arXiv subjects

Avanish Kumar

Publications and source records attributed to Avanish Kumar.

13 recordsLinked to original sources

arXiv2026

Shear Banding in Amorphous Solids as a Nonlinear Screened Soft Mode Instability

Shear banding is a well-known and widespread instability in strained solids: under external strain, the deformation localizes along a line in two dimensions or a plane in three dimensions. Developing a proper theoretical description of this phenomenon is key to understanding mechanical failure in solid materials. Very recently, a nonlinear theory extending classical elasticity to include plastic deformations as topological charges was proposed, offering detailed predictions on the nature and consequences of the shear-banding instability. The theory derives a Hessian operator whose lowest eigenvalue vanishes at the onset of instability, and the corresponding critical eigenmode describes the displacement field across the shear band. The resulting soft mode possesses the selected localization scale and subsequently saturates into a finite-width shear band. The aim of this Letter is to examine this theory numerically, establishing the role of topological screening and nonlinear instability as the mechanisms governing shear banding during athermal quasistatic deformation. We show that the displacement profile around the shear band is directly determined by the screening parameter and the nonlinear coefficient, thereby quantitatively verifying the theoretical predictions. Our results demonstrate that shear banding differs fundamentally from fracture: it arises from a nonlinear instability of an elastic field screened by plastic deformations. This establishes topological screening as the essential mechanism governing shear banding in amorphous solids.

cond-mat.soft↗

arXiv2026

Analytic Nonlinear Theory of Shear Banding in Amorphous Solids

The aim of this paper is to offer an analytic theory of the shear banding instability in amorphous solids that are subjected to athermal quasi-static shear. To this aim we derive nonlinear equations for the displacement field, including the consequences of plastic deformation on the mechanical response of amorphous solids. The plastic events collectively induce distributed dipoles that are responsible for screening effects and the creation of typical length-scales that are absent in classical elasticity theory. The nonlinear theory exposes an instability that results in the creation of shear bands. By solving the weakly nonlinear amplitude equation we present analytic expressions for the displacement fields that is associated with shear bands, explaining the role of the elastic moduli that determine the width of a shear band from ductile to brittle characteristics. We derive an energy functional whose Hessian possesses an eigenvalue that goes to zero at the shear-banding instability, providing a prediction for the critical value of the accumulated stress that results in an instability.

cond-mat.stat-mech↗

arXiv2024

Odd Dipole Screening in Radial Inflation

The inflation of an inner radial (or spherical) cavity in an amorphous solids confined in a disk (or a sphere), served as a fruitful case model for studying the effects of plastic deformations on the mechanical response. It was shown that when the field associated with Eshelby quadrupolar charges is non-uniform, the displacement field is riddled with dipole charges that screen elasticity, reminiscent of Debye monopoles screening in electrostatics. In this paper we look deeper into the screening phenomenon, taking into account the consequences of irreversibility that are associated with the breaking of Chiral symmetry. We consider the equations for the displacement field with the presence of ``Odd Dipole Screening", solve them analytically and compare with numerical simulations. Suggestions how to test the theory in experiments are provided.

cond-mat.dis-nn↗

arXiv2023

Elasticity, plasticity and screening in amorphous solids: a short review

The aim of this short review is to summarize the developing theory aimed at describing the effect of plastic events in amorphous solids on its emergent mechanics. Experiments and simulations present anomalous mechanical response of amorphous solids where quadrupolar plastic events collectively induce distributed dipoles that are analogous to dislocations in crystalline solids. The novel theory is described, and a number of pertinent examples are provided, including the comparison of theoretical prediction to simulations or experiments.

cond-mat.stat-mech↗

arXiv2023

The Eshelby problem in amorphous solids

The ``Eshelby problem" refers to the response of a 2-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called ``Eshelby Kernel" which was derived for purely elastic (infinite) material, but has been employed extensively to model the redistribution of stress after plastic events in amorphous solids with finite boundaries. Here we discuss and solve the Eshelby problem directly for amorphous solids, taking into account possible screening effects and realistic boundary conditions. We find major modifications compared to the classical Eshelby solution. These modification are needed for modeling correctly the spatial responses to plastic events in amorphous solids.

cond-mat.mtrl-sci↗

arXiv2023

Disorder Induced Nonlinear Mode Coupling and Symmetry Breaking in Amorphous Solids

Applying very small purely radial strains on amorphous solids in radial geometry one observes elastic responses that break the radial symmetry. Without any plasticity involved, the responses indicate nonlinear mode coupling contributions even for minute strains. We show that these symmetry-breaking responses are due to disorder, typical to amorphous configurations. The symmetry breaking responses are quantitatively explained using the classical Michell solutions which are excited by mode coupling.

cond-mat.soft↗

arXiv2022

Anomalous Elasticity in Classical Glass-formers

Amorphous solids under mechanical strains are prone to plastic responses. Recent work showed that in amorphous granular system these plastic events, that are typically quadrupolar in nature, can screen the elastic response. When the density of the quadrupoles is high, the gradients of the quadrupole field act as emergent dipole sources, leading to qualitative changes in the mechanical response, as seen for example in the displacement field. In this paper we examine the effect of screening in classical glass formers. These are made of point particles that interact via binary forces. Both inverse power law forces and Lennard-Jones interactions are examined, and it is shown that in both cases the elastic response can be strongly screened, in agreement with the novel theory. The degree of deviation from classical elasticity theory is parameterized by a proposed new measure that is shown to have a functional dependence of on the amount of energy lost to plastic responses.

cond-mat.mtrl-sci↗

arXiv2021

Density of Quasi-localized Modes in Glasses: where are the Two-Level Systems?

The existence of a constant density of two-level systems (TLS) was proposed as the basis of some intriguing universal aspects of glasses at ultra-low temperatures. Here we ask whether their existence is necessary for explaining the universal density of states quasi-localized modes (QLM) in glasses at ultra-low temperatures. A careful examination of the QLM that exist in a generic atomistic model of a glass former reveals at least two types of them, each exhibiting a different density of states, one depending on the frequency as $\omega^3$ and the other as $\omega^4$. The properties of the glassy energy landscape that is responsible for the two types of modes is examined here, explaining the analytic feature responsible for the creations of (at least) two families of QLM's. Although adjacent wells certainly exist in the complex energy landscape of glasses, doubt is cast on the relevance of TLS for the universal density of QLM's.

cond-mat.stat-mech↗

arXiv2019

Particles confined in arbitrary potentials with a class of finite-ranged interactions

In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a class of pairwise interaction potentials $V_\text{int}(r)$ (where $r$ is distance between a pair of particles) such that $ V_\text{int} \sim |r|^{-k}$ when $r \to 0$. We consider the case where every particle is interacting with $d$ (finite range parameter) number of particles to its left and right. Due to the intricate interplay between external confinement, pairwise repulsion and entropy, the density exhibits markedly distinct behavior in three regimes $k>0$, $k \to 0$ and $k<0$. From this field theory, we compute analytically the average density profile for large $N$ in these regimes. We show that the contribution from interaction dominates the collective behaviour for $k > 0$ and the entropy contribution dominates for $k<0$, and both contributes equivalently in the $k\to 0$ limit (finite range log-gas). Given the fact that these family of systems are of broad relevance, our analytical findings are of paramount importance. These results are in excellent agreement with brute-force Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2019

Quantum Chaotic Systems and Random Matrix Theory

This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical perspective. Subsequently there have been novel applications to diverse areas, e.g., atomic and molecular physics, mesoscopic and nanoscopic systems, microwave cavities, econophysics, biological sciences, communication theory. This article is designed to be accessible at the graduate and post-doctoral level.

cond-mat.stat-mech↗

arXiv2019

Finite-Range Coulomb Gas Models I: Some Analytical Results

Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas (FRCG) models as a generalization of the Dyson models with a finite range of eigenvalue interactions. As the range of interaction increases, there is a transition from Poisson statistics to classical random matrix statistics. These models yield new universality classes of random matrix ensembles. They also provide a theoretical framework to study banded random matrices, and dynamical systems whose matrix representation can be written in the form of banded matrices.

cond-mat.stat-mech↗

arXiv2019

Finite-Range Coulomb Gas Models II: Applications to Quantum Kicked Rotors and Banded Random Matrices

In paper I of this two-stage exposition, we introduced finite-range Coulomb gas (FRCG) models, and developed an integral-equation framework for their study. We obtained exact analytical results for $d = 0,1,2 $, where d denotes the range of eigenvalue interaction. We found that the integral-equation framework was not analytically tractable for higher values of $d$. In this paper II, we develop a Monte Carlo (MC) technique to study FRCG models. Our MC simulations provide a solution of FRCG models for arbitrary $d$. We show that, as d increases, there is a transition from Poisson to Wigner-Dyson classical random matrix statistics. Thus FRCG models provide a novel route for transition from Poisson to Wigner-Dyson statistics. The analytical formulation obtained in paper I, and MC techniques developed in this paper II, are used to study banded random matrices (BRM) and quantum kicked rotors (QKR). We demonstrate that, for a BRM of bandwidth $b$ and a QKR of chaos parameter $\alpha$, the appropriate FRCG model has range $d=b^2/N=\alpha^2/N$, for $N \rightarrow \infty $. Here, N is the dimensionality of the matrix in BRM, and the evolution operator matrix in QKR.

cond-mat.stat-mech↗

arXiv2017

Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte-Carlo simulations. These models yield new universality classes, and provide a theoretical framework for study of banded random matrices (BRM) and quantum kicked rotors (QKR). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter {\alpha}, the appropriate FRCG model has the effective range d = (b^2)/N = ({\alpha}^2)/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

cond-mat.stat-mech↗