arXiv subjects

Gyula I. Tóth

Publications and source records attributed to Gyula I. Tóth.

At least 19 recordsLinked to original sources

arXiv2026

Liquid bridges between horizontal cylinders: effects of gravity and electric fields

Liquid bridges suspended between two parallel horizontal cylinders are studied using experiments, reduced-order mathematical modelling and numerical simulations. Both non-electrified and electrified configurations are considered, with the cylinders acting as electrodes between which a potential difference can be applied. The initial focus is on equilibrium bridge shapes, while the dynamics is examined only in the non-electrified case. In the experiments, transformer-oil bridges are investigated and modelled as perfect dielectrics. The electric field counteracts the gravitational effects and causes the bridges to rise and become flatter, with shapes that are well described by Young--Laplace-type equations containing non-local electric-field contributions evaluated using a boundary-element method. Bifurcation diagrams of these solutions are constructed by pseudo-arclength continuation to characterise the dependence of bridge shapes on liquid volume and electric-field strength. In the absence of an electric field, the transient relaxation to equilibrium is analysed using a reduced-order model developed using Onsager's variational principle, with comparison to direct numerical simulations. The steady states predicted by the reduced-order model agree closely with those of the full formulation over a wide parameter range, and the dynamics is well captured in the overdamped regime.

physics.flu-dyn↗

arXiv2026

Isotropic random walks and Brownian diffusion on complex projective space

We show that isotropic random walks on the complex projective space provide a canonical and analytically tractable stochastic-geometric framework for the exploration of quantum-state space. The approach combines harmonic analysis on compact rank-one symmetric spaces with stochastic pure-state evolution and yields explicit analytical expressions for transition kernels, fidelity statistics, and geometric observables associated with the Fubini--Study metric. In particular, the framework provides a solvable reference model for isotropic depolarization and Haar equilibration, reproducing Haar-random fidelity statistics and the invariant measure on projective Hilbert space without specifying a microscopic Lindblad generator. In the short-time regime, the stochastic evolution converges to Brownian diffusion generated by the Fubini--Study Laplace--Beltrami operator, while the long-time limit exhibits concentration-of-measure behaviour characteristic of high-dimensional random quantum states. We further derive analytical and asymptotic results for the first-passage-time problem, including closed-form expressions in the Brownian limit for the mean first passage time and the long-time tail of the first-passage-time distribution. For high-fidelity target states, the mean first passage time exhibits a strong dimension-dependent divergence originating from the concentration properties of the Fubini--Study geometry.

quant-ph↗

arXiv2024

Hydrodynamic Density Functional Theory of simple dissipative fluids

In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the one-particle probability density function around Local Thermodynamic Equilibrium, (ii) the assumption of decoupled particle positions and momenta, and (iii) the variational principle. It is shown that there exists a class of free energy functionals for which the conventional thermodynamic formalism can be naturally adopted for non-equilibrium scenarios, and describes entropy monotonic fluid flow in isolated systems. Furthermore, the analysis of the general continuum equations revealed the possibility of a non-local transport mode of energy in highly compressible dense fluids.

cond-mat.stat-mech↗

arXiv2022

Thermodynamics, formation dynamics and structural correlations in the bulk amorphous phase of the phase-field crystal model

We investigate bulk thermodynamic and microscopic structural properties of amorphous solids in the framework of the phase-field crystal (PFC) model. These are metastable states with a non-uniform density distribution having no long-range order. From extensive numerical simulations we determine the distribution of free energy density values in varying size amorphous systems and also the point-to-set correlation length, which is the radius of the largest volume of amorphous one can take while still having the particle arrangements within the volume determined by the particle ordering at the surface of the chosen volume. We find that in the thermodynamic limit, the free energy density of the amorphous tends to a value that has a slight dependence on the initial state from which it was formed -- i.e.\ it has a formation history dependence. The amorphous phase is observed to form on both sides of the liquid linear-stability limit, showing that the liquid to amorphous transition is first order, with an associated finite free energy barrier when the liquid is metastable. In our simulations this is demonstrated when noise in the initial density distribution is used to induce nucleation events from the metastable liquid. Depending on the strength of the initial noise, we observe a variety of nucleation pathways, in agreement with previous results for the PFC model, and which show that amorphous precursor mediated multi-step crystal nucleation can occur in colloidal systems.

cond-mat.soft↗

arXiv2021

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rimini-Weber (GRW) theory, continuous spontaneous localization (CSL) model, Diósi-Penrose model, and dissipative GRW model - in the Wigner framework. The resulting master equations are approximated by Fokker-Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert's suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.

quant-ph↗

arXiv2021

Dynamical density functional theory for the drying and stratification of binary colloidal dispersions

We develop a dynamical density functional theory based model for the drying of colloidal films on planar surfaces. We consider mixtures of two different sizes of hard-sphere colloids. Depending on the solvent evaporation rate and the initial concentrations of the two species, we observe varying degrees of stratification in the final dried films. Our model predicts the various structures described in the literature previously from experiments and computer simulations, in particular the small-on-top stratified films. Our model also includes the influence of adsorption of particles to the interfaces.

cond-mat.soft↗

arXiv2020

Phase-field modeling of biomineralization in mollusks and corals: Microstructure vs. formation mechanism

While biological crystallization processes have been studied on the microscale extensively, models addressing the mesoscale aspects of such phenomena are rare. In this work, we investigate whether the phase-field theory developed in materials science for describing complex polycrystalline structures on the mesoscale can be meaningfully adapted to model crystallization in biological systems. We demonstrate the abilities of the phase-field technique by modeling a range of microstructures observed in mollusk shells and coral skeletons, including granular, prismatic, sheet/columnar nacre, and sprinkled spherulitic structures. We also compare two possible micromechanisms of calcification: the classical route via ion-by-ion addition from a fluid state and a non-classical route, crystallization of an amorphous precursor deposited at the solidification front. We show that with appropriate choice of the model parameters microstructures similar to those found in biomineralized systems can be obtained along both routes, though the timescale of the non-classical route appears to be more realistic. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be understood with simple math, and simulated by phase-field theory.

cond-mat.mtrl-sci↗

arXiv2019

Phase-field modeling of crystal nucleation in undercooled liquids -- A review

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the conventional phase-field approaches that rely on spatially averaged (coarse grained) order parameters in capturing freezing, and by the recently developed phase-field crystal models that work on the molecular scale, while employing time averaged particle densities, and are regarded as simple dynamical density functional theories of classical particles. Besides simpler cases of homogeneous and heterogeneous nucleation, phenomena addressed by these techniques include precursor assisted nucleation, nucleation in eutectic and phase separating systems, phase selection via competing nucleation processes, growth front nucleation (a process, in which grains of new orientations form at the solidification front) yielding crystal sheaves and spherulites, and transition between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies.

cond-mat.mtrl-sci↗

arXiv2014

A GPU cluster optimized multigrid scheme for computing unsteady incompressible fluid flow

A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units (GPUs). It is shown that the total number of the synchronization events can be significantly reduced when a deep, 2h grid hierarchy is replaced with a two-level scheme using 16h-32h restriction, fitting to the the width of the SIMD engine of modern CPUs and GPUs. In addition, optimal memory transfer is also ensured, since no strided memory access is required. We report increasing arithmetic intensity of the smoothing steps when compared to the conventional additive correction multigrid (ACM), however it is counterbalanced in runtime by the decreasing number of the expensive restriction steps. A systematic construction methodology for the coarse grid stencil is also presented that helps in moderating the excess arithmetic intensity associated with the aggressive coarsening. Our higher order interpolated stencil improves convergence rate via minimizing spurious interference between the coarse and the fine scale solutions. The method is demonstrated on solving the pressure equation for 2D incompressible fluid flow: The benchmark setups cover shear driven laminar flow in cavity, and direct numerical simulation (DNS) of a turbulent jet. We have compared our scheme to the ACM in terms of the arithmetic intensity of the iterations and the number of the synchronization calls required. Also the strong scaling is plotted for our scheme when using a hybrid OpenCl/MPI based parallelization.

math.NA↗

arXiv2014

Crystallization: Colloidal suspense

According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase - but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different structures can develop.

cond-mat.mtrl-sci↗

arXiv2014

Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model

Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous precursor forms, and the crystalline phase appears via heterogeneous nucleation in/on the precursor cluster. Herein, we review recent results by a simple dynamical density functional theory, the phase-field crystal model, for (precursor-mediated) homogeneous and heterogeneous nucleation of nanocrystals. It will be shown that the mismatch between the lattice constants of the nucleating crystal and the substrate plays a decisive role in determining the contact angle and nucleation barrier, which were found to be non-monotonic functions of the lattice mismatch. Time dependent studies are essential as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning.

cond-mat.mtrl-sci↗

arXiv2014

Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model

The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at various reduced temperatures in the range $ε\in\left[0,0.5\right]$. While the maximum free energy corresponds to the $\left\{ 100\right\} $ orientation for all $ε$ values, the minimum is realized by the $\left\{ 111\right\} $ direction for small $ε\,(<0.13)$, and by the $\left\{ 211\right\} $ orientation for higher $ε$. The predicted dependence on the reduced temperature is consistent with the respective mean field critical exponent. The results are fitted with an eight-term Kubic harmonic series, and are used to create stereographic plots displaying the anisotropy of the interface free energy. We have also derived the corresponding Wulff shapes that vary with increasing $ε$ from sphere to a polyhedral form that differs from the rhombo-dodecahedron obtained previously by growing a bcc seed until reaching equilibrium with the remaining liquid.

cond-mat.mtrl-sci↗

arXiv2014

Beyond the Ginzburg-Landau theory of freezing: Anisotropy of the interfacial free energy in the Phase-Field Crystal model

This paper re-visits the weakly fourth order anisotropic Ginzburg-Landau (GL) theory of freezing. First we determine the anisotropy of the interfacial free energy in the Phase-Field Crystal (PFC) model analytically, and prove that it remains finite at the critical point as a direct consequence of the one-mode dominance of the model. Next, we derive the leading order PFC amplitude model and show the formal analogy to traditional weakly 4th order anisotropic GL theories. We conclude that the material-independent anisotropy appearing in emergent GL theory coincides with the remnant anisotropy of the generating PFC model. As a result, we show that the reduced temperature ε does not enter into the interfacial free energy anisotropy for metallic materials in both the Phase-Field Crystal model and the emerging Ginzburg-Landau theories. Finally, we investigate the possible pathways of calibrating anisotropic Ginzburg-Landau theories.

cond-mat.mtrl-sci↗

arXiv2013

Nonlinear hydrodynamic theory of crystallization

We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology, which allows a direct coupling between the free energy functional of the classical Density Functional Theory and the Navier-Stokes equation. Contrary to the Ginzburg-Landau type amplitude theories, the dynamic response to elastic deformations is described by parameter-free kinetic equations. Employing our approach to the free energy functional of the Phase-Field Crystal model, we recover the classical spectrum for the phonons and the steady-state growth fronts. The capillary wave spectrum of the equilibrium crystal-liquid interface is in a good qualitative agreement with the molecular dynamics simulations.

cond-mat.mtrl-sci↗

arXiv2012

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.

cond-mat.soft↗

arXiv2011

Amorphous nucleation precursor in highly nonequilibrium fluids

Dynamical density functional simulations reveal structural aspects of crystal nucleation in undercooled liquids: the first appearing solid is amorphous, which promotes the nucleation of bcc crystals, but suppresses the appearance of the fcc and hcp phases. These findings are associated with features of the effective interaction potential deduced from the amorphous structure.

cond-mat.mtrl-sci↗

arXiv2010

Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2d and 3d

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3d, and determine the line free energy in 2d, the height of the nucleation barrier in 2d and 3d for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from sphere to the specific faceted shapes: rhombic-dodecahedron (bcc), truncated-octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic, which anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggrega-tion in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simula-tions. Finally, we present results for eutectic solidification in a binary PFC model.

cond-mat.mtrl-sci↗

arXiv2010

Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning

We apply a simple dynamical density functional theory, the phase-field-crystal (PFC) model, to describe homogeneous and heterogeneous crystal nucleation in 2d monodisperse colloidal systems and crystal nucleation in highly compressed Fe liquid. External periodic potentials are used to approximate inert crystalline substrates in addressing heterogeneous nucleation. In agreement with experiments in 2d colloids, the PFC model predicts that in 2d supersaturated liquids, crystalline freezing starts with homogeneous crystal nucleation without the occurrence of the hexatic phase. At extreme supersaturations crystal nucleation happens after the appearance of an amorphous precursor phase both in 2d and 3d. We demonstrate that contrary to expectations based on the classical nucleation theory, corners are not necessarily favourable places for crystal nucleation. Finally, we show that adding external potential terms to the free energy, the PFC theory can be used to model colloid patterning experiments.

cond-mat.mtrl-sci↗