arXiv subjects

Prashant K. Purohit

Publications and source records attributed to Prashant K. Purohit.

At least 19 recordsLinked to original sources

arXiv2026

Finite strain homogenization of periodic rod networks with application to semi-flexible biopolymers

In this work, we adopt a finite strain computational homogenization approach to characterize the response of semi-flexible biopolymer networks modeled as idealized 8- and 14-chain periodic networks. We use the geometrically exact special Cosserat rod theory to model the microscale fibers forming these 8- and 14-chain networks. This allows us to capture arbitrarily large microscale deformations. Both macroscopic strain- and stress-driven homogenization are performed to study the macroscopic uniaxial tension, compression and simple shear responses. Several phenomena unique to biopolymer networks are recovered such as strain-stiffening and volume shrinkage under uniaxial tension, softening under compression and reverse Poynting effect under simple shear. We find that nonlinearity and non-affine deformation at microscale, especially bending and buckling of microscale fibers, plays an important role in these phenomena. We obtain the postbuckled solutions of the homogenization problem using a nonlinear, imperfection-free path following approach and also check for their stability. We further compare our homogenization results with experimental data for uniaxial tension and compression of biofilament networks and find good agreement. When the fibers are replaced by helical rods in the 8-chain unit cell, we are also able to capture the enlarged stretching behaviour as shown in recently fabricated compliant metastructures.

cond-mat.soft↗

arXiv2026

Design principles for energy dissipation in viscoelastic network metamaterials

Mechanical energy dissipation in networked materials is relevant for applications from vibration isolation to impact protection, yet identifying optimal dissipative architectures in large disordered truss networks is computationally prohibitive with conventional finite element methods. We develop an efficient graph Laplacian-based spectral framework for viscoelastic truss networks, in which the full continuum dynamics of each rod are retained exactly and the problem size scales with the number of joints rather than element-level discretization points. Using this framework, we investigate how redistributing cross-sectional areas within a network (without changing material composition) controls energy dissipation. We find that random redistribution typically reduces dissipation relative to a uniform baseline, while gradient-based optimization yields nontrivial architectures whose form is governed by the intrinsic attenuation length of the base material. Focusing on driving frequencies near a global resonant mode of the network, we show that the optimal mass distribution decays from the source (driven joint) with the attenuation length scale, and at small attenuation lengths the optimal architecture is independent of the boundary conditions. These results motivate future studies of dissipation length scale based design principles on more complex disordered architectures and provide an efficient computational framework for exploring such structures at scale.

cond-mat.soft↗

arXiv2026

An Octahedral Fibrous Constitutive Model for Heart Valve Mechanics and Function

Fibrous soft tissues derive their nonlinear mechanical response from networks of extracellular matrix fibers, whose organization gives rise to strain stiffening, the reverse Poynting effect, and anisotropic mechanical behavior. Motivated by these coupled features, we develop an anisotropic hyperelastic model for fibrous biological tissues that accounts for the contribution of the fiber network under both tensile and compressive deformation. We calibrate the model to experimental data for mitral valve leaflets using an inverse finite element approach that is coupled to automatic differentiation to facilitate efficient parameter calibration. Using the calibrated model, we investigate how anisotropy and fiber reorientation affect valve deformation under physiological loading. The results show that greater leaflet compliance in the radial direction yields proper valve closure, whereas localized fiber reorientation leads to stress concentrations that may promote progressive functional degradation. Fiber reorientation that makes the circumferential direction more compliant than the radial direction compromises valve closure and leads to mitral regurgitation. Chordal softening further amplifies the severity of this regurgitant response. These findings suggest that alterations in fiber architecture, especially when accompanied by chordal degradation, can contribute to the onset and progression of mitral valve incompetence.

q-bio.TO↗

arXiv2026

On the Statistical Mechanics of Active Membranes: Some Selected Results

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy consuming proteins. In this work, we employ a nonequilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation based assays of active membrane behavior.

cond-mat.soft↗

arXiv2025

Instabilities and Phase Transformations in Architected Metamaterials: a Gradient-Enhanced Continuum Approach

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transformations. Their macroscopic response--including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior--remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. We propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic--staggered strategy. Simulations capture densification fronts, forward and reverse transformations, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected materials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

physics.comp-ph↗

arXiv2025

Fracture of disordered and stochastic lattice materials

The failure of mechanical metamaterials is a function of the interplay between the properties of the base material and the microstructural geometry. Stochastic failure properties of the base material and disordered microstructural geometries can contribute to variations in the global failure mechanics that are not captured in traditional analyses of ordered, deterministic architected materials. We present a probabilistic framework that couples stochastic material failure and geometric disorder to predict failure in lattice mechanical metamaterials. These predictions are verified through finite element analysis, which confirm that disorder and stochasticity affect both the mean and variance of the damage initiation load in a lattice, with average failure loads being generally reduced and variance increasing with higher levels of disorder and stochasticity. The fracto-cohesive length and representative volume element size are also predicted and constrain the minimum defect and lattice sizes, respectively, for failure to be considered a fracture process. The framework is extended to consider the fracture behavior of the lattice, the development of damage zones, and their impact on the steady-state fracture toughness.

cond-mat.mtrl-sci↗

arXiv2025

On a structure preserving closure of Langevin dynamics

Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free energy. To do so, we significantly extend the recent Stochastic Thermodynamics with Internal Variables (STIV) framework, a method for producing macroscopic thermodynamic models far-from-equilibrium from the underlying mesoscopic dynamics and an approximate probability density of states parameterized with so-called internal variables. Though originally explored for Gaussian probability distributions, we here allow for an arbitrary choice of the approximate probability density while retaining a gradient flow dynamics. This greatly extends its range of applicability and automatically ensures consistency with the second law of thermodynamics, without the need for secondary verification. We demonstrate numerical convergence, in the limit of increasing internal variables, to the true probability density of states for both a multi-modal relaxation problem, a protein diffusing on a strand of DNA, and for an externally driven particle in a periodic landscape. Finally, we provide a reformulation of STIV with the quasi-equilibrium approximations in terms of the averages of observables of the mesostate, and show that these, too, obey a gradient flow.

cond-mat.stat-mech↗

arXiv2024

Kinetically arrested clusters in active filament arrays

We use Brownian dynamics simulations and theory to study the over-damped spatiotemporal dynamics and pattern formation in a fluid-permeated array of equally spaced, active, elastic filaments that are pinned at one end and free at the other. The filaments are modeled as connected colloidal chains with activity incorporated via compressive follower forces acting along the filament backbone. The length of the chains is smaller than the thermal persistence length. For a range of filament separation and activity values, we find that the filament array eventually self-assembles into a series of regularly spaced, kinetically arrested, compact clusters. Filament activity, geometry, elasticity, and grafting density are each seen to crucially influence the size, shape, and spacing of emergent clusters. Furthermore, cluster shapes for different grafting densities can be rescaled into self-similar forms with activity-dependent scaling exponents. We derive theoretical expressions that relate the number of filaments in a cluster and the spacing between clusters, to filament activity, filament elasticity, and grafting density. Our results provide insight into the physical mechanisms involved in the initiation of clustering and suggest that steric contact forces and friction balance active forces and filament elasticity to stabilize the clusters. Our simulations suggest design principles to realize filament-based clusters and similar self-assembling biomimetic materials using active colloids or synthetic microtubule-motor systems.

cond-mat.soft↗

arXiv2024

A statistical mechanics derivation and implementation of non-conservative phase field models for front propagation in elastic media

Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical phenomena. However, despite its widespread success, phase field modeling remains largely driven by phenomenological justifications except in a handful of instances. In this work, we leverage a recently developed statistical mechanics framework for non-equilibrium phenomena, called Stochastic Thermodynamics with Internal Variables (STIV), to provide the first derivation of a phase field model for front propagation in a one dimensional elastic medium without appeal to phenomenology or fitting to experiments or simulation data. In the resulting model, the variables obey a gradient flow with respect to a non-equilibrium free energy, although notably, the dynamics of the strain and phase variables are coupled, and while the free energy functional is non-local in the phase field variable, it deviates from the traditional Landau-Ginzburg form. Moreover, in the systems analyzed here, the model accurately captures stress induced nucleation of transition fronts without the need to incorporate additional physics. We find that the STIV phase field model compares favorably to Langevin simulations of the microscopic system and we provide two numerical implementations enabling one to simulate arbitrary interatomic potentials.

cond-mat.stat-mech↗

arXiv2023

A statistical mechanics framework for constructing non-equilibrium thermodynamic models

Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of non-equilibrium systems. But despite tremendous efforts, a universal theory of non-equilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex non-equilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data, or on running concurrent simulations at the particle level. Instead, we provide a framework for deriving stand-alone macroscopic thermodynamics models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework's effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double stranded DNA, thus producing, to the authors' knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers.

cond-mat.stat-mech↗

arXiv2021

Statistical mechanics of a dielectric polymer chain in the force ensemble

Constitutive modeling of dielectric elastomers has been of long standing interest in mechanics. Over the last two decades rigorous constitutive models have been developed that couple the electrical response of these polymers with large deformations characteristic of soft solids. A drawback of these models is that unlike classic models of rubber elasticity they do not consider the coupled electromechanical response of single polymer chains which must be treated using statistical mechanics. The objective of this paper is to compute the stretch and polarization of single polymer chains subject to a fixed force and fixed electric field using statistical mechanics. We assume that the dipoles induced by the applied electric field at each link do not interact with each other and compute the partition function using standard techniques. We then calculate the stretch and polarization by taking appropriate derivatives of the partition function and obtain analytical results in various limits. We also perform Markov chain Monte Carlo simulations using the Metropolis and umbrella sampling methods, as well as develop a new sampling method which improves convergence by exploiting a symmetry inherent in dielectric polymer chains. The analytical expressions are shown to agree with the Monte Carlo results over a range of forces and electric fields. Our results complement recent work on the statistical mechanics of electro-responsive chains which obtains analytical expressions in a different ensemble.

cond-mat.soft↗

arXiv2021

On the dissipation at a shock wave in an elastic bar

This paper aims to quantitatively relate the energy dissipated at a shock wave in a nonlinearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. In contrast to a phase boundary, there is no kinetic relation associated with a shock wave. Three one-dimensional dynamic impact problems are studied: Problem 1 concerns a nonlinearly elastic bar, Problem 2 a discrete chain of particles, and Problem 3 a continuum with a strain gradient term in the constitutive relation. In the impact problem considered, the free boundary of each initially quiescent body is subjected to a sudden velocity that is then held constant for all subsequent time. There is energy dissipation at the shock in Problem 1 but Problems 2 and 3 are conservative. Problem 1 is solved analytically, Problem 2 numerically and an approximate solution to Problem 3 is constructed using modulation theory. The rate of increase of the oscillatory energy in Problems 2 and 3 are calculated and compared with the dissipation rate at the shock in Problem 1. The results indicate that the former is a good measure of the latter.

physics.class-ph↗

arXiv2021

Wave manipulation using a bistable chain with reversible impurities

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal testbeds for supporting nonlinear wave dynamical features including transition and (supersonic) solitary waves. We show that bistable chains can support the propagation of subsonic wavepackets which in turn can be trapped by a low-energy phase to induce energy localization. The spatial distribution of these energy foci strongly affects the propagation of linear waves, typically causing scattering, but, in special cases, leading to a reflectionless mode analogous to the Ramsauer-Townsend (RT) effect. Further, we show that the propagation of nonlinear waves can spontaneously generate or remove additional foci, which act as effective "impurities". This behavior serves as a novel mechanism for reversibly programming the dynamic response of bistable chains.

nlin.PS↗

arXiv2021

Bacterial activity hinders particle sedimentation

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and industrial processes. Here, we investigate sedimentation dynamics of passive particles in a fluid as a function of bacteria E. coli concentration. Results show that the presence of swimming bacteria significantly reduces the speed of the sedimentation front even in the dilute regime, in which the sedimentation speed is expected to be independent of particle concentration. Furthermore, bacteria increase the dispersion of the passive particles, which determines the width of the sedimentation front. For short times, particle sedimentation speed has a linear dependence on bacterial concentration. Mean square displacement data shows, however, that bacterial activity decays over long experimental (sedimentation) times. An advection-diffusion equation coupled to bacteria population dynamics seems to capture concentration profiles relatively well. A single parameter, the ratio of single particle speed to the bacteria flow speed can be used to predict front sedimentation speed.

physics.flu-dyn↗

arXiv2020

A continuum model for the growth of dendritic actin networks

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.

physics.bio-ph↗

arXiv2018

Elasticity as the basis of allostery in DNA

Allosteric interactions in DNA are crucial for various biological processes. These interactions are quantified by measuring the change in free energy as a function of the distance between the binding sites for two ligands. Here we show that trends in the interaction energy of ligands binding to DNA can be explained within an elastic birod model. The birod model accounts for the deformation of each strand as well as the change in stacking energy due to perturbations in position and orientation of the bases caused by the binding of ligands. The strain fields produced by the ligands decay with distance from the binding site. The interaction energy of two ligands decays exponentially with the distance between them and oscillates with the periodicity of the double helix in quantitative agreement with experimental measurements. The trend in the computed interaction energy is similar to that in the perturbation of groove width produced by the binding of a single ligand which is consistent with molecular simulations. Our analysis provides a new framework to understand allosteric interactions in DNA and can be extended to other rod-like macromolecules whose elasticity plays a role in biological functions.

physics.bio-ph↗

arXiv2018

Allosteric interactions in a birod model of DNA

Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory of DNA elasticity remains a challenge. Here we quantify allosteric interactions between two entities bound to DNA by using the theory of birods. We recognize that molecules bound to DNA cause local deformations that can be captured in a birod model which consists of two elastic strands interacting via an elastic web representing the base-pairs. We show that the displacement field caused by bound entities decays exponentially with distance from the binding site. We compute the interaction energy between two proteins on DNA as a function of distance between them and find that it decays exponentially while oscillating with the periodicity of the double-helix, in excellent agreement with experiments. The decay length of the interaction energy can be determined in terms of the mechanical properties of the strands and the webbing in our birod model, and it varies with the GC content of the DNA. Our model provides a framework for viewing allosteric interactions in DNA within the ambit of configurational forces of continuum elasticity.

cond-mat.soft↗

arXiv2017

Sedimentation and diffusion of passive particles in suspensions of swimming Escherichia coli

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and artificial environments. Here, we experimentally investigate sedimentation of passive particles in water containing various concentrations of the bacterium E. coli. Results show that the presence of living bacteria reduces the velocity of the sedimentation front even in the dilute regime, where the sedimentation velocity is expected to be independent of particle concentration. Bacteria increase the effective diffusion coefficient of the passive particles, which determines the width of the sedimentation front. For higher bacteria concentration, we find the development of two sedimentation fronts due to bacterial death. A model in which an advection-diffusion equation describing the settling of particles under gravity is coupled to the population dynamics of the bacteria seems to capture the experimental trends relatively well.

physics.flu-dyn↗