arXiv subjects

S. S. Ashwin

Publications and source records attributed to S. S. Ashwin.

14 recordsLinked to original sources

arXiv2023

Phase ordering in the near-critical regime of the Alzheimer's and normal brain

Criticality, observed during second-order phase transitions, is an emergent phenomenon. The brain operates near criticality, where complex systems exhibit high correlations. The critical brain hypothesis suggests that the brain becomes an efficient learning system in this state but poor in memory, while sub-criticality enhances memory but inhibits learning. As a system approaches criticality, it develops "domain"-like regions with competing phases and increased spatiotemporal correlations that diverge. The dynamics of these domains depend on the system's proximity to criticality. This study investigates the phase ordering properties of a spin-lattice model derived from Alzheimer's and cognitively normal subjects, expecting significant differences in their proximity to criticality. However, our findings show no conclusive distinction in the distal properties from criticality, as reflected in the phase ordering behavior of the Alzheimer's and cognitively normal brain.

cond-mat.stat-mech↗

arXiv2023

Closed form Eigenvalues of Randomly Segmented Tridiagonal quasi-Toeplitz Matrices: Random Rouse block copolymer

We calculate the eigenvalues of a class of random matrices, namely the randomly segmented tridiagonal quasi-Toeplitz (rstq-T) matrix, in exact closed-form. The contexts under which these matrices arise are ubiquitous in physics. In our case, they arise when studying the dynamics of a Rouse polymer embedded in random environments. Unlike in the case of Rouse polymers in homogeneous environments, where the dynamics give rise to a circulant matrix and the diagonalization is achieved easily via a Fourier transform, analytical diagonalization of the rstq-T matrix has remained unsolved thus far. We analytically calculate the spectral distribution of the rstq-T matrix, which is able to capture the effect of disorder on the modes.

cond-mat.stat-mech↗

arXiv2019

A Kinetically Constrained Model with a Thermodynamic Flavor

Kinetically constrained models (KCM) generically have trivial thermodynamics and yet manifest rich glassy dynamics. In order to resolve the thermodynamics-dynamics disconnect in KCMs, we derive a KCM by coarse-graining a non-trivial thermodynamic model with a solvable partition function. Blending of thermodynamics to the KCM makes the role of landscape properties on the relaxation times, fragility and its crossover analytically transparent. Using Bethe ansatz, we calculate the time-dependent $N$-point probability function in the distinct dynamical regimes of the landscapes; the contribution of the glassy term is identified.

cond-mat.stat-mech↗

arXiv2019

Organization of fast and slow chromatin revealed by single-nucleosome dynamics

Understanding chromatin organization and dynamics is important since they crucially affect DNA functions. In this study, we investigate chromatin dynamics by statistically analyzing single-nucleosome movement in living human cells. Bi-modal nature of the mean squared displacement distribution of nucleosomes allows for a natural categorization of the nucleosomes as fast and slow. Analyses of the nucleosome-nucleosome correlation functions within these categories along with the density of vibrational modes show that the nucleosomes form dynamically correlated fluid regions, i.e., dynamic domains of fast and slow nucleosomes. Perturbed nucleosome dynamics by global histone acetylation or cohesin inactivation indicate that nucleosome-nucleosome interactions along with tethering of chromatin chains organize nucleosomes into fast and slow dynamic domains. A simple polymer model is introduced, which shows the consistency of this dynamic domain picture. Statistical analyses of single-nucleosome movement provide rich information on how chromatin is dynamically organized in a fluid manner in living cells.

cond-mat.soft↗

arXiv2014

Epigenetic Dynamics of Cell Reprogramming

Reprogramming is a process of transforming differentiated cells into pluripotent stem cells by inducing specific modifying factors in the cells. Reprogramming is a non-equilibrium process involving a collaboration at levels separated by orders of magnitude in time scale, namely transcription factor binding/unbinding, protein synthesis/degradation, and epigenetic histone modification. We propose a model of reprogramming by integrating these temporally separated processes and show that stable states on the epigenetic landscape should be viewed as a superposition of basin minima generated in the fixed histone states. Slow histone modification is responsible for the narrow valleys connecting the pluripotent and differentiated states on the epigenetic landscape, and the pathways which largely overlap with these valleys explain the observed heterogeneity of latencies in reprogramming. We show that histone dynamics also creates an intermediary state observed in experiments. A change in the mechanism of histone modification alters the pathway to bypass the barrier, thereby accelerating the reprogramming and reducing the heterogeneity of latencies.

q-bio.MN↗

arXiv2012

A Fragile-Strong Fluid Crossover and Universal Relaxation Times in a Confined Hard Disc Fluid

We show that a system of hard discs confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single master curve when rescaled by the relaxation times and temperatures of the crossover. Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adams-Gibbs relation does not predict the relaxation behavior. We also show that a facilitated dynamics description of the system, where kinetically excited regions are identified with local packing arrangements of the discs, successfully describes the fragile-strong crossover.

cond-mat.soft↗

arXiv2012

The Inherent Structure Landscape Connection Between Liquids, Granular materials and the Jamming Phase Diagram

We provide a comprehensive picture of the jamming phase diagram by connecting the athermal, granular ensemble of jammed states and the equilibrium fluid through the inherent structure paradigm for a system hard discs confined to a narrow channel. The J-line is shown to be divided into packings that are thermodynamically accessible from the equilibrium fluid and inaccessible packings. The J-point is found to occur at the transition between these two sets of packings and is located at the maximum the inherent structure distribution. A general thermodynamic argument suggests that the density of the states at the configurational entropy maximum represents a lower bound on the J-point density in hard sphere systems. Finally, we find that the granular and fluid systems only occupy the same set of inherent structures, under the same thermodynamic conditions, at two points, corresponding to zero and infinite pressures, where they sample the J-point states and the most dense packing respectively.

cond-mat.soft↗

arXiv2011

Calculations of the Structure of Basin Volumes for Mechanically Stable Packings

There are a finite number of distinct mechanically stable (MS) packings in model granular systems composed of frictionless spherical grains. For typical packing-generation protocols employed in experimental and numerical studies, the probabilities with which the MS packings occur are highly nonuniform and depend strongly on parameters in the protocol. Despite intense work, it is extremely difficult to predict {\it a priori} the MS packing probabilities, or even which MS packings will be the most versus the least probable. We describe a novel computational method for calculating the MS packing probabilities by directly measuring the volume of the MS packing `basin of attraction', which we define as the collection of initial points in configuration space at {\it zero packing fraction} that map to a given MS packing by following a particular dynamics in the density landscape. We show that there is a small core region with volume $V^c_n$ surrounding each MS packing $n$ in configuration space in which all initial conditions map to a given MS packing. However, we find that the MS packing probabilities are very weakly correlated with core volumes. Instead, MS packing probabilities obtained using initially dilute configurations are determined by complex geometric features of the basin of attraction that are distant from the MS packing.

cond-mat.soft↗

arXiv2011

Edwards entropy and compactivity in a model of granular matter

Formulating a statistical mechanics for granular matter remains a significant challenge, in part, due to the difficulty associated with a complete characterization of the systems under study. We present a fully characterized model of a granular material consisting of $N$ two-dimensional, frictionless, hard discs, confined between hard walls, including a complete enumeration of all possible jammed structures. We show the properties of the jammed packings are independent of the distribution of defects within the system and that all the packings are isostatic. This suggests the assumption of equal probability for states of equal volume, which provides one possible way of constructing the equivalent of a microcanonical ensemble, is likely to be vaild for our model. An application of the second law of thermodynamics involving two subsystems in contact shows that the expected spontaneous equilibration of defects between the two is accompanied by an increase in entropy and that the equilibirum, obtained by entropy maximization, is characterized by the equality of compactivities. Finally, we explore the properties of the equivalent to the canonical ensemble for this system.

cond-mat.soft↗

arXiv2009

The Complete Jamming Landscape of Confined Hard Discs

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $σ$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/σ< 2$. By considering all possible local packing arrangements, the generalized ensemble partition function of jammed states is obtained using the transfer matrix method, which allows us to calculate the configurational entropy and the equation of state for the packings. Exploring the relationship between structural order and packing density, we find that the geometric frustration between local packing environments plays an important role in determining the density distribution of jammed states and that structural "randomness" is a non-monotonic function of packing density. Molecular dynamics simulations show that the properties of the equilibrium liquid are closely related to those of the landscape.

cond-mat.soft↗

arXiv2009

A Tiling Approach to Counting Inherent Structures in Hard Potential Systems

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure corresponds to a collectively jammed configuration. This work develops a tiling based approach to counting inherent structures that constructs packings by combining sets of elementary locally jammed structures but eliminates those final packings that either, do not tile space, or are not collectively jammed, through the use of tile incompatibility rules. The resulting theory contains a number of geometric quantities, such as the number of growth sites on a tile and the number of tile compatibilities that provide insight into the number of inherent structures in certain limits. We also show that these geometric quantities become quite simple in a system of highly confined hard discs.

cond-mat.stat-mech↗

arXiv2008

Gaussian approximation to single particle correlations at and below the picosecond scale for Lennard-Jones and nanoparticle fluids

To describe short-time (picosecond) and small-scale (nanometre) transport in fluids, a Green's function approach was recently developed. This approach relies on an expansion of the distribution of single particle displacements around a Gaussian function, yielding an infinite series of correction terms. Applying a recent theorem [Van Zon and Cohen, J. Stat. Phys. 123, 1-37 (2006)] shows that for sufficiently small times the terms in this series become successively smaller, so that truncating the series near or at the Gaussian level might provide a good approximation. In the present paper, we derive a theoretical estimate for the time scale at which truncating the series at or near the Gaussian level could be supposed to be accurate for equilibrium nanoscale systems. In order to numerically estimate this time scale, the coefficients for the first few terms in the series are determined in computer simulations for a Lennard-Jones fluid, an isotopic Lennard-Jones mixture and a suspension of a Lennard-Jones-based model of nanoparticles in a Lennard-Jones fluid. The results suggest that for Lennard-Jones fluids an expansion around a Gaussian is accurate at time scales up to a picosecond, while for nanoparticles in suspension (a nanofluid), the characteristic time scale up to which the Gaussian is accurate becomes of the order of five to ten picoseconds.

cond-mat.stat-mech↗

arXiv2006

Short-time fluctuations of displacements and work

A recent theorem giving the initial behavior of very short-time fluctuations of particle displacements in classical many-body systems is discussed. It has applications to equilibrium and non-equilibrium systems, one of which is a series expansion of the distribution of work fluctuations around a Gaussian function. To determine the time-scale at which this series expansion is valid, we present preliminary numerical results for a Lennard-Jones fluid. These results suggest that the series expansion converges up to time scales on the order of a picosecond, below which a simple Gaussian function for the distribution of the displacements can be used.

cond-mat.stat-mech↗

arXiv2006

The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids

A liquid can exist under conditions of thermodynamic stability or metastability within boundaries defined by the liquid-gas spinodal and the glass transition line. The relationship between these boundaries has been investigated previously using computer simulations, the energy landscape formalism, and simplified model calculations. We calculate these stability boundaries semi-analytically for a model glass forming liquid, employing accurate liquid state theory and a first-principles approach to the glass transition. These boundaries intersect at a finite temperature, consistent with previous simulation-based studies.

cond-mat.soft↗