arXiv subjects

V. L. Kulinskii

Publications and source records attributed to V. L. Kulinskii.

At least 19 recordsLinked to original sources

arXiv2025

Liquid-gas state regularities as a manifestation of global isomorphism with the Ising model

Liquid-gas equilibrium is considered using the global isomorphism with the Ising-like (lattice gas) model. Such an approach assumes the existence of the order parameter in terms of which the symmetry of binodal is restored not only in the vicinity of the critical point (critical isomorphism) but also globally in the whole coexistence region. We show how the empirical law of the rectilinear density diameter of the liquid-gas binodal allows us to derive a rather simple form of the isomorphism transformation between the fluid and lattice gas model of Ising-type. The relations for critical parameters which follow from such isomorphism are tested on a variety of fluid systems, both real and model ones. Moreover, we consider the phase equilibrium in polymer solutions and the Flory $θ$-point as the extreme state of such equilibrium within our approach. The most crucial testing in 2D case is using the Onsager exact solution of the Ising model, and we represent the results of our approach to the calculation of critical point parameters of monolayers for noble gases and the surface tension.

cond-mat.soft↗

arXiv2019

Thermalization of non-stochastic Hamiltonian systems

Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics. The key link in this connection is stochasticity, which translates the deterministic evolution of a dynamical system to its probabilistic exploration of the state space. To-date research focuses on determining the conditions of stochasticity for particular systems. Here we propose an alternative agenda and prove thermalization for non-stochastic Hamiltonian systems. This shows that thermalization happens in both stochastic and non-stochastic systems, reducing the need to rely on stochasticity in a "coarse-grained" analysis. The result is valid for an arbitrary classical Hamiltonian system and does not rely on the thermodynamic limit or the particular form of the interaction potential. It utilizes the property of adiabatic invariance, and reveals a deep relation between the structure of the microscopic Hamiltonian and macroscopic thermodynamics.

cond-mat.stat-mech↗

arXiv2018

Thermodynamics without ergodicity

We show that fundamental thermodynamic relations can be derived from deterministic mechanics for a non-ergodic system. This extend a similar derivation for ergodic systems and suggests that ergodicity should not be considered as a requirement for a system to exhibit a thermodynamic behavior. Our analysis emphasizes the role of adiabatic invariants in deterministic description and strengthens the link between mechanics and thermodynamics. In particular, we argue that macroscopic thermodynamic behavior of a system is caused by the existence of different time scales in its deterministic microscopic evolution.

cond-mat.stat-mech↗

arXiv2015

Physical interpretation of point-like interactions of one-dimensional Schrödinger operator

We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schrödinger operator of free spinless particle. Despite its model and rather abstract character this question is worth of investigation due to application for one-dimensional nanostructures. The main result is the physical interpretation of peculiar self-adjoint extension with discontinuity of both the probability density and the derivative of the wave function. We show that this case differs very much from other three which were considered before and corresponds to the presence of mass-jump in a sense of works of Ganella et. al., (Journal of Physics A: Mathematical and Theoretical 42, 465207 (2009)) along with the quantized magnetic flux. Real physical system which can be modeled by such boundary conditions is the localized quantazied flux in the Josephson junction of two superconductors with different effective masses of the elementary excitations.

math-ph↗

arXiv2013

Zero-range potential model for the study of the ground states near the vortex core in the quantum limit

We propose the treatment of the lowest bound states near the vortex core on the basis of the self-adjoint extension of the Hamiltonian with the localized magnetic flux of Aaronov-Bohm type. It is shown that in the limit {\varkappa} >> 1 the potential for the vortex core excitations can be treated in terms of the generalized zero-range potential method. The spectrum of the Caroli-de Gennes-Matricon states is obtained and the comparison with the numerical calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)] is performed. The analytical expression for the ground state energy depending on the boundary condition parameter b was obtained by us.

cond-mat.supr-con↗

arXiv2011

Peculiarities in the behavior of the entropy diameter for molecular liquids as the reflection of molecular rotations and the excluded volume effects

The behavior of the diameter of the coexistence curve in terms of the entropy and the corresponding diameter are investigated. It is shown that the diameter of the coexistence curve in term of the entropy is sensitive to the change in the character of the rotational motion of the molecule in liquid phase which is governed by the short range correlations. The model of the compressible effective volume is proposed to describe the phase coexistence both in terms of the density and the entropy.

cond-mat.stat-mech↗

arXiv2010

On the relation between Vicsek and Kuramoto models of spontaneous synchronization

The Vicsek model for the self-propelled particles is investigated with the respect to the introduction of the stochastic perturbation of the dynamics. It is shown that such a dependence can be thought in terms of the isomorphism of the Vicsek model with the Kuramoto model of spontaneous synchronization. They are isomorphic at least within the mean-field approach. The isomorphism between two models allows to state the dependence of the type of the transition in Vicsek model on the noise perturbation. Two types of noise the scalar and the vector ones lead to qualitatively different behavior with continuous and the discontinuous transition to ordered state correspondingly. New type of the stochastic perturbation - ``mixed`` noise is proposed. It is the weighted superposition of the scalar and vector noises. The corresponding phase diagram ``noise amplitude vs. interaction strength`` is obtained and the tricritical behavior for Vicsek model is demonstrated.

cond-mat.stat-mech↗

arXiv2010

The kinetic regime of the Vicsek model

We consider the dynamics of the system of self propelling particles modeled via the Vicsek algorithm in continuum time limit. It is shown that the alignment process for the velocities can be subdivided into two regimes: "fast" kinetic and "slow" hydrodynamic ones. In fast kinetic regime the alignment of the particle velocity to the local neighborhood takes place with characteristic relaxation time. So that the bigger regions arise with the velocity alignment. These regions align their velocities thus giving rise to hydrodynamic regime of the dynamics. We propose the mean-field like approach in which we take into account the correlations between density and velocity. The comparison of the theoretical predictions with the numerical simulations is given. The relation between Vicsek model in the zero velocity limit and the Kuramoto model is stated. The mean-field approach accounting for the dynamic change of the neighborhood is proposed. The nature of the discontinuity of the dependence of the order parameter in case of vectorial noise revealed in Gregorie and Chaite, Phys. Rev. Lett., {\bf 92}, 025702 (2004) is discussed and the explanation of it is proposed.

cond-mat.stat-mech↗

arXiv2010

The vortex pinning on the cylindrical defects and the electronic structure of the vortex core

The model of the Abrikosov vortex pinning on a cylindrical defect is proposed. It is shown that in the limit $\varkappa \gg 1$ the potential for the vortex core excitations can be treated in terms of the zero-range potentials method. Using the variational method the estimates for the energy of pinning, the pinning force and the density of critical current defect are obtained.

cond-mat.supr-con↗

arXiv2010

Global isomorphism between the Lenard-Jones fluids and the Ising model

The interpretation of the linear character of the observable classic rectilinear diameter law and the linear character of the Zeno-line (unit compressibility line Z=1) on the basis of global isomorphism between Ising model (Lattice Gas) and simple fluid is proposed. The correct definition of the limiting nontrivial Zeno state is given and its relation with the locus of the critical point is derived within this approach. We show that the liquid-vapor part of the phase diagram of the molecular fluids can be described as the isomorphic image of the phase diagram of the Lattice Gas. It is shown how the the position of the critical points of the fluids of the Lenard-Jones type can be determined basing on the scaling symmetry. As a sequence the explanation of the well known fact about "global" cubic character of the coexistence curve of the molecular fluids is proposed.

cond-mat.stat-mech↗

arXiv2010

Simple geometrical interpretation of the linear character for the Zeno-line and the rectilinear diameter

The unified geometrical interpretation of the linear character of the Zeno-line (unit compressibility line Z=1) and the rectilinear diameter is proposed. We show that recent findings about the properties of the Zeno-line and striking correlation with the rectilinear diameter line as well as other empirical relations can be naturally considered as the consequences of the projective isomorphism between the real molecular fluids and the lattice gas (Ising) model.

cond-mat.stat-mech↗

arXiv2009

Surprising properties of water on its binodal as the reflection of the specificity of intermolecular interactions

In the paper the behavior of density (or specific volume), the heat of evaporation and entropy per molecule for normal and heavy water on their coexistence curves is discussed. The special attention is paid on the physical nature of the similarity in the behavior of density and the heat of evaporation for water and argon as well as the nearest water homolog $H_{2} S$. It is shown that the appearance of this similarity is a consequence of the rotational motion of water molecules, which averages the inter-particle potential in water and leads it to the argon-like form. To describe the fine distinctions in the behavior of the binodals for water and argon the dependence of the proper molecular volume on pressure is taken into account. In accordance with this often used the van der Waals and Carnahan-Starling equations of states are modified. The very surprising behavior of the entropy diameter for water is analyzed. It is shown that the nontrivial details of the temperature dependence for the entropy diameter is directly connected with the peculiarities of the rotational motion of molecules in water. The effect of strong dimerization of water molecules in the fluctuation region near the critical point is studied in details. The inner rotation of monomers forming the dimer $(D_{2} O)_{2} $ near the critical point is discovered.

cond-mat.stat-mech↗

arXiv2009

Is the thermodynamic behavior of the noble fluids consistent with the Principle of Corresponding States?

The applicability of the Principle of Corresponding States (PCS) for the noble fluids is discussed. We give the thermodynamic evidences for the dimerization of the liquid phase in heavy noble gases like argon, krypton etc. which manifest itself in deviation from the PCS. The behavior of the rectilinear diameter of the entropy and the density is analyzed. It is shown that these characteristics are very sensitive to the dimerization process which takes place in the liquid phase of heavy noble gases.

cond-mat.stat-mech↗

arXiv2008

The nature of the rectilinear diameter singularity

The rigorous explanation for the term $| t |^{2β}$ in the rectilinear diameter equation is given ($t = (T_c-T)/T_c$, $β$ is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric is constructed within the canonical formalism. It is shown that the ratio of the amplitudes $\f{D_{2β}}{D_{1-α}}$ before $|t|^{2β}$ and $|t|^{1-α}$ where $α$ determines the behavior of the heat capacity, takes the universal character. The analysis of entropy for argon and water leads to $β= 0.33$ and $\f{D_{2-β}}{D_{1-α}}\approx - 3.5$.

cond-mat.stat-mech↗

arXiv2007

Asymmetry of the Hamiltonian and the Tolman's length

Using the canonical transformation of the order parameter which restores the Ising symmetry of the Hamiltonian we derive the expression for the Tolman length as a sum of two terms. One of them is the term generated by the fluctuations of the order parameter the other one is due to the entropy. The leading singular behavior of the Tolman length near the critical point is analyzed. The obtained results are in correspondence with that of M.A. Anisimov, Phys. Rev. Lett., \textbf{98} 035702 (2007).

cond-mat.stat-mech↗

arXiv2006

Collective Behavior of Self Propelling Particles with Kinematic Constraints; The relation between the discrete and the continuous description

In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we derive the continuous hydrodynamic model from the discrete description. The similarities and differences between the resulting model and the hydrodynamic model postulated in our previous papers are discussed. The results clarify the assumptions used to obtain a continuous description.

physics.flu-dyn↗

arXiv2006

Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow, linear and radially symmetric (vortical) flow, are possible. In this paper we consider the stability properties of these stationary flows. We show, using a linear stability analysis, that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations. A similar analysis of the stability of the vortical solution is found to be not conclusive.

physics.flu-dyn↗

arXiv2006

$μ$-model for the statics of dry granular medium

We propose the description of the granular matter which is based on distribution of dry friction coefficients. Using such a concept and a simple one-dimensional packing of grains we solve the silo problem. The friction coefficients at contacts are determined both by geometry of packing configuration and the stress distribution in a medium. Within such an approach the Janssen coefficient is determined and its dependence on the particle-particle and boundary-particle friction coefficients is obtained. Also we investigate the conditions for the appearance of the maximum in the pressure distribution with the depth with overweight on top. As an outcome of our work we propose the general framework to the description of the granular matter as a continual medium which is characterized by the field of the dry friction tensor.

cond-mat.soft↗