting processes in one dimension and random matrices, based on the reflection principle. There...     

Optical Mueller matrices in terms of geometric algebra

Connection between optical Mueller matrices and geometrical (Clifford) algebra multivectors is established. It is shown that starting from 3-dimensional (3D) Cl_3,0 algebra and using isomorphism between Cl_3,0 and even Cl_3,1⁺ subalgebra one can generate canonical Mueller matrices and their combinations that describe an optical system. It appears that representation of polarization devices in terms of geometric algebra is very compact and, in contrast to Mueller matrix approach, there is no need for speculative physical restrictions. If needed, properties of media can be logically introduced into Maxwell equation in a form of Clifford algebra via constitutive relations. Since representation of polarization by Cl_3,1 algebra is Lorentz invariant it allows to include relativistic effects of moving bodies on light polarization as well. In this paper only simple examples of connection between Mueller matrices and geometric algebra multivectors is presented.     

Internal space-time symmetries of particles derivable from periodic systems in optics

While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into three conjugate classes depending on their traces, optical systems force us to establish continuity from one class to another. It is noted that those three classes are equivalent to three different branches of Wigner’s little groups dictating the internal space-time symmetries massive, massless, and imaginary-mass particles. It is shown that the periodic systems in optics can also be described by the same class-based matrix algebra. The optical system allow us to make continuous, but not analytic, transitions from massiv to massless, and massless to imaginary-mass cases.     

Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

We consider holomorphic deformations of Fuchsian systems parameterized by the pole loci. It is well known that, in the case when the residue matrices are non-resonant, such a deformation is isomonodromic if and only if the residue matrices satisfy the Schlesinger system with respect to the parameter. Without the non-resonance condition this result fails: there exist non-Schlesinger isomonodromic deformations. In the present article we introduce the class of the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal deformation is also an isomonodromic one. In general, the class of the isomonodromic deformations is much richer than the class of the isoprincipal deformations, but in the non-resonant case these classes coincide. We prove that a deformation is isoprincipal if and only if the residue matrices satisfy the Schlesinger system. This theorem holds in the general case, without any assumptions on the spectra of the residue matrices of the deformation. An explicit example illustrating isomonodromic deformations, which are neither isoprincipal nor meromorphic with respect to the parameter, is also given.The research of Victor Katsnelson was supported by the Minerva Foundation.     

Impedance theory of sound scattering: General relations

The problem of sound scattering by an elastic body of arbitrary geometry in an acoustic medium is solved by the impedance method. It is shown that, for a complete solution, three impedance matrices are necessary: one of them characterizes the scatterer and the other two, the medium. The scattering matrices and other characteristics of the solution are expressed through the incident field and these three impedance matrices. The necessary general relations are presented, and the most important particular cases are considered. Three new representations of the diffraction field are proposed in the form of a sum of two components obtained as solutions to two simpler boundary-value problems. Original Russian Text ￠ Yu.I. Bobrovnitskiĭ, 2006, published in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 5, pp. 601–606.     

Twisted h-spacetimes and invariant equations

We analyze the h-deformations of the Lorentz group and their associated spacetimes. We prove that they have a twisted character and give explicitly the twisting matrices. After studying the representations of one of the deformed spacetime algebras, we discuss the Klein-Gordon operator. It is found that the h-deformed d’Alembertian has plane wave solutions of the same form as the standard ones. We also give explicit expressions for the h-gamma matrices defining the associated Dirac equations.     

Investigation of thermoluminescence of natural zircon relevant to dating application

The thermoluminescence (TL) characteristics of natural zircons from Vietnam were studied for potential application to TL dating. All the glow curves of samples irradiated by gamma radiation or UV light showed a complex structure that consisted of a low temperature part (LTP) and a high temperature part (HTP). The TL emission spectra and monochromatic glow curves indicate that the two main impurities governing the TL emission are Dy³⁺ (LTP) and Tb³⁺ (HTP). The anomalous fading of the TL signal was assigned to the emission associated with Dy³⁺ whereas the 545 nm emission associated with Tb3⁺, exhibits significantly lower fading and consequently more suitable for TL dating.     

Entanglement correlation in mixed states for anharmonic vibrations in ozone

Entanglement dynamics of anharmonic vibrations in molecule O₃ is studied in terms of the linear entropy and negativity with various initial states that are, respectively, taken to be the mixed density matrices of coherent states on each normal mode. It is shown that with a suitable parameter in initial states, the entropy in one mode can be positively correlated or anti-correlated with negativity. The behavior of correlation between two entropies for two modes, negativity, and mutual entropy is discussed as well.     

Spectroscopic and laser properties of photoexcited organic fluorescers embedded in composite gel systems

The spectral luminescence and lasing characteristics of rhodamine 101T and phenalemine 512 embedded in simple and composite gel matrices of different compositions based on tetraethoxysilane were excited by XeCl laser radiation and the second harmonic of a Nd:YAG laser. It is established that a dye interacts with a solid matrix through formation of donor-acceptor and hydrogen-bonded solvates. The dependence of the lasing efficiency on the excitation intensity was determined, as well as the laser photostability of gel systems with dyes. It is shown that the pump conversion efficiency and the laser photostability of dyes in composite gel systems are higher than in simple gel matrices.     

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto(GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective,reliable and does not require any restrictive assumptions for nonlinear terms.     

Quantum Integrability in Systems with Finite Number of Levels

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We argue that if the matrices depend on a (real) parameter, one can define quantum integrability from this feature alone, leading to specific results such as exact solvability, Poissonian energy level statistics and to level crossings.     

热压处理对Nd0.7Sr0.3MnO3陶瓷磁电输运影响

在温度1273 K、压强9 GPa条件下对固相烧结Nd_0.7Sr_0.3MnO₃陶瓷样品进行热压处理. 结果发现, 处理后样品的晶体结构和空间群没有改变, 但晶胞参数和结构参数, 特别是样品的显微结构发生了很大变化. 这些变化对样品的磁电输运产生显著影响: 在磁性上, 热压样品的低温饱和磁矩减小并出现磁矩排列弥散特点; 在电输运方面, 当负载电流小于1.5 mA时, 与烧结样品一样, 热压样品不产生电致电阻 (ER) 效应, 并在金属-绝缘体转变点出现最大磁电阻 (MR). 但在低温下, 热压样品仍有较大MR值. 当负载电流超过1.5 mA时, 热压样品原R-T曲线中的电阻峰替变为一电阻平台, 且随负载电流增大, 平台逐渐宽化, 阻值减小, 出现ER行为. 有趣的是, 在外磁场作用下, 电阻平台随外场增大逐渐变窄、消失并又演变为一电阻峰. 这些奇特的输运行为除与热压处理导致样品晶粒绝缘化有关外, 可能还与热压导致粒间相的形成有关.     

Measuring distances between complex networks

A previously introduced concept of higher order neighborhoods in complex networks, [R.F.S. Andrade, J.G.V. Miranda, T.P. Lobão, Phys. Rev. E 73 (2006) 046101] is used to define a distance between networks with the same number of nodes. With such measure, expressed in terms of the matrix elements of the neighborhood matrices of each network, it is possible to compare, in a quantitative way, how far apart in the space of neighborhood matrices two networks are. The distance between these matrices depends on both the network topologies and the adopted node numberings. While the numbering of one network is fixed, a Monte Carlo algorithm is used to find the best numbering of the other network, in the sense that it minimizes the distance between the matrices. The minimal value found for the distance reflects differences in the neighborhood structures of the two networks that arise only from distinct topologies. This procedure ends up by providing a projection of the first network on the pattern of the second one. Examples are worked out allowing for a quantitative comparison for distances among distinct networks, as well as among distinct realizations of random networks.     

Correlations for the circular Dyson brownian motion model with Poisson initial conditions

The circular Dyson brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the initial condition that the particles are non-interacting (Poisson statistics). Jack polynomial theory is used to derive a simple exact expression for the density-density correlation with the position of one particle specified in the initial state, and the position of one particle specified at time τ, valid for all β > 0. The same correlation with two particles specified in the initial state is also derived exactly, and some special cases of the theoretical correlations are illustrated by comparison with the empirical correlations calculated from the eigenvalues of certain parameter-dependent Gaussian random matrices. Application to fluctuation formulas for time-displaced linear statistics in made.     

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.