Using video microscopy, we investigated melting of a two-dimensional colloidal system, formed by glycerol droplets at the free surface of a nematic liquid crystalline layer. Analyzing different structure correlation functions, we conclude that melting occurs through an intermediate hexatic phase, as predicted by the KosterlitzThouless-Halperin-Nelson-Young(KTHNY) theory. However, the temperature range of the intermediate phase is rather narrow, 1 • C, and the characteristic critical power law decays of the correlation functions are not fully developed. We conclude that the melting of our 2D systems qualitatively occurs according to KTHNY, although quantitative details of the transition scenario may partly depend on the details of interparticle interaction.
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial nonhomogeneous distribution of particles, i.e. cluster formation. For these clusters are evaluated: their size, the number of particles in a cluster, and the temperature of phase transition to the cluster state. Three systems are under consideration: electrons on the liquid helium surface, particles interacting by the shielding Coulomb potential, which are found under the effect of an elastic field (e.g. nucleons in a nucleus), and gravitating masses with the Hubble expansion.
The stationary distribution function of Brownian particles in a nonequilibrium dusty plasma is calculated with regard to electron and ion absorption by grains. The distribution is shown to be considerably different from the distribution function of ordinary Brownian particles in thermal equilibrium. A criterion for the grain-structure formation in a nonequilibrium dusty plasma is derived.
We investigated the behaviour of colloidal particles suspended in nematic liquid crystals. These colloidal particles interact through elastic deformation of the nematic director field which can result in nontrivial collective behavior, leading to the formation of spatially modulated structures. In this paper, the formation of lattice structures is described both by computer simulations and by analytical theory. Effective interactions of the pairs of spherical macroparticles suspended in nematic liquid crystals have been suggested by many authors. Using these pairwise interactions, spatial structures are obtained by means of dynamic simulations. We have suggested a number of possible structures, which may be formed in multi-macroparticle systems. Regions of temperatures and concentrations are determined in which such a structure might appear.
The field theory approach to statistical description of the system of gravitational interacting particles is proposed in order to describe spatially inhomogeneous structures. A nonperturbutive calculation of the partition function is demonstrated for such a system. Spatially inhomogeneous system's state -cluster is considered. The spatial distribution function, cluster's size and the conditions of phase transition to the collapsed phase are determined exactly in this approach. : 23.23.+x, 56.65.Dy The statistical description of the of interacting particles has attracted a permanent attention. A few model systems of interacting particles are known, as far as the partition function can be exactly evaluated, at least, in the thermodynamic limit. The gravitation system does not have an exact solution so far. The problem of mean-field thermodynamics of self-gravitational system lies in the possible collapse in this system. An important point, which emerges from these studies and which is quite obvious is the non-extensiveness of the usual thermodynamic function in the thermodynamic limit, when the number of particle N → ∞. But the example of scaling consideration suggests an extensive homogeneous mean field in thermodynamic limit when the N → ∞ [1]. The formation of the spatial inhomogeneous distribution of the particle and field distribution which accompanies the gravitational interaction requires another approach which can describe the cluster formation which is related as collapsing states. In this paper the developed approach [3][4][5] suggests a statistical description of gravitational interacting particles of the system with regard to cluster formation. Systems with spatially inhomogeneous particle distributions are described in terms of various approaches. Within this approach, special methods [3][4][5] have been proposed concerning the selection of states with thermodynamically stable spatially inhomogeneous particle distributions. When describing a wide range of systems of interacting particles with regard to the type of statistics but neglecting the quantum correlations, so that the interaction is treated in the classical manner, we can write the Hamiltonian of the system as given by [2,3,10,12] Key words: gravitational interaction, cluster, spatially inhomogeneous distribution, collapse, soliton solution PACSwhere ε s is the additive part of the particle energy in the state s which is equal to the kinetic energy in most cases, W ss are attraction energies for the particles in the states s and s . The macroscopic states of the system are described by a set of occupation numbers n s . Index s labels an individual particle state; it can also correspond to a fixed site of the Ising lattice [10], whose explicit form is irrelevant in the continuum approximation. This expression for the Hamiltonian also holds for the model of substitution and interstitial solid solutions with two atom species present [2]. It is clear that to calculate the partition function is a rather involved problem even in the case of the...
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