Spatially modulated structures in nematic colloids: Statistical thermodynamics and kinetics

We examine the spatial distribution of rigid-sphere-like particles in a nematic host. Using a continuum model we analyse the conditions necessary for the appearance of a modulated lamellar structure. There is a long-range effective interaction between the particles, which can lead to the formation of superstructures. In general, this interaction includes several contributions: van der Waals-type direct interaction and indirect interaction via the director field distortions. The latter depends on the temperature of the sample, the coupling energy between a colloidal particle and a nematic host, and the particle concentration. This effective interaction controls the spatial structure and the kinetic properties of the system. We obtained the analytical expression for the temperature when the system loses the stability with respect to the modulated structure formation. Typical contours of the diffuse light scattering are presented.     

Statistical approach to partial equilibrium analysis

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.     

Coherent approach to analysis of modulated optical radiation

A method is proposed for determining the modulation parameters of optical radiation that does not require wide-band photodetectors for modulation at high and microwave frequencies. The method is based on measurement of the time coherence of optical radiation containing a modulation signal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 25–28, April, 1930.     

Spectral-morphological analysis of acoustical images of biological tissues and composite structures: I. Statistical approach

The problem of classifying images of different biological tissues and composite structures is solved using the spectral and morphological analysis based on the Bayesian method for statistical hypothesis verification. The basis functions are constructed from a learning set. The spectral approach and its particular realizations in the form of Bartlett’s and Pisarenko’s methods adapted to the problem are considered. An extension of the spectral approach to the more general spectral-morphological classification is proposed. The latter takes into account the spatial-spectrum features of the structure types to be classified, as well as their morphological features, which manifest themselves in a correlation between the expansion coefficients. The characteristic properties of the spectral and spectral-morphological approaches are discussed using numerical classification examples. The method is generalized to the classification of multiparameter images of structures, which may be represented, for example, by the distributions of the sound velocity, density, absorption, and values of the nonlinear parameter.     

Statistical approach to the analysis of cell desynchronization data

Experimental measurements on semi-synchronous tumor cell populations show that after a few cell cycles they desynchronize completely, and this desynchronization reflects the intercell variability of cell-cycle duration. It is important to identify the sources of randomness that desynchronize a population of cells living in a homogeneous environment: for example, being able to reduce randomness and induce synchronization would aid in targeting tumor cells with chemotherapy or radiotherapy. Here we describe a statistical approach to the analysis of the desynchronization measurements that is based on minimal modeling hypotheses, and can be derived from simple heuristics. We use the method to analyze existing desynchronization data and to draw conclusions on the randomness of cell growth and proliferation.     

Phase shift analysis of modulated photocurrent: A new approach to determining the energy scale

One of the major problems of the method of phase shift analysis of modulated photocurrent for studying the density of states in the energy gap of amorphous semiconductors has been the determination of the energy scale corresponding to this DOS profile. This study presents a new way of dealing with this problem. This new method is especially useful in the case where the DOS profile lacks a characteristic peak. A computer analysis is used to confirm the validity of this method and to demonstrate how it can be used.     

Diffraction from modulated structures III. Partially modulated structures and polydisperzity of zones

The present paper deals with the generalization of a model of modulated structures proposed in part II (Czech. J. Phys. B19 (1969), 1343) in that both the inner and the outer parts of the zones have variable number of atomic planes. The formula for the diffracted intensity from the assembly of such zones embedded in the matrix is also given.     

用动力学方法研究原子分子碰撞过程中的统计平均问题

动力学李代数方法在研究原子分子碰撞问题中是一种很重要的方法.在计算过程中我们用密度算子导出了物理量的统计平均值.同时我们用时间演化算子计算了振转能量的跃迁几率.作为例子我们用此方法计算了H2和He的碰撞问题.     

Phase amplitude decoupling in modulated structures

We examine under what conditions phase and amplitude modulations are decoupled in a modulated structure, within a Landau Ginzburg approach. For the general case of a pth order commensurability, the condition for phase amplitude decoupling depends on the leading anharmonic terms in the Landau Ginzburg free energy. For a 2Mth order leading anharmonic term, the case p = 2M is a border line case. For p > 2M, phase and amplitude are decoupled near the disordered-incommensurate transition temperature, while they are not for p < 2M. In the latter case decoupling occurs at lower temperatures. We discuss the case of deuterated thiourea, which exhibits a commensurate pinning for p = 9 at T = 191 K.     

On the theory of modulated structures

Summary The reasons of the modulated structure formation through the second-order phase transition are briefly reviewed. Particular attention is paid to the relatively new case of the modulated structure formation due to the high-order invariants, linear in the order parameter gradients. Conditions of instability of the uniform state are discussed. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Symmetry approach to the analysis of coherent structures in quantum optics: Foundations and examples

A general symmetry method for the discovery and analysis of hidden coherent structures in quantum models with an invariant Hamiltonian is proposed. The method is based on the mathematical concept of dual algebraic pairs, which unifies the actions of invariance groups and algebras of dynamic symmetry. Its efficiency is illustrated by the examples of biphotons and the invariant treatment of unpolarized light quasi-spin clusters, and “optical atoms” in nonlinear quantum-optical models.     

Statistical physics approach to graphical games: local and global interactions

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.     

A thermostatistical approach to protein structures

In this study, the relation between the additional heat capacities of proteins have been obtained. The expressions for the increments of enthalpy , entropy and Gibbs energy which are encountered in the dissolving of the proteins in water, have been calculated. Partition functions of proteins are related to the macrothermodynamical quantities with the help of free energies. In order to endeavour the structure of the proteins, the theoretical calculations of thermostatistical mechanics are fitted to the data of experimental results.     

Statistical mechanical approach to lossy data compression: Theory and practice

The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the perceptron-based code saturates the theoretically achievable limit in most cases although exactly performing the compression is computationally difficult. To resolve this difficulty, we provide a computationally tractable approximation algorithm using belief propagation (BP), which is a current standard algorithm of probabilistic inference. Introducing several approximations and heuristics, the BP-based algorithm exhibits performance that is close to the achievable limit in a practical time scale in optimal cases.     

Statistical approach to the measurement of velocity field

Present paper describes the principle and applications of a velocity measurement using statistical analysis of visualized flow images. The authors have developed a new algorithm for the measurement using the passing probability of a particle. It is known that this kind methods gives the total flow speed at each pixel unit. In this study, the method is extended by forming the governing equation using the Lagrange’s differentiation. The process is similar to the so-called spatio-temporal derivative method. The extension of the equation enables to measure the velocity components with the help of the statistical technique. The idea is based on the fact that the temporal derivative of luminance function is proportional to the vector product of the flow velocity and the gradient of luminance function in space which gives the velocity component normal to the edge of particle image. This is easy to apply on the three-dimensional flow field.