arXiv subjects

Ulf R. Pedersen

Publications and source records attributed to Ulf R. Pedersen.

At least 19 recordsLinked to original sources

arXiv2026

Randium: A minimal model of universal viscous liquid dynamics

When liquids are cooled and crystallization is avoided, their dynamics slow dramatically and the material eventually solidifies into an amorphous glass. Experiments show that chemically distinct glass forming liquids share universal features in both the spectral shape and the temperature dependence of the primary structural relaxation. We introduce Randium, a generic, energetically coarse-grained minimal model of viscous liquids. The model, inspired by results from atomistic molecular-dynamics simulations, is implemented on a two-dimensional lattice with Gaussian-distributed nearest-neighbor interactions. Temperature is the only control parameter, and at low temperatures, dynamic facilitation and dynamical heterogeneity emerge from simple nearest-neighbor rearrangements. The relaxation spectra obey time-temperature superposition, and they reproduce shapes observed experimentally for chemically distinct systems. The temperature dependence of the structural-relaxation time follows parabolic scaling, and the relaxation time grows exponentially with the heterogeneity length scale. The mean-squared displacement collapses onto the universal master curve of the random barrier model. The absence of elasticity-induced facilitation in Randium shows that this is not required for universal viscous-liquid dynamics. Other explanations for universal relaxation are discussed in light of Randium.

cond-mat.soft↗

arXiv2025

Theory of Generalized Hertzian Hyperspheres

While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized Hertzian hyperspheres, where particles interact via a finite-range repulsive potential that allows slight overlaps. Well-studied examples of this class include particles with harmonic repulsions, Hertzian spheres, and Hertzian disks. We derive closed-form expressions for thermodynamic properties, coexistence pressures, and scaling laws governing structure and dynamics. The theory predicts how quantities scale with temperature, density, spatial dimension, and potential softness. These theoretical predictions are tested through numerical simulations in dimensions ranging from one to eight.

cond-mat.soft↗

arXiv2024

Microscopic Theory of Density Scaling: Coarse-Graining in Space and Time

Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through experiments, offers an efficient means for exploring a vast range of time scales along a one-dimensional phase diagram. However, the theoretical foundation provided by isomorph theory is of limited use for molecular systems, since currently no first-principles theory exists that can explain the origins of density scaling or make predictions based on it. In this work, we propose a first-principles framework employing coarse-graining in space and time. Spatial coarse-graining reduces a molecule to a center-of-mass-level description by eliminating fast degrees of freedom, while temporal coarse-graining involves averaging fluctuations or correlation functions over characteristic time scales. We show that both approaches enable ab initio estimation of the density scaling coefficient for ortho-terphenyl, consistent with experimental values. Building on these findings, we employ excess entropy scaling to derive a microscopic theory that underpins density scaling from fully atomistic simulations. Our results illuminate the role of coarse-graining in assessing slow fluctuations in molecules and unravel the microscopic nature of density scaling. Ultimately, our proposed framework enables systematic bottom-up approaches for predicting transport coefficients that are otherwise experimentally inaccessible and computationally prohibitive.

cond-mat.soft↗

arXiv2023

Comparing zero-parameter theories for the WCA and harmonic-repulsive melting lines

The melting line of the Weeks-Chandler-Andersen (WCA) system was recently determined accurately and compared to the predictions of four analytical hard-sphere approximations [Attia et al., J. Chem. Phys. 157, 034502 (2022)]. Here, we study an alternative zero-parameter prediction based on the isomorph theory, the input of which relate to properties at a single reference state point on the melting line. The two central assumptions made are that the harmonic-repulsive potential approximates the WCA potential and that pair collisions are uncorrelated. The new approach gives excellent predictions at high temperatures, while the hard-sphere-theory based predictions are better at lower temperatures. Supplementing the WCA investigation, the face-centered-crystal to fluid coexistence line is determined for a system of harmonic-repulsive particles and compared to the zero-parameter theories. The results indicate that the excellent isomorph-theory predictions for the WCA potential at higher temperatures may be partly due to a cancellation of errors between the two above-mentioned assumptions.

cond-mat.stat-mech↗

arXiv2022

Isomorph invariance in the liquid and plastic-crystal phases of asymmetric-dumbbell models

We present a numerical study of the asymmetric dumbbell model consisting of ``molecules'' constructed as two different-sized Lennard-Jones spheres connected by a rigid bond. In terms of the largest (A) particle radius, we report data for the structure and dynamics of the liquid phase for the bond lengths 0.05, 0.1, 0.2, and 0.5, and analogous data for the plastic-crystal phase for the bond lengths 0.05, 0.1, 0.2, and 0.3. Structure is probed by means of the AA, AB, and BB radial distribution functions. Dynamics is probed via the A and B particle mean-square displacement as functions of time and via the rotational time-autocorrelation function. Consistent with the systems' strong virial potential-energy correlations, the structure and dynamics are found to be isomorph invariant to a good approximation in reduced units, while they generally vary considerably along isotherms of the same (20%) density variation. Even the rotational time-autocorrelation function, which due to the constant bond length is not predicted to be isomorph invariant, varies more along isotherms than along isomorphs. Our findings provide the first validation of isomorph-theory predictions for plastic crystals for which isomorph invariance, in fact, is found to apply better than in the liquid phase of asymmetric-dumbbell models.

cond-mat.soft↗

arXiv2022

Comparing four hard-sphere approximations for the low-temperature WCA melting line

By combining interface-pinning simulations with numerical integration of the Clausius-Clapeyron equation we determine accurately the melting-line coexistence pressure and fluid/crystal densities of the Weeks-Chandler-Andersen (WCA) system covering four decades of temperature. The data are used for comparing the melting-line predictions of the Boltzmann, Andersen-Weeks-Chandler, Barker-Henderson, and Stillinger hard-sphere approximations. The Andersen-Weeks-Chandler and the Barker-Henderson theories give the most accurate predictions, and they both work excellently in the zero-temperature limit for which analytical expressions are derived here.

cond-mat.stat-mech↗

arXiv2021

An extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures

This paper studies numerically the Weeks-Chandler-Andersen (WCA) system, which is shown to obey hidden scale invariance with a density-scaling exponent that varies from below 5 to above 500. This unprecedented variation makes it advantageous to use the fourth-order Runge-Kutta algorithm for tracing out isomorphs. Good isomorph invariance of structure and dynamics is observed over more than three orders of magnitude temperature variation. For all state points studied, the virial potential-energy correlation coefficient and the density-scaling exponent are controlled mainly by the temperature. Based on the assumption of statistically independent pair interactions, a mean-field theory is developed that rationalizes this finding and provides an excellent fit to data at low temperatures and densities.

cond-mat.soft↗

arXiv2020

Solid-liquid coexistence of the noble elements. I. Theory illustrated by the case of argon

The noble elements constitute the simplest group of atoms. At low temperatures or high pressures they freeze into the face-centered cubic (fcc) crystal structure (except helium). We perform molecular dynamics using the recently proposed simplified ab initio atomic (SAAP) potential [Deiters and Sadus, J. Chem. Phys. 150, 134504 (2019)] . This potential is parameterized using data from accurate ab initio quantum mechanical calculations by the coupled-cluster approach on the CCSD(T) level. We compute the fcc freezing lines for Argon and find a great agreement with the experimental values. At low pressures, this agreement is further enhanced by using many-body corrections. Hidden scale invariance of the potential energy function is validated by computing lines of constant excess entropy (configurational adiabats) and shows that mean square displacement and the static structure factor are invariant. These lines (isomorphs) can be generated from simulations at a single state-point by having knowledge of the pair potential. The isomorph theory for the solid-liquid transition is used to accurately predict the shape of the freezing line in the pressure-temperature plane, the shape in the density-temperature plane, the entropy of melting and the Lindemann parameters along the melting line. We finally predict that the body-centered cubic (bcc) crystal is stable at high pressures.

cond-mat.mtrl-sci↗

arXiv2019

Glass-forming ability of Lennard-Jones trimers

Melting temperatures at ambient pressure of systems of isosceles Lennard-Jones trimers with angles ranging from 70 degrees to 100 degrees are determined. Two crystal structures are considered: a distorted body centered cubic structure and a distorted face centered cubic structure with preferred angles of 77 and 96 degrees, respectively. Liquid dynamics are slowed down when the angle is increased. A trimer angle of 83 degrees yields the largest distance between isochrones and the melting temperature, suggesting that this value gives the optimal glass-forming ability. It is conjectured that better glass-formers may be found at angles larger than the ones considered in this study.

cond-mat.mtrl-sci↗

arXiv2018

Statistics of small length scale density fluctuations in supercooled viscous liquids

Many successful theories of liquids near the melting temperature assume that small length scale density fluctuations follow Gaussian statistics. In this paper I present numerical investigations of fluctuations in the supercooled viscous regime using an enhance sampling method. I present results for the single component Lennard-Jones liquid, the Kob-Andersen binary mixture, the Wahnström binary mixture, the Lewis-Wahnström model of ortho-terphenyl and for the TIP4P/Ice model of water. Results show that the Gaussian approximation persist to a good degree into the supercooled viscous regime, however, the approximation is less accurate at low temperatures. I relate the non-Gaussian fluctuations to crystalline configurations. Implications to theories of the glass transition are discussed.

cond-mat.stat-mech↗

arXiv2018

Experimental evidence of a state-point dependent scaling exponent of liquid dynamics

A large class of liquids have hidden scale invariance characterized by a scaling exponent. In this letter we present experimental evidence that the scaling exponent of liquid dynamics is state-point dependent for the glass-forming silicone oil tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). From dynamic and thermodynamic properties at equilibrium, we use a method to estimate the value of $γ$ at any state point of the pressure-temperature plane, both in the supercooled and normal liquid regimes. We find agreement between the average exponents and the value obtained by superposition of relaxation times over a large range of state-points. We confirm the state-point dependence of $γ$ by reanalyzing data of 20 metallic liquids and two model liquids.

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↗

arXiv2017

Variation along liquid isomorphs of the driving force for crystallization

We investigate the variation of the driving force for crystallization of a supercooled liquid along isomorphs, curves along which structure and dynamics are invariant. The variation is weak, and can be predicted accurately for the Lennard-Jones fluid using a recently developed formalism and data at a reference temperature. More general analysis allows interpretation of experimental data for molecular liquids such as dimethyl phthalate and indomethacin, and suggests that the isomorph scaling exponent $γ$ in these cases is an increasing function of density, although this cannot be seen in measurements of viscosity or relaxation time.

cond-mat.stat-mech↗

arXiv2015

Hidden scale invariance of metals

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between thermal fluctuations between virial and potential-energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the dense part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Gr{ü}neisen parameter, are in good agreement with experimental values for 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W and Hg), most post-transition metals (Ga, In, Sn, and Tl) and the metalloids Si and Ge cannot be explained by the IPL assumption. Thus, hidden scale invariance can be present even when the IPL-approximation is inadequate. The virial-energy correlation coefficient of iron and phosphorous is shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Gr{ü}neisen equation of state and a number of well-known empirical melting and freezing rules.

cond-mat.stat-mech↗

arXiv2014

Isomorph invariance of classical crystals' structure and dynamics

This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework, which is generally a good description except significantly below melting. The existence of isomorphs for crystals is validated by simulations of particles interacting via the Lennard-Jones pair potential arranged into a face-centered cubic (FCC) crystalline structure; the slow vacancy-jump dynamics of a defective FCC crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal model does not exhibit isomorph invariances. Other systems simulated, though in less detail, are the Wahnstrom binary Lennard-Jones crystal with the ${\rm MgZn_2}$ Laves crystal structure, monatomic FCC crystals of particles interacting via the Buckingham pair potential and via a novel purely repulsive pair potential diverging at a finite separation, an ortho-terphenyl molecular model, and SPC/E hexagonal ice. Except for NaCl and ice, the crystals simulated all have isomorphs. Based on these findings and previous simulations of liquid models, we conjecture that crystalline solids with isomorphs include most or all formed by atoms or molecules interacting via metallic or van der Waals forces, whereas covalently- or hydrogen-bonded crystals are not expected to have isomorphs. Crystals of ions or dipolar molecules constitute a limiting case for which isomorphs are only expected when the Coulomb interactions are relatively weak. We briefly discuss the consequences of the findings for theories of melting and crystallization.

cond-mat.stat-mech↗

arXiv2014

Computing the crystal growth rate by the interface pinning method

An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between super-cooling and average growth velocity. Here we show that this coefficient can be computed in a single equilibrium simulation using the interface pinning method where two-phase configurations are stabilized by adding an spring-like bias field coupling to an order-parameter that discriminates between the two phases. Crystal growth is a Smoluchowski process and the crystal growth rate can therefore be computed from the terminal exponential relaxation of the order parameter. The approach is investigated in detail for the Lennard-Jones model. We find that the kinetic coefficient scales as the inverse square-root of temperature along the high temperature part of the melting line. The practical usability of the method is demonstrated by computing the kinetic coefficient of the elements Na, Mg, Al and Si from first principles. It is briefly discussed how a generalized version of the method is an alternative to forward flux sampling methods for computing rates along trajectories of rare events.

cond-mat.stat-mech↗

arXiv2013

Direct calculation of the solid-liquid Gibbs free energy difference in a single equilibrium simulation

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs.

cond-mat.stat-mech↗