arXiv subjects

Victor M. Pergamenshchik

Publications and source records attributed to Victor M. Pergamenshchik.

4 recordsLinked to original sources

arXiv2026

Taming of free volume in statistical mechanics of the hard disks model

We turn the long time puzzle of the free volume, known for its highly irregular form, into exact analytical formulae and develop statistical mechanics of the hard disk model. The free volume is exactly expressed in terms of the intersection areas of up to five exclusion circles, which can be computed analytically as functions of disk coordinates. In turn, the free volume determines the partition function and entropy. The partition function is shown to factorize into a product of free volumes and admits two exact limiting forms corresponding to gaslike and liquidlike regimes. From this construction, using Monte Carlo-generated disk coordinates, the entropy and pressure are obtained analytically and recover the known equation of state of hard disks in almost entire density range up to the close packing. At intermediate densities, the theory reveals a mixed liquid regime associated with defect formation preceding the hexagonal ordering. The intersection area of five disks emerges as a scalar measure of the local hexagonal order. The theory can be directly adopted for the hard sphere model.

cond-mat.stat-mech↗

arXiv2023

Colloidal Directional Structures at a Nematic Liquid Crystal-Air Interface

We present a variety of structures formed by colloidal droplets at a nematic liquid crystal-air interface, where the elastic dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions are all essentially involved. The colloidal structures observed not only include chains with kinks or clusters, but also comprise directional structures, such as directional chains and branches, whose direction is associated with the tilting director in the liquid crystal layer. The dipole-quadrupole interaction, originating from the polydispersity of the droplets, plays a central role for the formation of these directional structures. Clusters consisting of directional branches and chains are also observed and found to be fractal statistically.

cond-mat.soft↗

arXiv2016

Active shape-morphing elastomeric colloids in short-pitch cholesteric liquid crystals

Active elastomeric liquid crystal particles with initial cylindrical shapes are obtained by means of soft lithography and polymerization in a strong magnetic field. Gold nanocrystals infiltrated into these particles mediate energy transfer from laser light to heat, so that the inherent coupling between the temperature-dependent order and shape allows for dynamic morphing of these particles and well-controlled stable shapes. Continuous changes of particle shapes are followed by their spontaneous realignment and transformations of director structures in the surrounding cholesteric host, as well as locomotion in the case of a nonreciprocal shape morphing. These findings bridge the fields of liquid crystal solids and active colloids, may enable shape-controlled self-assembly of adaptive composites and light-driven micromachines, and can be understood by employing simple symmetry considerations along with electrostatic analogies.

cond-mat.soft↗

arXiv2016

Maximum entropy states of collisionless systems with long-range interaction and different degrees of mixing

Dynamics of many-particle systems with long-range interaction is collisionless and governed by the Vlasov equation. This dynamics is a flow of a six-dimensional incompressible liquid with uncountable integrals of motion. If the flow possesses the statistical property of mixing, each liquid element spreads over the entire accessible space. I derive the equilibrium microcanonical maximum entropy states of this liquid for different degrees of mixing $M$. This $M$ is the number of liquid elements which are statistically independent. To count microstates of a liquid, I develop analog of the discrete combinatorics for continuous systems by introducing the ensemble of phase subspaces and making contact with the Shannon-McMillan-Breiman theorem from the ergodic theory. If $M$ is much larger than the total number of particles $N$, then the equilibrium distribution function (DF) is found to be exactly of the Fermi-Dirac form. If the system is ergodic but without mixing, $M=0$, the DF is a formal expression which coincides with the famous DF obtained by Lynden-Bell. If the mixing is incomplete and $M\sim N$, the exponentials, which are present in Lynden-Bell's DF, appear with certain weight given by the entropy of mixing. For certainty, the \ long-range interaction is taken in the form of the Newton and Coulomb potential in three dimensional space, but the applicability of the method developed in the paper is not restricted to this case. The analogy of the obtained statistics to the Fermi-Dirac statistics allows for expressing the entropy of the system via its total energy and chemical potentials of liquid's elements. The effect of the long-range interaction to the basic thermodynamic relations is demonstrated.

cond-mat.stat-mech↗