arXiv subjects

Surajit Sengupta

Publications and source records attributed to Surajit Sengupta.

At least 19 recordsLinked to original sources

arXiv2025

Activated solids: Spontaneous deformations, non-affine fluctuations, softening, and failure

Internal activity can fundamentally reshape the mechanical behavior of solids, yet its role in softening and failure remains incompletely understood. In this study, we investigate spontaneous deformations in activated solids via non-affine fluctuations that quantify local rearrangements relative to global strain. Using scaling analysis and numerical simulations, we show that non-affinity in crystalline solids grows quadratically with active speed, increases linearly with persistence time before saturating, and scales inversely with the distance to the melting density. Spatial correlations reveal an activity-dependent growing correlation length, while relaxation dynamics are governed by the active persistence time. With increasing activity, the distributions of local non-affinity broaden, become more skewed, and develop heavy tails, eventually forming a secondary maximum that signals coexisting small and large non-affinities; this heterogeneity precedes defect formation and two-step melting from solid to hexatic and ultimately to fluid. Finally, we demonstrate that spatially patterned activation provides a simple route to locally induce non-affinity and mechanical softening. Our predictions are experimentally testable and suggest a pathway to tunable mechanics in adaptive metamaterials, with implications for mechanical regulation in biological systems.

cond-mat.soft↗

arXiv2021

Emergent power-law interactions in disordered crystals

We derive exact results for the fluctuations in energy produced by microscopic disorder in near-crystalline athermal systems. Our formalism captures the heterogeneity in the elastic energy of polydispersed soft disks in energy-minimized configurations. We use this to predict the distribution of interaction energy between two defects in a disordered background. We show this interaction energy displays an average power-law behaviour $\langle δE \rangle \sim Δ^{-4}$ at large distances $Δ$ between the defects. These interactions upon disorder average also display the sixfold symmetry of the underlying reference crystal. Additionally, we show that the fluctuations in the interaction energy encode the athermal correlations introduced by the disordered background. We verify our predictions with energy minimized configurations of polydispersed soft disks in two dimensions.

cond-mat.soft↗

arXiv2021

Pattern stabilisation in swarms of programmable active matter: a probe for turbulence at large length scales

We propose an algorithm for creating stable, ordered, swarms of active robotic agents arranged in any given pattern. The strategy involves suppressing a class of fluctuations known as "non-affine" displacements, viz. those involving non-linear deformations of a reference pattern, while all (or most) affine deformations are allowed. We show that this can be achieved using precisely calculated, fluctuating, thrust forces associated with a vanishing average power input. A surprising outcome of our study is that once the structure of the swarm is maintained at steady state, the statistics of the underlying flow field is determined solely from the statistics of the forces needed to stabilize the swarm.

cond-mat.soft↗

arXiv2020

Athermal fluctuations in disordered crystals

We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions.

cond-mat.soft↗

arXiv2020

Wrinkles, folds and ripplocations: unusual deformation structures of confined elastic sheets at non-zero temperatures

We study the deformation of a fluctuating crystalline sheet confined between two flat rigid walls as a simple model for layered solids where bonds among atoms {\it within} the same layer are much stronger than those {\it between} layers. When subjected to sufficiently high loads in an appropriate geometry, these solids deform and fail in unconventional ways. Recent experiments suggest that configurations named {\it ripplocations}, where a layer folds backwards over itself, are involved. These structures are distinct and separated by large free energy barriers from smooth {\it ripples} of the atomic layers that are always present at any non-zero temperature. We use Monte Carlo simulation in combination with an umbrella sampling technique to obtain conditions under which such structures form and study their specific experimental signatures.

cond-mat.soft↗

arXiv2019

A nucleation theory for yielding of nearly defect-free crystals: understanding rate dependent yield points

Experiments and simulations show that when an initially defect free rigid crystal is subjected to deformation at a constant rate, irreversible plastic flow commences at the so-called {\em yield point}. The yield point is a weak function of the deformation rate, which is usually expressed as a power law with an extremely small non-universal exponent. We re-analyze a representative set of published data on nanometer sized, mostly defect free, Cu, Ni and Au crystals in the light of a recently proposed theory of yielding based on nucleation of stable stress-free regions inside the metastable rigid solid. The single relation derived here, which is {\em not} a power law, explains data covering {\em fifteen} orders of magnitude in time scales.

cond-mat.mtrl-sci↗

arXiv2019

Exploring the link between crystal defects and non-affine displacement fluctuations

We generalize, and then use, a recently introduced formalism to study thermal fluctuations of atomic displacements in several two and three dimensional crystals. We study both close packed as well as open crystals with multi atom bases. Atomic displacement fluctuations in a solid, once coarse-grained over some neighborhood may be decomposed into two mutually orthogonal components. In any dimension $d$ there are always $d^2$ {\em affine} displacements representing local strains and rotations of the ideal reference configuration. In addition, there exists a number of {\em non-affine} localized displacement modes that cannot be represented as strains or rotations. The number of these modes depends on $d$ and the size of the coarse graining region. All thermodynamic averages and correlation functions concerning the affine and non-affine displacements may be computed within a harmonic theory. We show that for compact crystals, such as the square and triangular in $d=2$ and the simple, body-centered and face-centered cubic crystals in $d=3$, a single set of $d-$fold degenerate modes always dominate the non-affine sub-space and are separated from the rest by a large gap. These modes may be identified with specific precursor configurations that lead to lattice defects. Deformation mechanisms such as lattice slips and stacking faults in close packed crystals can also be understood within this framework. The qualitative features of these conclusions are expected to be independent of the details of the atomic interactions.

cond-mat.stat-mech↗

arXiv2019

Orientational correlations in fluids with quenched disorder

Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting non-monotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible.

cond-mat.soft↗

arXiv2018

Plastic deformation of a permanently bonded network: stress relaxation by pleats

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing `pleats'; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local {\em non-affine} displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain -- field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

cond-mat.soft↗

arXiv2018

Do thermodynamically stable rigid solids exist?

Customarily, crystalline solids are defined to be {\em rigid} since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the {\em metastable} state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then employed to obtain the equilibrium free energy as a function of this variable. Our results lead to a new view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable by switching on an external field, which penalises particle rearrangements. This produces a line of first-order phase transitions in the field - strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

cond-mat.mtrl-sci↗

arXiv2017

Translationally invariant colloidal crystal templates

We show that dynamic, feed-back controlled optical traps, whose positions depend on the instantaneous local configuration of particles in a pre-determined way, can stabilise colloidal particles in finite lattices of ${\it any}$ given symmetry. Unlike in a static template, the crystal so formed is translationally invariant and retains all possible zero energy modes. We demonstrate this ${\it in-silico}$ by stabilising the unstable two-dimensional ${\it square}$ lattice in a model soft solid with isotropic interactions.

cond-mat.soft↗

arXiv2017

Contrasting the dynamics of elastic and non-elastic deformations across an experimental colloidal Martensitic transition

We present a framework to segregate the roles of elastic and non-elastic deformations in the examination of real-space experiments of solid-solid Martensitic transitions. The Martensitic transformation of a body-centred-tetragonal(BCT) to a body-centred-orthorhombic(BCO) crystal structure has been studied in a model system of micron-scale ionic microgel colloids. Non-affine fluctuations, i.e., displacement fluctuations that do not arise from purely elastic(affine) deformations, are detected in particle configurations acquired from the experiment. Tracking these fluctuations serves as a highly sensitive tool in signaling the onset of the Martensitic transition and precisely locating particle rearrangements occurring at length scales of a few particle diameters. Particle rearrangements associated with non-affine displacement modes become increasingly favorable during the transformation process. The nature of the displacement fluctuation modes that govern the transformation are shown to be different from those predominant in an equilibrium crystal. We show that BCO crystallites formed through shear may, remarkably, co-exist with those resulting from local rearrangements within the same sample.

cond-mat.soft↗

arXiv2017

Statistics of non-affine defect precursors: tailoring defect densities in colloidal crystals using external fields

Coarse-graining atomic displacements in a solid produces both local affine strains and "non-affine" fluctuations. Here we study the equilibrium dynamics of these coarse grained quantities to obtain space-time dependent correlation functions. We show how a subset of these thermally excited, non-affine fluctuations act as precursors for the nucleation of lattice defects and suggest how defect probabilities may be altered by an {\it experimentally realisable} "external" field conjugate to the global non-affinity parameter. Our results are amenable to verification in experiments on colloidal crystals using commonly available holographic laser tweezer and video microscopy techniques, and may lead to simple ways of controlling the defect density of a colloidal solid.

cond-mat.soft↗

arXiv2016

Excess vibrational modes of a crystal in an external non-affine field

Thermal displacement fluctuations in a crystal may be classified as either "affine" or "non-affine". While the former couples to external stress with familiar consequences, the response of a crystal when {\em non-affine} displacements are enhanced using the thermodynamically conjugate field, is relatively less studied. We examine this using a simple model of a crystal in two dimensions for which analytical calculations are possible. Enhancing non-affine fluctuations destabilises the crystal. The population of small frequency phonon modes increases, with the phonon density of states shifting, as a whole, towards zero frequency. Even though the crystal is free of disorder, we observe growing length and time scales. Our results, which may have implications for the glass transition and structural phase transitions in solids, are compared to molecular dynamics simulations. Possibility of experimental verification of these results is also discussed.

cond-mat.soft↗

arXiv2016

Amorphization of a crystalline solid by plastic deformation

We demonstrate that plastic deformation in solids is associated with a dynamic transition that is reminiscent to the transition from a superconducting to a mixed phase in Type II superconductors. We report analytic calculations, extensive molecular dynamics and sequential umbrella sampling Monte Carlo simulations of a two dimensional triangular crystalline solid undergoing plastic deformation under strain. The solid consists of particles connected by harmonic springs. Non-affine displacement fluctuations of the solid are enhanced using an external field, causing a rich deformation behaviour. The external field leads to a mixed phase, where defect and stress-free crystallites are surrounded by a network of amorphous regions with large local internal stress --- a "stress Meissner" effect. The transition shows slow ageing dynamics caused by the presence of many competing, non-crystalline free-energy minima. Under uniform uniaxial strain, this amorphization transition gives rise to irreversible plastic deformation with the amorphous regions appearing as band-like structures. Our results may be checked by careful experiments on colloidal crystals using holographic optical tweezers.

cond-mat.soft↗

arXiv2016

Equilibrium and dynamic pleating of a crystalline bonded network

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness", i.e.~the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The {\em kinetics} of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a {\em metastable} phase with the stress now localised in a {\em disordered} arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps.

cond-mat.soft↗

arXiv2015

Excess Vibrational Density of States and the Brittle to Ductile Transition in Crystalline and Amorphous Solids

The conditions which determine whether a material behaves in a brittle or ductile fashion on mechanical loading are still elusive and comprise a topic of active research among materials physicists and engineers. In this study, we present results of {\em in silico} mechanical deformation experiments from two very different model solids in two and three dimensions. The first consists of particles interacting with isotropic potentials and the other has strongly direction dependent interactions. We show that in both cases, the excess vibrational density of states is the fundamental quantity which characterises the ductility of the material. Our results can be checked using careful experiments on colloidal solids.

cond-mat.soft↗

arXiv2015

Non-affine fluctuations and the Statistics of Defect Precursors in the Planar Honeycomb Lattice

Certain localised displacement fluctuations in the planar honeycomb lattice may be identified as precursors to topological defects. We show that these fluctuations are among the most pronounced {\em non-affine} distortions of an elemental coarse graining volume of the honeycomb structure at non zero temperatures. We obtain the statistics of these precursor modes in the canonical ensemble, evaluating exactly their single point and two-point spatio-temporal distributions, for a lattice with harmonic nearest neighbour and next near neighbour bonds. As the solid is destabilised by tuning interactions, the precursor fluctuations diverge and correlations become long-lived and long-ranged.

cond-mat.mtrl-sci↗