arXiv subjects

Lorenzo Costigliola

Publications and source records attributed to Lorenzo Costigliola.

At least 19 recordsLinked to original sources

arXiv2026

Property-dependent material times

We analyze simulations of physical aging following large temperature up-jumps from equilibrated, slowly relaxing states. Specifically, we consider up-jumps from temperatures T=0.43 and T=0.37 to T=0.48 in a binary Lennard-Jones mixture. The Tool-Narayanaswamy (TN) concept of a universal material time was recently shown to become less effective in rationalizing the aging response for such large jumps [Amari et al., Phys. Rev. E 113, 045411 (2026)]. Here, we investigate whether the performance of the TN formalism can be improved by assigning a separate material time to each observable. We examine the potential-energy time-autocorrelation function, the self-intermediate scattering function, and the time-dependent mean-square displacement. As part of this study, we perform a detailed analysis of the extent to which the triangular relation, a necessary condition for the existence of a material time, is satisfied. We find that, for all three properties, the best data collapse is obtained when each property is parameterized by its own material time. The degree of improvement varies considerably among the observables, however; it is most pronounced for the mean-square displacement.

cond-mat.soft↗

arXiv2026

Large temperature-up-jump simulations of a binary Lennard-Jones system

This paper presents simulations of the physical aging of a binary Kob-Andersen-type Lennard-Jones liquid following large temperature up-jumps from equilibrated states of high relaxation time. The purpose is to investigate how well the Tool-Narayanaswamy (TN) material-time concept works for this rather extreme case of aging. First the triangular relation of the potential energy is investigated. This is found to be well obeyed, making it possible to define a potential-energy-based material time $ξ$. We proceed to study aging toward equilibrium at the final temperature 0.48 for jumps from the two temperatures 0.43 and 0.37 (primarily), monitoring the following five quantities: the potential energy, the self-intermediate scattering function, the mean-square displacement, the dynamic susceptibility $χ_4$, and the non-Gaussian parameter $α_2$. The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference $ξ_2-ξ_1$. This is found to work better for the $0.43\to 0.48$ temperature jump than for the $0.37\to 0.48$ jump. Our findings thus confirm the general understanding that the TN aging formalism works best for systems that are never very far from equilibrium. This raises two questions for future work: Is the collapse significantly improved if each aging quantity is allowed its own material time? Can better collapse be obtained if the material-time is generalized to be locally defined (in order to reflect dynamic heterogeneity)?

cond-mat.soft↗

arXiv2025

Swap Monte Carlo for diatomic molecules

In recent years the Swap Monte Carlo algorithm has led to remarkable progress in equilibrating supercooled model liquids at low temperatures. Applications have so far been limited to systems composed of spherical particles, however, whereas most real-world supercooled liquids are molecular. We here introduce a simple size-polydisperse molecular model that allows for efficient thermal equilibration in silico with the Swap Monte Carlo method, resulting in an estimated speedup of 1,000-1,000,000 at moderate polydispersity (5-10%). The model exhibits little difference between size-resolved orientational time-autocorrelation functions.

cond-mat.soft↗

arXiv2025

Interpolating between pair-potential systems

This paper studies liquid-model systems with almost identical constant-potential-energy hypersurfaces. We simulated continuous interpolations between such systems, specifically between the Lennard-Jones (LJ), Weeks-Chandler-Andersen (WCA), exponent 12 inverse-power-law (IPL), and Yukawa (YK) pair-potential systems. Structure and dynamics were monitored via the radial distribution function and the time-dependent mean-square displacement, respectively. In terms of the interpolation parameter lambda, we argue that two systems have very similar constant-potential-energy hypersurfaces if the potential energies of configurations rarely cross when plotted as functions of lambda. Such absence of "level crossing" applies to a very good approximation for the LJ to WCA transformation, and it also applies to a quite good approximation for the LJ to IPL and the YK to YK transformations (the latter varies the screening length). In all cases, structure and dynamics are shown to be almost invariant as functions of lambda. The density is kept constant when lambda is varied. Temperature must generally be adjusted with lambda, which is done by an iterative "reduced-force-matching" method with no free parameters. We also apply the interpolation strategy to two versions of the Kob-Andersen (KA) binary LJ system and show that a recently introduced shifted-force-cutoff version of this system has constant-potential-energy hypersurfaces, which are almost identical to those of the original KA system. This result rationalizes the previously established fact that the two KA versions have virtually identical physics.

cond-mat.soft↗

arXiv2025

$NVU$ view on energy polydisperse Lennard-Jones systems

When energy polydispersity is introduced into the Lennard-Jones (LJ) system, there is little effect on structure and dynamics [Ingebrigtsen and Dyre, J. Phys. Chem. B 127, 2837 (2023)]. For instance, at a given state point both the radial distribution function and the mean-square displacement as a function of time are virtually unaffected by even large energy polydispersity, which is in stark contrast to what happens when size polydispersity is introduced. We here argue -- and validate by simulations of up to 30\% polydispersity -- that this almost invariance of structure and dynamics reflects an approximate invariance of the constant-potential-energy surface. Because $NVU$ dynamics defined as geodesic motion at constant potential energy is equivalent to Newtonian dynamics in the thermodynamic limit, the approximate invariance of the constant-potential-energy surface implies virtually the same physics of energy polydisperse LJ systems as of the standard single-component version. In contrast, the constant-potential-energy surface is significantly affected by introducing size polydispersity.

cond-mat.soft↗

arXiv2025

Freezing, melting and the onset of glassiness in binary mixtures

We clarify the relationship between freezing, melting, and the onset of glassy dynamics in a prototypical glass-forming mixture model. Our starting point is a precise operational definition of the onset of glassiness, as expressed by the emergence of inflections in time-dependent correlation functions. By scanning the temperature-composition phase diagram of the mixture, we find a disconnect between the onset of glassiness and freezing. Surprisingly, however, the onset temperature closely tracks the melting line, along which the excess entropy is approximately constant. At fixed composition, all characteristic temperatures display nonetheless similar pressure dependencies, which are very well predicted by the isomorph theory. While our results rule out a general connection between thermodynamic metastability and glassiness, they call for a reassessment of the role of crystalline precursors in glass-forming liquids.

cond-mat.soft↗

arXiv2024

Time reversibility during the ageing of materials

Physical ageing is the generic term for irreversible processes in glassy materials resulting from molecular rearrangements. One formalism for describing such ageing processes involves the concept of material time, which may be thought of as time measured on a clock whose rate changes as the glass ages. Experimental determination of material time has so far not been realized, however. Here, we show how dynamic light-scattering measurements provide a way forward. We determined the material time for an ageing sample of the glass-former 1-phenyl-1-propanol after temperature jumps close to the glass transition from the time-autocorrelation function of the intensity fluctuations probed by multispeckle dynamic light scattering. These fluctuations are shown to be stationary and reversible when regarded as a function of the material time. The glass-forming colloidal synthetic clay Laponite and a chemically ageing curing epoxy are also shown to display material-time-reversible scattered-light intensity fluctuations, and simulations of an ageing binary system monitoring the potential energy confirm material-time reversibility. In addition to demonstrating direct measurements of the material time, our findings identify a fundamental property of ageing in quite different contexts that presents a challenge to the current theories of ageing.

cond-mat.soft↗

arXiv2024

Complexity Scaling of Liquid Dynamics

According to excess-entropy scaling, dynamic properties of liquids like viscosity and diffusion coefficient are determined by the entropy. This link between dynamics and thermodynamics is increasingly studied and of interest also for industrial applications, but hampered by the challenge of calculating entropy efficiently. Utilizing the fact that entropy is basically the Kolmogorov complexity, which can be estimated from optimal compression algorithms [Avinery et al., Phys. Rev. Lett. 123, 178102 (2019); Martiniani et al., Phys. Rev. X 9, 011031 (2019)], we here demonstrate that the diffusion coefficients of four simple liquids follow a quasiuniversal exponential function of the optimal compression length of a single equilibrium configuration. We conclude that "complexity scaling" has the potential to become a useful tool for estimating dynamic properties of any liquid from a single configuration.

cond-mat.soft↗

arXiv2023

Active-parameter polydispersity in the 2d ABP Yukawa model

In both experiments and simulations the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional Active Brownian Particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity $v_0$. Uniform and binary parameter distributions are considered in both the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of $v_0$ polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e., a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

cond-mat.soft↗

arXiv2023

Active-matter isomorphs in the size-polydisperse Ornstein-Uhlenbeck Lennard-Jones model

This paper studies size-polydisperse Lennard-Jones systems described by active Ornstein-Uhlenbeck particle dynamics. The focus is on the existence of isomorphs (curves of invariant structure and dynamics) in the model's three-dimensional phase diagram. Isomorphs are traced out from a single steady-state configuration by means of the configurational-temperature method. Good invariance of the reduced-unit radial distribution function and the mean-square displacement as a function of time is demonstrated for three uniform-distribution polydispersities, 12%, 23%, and 29%. Comparing to active-matter isomorphs generated by the analytical direct-isomorph-check method, the latter give somewhat poorer invariance of the structure, but better invariance of the dynamics. We conclude that both methods can be used to quickly get an overview of the phase diagram of polydisperse AOUP models involving a potential-energy function obeying the hidden-scale-invariance property required for isomorph theory to apply.

cond-mat.soft↗

arXiv2023

Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model

This paper shows that the configurational temperature of liquid-state theory, $\Tc$, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's $\Tc$ for a uniform scaling of all particle coordinates. The resulting equations are justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, demonstrating lines of approximate reduced-unit invariance of the radial distribution function and time-dependent mean-square displacement.

cond-mat.soft↗

arXiv2023

Configurational temperature in active matter. II. Quantifying the deviation from thermal equilibrium

This paper suggests using the configurational temperature $\Tc$ for quantifying how far an active-matter system is from thermal equilibrium. We measure this ``distance'' by the ratio of the systemic temperature $\Ts$ to $\Tc$, where $\Ts$ is the canonical-ensemble temperature for which the average potential energy is equal to that of the active-matter system. $\Tc$ is ``local'' in the sense that it is the average of a function, which only depends on how the potential energy varies in the vicinity of a given configuration; in contrast $\Ts$ is a global quantity. The quantity $\Ts/\Tc$ is straightforward to evaluate in a computer simulation; equilibrium simulations in conjunction with a single steady-state active-matter configuration are enough to determine $\Ts/\Tc$. We validate the suggestion that $\Ts/\Tc$ quantifies the deviation from thermal equilibrium by data for the radial distribution function of 3d Kob-Andersen and 2d Yukawa active-matter models with active Ornstein-Uhlenbeck and active Brownian Particle dynamics. Moreover, we show that $\Ts/\Tc$, structure, and dynamics of the homogeneous phase are all approximately invariant along the motility-induced phase separation (MIPS) boundary in the phase diagram of the 2d Yukawa model. The measure $\Ts/\Tc$ is not limited to active matter; it can be used for quantifying how far any system involving a potential-energy function, e.g., a driven Hamiltonian system, is from thermal equilibrium.

cond-mat.soft↗

arXiv2022

Single-parameter aging in the weakly nonlinear limit

Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials like polymers and inorganic glasses, both in production and during subsequent use. The Narayanaswamy theory from 1971 describes physical aging - an inherently nonlinear phenomenon - in terms of a linear convolution integral over the so-called material time $ξ$. The resulting "Tool-Narayanaswamy (TN) formalism" is generally recognized to provide an excellent description of physical aging for small, but still highly nonlinear temperature variations. The simplest version of the TN formalism is single-parameter aging according to which the clock rate $dξ/dt$ is an exponential function of the property monitored [T. Hecksher et al., J. Chem. Phys. 142, 241103 (2015)]. For temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation for property monitored, involving a system-specific function. The present paper shows analytically that the solution to this equation to first order in the temperature variation has a universal expression in terms of the zeroth-order solution, $R_0(t)$. Numerical data for a binary Lennard-Jones glass former probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging correctly from $R_0(t)$ (which by the fluctuation-dissipation theorem is the normalized equilibrium potential-energy time-autocorrelation function).

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↗

arXiv2022

Connecting Entropy Scaling and Density Scaling

It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The two-body residual entropy is demonstrated to not be a suitable surrogate for the total residual entropy in the gas phase. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent is related to the two-body interactions.

physics.chem-ph↗

arXiv2020

Density scaling of generalized Lennard-Jones fluids in different dimensions

Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.

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

Density-scaling exponents and virial potential-energy correlation coefficients for the (2n,n) Lennard-Jones system

This paper investigates the relation between the density-scaling exponent $γ$ and the virial potential-energy correlation coefficient $R$ at several thermodynamic state points in three dimensions for the generalized $(2n,n)$ Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard $n=6$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $γ\cong 3nR/d$ in $d$ dimensions. This result is discussed in light of the approximate "extended inverse power law" description of generalized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)]. In the plot of $γ$ versus $R$ there is in all cases a transition around $R\approx 0.9$, above which $γ$ starts to decrease as $R$ approaches unity. This is consistent with the fact that $γ\rightarrow 2n/d$ for $R\rightarrow 1$, a limit that is approached at high densities and/or temperatures at which the repulsive $r^{-2n}$ term dominates the physics.

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