arXiv subjects

Grzegorz Szamel

Publications and source records attributed to Grzegorz Szamel.

At least 55 records · Page 3Linked to original sources

arXiv2019

Mode-coupling theory for the steady-state dynamics of active Brownian particles

We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a many-particle evolution equation for the probability distribution of the particles' positions. Second, we use projection operator technique and a mode-coupling-like factorization approximation to derive an equation of motion for the density correlation function. The nonequilibrium character of the active system manifests itself through the presence of a steady-state correlation function that quantifies spatial correlations of microscopic steady-state currents of the particles. This function determines the dependence of the short-time dynamics on the activity. It also enters into the expression for the memory matrix and thus influences the long-time glassy dynamics.

cond-mat.soft↗

arXiv2019

Theory for the single-particle dynamics in glassy mixtures with particle size swaps

We present a theory for the single-particle dynamics in binary mixtures with particle size swaps. The general structure of the theory follows that of the theory for the collective dynamics in binary mixtures with particle size swaps, which we developed previously [G. Szamel, Phys. Rev. E 98, 050601(R) (2018)]. Particle size swaps open up an additional relaxation channel, which speeds up both the collective dynamics and the single-particle dynamics. To make explicit predictions, we resort to a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. We show that, like in the standard mode-coupling theory, the single-particle motion becomes arrested at the dynamic glass transition predicted by the theory for the collective dynamics. We compare the non-ergodicity parameters predicted by our mode-coupling-like approach for the an equimolar binary hard sphere mixture with particle size swaps with the non-ergodicity parameters predicted by the standard mode-coupling theory for the same system without swaps. Our theory predicts that the "cage size" is bigger in the system with particle size swaps.

cond-mat.soft↗

arXiv2019

Perspective: Nonequilibrium glassy dynamics in dense systems of active particles

Despite the diversity of materials designated as active matter, virtually all active systems undergo a form of dynamic arrest when crowding and activity compete, reminiscent of the dynamic arrest observed in colloidal and molecular fluids undergoing a glass transition. We present a short perspective on recent and ongoing efforts to understand how activity competes with other physical interactions in dense systems. We first review recent experimental work on active materials that uncovered both classic signatures of glassy dynamics and intriguing novel phenomena at large density. We introduce a minimal model of self-propelled particles where the competition between interparticle interactions, crowding, and self-propulsion can be studied in great detail. We discuss more complex models that include some additional, material-specific ingredients. We end with some general perspectives on dense active materials, suggesting directions for future research, in particular for theoretical work.

cond-mat.soft↗

arXiv2019

Low-frequency vibrational modes of stable glasses

We numerically study the evolution of the vibrational density of states $D(ω)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(ω) \sim ω^2$) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes instead obey $D(ω) \sim ω^4$, irrespective of the glass stability. However, the prefactor of this quartic law becomes smaller in more stable glasses, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glass stability and soft vibrational motion in amorphous solids.

cond-mat.soft↗

arXiv2018

A theory for the dynamics of glassy mixtures with particle size swaps

We present a theory for the dynamics of a binary mixture with particle size swaps. The theory is based on a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. The theory shows that, in accordance with physical intuition, particle size swaps open up an additional channel for the relaxation of density fluctuations. Thus, allowing swaps speeds up the dynamics and moves the dynamic glass transition towards higher densities and/or lower temperatures. We calculate an approximate dynamic glass transition phase diagram for an equimolar binary hard sphere mixture. We find that in the presence of particle size swaps, with increasing ratio of the hard sphere diameters the dynamic glass transition line moves towards higher volume fractions, up to the ratio of the diameters approximately equal to 1.2, and then saturates. We comment on the implications of our findings for the theoretical description of the glass transition.

cond-mat.soft↗

arXiv2018

Viscoelastic shear stress relaxation in two-dimensional glass forming liquids

Translational dynamics of two-dimensional glass forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation and well developed plateaus are observed in orientational correlation functions. It has been suggested that by monitoring translational motion of particles relative to that of their neighbors, one can recover characteristic features of glassy dynamics and thus disentangle the Mermin-Wagner fluctuations from the two-dimensional glass transition. Here we use molecular dynamics simulations to study viscoelastic relaxation in two and three dimensions. We find different behavior of the dynamic modulus below the onset of slow dynamics (determined by the orientational or cage-relative correlation functions) in two and three dimensions. The dynamic modulus for two-dimensional supercooled fluids is more stretched than for three-dimensional supercooled fluids and it does not exhibit a plateau, which implies the absence of glassy viscoelastic relaxation. At lower temperatures, the two-dimensional dynamic modulus starts exhibiting an intermediate time plateau and decays similarly to the three-dimensional dynamic modulus. The differences in the glassy behavior of two- and three-dimensional glass forming fluids parallel differences in the ordering scenarios in two and three dimensions.

cond-mat.soft↗

arXiv2018

A Microscopic Model of the Stokes-Einstein Relation in Arbitrary Dimension

The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.

cond-mat.stat-mech↗

arXiv2017

How active forces influence nonequilibrium glass transitions

Dense assemblies of self-propelled particles undergo a nonequilibrium form of glassy dynamics. Physical intuition suggests that increasing departure from equilibrium due to active forces fluidifies a glassy system. We falsify this belief by devising a model of self-propelled particles where increasing departure from equilibrium can both enhance or depress glassy dynamics, depending on the chosen state point. We analyze a number of static and dynamic observables and suggest that the location of the nonequilibrium glass transition is primarily controlled by the evolution of two-point static density correlations due to active forces. The dependence of the density correlations on the active forces varies non-trivially with the details of the system, and is difficult to predict theoretically. Our results emphasize the need to develop an accurate liquid state theory for nonequilibrium systems.

cond-mat.soft↗

arXiv2017

A simple theory for the dynamics of mean-field-like models of glass-forming fluids

We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [PRL 116, 015902 (2016)]. Our approach provides an alternative, physically motivated derivation of this result.

cond-mat.dis-nn↗

arXiv2017

Evaluating linear response in active systems with no perturbing field

We present a method for the evaluation of time-dependent linear response functions for systems of active Ornstein-Uhlenbeck particles from unperturbed simulations. The method is inspired by the Malliavin weights sampling method proposed by Warren and Allen [Phys. Rev. Lett. 109, 250601 (2012)] for systems of Brownian particles. We illustrate our method by evaluating a linear response function for a single active particle in an external harmonic potential. As an application, we calculate the time-dependent mobility function and an effective temperature, defined through the Einstein relation between the self-diffusion and mobility coefficients, for a system of active particles interacting via a screened-Coulomb potential. We find that this effective temperature decreases with increasing persistence time of the self-propulsion. Initially, for not too large persistence times, it changes rather slowly, but then it decreases markedly when the persistence length of the self-propelled motion becomes comparable with the particle size.

cond-mat.soft↗

arXiv2016

Kinetic stability and energetics of simulated glasses created by constant pressure cooling

We use computer simulations to study the cooling rate dependence of the stability and energetics of model glasses created at constant pressure conditions and compare the results with glasses formed at constant volume conditions. To examine the stability, we determine the time it takes for a glass cooled and reheated at constant pressure to transform back into a liquid, $t_{\mathrm{trans}}$, and calculate the stability ratio $S = t_{\mathrm{trans}}/τ_α$, where $τ_α$ is the equilibrium relaxation time of the liquid. We find that, for slow enough cooling rates, cooling and reheating at constant pressure results in a larger stability ratio $S$ than for cooling and reheating at constant volume. We also compare the energetics of glasses obtained by cooling while maintaining constant pressure with those of glasses created by cooling from the same state point while maintaining constant volume. We find that cooling at constant pressure results in glasses with lower average potential energy and average inherent structure energy. We note that in model simulations of the vapor deposition process glasses are created under constant pressure conditions, and thus they should be compared to glasses obtained by constant pressure cooling.

cond-mat.soft↗

arXiv2016

The nonequilibrium glassy dynamics of self-propelled particles

We study the glassy dynamics taking place in dense assemblies of athermal active particles that are driven solely by a nonequilibrium self-propulsion mechanism. Active forces are modeled as an Ornstein-Uhlenbeck stochastic process, characterized by a persistence time and an effective temperature, and particles interact via a Lennard-Jones potential that yields well-studied glassy behavior in the Brownian limit, obtained as the persistence time vanishes. By increasing the persistence time, the system departs more strongly from thermal equilibrium and we provide a comprehensive numerical analysis of the structure and dynamics of the resulting active fluid. Finite persistence times profoundly affect the static structure of the fluid and give rise to nonequilibrium velocity correlations that are absent in thermal systems. Despite these nonequilibrium features, for any value of the persistence time we observe a nonequilibrium glass transition as the effective temperature is decreased. Surprisingly, increasing departure from thermal equilibrium is found to promote (rather than suppress) the glassy dynamics. Overall, our results suggest that with increasing persistence time, microscopic properties of the active fluid change quantitatively, but the broad features of the nonequilibrium glassy dynamics observed with decreasing the effective temperature remain qualitatively similar to those of thermal glass-formers.

cond-mat.soft↗

arXiv2016

Dynamic heterogeneity in two-dimensional supercooled liquids: comparison of bond-breaking and bond-orientational correlations

We compare the spatial correlations of bond-breaking events and bond-orientational relaxation in a model two-dimensional liquid undergoing Newtonian dynamics. We find that the relaxation time of the bond-breaking correlation function is much longer than the relaxation time of the bond-orientational correlation function and self-intermediate scattering function. However, the relaxation time of the bond-orientational correlation function increases faster with decreasing temperature than the relaxation time of the bond-breaking correlation function and the self-intermediate scattering function. Moreover, the dynamic correlation length that characterizes the size of correlated bond-orientational relaxation grows faster with decreasing temperature than the dynamic correlation length that characterizes the size of correlated bond-breaking events. We also examine the ensemble-dependent and ensemble-independent dynamic susceptibilities for both bond-breaking correlations and bond-orientational correlations. We find that for both correlations, the ensemble-dependent and ensemble-independent susceptibilities exhibit a maximum at nearly the same time, and this maximum occurs at a time slightly shorter than the peak position of the dynamic correlation length.

cond-mat.stat-mech↗

arXiv2015

A theory for the dynamics of dense systems of athermal self-propelled particles

We present a derivation of a recently proposed theory for the time dependence of density fluctuations in stationary states of strongly interacting, athermal, self-propelled particles. The derivation consists of two steps. First, we start from the equation of motion for the joint distribution of particles' positions and self-propulsions and we integrate out the self-propulsions. In this way we derive an approximate, many-particle evolution equation for the probability distribution of the particles' positions. Second, we use this evolution equation to describe the time dependence of steady-state density correlations. We derive a memory function representation of the density correlation function and then we use a factorization approximation to obtain an approximate expression for the memory function. In the final equation of motion for the density correlation function the non-equilibrium character of the active system manifests itself through the presence of a new steady-state correlation function that quantifies spatial correlations of the velocities of the particles. This correlation function enters into the frequency term, and thus it describes the dependence of the short-time dynamics on the properties of the self-propulsions. More importantly, the correlation function of particles' velocities enters into the vertex of the memory function and through the vertex it modifies the long-time glassy dynamics.

cond-mat.soft↗

arXiv2015

Reduced strength and extent of dynamic heterogeneity in a strong glass former as compared to fragile glass formers

We examined dynamic heterogeneity in a model tetrahedral network glass-forming liquid. We used four-point correlation functions to extract dynamic correlation lengths xi_4^a(t) and susceptibilities chi_4^a(t) corresponding to structural relaxation on two length scales a. One length scale corresponds to structural relaxation at nearest neighbor distances and the other corresponds to relaxation of the tetrahedral structure. We find that the dynamic correlation length xi_4^{a} grows much slower with increasing relaxation time than for model fragile glass formers. We also find that chi_4^a ~ (xi_4^a)^z for a range of temperatures, but z < 3 at the lowest temperatures examined in this study. However, we do find evidence that the temperature where Stokes-Einstein violation begins marks a temperature where there is a change in the character of dynamically heterogeneous regions. Throughout the paper, we contrast the structure and dynamics of a strong glass former with that of a representative fragile glass former.

cond-mat.soft↗

arXiv2015

On the coarse-grained density and compressibility of a non-ideal crystal

The isothermal compressibility of a general crystal is derived and discussed within (classical) density functional theory. Starting from the microscopic particle density, we carefully coarse grain to obtain the thermodynamic compressibility and the long wavelength limits of the correlation functions of elasticity theory. We explicitly show that the isothermal compressibility is not the wavevector to zero limit of the (total) density correlation function. The latter also cannot be obtained from the static structure factor measured in a scattering experiment.

cond-mat.soft↗

arXiv2015

On the coarse-grained density and compressibility of non-ideal crystals: general theory and an application to cluster crystals

The isothermal compressibility of a general crystal is analyzed within classical density functional theory. Our approach can be used for homogeneous and unstrained crystals containing an arbitrarily high density of local defects. We start by coarse-graining the microscopic particle density and then obtain the long wavelength limits of the correlation functions of elasticity theory and the thermodynamic derivatives. We explicitly show that the long wavelength limit of the microscopic density correlation function differs from the isothermal compressibility. It also cannot be obtained from the static structure factor measured in a scattering experiment. We apply our theory to crystals consisting of soft particles which can multiply occupy lattice sites ('cluster crystals'). The multiple occupancy results in a strong local disorder over an extended range of temperatures. We determine the cluster crystals' isothermal compressibility, the fluctuations of the lattice occupation numbers and their correlation functions, and the dispersion relations. We also discuss their low-temperature phase diagram.

cond-mat.soft↗

arXiv2015

Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory

We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. The simulations reveal that when the persistence time of the self-propelled particles is increased, the local structure becomes more pronounced whereas the long-time dynamics first accelerates and then slows down. These seemingly contradictory evolutions are explained by constructing a nonequilibrium mode-coupling-like theory for interacting self-propelled particles. To predict the collective dynamics the theory needs the steady state structure factor and the steady state correlations of the local velocities. It yields nontrivial predictions for the glassy dynamics of self-propelled particles in qualitative agreement with the simulations.

cond-mat.soft↗