arXiv subjects

Roshan Maharana

Publications and source records attributed to Roshan Maharana.

7 recordsLinked to original sources

arXiv2026

Monte-Carlo study of Compositional Heterogeneity in Multicomponent Cluster Crystals

Soft (sub)micron-sized particles with bounded interactions can form cluster crystals, periodic structures in which multiple particles occupy the same lattice site. While the thermodynamics of monodisperse cluster crystals is well understood, less is known about how compositional disorder affects their stability. Using Monte Carlo simulations and density functional theory we show that binary cluster crystals undergo a density driven transition from a homogeneous mixed state to a heterogeneous ``alloy" like solid in which lattice sites spontaneously differentiate into populations with distinct compositions and occupancies while preserving the underlying crystal symmetry. The transition is accompanied by a sharp increase in the equilibrium lattice site density and by increased compositional fluctuations, but we see no evidence for macroscopic phase separation. We demonstrate that this transition is governed by competition between clustering and demixing instabilities and derive a simple scaling law for the demixing density as a function of temperature, composition, and particle size mismatch, in quantitative agreement with simulation.

cond-mat.soft↗

arXiv2024

Instabilities govern the low-frequency vibrational spectrum of amorphous solids

Amorphous solids exhibit an excess of low-frequency vibrational modes beyond the Debye prediction, contributing to their anomalous mechanical and thermal properties. Although a $ω^4$ power-law scaling is often proposed for the distribution of these modes, the precise exponent remains a subject of debate. In this study, we demonstrate that boundary-condition-induced instabilities play a key role in this variability. We identify two distinct types of elastic branches that differ in the nature of their energy landscape: Fictitious branches, where shear minima cannot be reached through elastic deformation alone and require plastic instabilities, and True branches, where elastic deformation can access these minima. Configurations on Fictitious branches show a vibrational density of states (VDoS) scaling as $D(ω) \sim ω^3$, while those on True elastic branches under simple and pure shear deformations exhibit a scaling of $D(ω) \sim ω^{5.5}$. Ensemble averaging over both types of branches results in a VDoS scaling of $D(ω) \sim ω^4$. Additionally, solids relaxed to their shear minima, with no residual shear stress, display a steeper scaling of $D(ω) \sim ω^{6.5}$ in both two and three dimensions. We propose two limiting behaviors for amorphous solids: if the system size is increased without addressing instabilities, the low-frequency VDoS scales with an exponent close to $3$. Conversely, by removing residual shear stress before considering large system sizes, the VDoS scales as $D(ω) \sim ω^{6.5}$.

cond-mat.soft↗

arXiv2024

Efficient Simulation of Deformable Particles

We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed particle based on the geometrical as well as physical properties of the particles, such as their size and elasticity. The model also accounts for the conservation of energy associated with the particle shape during interaction with other particles as well as with rigid walls. To verify the accuracy of the shape of the deformed particles, we start with a single deformable particle in an overcompressed box which we compare with the numerically simulated deformable polygon (DP) model. Then we extend our method to a jammed packing of deformable particles which we also verify through the DP model. We also provide a protocol to calculate the total force acting on such deformable particles solely based on their deformation and to obtain both athermal jammed packings as well as packings in thermal equilibrium.

cond-mat.soft↗

arXiv2024

Universal stress correlations in crystalline and amorphous packings

We present a universal characterization of stress correlations in athermal systems, across crystalline to amorphous packings. Via numerical analysis of static configurations of particles interacting through harmonic as well as Lennard-Jones potentials, for a variety of preparation protocols and ranges of microscopic disorder, we show that the properties of the stress correlations at large lengthscales are surprisingly universal across all situations, independent of structural correlations, or the correlations in orientational order. In the near-crystalline limit, we present exact results for the stress correlations for both models, which work surprisingly well at large lengthscales, even in the amorphous phase. Finally, we study the differences in stress fluctuations across the amorphization transition, where stress correlations reveal the loss of periodicity in the structure at short lengthscales with increasing disorder.

cond-mat.soft↗

arXiv2023

Stress correlations in near-crystalline packings

We derive exact results for stress correlations in near-crystalline systems in two and three dimensions. We study energy minimized configurations of particles interacting through Harmonic as well as Lennard-Jones potentials, for varying degrees of microscopic disorder and quenched forces on grains. Our findings demonstrate that the macroscopic elastic properties of such near-crystalline packings remain unchanged within a certain disorder threshold, yet they can be influenced by various factors, including packing density, pressure, and the strength of inter-particle interactions. We show that the stress correlations in such systems display anisotropic behavior at large lengthscales and are significantly influenced by the pre-stress of the system. The anisotropic nature of these correlations remains unaffected as we increase the strength of the disorder. Additionally, we derive the large lengthscale behavior for the change in the local stress components that shows a $1/r^d$ radial decay for the case of particle size disorder and a $1/r^{d-1}$ behavior for quenched forces introduced into a crystalline network. Finally, we verify our theoretical results numerically using energy-minimised static particle configurations.

cond-mat.soft↗

arXiv2022

First contact breaking distributions in strained disordered crystals

We derive exact probability distributions for the strain ($ε$) at which the first stress drop event occurs in uniformly strained disordered crystals, with quenched disorder introduced through polydispersity in particle sizes. We characterize these first stress drop events numerically as well as theoretically, and identify them with the first contact breaking event in the system. Our theoretical results are corroborated with numerical simulations of quasistatic volumetric strain applied to disordered near-crystalline configurations of athermal soft particles. We develop a general technique to determine the $distribution$ of strains at which the first stress drop events occur, through an exact mapping between the cumulative distribution of first contact breaking events and the volume of a convex polytope whose dimension is determined by the number of defects $N_d$ in the system. An exact numerical computation of this polytope volume for systems with small numbers of defects displays a remarkable match with the distribution of strains generated through direct numerical simulations. Finally, we derive the distribution of strains at which the first stress drop occurs, assuming that individual contact breaking events are uncorrelated, which accurately reproduces distributions obtained from direct numerical simulations.

cond-mat.soft↗

arXiv2022

Athermal fluctuations in three dimensional disordered crystals

We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyze the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed perturbation expansion about the crystalline ordered state to three dimensional systems. This allows us to exactly predict changes in positions and forces as a response to the changes in particle radii. We show that fluctuations in forces orthogonal to the lattice directions are highly constrained as compared to the fluctuations along lattice directions. Additionally, we analyze the correlations in the displacement fields produced by the microscopic disorder, which we show displays long ranged behaviour.

cond-mat.soft↗