arXiv subjects

Elijah Flenner

Publications and source records attributed to Elijah Flenner.

At least 55 records · Page 3Linked to original sources

arXiv2012

Glassy dynamics of partially pinned fluids: an alternative mode-coupling approach

We use a simple mode-coupling approach to investigate glassy dynamics of partially pinned fluid systems. Our approach is different from the mode-coupling theory developed by Krakoviack [Phys. Rev. Lett. 94, 065703 (2005), Phys. Rev. E 84, 050501(R) (2011)]. In contrast to Krakoviack's theory, our approach predicts a random pinning glass transition scenario that is qualitatively the same as the scenario obtained using a mean-field analysis of the spherical p-spin model and a mean-field version of the random first-order transition theory. We use our approach to calculate quantities which are often considered to be indicators of growing dynamic correlations and static point-to-set correlations. We find that the so-called static overlap is dominated by the simple, low pinning fraction contribution. Thus, at least for randomly pinned fluid systems, only a careful quantitative analysis of simulation results can reveal genuine, many-body point-to-set correlations.

cond-mat.dis-nn↗

arXiv2011

Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Computer simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in explaining and predicting the resulting stationary structures (corresponding to the lowest adhesion energy state). Here we present two alternatives to the MMC approach for modeling cellular motion and self-assembly: (1) a kinetic Monte Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC, both KMC and CPD methods are capable of simulating the dynamics of the cellular system in real time. In the KMC approach a transition rate is associated with possible rearrangements of the cellular system, and the corresponding time evolution is expressed in terms of these rates. In the CPD approach cells are modeled as interacting cellular particles (CPs) and the time evolution of the multicellular system is determined by integrating the equations of motion of all CPs. The KMC and CPD methods are tested and compared by simulating two experimentally well known phenomena: (1) cell-sorting within an aggregate formed by two types of cells with different adhesivities, and (2) fusion of two spherical aggregates of living cells.

physics.bio-ph↗

arXiv2011

Emergence of Long-range Correlations and Rigidity at the Dynamic Glass Transition

At the microscopic level, equilibrium liquid's translational symmetry is spontaneously broken at the so-called dynamic glass transition predicted by the mean-field replica approach. We show that this fact implies the emergence of Goldstone modes and long-range density correlations. We derive and evaluate a new statistical mechanical expression for the glass shear modulus.

cond-mat.stat-mech↗

arXiv2011

Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction phi_c. First, we characterize the system's dynamics. Then, we utilize a new method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble independent dynamic susceptibility chi_4(t) and the dynamic correlation length xi(t) for a range of times between the beta and alpha relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction independent curve xi(t) ~ ln(t). For longer times, xi(t) departs from this curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation tau_alpha ~ exp[xi(tau_alpha)] between the alpha relaxation time, tau_alpha, and the dynamic correlation length at this time, xi(tau_alpha), we also find a similar correlation for the diffusion coefficient D ~ exp[xi(tau_alpha)^theta] with theta approximately 0.6. We discuss the relevance of these findings for different theories of the glass transition.

cond-mat.soft↗

arXiv2010

Dynamic heterogeneity in a glass forming fluid: susceptibility, structure factor and correlation length

We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80 000 particle system to test a new procedure to evaluate a dynamic correlation length xi(t): we determine the ensemble independent dynamic susceptibility chi_4(t) and use it to facilitate evaluation of xi(t) from the small wave vector behavior of the four-point structure factor. We analyze relations between the alpha relaxation time tau_alpha, chi_4(tau_alpha), and xi(tau_alpha). We find that mode-coupling like power laws provide a reasonable description of the data over a restricted range of volume fractions, but the power laws' exponents differ from those predicted by the inhomogeneous mode-coupling theory. We find xi(tau_alpha) ~ ln(tau_alpha) over the full range of volume fractions studied, which is consistent with Adams-Gibbs-type relation.

cond-mat.soft↗

arXiv2009

Scaling of the glassy dynamics of soft repulsive particles: a mode-coupling approach

We combine the hyper-netted chain approximation of liquid state theory with the mode-coupling theory of the glass transition to analyze the structure and dynamics of soft spheres interacting via harmonic repulsion. We determine the locus of the fluid-glass dynamic transition in a temperature -- volume fraction phase diagram. The zero-temperature (hard sphere) glass transition influences the dynamics at finite temperatures in its vicinity. This directly implies a form of dynamic scaling for both the average relaxation time and dynamic susceptibilities quantifying dynamic heterogeneity. We discuss several qualitative disagreements between theory and existing simulations at equilibrium. Our theoretical results are, however, very similar to numerical results for the driven athermal dynamics of repulsive spheres, suggesting that `mean-field' mode-coupling approaches might be good starting points to describe these nonequilibrium dynamics.

cond-mat.stat-mech↗

arXiv2009

Diverging length scale of the inhomogeneous mode-coupling theory: a numerical investigation

Biroli et al.'s extension of the standard mode-coupling theory to inhomogeneous equilibrium states [Phys. Rev. Lett. 97, 195701 (2006)] allowed them to identify a characteristic length scale that diverges upon approaching the mode-coupling transition. We present a numerical investigation of this length scale. To this end we derive and numerically solve equations of motion for coefficients in the small q expansion of the dynamic susceptibility $χ_{\mathbf{q}}(\mathbf{k};t)$ that describes the change of the system's dynamics due to an external inhomogeneous potential. We study the dependence of the characteristic length scale on time, wave-vector, and on the distance from the mode-coupling transition. We verify scaling predictions of Biroli et al. In addition, we find that the numerical value of the diverging length scale qualitatively agrees with lengths obtained from four-point correlation functions. We show that the diverging length scale has very weak k dependence, which contrasts with very strong $k$ dependence of the $q\to 0$ limit of the susceptibility, $χ_{\mathbf{q}=0}(\mathbf{k};t)$. Finally, we compare the diverging length obtained from the small q expansion to that resulting from an isotropic approximation applied to the equation of motion for the dynamic susceptibility $χ_{\mathbf{q}}(\mathbf{k};t)$.

cond-mat.stat-mech↗

arXiv2009

Anisotropic spatially heterogeneous dynamics on the $α$ and $β$ relaxation time scales studied via a four-point correlation function

We examine the anisotropy of a four-point correlation function $G_4(\vec{k},\vec{r};t)$ and it's associated structure factor $S_4(\vec{k},\vec{q};t)$ calculated using Brownian Dynamics computer simulations of a model glass forming system. These correlation functions measure the spatial correlations of the relaxation of different particles, and we examine the time and temperature dependence of the anisotropy. We find that the anisotropy is strongest at nearest neighbor distances at time scales corresponding to the peak of the non-Gaussian parameter $α_2(t) = 3 < δr^4(t) >/[ 5 < δr^2(t) >^2] - 1$, but is still pronounced around the $α$ relaxation time. We find that the structure factor $S_4(\vec{k},\vec{q};t)$ is anisotropic even for the smallest wave vector accessible in our simulation suggesting that our system (and other systems commonly used in computer simulations) may be too small to extract the $\vec{q} \to 0$ limit of the structure factor. We find that the determination of a dynamic correlation length from $S_4(\vec{k},\vec{q};t)$ is influenced by the anisotropy. We extract an effective anisotropic dynamic correlation length from the small $q$ behavior of $S_4(\vec{k},\vec{q};t)$.

cond-mat.soft↗

arXiv2008

Three-point susceptibilities $χ_n(k;t)$ and $χ_n^s(k;t)$: mode-coupling approximation

Recently, it was argued that a three-point susceptibility equal to the density derivative of the intermediate scattering function, $χ_n(k;t) = d F(k;t)/d n$, enters into an expression for the divergent part of an integrated four-point dynamic density correlation function of a colloidal suspension [Berthier \textit{et al.}, J. Chem. Phys. \textbf{126}, 184503 (2007)]. We show that, within the mode-coupling theory, the equation of motion for $χ_n(k;t)$ is essentially identical as the equation of motion for the $\mathbf{q}\to 0$ limit of the three-point susceptibility $χ_{\mathbf{q}}(\mathbf{k};t)$ introduced by Biroli \textit{et al.} [Phys. Rev. Lett. \textbf{97}, 195701 (2006)]. We present a numerical solution of the equation of motion for $χ_n(k;t)$. We also derive and numerically solve an equation of motion for the density derivative of the self-intermediate scattering function, $χ_n^s(k;t) = d F^s(k;t)/d n$. We contrast the wave vector dependence of $χ_n(k;t)$ and $χ_n^s(k;t)$.

cond-mat.soft↗

arXiv2008

Subdiffusion and lateral diffusion coefficient of lipid atoms and molecules in phospholipid bilayers

We use a long, all-atom molecular dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine (DMPC) lipid bilayer. From the analysis of a 0.1 $μ$s MD trajectory we find that the time evolution of the mean square displacement, [δ{r}(t)]^2, of lipid atoms and molecules exhibits three well separated dynamical regions: (i) ballistic, with [δ{r}(t)]^2 ~ t^2 for t < 10 fs; (ii) subdiffusive, with [δ{r}(t)]^2 ~ t^β with β<1, for 10 ps < t < 10 ns; and (iii) Fickian diffusion, with [δ{r}(t)]^2 ~ t for t > 30 ns. We propose a memory function approach for calculating [δ{r}(t)]^2 over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamics structure factor measured in neutron scattering experiments.

physics.bio-ph↗

arXiv2007

Relating Biophysical Properties Across Scales

A distinguishing feature of a multicellular living system is that it operates at various scales, from the intracellular to organismal. Very little is known at present on how tissue level properties are related to cell and subcellular properties. Modern measurement techniques provide quantitative results at both the intracellular and tissue level, but not on the connection between these. In the present work we outline a framework to address this connection. We specifically concentrate on the morphogenetic process of tissue fusion, by following the coalescence of two contiguous multicellular aggregates. The time evolution of this process can accurately be described by the theory of viscous liquids. We also study fusion by Monte Carlo simulations and a novel Cellular Particle Dynamics (CPD) model, which is similar to the earlier introduced Subcellular Element Model (Newman, 2005). Using the combination of experiments, theory and modeling we are able to relate the measured tissue level biophysical quantities to subcellular parameters. Our approach has validity beyond the particular morphogenetic process considered here and provides a general way to relate biophysical properties across scales.

physics.bio-ph↗

arXiv2006

Anisotropic spatially heterogeneous dynamics in a model glass-forming binary mixture

We calculated a four-point correlation function G_4(k,r;t) and the corresponding structure factor S_4(k,q;t) for a model glass-forming binary mixture. These functions measure the spatial correlations of the relaxation of different particles. We found that these four-point functions are anisotropic and depend on the angle between vectors k and r (or q). The anisotropy is the strongest for times somewhat longer than the beta relaxation time but it is quite pronounced even for times comparable to the alpha relaxation time, tau_alpha. At the lowest temperatures S_4(k,q;tau_alpha) is strongly anisotropic even for the smallest wavevector q accessible in our simulation.

cond-mat.stat-mech↗

arXiv2006

Four-point susceptibility of a glass-forming binary mixture: Brownian dynamics

We study the four-point dynamic susceptibility $χ_4(t)$ obtained from Brownian dynamics computer simulations of the Kob-Andersen Lennard-Jones mixture. We compare the results of the simulations with qualitative predictions of the mode-coupling theory. In addition, we test an estimate of the four-point susceptibility recently proposed by Berthier \textit{et al.} [Science, \textbf{310}, 1797 (2005)].

cond-mat.soft↗

arXiv2005

Efficient Monte Carlo simulation of a glass forming binary mixture

We propose and use a novel, hybrid Monte Carlo algorithm that combines configurational bias particle swaps with parallel tempering. We use this new method to simulate a standard model of a glass forming binary mixture above and below the so-called mode-coupling temperature, Tmct. We find that an ansatz that was used previously to extrapolate thermodynamic quantities to temperatures below Tmct breaks down in the vicinity of the mode-coupling temperature. Thus, previous estimates of the so-called Kauzmann temperature need to be reexamined. Also, we find that the Adam-Gibbs relations D ~ exp(-a/TSc) and tau ~ exp(b/TSc), which connect the diffusion coefficient D and the relaxation time tau with the configurational entropy Sc, are valid for all temperatures for which the configurational and vibrational contributions to the free energy decouple.

cond-mat.soft↗

arXiv2005

Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation

We solved the mode-coupling equations for the Kob-Andersen binary mixture using the structure factors calculated from Brownian dynamics simulations of the same system. We found, as was previously observed, that the mode-coupling temperature, Tc, inferred from simulations is about two times greater than that predicted by the theory. However, we find that many time dependent quantities agree reasonably well with the predictions of the mode-coupling theory if they are compared at the same reduced temperature epsilon = (T-Tc)/Tc, and if epsilon is not too small. Specifically, the simulation results for the incoherent intermediate scattering function, the mean square displacement, the relaxation time and the self-diffusion coefficient agree reasonably well with the predictions of the mode-coupling theory. We find that there are substantial differences for the non-Gaussian parameter. At small reduced temperatures the probabilities of the logarithm of single particle displacements demonstrate that there is hopping-like motion present in the simulations, and this motion is not predicted by the mode-coupling theory. The wave vector dependent relaxation time is shown to be qualitatively different than the predictions of the mode-coupling theory for temperatures where hopping-like motion is present.

cond-mat.soft↗

arXiv2005

Time scale for the onset of Fickian diffusion in supercooled liquids

We propose a quantitative measure of a time scale on which Fickian diffusion sets in for supercooled liquids and use Brownian Dynamics computer simulations to determine the temperature dependence of this onset time in a Lennard-Jones binary mixture. The time for the onset of Fickian diffusion ranges between 6.5 and 31 times the $α$ relaxation time (the $α$ relaxation time is the characteristic relaxation time of the incoherent intermediate scattering function). The onset time increases faster with decreasing temperature than the $α$ relaxation time. Mean squared displacement at the onset time increases with decreasing temperature.

cond-mat.dis-nn↗

arXiv2005

Relaxation in a glassy binary mixture: Mode-coupling-like power laws, dynamic heterogeneity and a new non-Gaussian parameter

We examine the relaxation of the Kob-Andersen Lennard-Jones binary mixture using Brownian dynamics computer simulations. We find that in accordance with mode-coupling theory the self-diffusion coefficient and the relaxation time show power-law dependence on temperature. However, different mode-coupling temperatures and power laws can be obtained from the simulation data depending on the range of temperatures chosen for the power-law fits. The temperature that is commonly reported as this system's mode-coupling transition temperature, in addition to being obtained from a power law fit, is a crossover temperature at which there is a change in the dynamics from the high temperature homogeneous, diffusive relaxation to a heterogeneous, hopping-like motion. The hopping-like motion is evident in the probability distributions of the logarithm of single-particle displacements: approaching the commonly reported mode-coupling temperature these distributions start exhibiting two peaks. Notably, the temperature at which the hopping-like motion appears for the smaller particles is slightly higher than that at which the hopping-like motion appears for the larger ones. We define and calculate a new non-Gaussian parameter whose maximum occurs approximately at the time at which the two peaks in the probability distribution of the logarithm of displacements are most evident.

cond-mat.soft↗

arXiv2004

Lifetime of dynamic heterogeneities in a binary Lennard-Jones mixture

A four-time correlation function was calculated using a computer simulation of a binary Lennard-Jones mixture. The information content of the four-time correlation function is similar to that of four-time correlation functions measured in NMR experiments. The correlation function selects a sub-ensemble and analyzes its dynamics after some waiting time. The lifetime of the sub-ensemble selected by the four-time correlation function is calculated, and compared to the lifetimes of slow sub-ensembles selected using two different definitions of mobility, and to the $α$ relaxation time.

cond-mat.soft↗