arXiv subjects

Gyula I. Toth

Publications and source records attributed to Gyula I. Toth.

7 recordsLinked to original sources

arXiv2022

Emergent pseudo time-irreversibility in the classical many-body system of pair interacting particles

In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in the closed classical many-body system of pair interacting particles. First, exact continuum equations are derived to the Hamiltonian dynamics without the utilisation of statistical mechanics. Next, it is shown that the momentum density field incorporates the thermal degrees of freedom in the considered scaling limit, and therefore initial condition indicated pseudo time-irreversible solutions may exist to the dynamical equations. Numerical evidence for pseudo-irreversible thermal equilibration, heat and momentum transport is provided. Finally, the possible reasons of the numerically obtained non-diffusional relaxation of macroscopic order is discussed.

cond-mat.stat-mech↗

arXiv2020

A measure theoretical approach to non-uniform phases of matter with no long-range spatial order

In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the concentration of measure phenomenon to re-formulate partial differential equations for probability measures, which extends the concept of analytical solutions to random fields. A stochastic solution of an equation is such a non-singular probability measure, according to which the random variable is almost surely a solution to the equation. The general concept is applied for continuum theories, where the concept of symmetry breaking is extended to probability measures. The concept is practicable and predictive for non-local continuum mean-field theories of first order phase transitions. The results suggest that symmetry breaking must be present in stochastic stationary points of the energy on the level of the probability measure. This is in agreement with the observation that amorphous solid structures preserve local ordering.

cond-mat.stat-mech↗

arXiv2019

Phase-field modelling of the effect of density change on solidification revisited: Model development and analytical solutions for single component materials

In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of statistical physics, while the constitutive relations are developed in the framework of the standard Phase-field Theory, by following the variational formalism and the principles of non-equilibrium thermodynamics. To enhance the numerical practicality of the model, quasi-incompressible hydrodynamic equations are derived, where sound waves are absent (but density change is still possible), and therefore the time scale of solidification is accessible in numerical simulations. The model development is followed by a comprehensive mathematical analysis of the equilibrium and propagating 1-dimensional solid-liquid interfaces for different density-phase couplings. It is shown, that the fluid flow decelerates/accelerates the solidification front in case of shrinkage/expansion of the solid compared to the case when no density contrast is present between the phases. Furthermore, such a free energy construction is proposed, in which the equilibrium planar phase-field interface is independent from the density-phase coupling, and the equilibrium interface represents an exact propagating planar interface solution of the quasi-incompressible hydrodynamic equations. Our results are in excellent agreement with previous theoretical predictions.

cond-mat.mtrl-sci↗

arXiv2017

Hydrodynamic theory of freezing: Nucleation and polycrystalline growth

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Toth et al., J. Phys.: Condens. Matter 26, 055001 (2014)], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.

cond-mat.mtrl-sci↗

arXiv2016

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental {equations of continuum mechanics}, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. {Next the general definition of incompressibility is given}, which is taken into account {in the derivation} by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional), {and (ii) can} influence non-equilibrium pattern formation significantly.

cond-mat.soft↗

arXiv2015

Phase-feld theory of multi-component incompressible Cahn-Hilliard liquids

In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free energy functional is presented for arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and demonstrate, that the energy penalization for multi-component states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (4-component) systems. Simulations addressing liquid flow assisted spinodal decomposition in these systems are also presented.

cond-mat.mtrl-sci↗

arXiv2015

Consistent multiphase-field theory for interface driven multidomain dynamics

We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories, and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a new way of constructing the free energy surface, and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism; reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations; enables the use of arbitrary pairwise equilibrium interfacial properties; penalizes multiple junctions increasingly with the number of phases; ensures non-negative entropy production, and the convergence of the dynamic solutions to the equilibrium solutions; and avoids the appearance of spurious phases on binary interfaces. The new approach is tested for multi-component phase separation and grain coarsening.

cond-mat.mtrl-sci↗