arXiv subjects

Thomas B. Schrøder

Publications and source records attributed to Thomas B. Schrøder.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of viscous liquids and the Random Barrier Model

This paper combines the particle-swap Monte Carlo algorithm with long GPU molecular dynamics simulations to analyze the dynamics of a ternary Lennard-Jones glass-forming liquid in the extremely viscous regime. The focus is on the inherent dynamics, obtained by quenching configurations along the configuration-space trajectory into their inherent state. We compare how two functional forms, the von Schweidler law and the random barrier model (RBM) prediction in the extreme disorder limit, fit data for the inherent mean-squared displacement as a function of time. We find that the RBM, which has no dimensionless free parameters, generally fits the data better than the von Schweidler law, despite the latters one dimensionless free parameter. In particular, this implies that the RBM predicts the value of the diffusion coefficient from short-time simulation data more accurately than does the von Schweidler expression. It remains an open question why the RBM reproduces well the inherent data despite this models (unrealistic) assumption of identical energy minima.

cond-mat.soft↗

arXiv2025

Unified percolation scenario for the $α$ and $β$ processes in simple glass formers

Given the vast differences in interaction details, describing the dynamics of structurally disordered materials in a unified theoretical framework presents a fundamental challenge to condensed-matter physics and materials science. Here, we numerically investigate a double-percolation scenario for the two most important relaxation processes of supercooled liquids and glasses, the so-called alpha and beta relaxations. For several simple glass formers, we find that when monitoring the dynamic shear modulus as temperature is lowered from the liquid state, percolation of immobile particles takes place at the temperature locating the alpha process. Mirroring this, upon continued cooling into the glass state, the mobile-particle percolation transition pinpoints a beta process whenever the latter is well separated from the main (alpha) process. For two-dimensional systems under the same conditions, percolation of mobile and immobile particles occurs nearly simultaneously and no beta relaxation can be identified. Our findings suggest that a general description of glassy dynamics should be based on a percolation perspective.

cond-mat.soft↗

arXiv2025

Viscous liquid dynamics modeled as random walks within overlapping hyperspheres

The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the number of particles. We study random walks within overlapping hyperspheres in 12 to 45 dimensions, i.e., above the percolation threshold, utilizing an algorithm for on-the-fly placement of the hyperspheres in conjunction with the kinetic Monte Carlo method. We find behavior typical of viscous liquids; thus decreasing the hypersphere density (corresponding to decreasing the temperature) leads to a slowing down of the dynamics by many orders of magnitude. The shape of the mean-square displacement as a function of time is found to be similar to that of the Kob-Andersen binary Lennard-Jones mixture and the Random Barrier Model, which predicts well the frequency-dependent fluidity of nine glass-forming liquids of different chemistry [Bierwirth et al., Phys. Rev. Lett. $\mathbf{119}, 248001\,(2017)$].

cond-mat.soft↗

arXiv2024

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules

Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been shown to exist in molecular models with flexible bonds [A. E. Olsen et al., J. Chem. Phys. 145, 241103 (2016)]. We here present three force-based methods to trace out pseudoisomorphs based on a single configuration and test them on the asymmetric dumbbell and 10-bead Lennard-Jones chain models with bonds modeled as harmonic springs. The three methods are based on requiring that particle forces, center-of-mass forces, and torques, respectively, are invariant in reduced units. For each of the two investigated models we identify a method that works well for tracing out pseudoisomorphs, but these methods are not the same. Overall, it appears that the more internal degrees of freedom there are in the molecule studied, the less they affect the gross dynamical behavior. Moreover, the "internal" degrees of freedom (including rotation) do not appear to significantly affect the scaling behavior of the dynamical/transport coefficients provided some "quenching" is performed.

cond-mat.soft↗

arXiv2023

Scaling properties of liquid dynamics predicted from a single configuration: Small rigid molecules

Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the direct-isomorph-check method. Recently a new method based on the scaling properties of forces was introduced and shown to work very well for atomic systems [T. B. Schroder, Phys. Rev. Lett. 129, 245501 (2022)]. A unique feature of this method is that it only requires a single equilibrium configuration for tracing out an isomorph. We here test generalizations of this method to molecular systems and compare to simulations of three simple molecular models: the asymmetric dumbbell model of two Lennard-Jones spheres, the symmetric inverse-power-law dumbbell model, and the Lewis-Wahnström o-terphenyl model. We introduce and test two force-based and one torque-based methods, all of which require just a single configuration for tracing out an isomorph. Overall, the method based on requiring invariant center-of-mass reduced forces works best.

cond-mat.soft↗

arXiv2022

A toy model for viscous liquid dynamics

A simple model for viscous liquid dynamics is introduced. Consider the surface of the union of hyper-spheres centered at random positions inside a hypercube with periodic boundary conditions. It is argued and demonstrated by numerical simulations that at high dimensions geodetic flows on this surface is a good model for viscous liquid dynamics. It is shown that this simple model exhibits viscous dynamics for densities above the percolation threshold in $8$, $12$ and $16$ dimensions. Thus the slowing down of the dynamics, measured by the mean-squared displacement, extends to several orders of magnitude similarly to what is observed in other models for viscous dynamics. Furthermore, the shape of the mean-squared displacement is to a very good approximation the same as for the standard model in simulations of viscous liquids: the Kob-Andersen binary Lennard Jones mixture.

cond-mat.soft↗

arXiv2021

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase of the activation barrier $ΔE(T)$ with decreasing temperature $T$. A class of theoretical frameworks -- known as elastic models -- attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus $G_\infty(T)$. While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose that viscous slowing down is controlled by a mesoscopic elastic stiffness $κ(T)$, defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent states. First, we show that $κ(T)$ -- which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses -- increases more strongly with decreasing $T$ than the macroscopic inherent state shear modulus $G(T)$ in several computer liquids. Second, we show that the simple relation $ΔE(T)\proptoκ(T)$ holds remarkably well for some computer liquids, implying a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the $ΔE(T) \propto κ(T)$ relation holds, from those in which it does not, is that the latter feature highly granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. [Rest of abstract abridged]

cond-mat.soft↗

arXiv2021

Predicting scaling properties from a single fluid configuration

Time-dependent dynamical properties of a fluid can not be estimated from a single configuration without performing a simulation. Here we show, however, that the scaling properties of both structure and dynamics can be predicted from a single configuration. The new method is demonstrated to work very well for equilibrium dynamics of the Kob-Andersen Binary Lennard-Jones mixture. Furthermore, the method is applied to isobaric cooling where the liquid falls out of equilibrium and forms a glass, demonstrating that the method requires neither equilibrium nor constant volume conditions to work, in contrast to existing methods.

cond-mat.soft↗

arXiv2020

Solid-like mean-square displacement in glass-forming liquids

It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth \textit{et al.}, Phys. Rev. Lett. {\bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-temperature mean-square displacement is fitted well by the RBM prediction, which involves no shape parameters. This finding highlights the challenge of explaining why a simple model based on hopping of non-interacting particles in a fixed random energy landscape can reproduce the complex and highly cooperative dynamics of glass-forming liquids.

cond-mat.soft↗

arXiv2018

The EXP pair-potential system. II. Fluid phase isomorphs

This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial potential-energy correlations, the system's reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and two versions of the direct-isomorph-check method that allows for much larger density changes. Results from approximate methods are compared to those of the small-step method for each of three isomorphs generated by 230 one percent density increases, covering in all one decade of density variation. Both approximate methods work well.

cond-mat.soft↗

arXiv2018

The EXP pair-potential system. I. Fluid phase isotherms, isochores, and quasiuniversality

The exponentially repulsive EXP pair potential defines a system of particles in terms of which simple liquids' quasiuniversality may be explained [A. K. Bacher et al., Nat. Commun. 5, 5424 (2014); J. C. Dyre, J. Phys. Condens. Matter 28, 323001 (2016)]. This paper and its companion present a detailed simulation study of the EXP system. Here we study how structure monitored via the radial distribution function and dynamics monitored via the mean-square displacement as a function of time evolve along the system's isotherms and isochores. The focus is on the gas and liquid phases, which are distinguished pragmatically by the absence or presence of a minimum in the radial distribution function above its first maximum. An NVU-based proof of quasiuniversality is presented, and quasiuniversality is illustrated by showing that the structure of the Lennard-Jones system at four selected state points is well approximated by those of EXP pair-potential systems with the same reduced diffusion constant. The companion paper studies the EXP system's isomorphs, focusing also on the gas and liquid phases.

cond-mat.soft↗

arXiv2018

Crystallisation Instability in Glassforming Mixtures

Crucial to gaining control over crystallisation in multicomponent materials or accurately modelling rheological behaviour of magma flows is to understand the mechanisms by which crystal nuclei form. The microscopic nature of such nuclei, however, makes this extremely hard in experiments, while computer simulations have hitherto been hampered by their short timescales and small system sizes due to limited computational power. Here we use highly-efficient GPU simulation techniques to access system sizes around 100 times larger than previous studies. This makes it possible to elucidate the nucleation mechanism in a well-studied binary glassformer. We discover that the supercooled liquid is inherently unstable for system sizes of 10,000 particles and larger. This effect is due to compositional fluctuations leading to regions comprised of large particles only which rapidly nucleate. We argue that this mechanism provides a minimum rate of crystallisation in mixtures in general, and use our results to stabilise a model binary mixture and predict glassforming ability for the CuZr metallic glassformer.

cond-mat.soft↗

arXiv2018

Phase diagram of Kob-Andersen type binary Lennard-Jones mixtures

The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations the viscous KA system crystallizes, however, by phase separating into a pure A particle phase forming an FCC crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50\% small (B) particles showing, in particular, that the melting temperature of the standard KA system at liquid density $1.2$ is $1.028(3)$ in A particle Lennard-Jones units. At large B particle concentrations the system crystallizes into the CsCl crystal structure. The eutectic corresponding to the FCC and CsCl structures is cut-off in a narrow interval of B particle concentrations around 26\% at which the bipyramidal orthorhombic ${\rm PuBr_3}$ structure is the thermodynamically stable phase. The melting temperature's variation with B particle concentration at two other pressures, as well as at the constant density $1.2$, is estimated from the simulations at pressure $10.19$ using isomorph theory. Our data demonstrate approximate identity between the melting temperature and the onset temperature below which viscous dynamics appears. Finally, the nature of the solid-liquid interface is briefly discussed.

cond-mat.soft↗

arXiv2017

RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles

RUMD is a general purpose, high-performance molecular dynamics (MD) simulation package running on graphical processing units (GPU's). RUMD addresses the challenge of utilizing the many-core nature of modern GPU hardware when simulating small to medium system sizes (roughly from a few thousand up to hundred thousand particles). It has a performance that is comparable to other GPU-MD codes at large system sizes and substantially better at smaller sizes.RUMD is open-source and consists of a library written in C++ and the CUDA extension to C, an easy-to-use Python interface, and a set of tools for set-up and post-simulation data analysis. The paper describes RUMD's main features, optimizations and performance benchmarks.

physics.comp-ph↗

arXiv2016

"Pseudoisomorphs" in liquids with intramolecular degrees of freedom

Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be identified by requiring scale invariance of the inherent-structure reduced-unit low-frequency vibrational spectrum evaluated for a single equilibrium configuration. This rationalizes why excess-entropy scaling, density scaling, and isochronal superposition apply for many liquids with internal degrees of freedom.

cond-mat.soft↗

arXiv2016

A pair potential that reproduces the shape of isochrones in molecular liquids

Many liquids have curves (isomorphs) in their phase diagrams along which structure, dynamics, and some thermodynamic quantities are invariant in reduced units. A substantial part of their phase diagrams is thus effectively one dimensional. The shape of these isomorphs is described by a material-dependent function of density $h(ρ)$, which for real liquids is well approximated by a power law $ρ^γ$. However, in simulations, a power law is not adequate when density changes are large; typical models such as the Lennard-Jones liquid show that $γ(ρ) \equiv \mathrm{d} \ln h(ρ)/\mathrm{d} \ln ρ$ is a decreasing function of density. This paper presents results from computer simulations using a new pair potential that diverges at a nonzero distance and can be tuned to give a more realistic shape of $γ(ρ)$. Our results indicate that the finite size of molecules is an important factor to take into account when modeling liquids over a large density range.

cond-mat.soft↗

arXiv2016

Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion

The recent theoretical prediction by Maimbourg and Kurchan [arXiv:1603.05023] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension $d$ goes to infinity is investigated for the standard 12-6 Lennard-Jones fluid. This is done by computer simulations for $d=2,3,4$ going from the critical point along the critical isotherm/isochore to higher density/temperature. In all cases the virial potential-energy correlation coefficient increases significantly. For a given density and temperature relative to the critical point, with increasing number of dimension the Lennard-Jones system conforms better to the hidden-scale-invariance property characterized by high virial potential-energy correlations (a property that leads to the existence of isomorphs in the thermodynamic phase diagram, implying that it becomes effectively one-dimensional in regard to structure and dynamics). The present paper also gives the first numerical demonstration of isomorph invariance of structure and dynamics in four dimensions. Our findings emphasize the need for a universally applicable $1/d$ expansion in liquid-state theory; we conjecture that the systems known to obey hidden scale invariance in three dimensions are those for which the yet-to-be-developed $1/d$ expansion converges rapidly.

cond-mat.soft↗

arXiv2016

Freezing and melting line invariants of the Lennard-Jones system

The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of the isomorph theory. First the freezing/melting lines for LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phase. Structure is probed by the radial distribution function and the structure factor and dynamics is probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties by reference to the isomorph theory explains why known single-phase melting criteria holds, e.g., the Hansen-Verlet and the Lindemann criterion, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from the isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.

cond-mat.soft↗