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Madan Rao

Publications and source records attributed to Madan Rao.

At least 73 records · Page 4Linked to original sources

Non affine deformations and shape recovery in solids undergoing martensitic transformations

We study, using molecular dynamics simulations, the kinetics of shape recovery in a model solid undergoing transformations from square to a general rhombic lattice, the triangular lattice being included as a special case. We determine the necessary and sufficient conditions for such shape recovery in terms of the nature and dynamics of transient and localized {\em non-affine zones} which inevitably accompany the transformation.

cond-mat.mtrl-sci↗

Elastoplastic model for the dynamics of solid-solid transformations : role of non-affine deformation in microstructure selection

We study the nucleation dynamics of a model solid state transformation and the criterion for microstructure selection using a molecular dynamics (MD) simulation. Our simulations show a range of microstructures depending on the depth of quench. We closely follow the dynamics of the solid and find that transient {\em non-affine zones} (NAZ) are created at and evolve with the rapidly moving transformation front. The dynamics of these plastic regions determines the selection of microstructure. We formulate an {\it elastoplastic model} which couples the elastic strain to the non-affine deformation, and recover all the qualitative features of the MD simulation. Using this model, we construct a dynamical phase diagram for microstructure selection, in addition to making definite testable predictions.

cond-mat.mtrl-sci↗

Active elastic dimers: self-propulsion and current reversal on a featureless track

We present a Brownian inchworm model of a self-propelled elastic dimer in the absence of an external potential. Nonequilibrium noise together with a stretch-dependent damping form the propulsion mechanism. Our model connects three key nonequilibrium features -- position-velocity correlations, a nonzero mean internal force, and a drift velocity. Our analytical results, including striking current reversals, compare very well with numerical simulations. The model unifies the propulsion mechanisms of DNA helicases, polar rods on a vibrated surface, crawling keratocytes and Myosin VI. We suggest experimental realizations and tests of the model.

cond-mat.stat-mech↗

Stress relaxation in a perfect nanocrystal by coherent ejection of lattice layers

We show that a small crystal trapped within a potential well and in contact with its own fluid, responds to large compressive stresses by a novel mechanism -- the transfer of complete lattice layers across the solid-fluid interface. Further, when the solid is impacted by a momentum impulse set up in the fluid, a coherently ejected lattice layer carries away a definite quantity of energy and momentum, resulting in a sharp peak in the calculated phonon absorption spectrum. Apart from its relevance to studies of stability and failure of small sized solids, such coherent nanospallation may be used to make atomic wires or monolayer films.

cond-mat.soft↗

Chiral tilt texture domains in two dimensions

We study the shape and texture of finite domains comprising chiral/achiral molecules carrying a tilt field embedded in a 2-dimensional surface. Using a combination of simulations and {\it exact} variational calculations, we determine the equilibrium (mean field) phase diagram in the achiral and chiral cases. We find a variety of novel shapes and textures including a {\it spontaneously broken chiral texture} when the molecules are achiral. We show that chiral tilt-domains nucleating in a region of two-phase coexistence, {\it repel} each other, thereby preventing coalescence and further growth. Our work has implications for tilt texture domains in phospholipid monolayers and giant unilamellar vesicles (GUVs), nucleating domains of Sm-C$^*$ in Sm-A films, and chiral emulsions in Sm-A films.

cond-mat.soft↗

Shear flow induced isotropic to nematic transition in a suspension of active filaments

We study the effects of externally applied shear flow on a model of suspensions of motors and filaments, via the equations of active hydrodynamics [PRL {\bf 89} (2002) 058101; {\bf 92} (2004) 118101]. In the absence of shear, the orientationally ordered phase of {\it both} polar and apolar active particles is always unstable at zero-wavenumber. An imposed steady shear large enough to overcome the active stresses stabilises both apolar and moving polar phases. Our work is relevant to {\it in vitro} studies of active filaments, the reorientation of endothelial cells subject to shear flow and shear-induced motility of attached cells.

cond-mat.soft↗

Fluctuation induced chiral symmetry breaking in autocatalytic reaction-diffusion systems

We show how spatiotemporal fluctuations can induce spontaneous symmetry breaking in systems which are perfectly symmetric in the absence of fluctuations. We illustrate this in the context of the autocatalytic production of chiral enantiomers from achiral reactants in reaction-diffusion systems. The mean field steady state is chiral symmetric; spatiotemporal fluctuations induce a novel (molecular) chiral ordering and sharp phase transitions including reentrance. We discuss its implications in the context of the emergence of molecular homochirality.

cond-mat.soft↗

Nonequilibrium steady states of the isotropic classical magnet

We drive a d-dimensional Heisenberg magnet using a spatially anisotropic current of mobile particles or heat. The continuum Langevin equation is analyzed using a dynamical renormalization group, stability analysis and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be `controlled' in a robust manner to target spatially periodic steady states with helical order. We discuss several physical realizations of this model and make definite predictions which could be tested in experimental or model lattice systems.

cond-mat.soft↗

Rheology of Active-Particle Suspensions

We study the interplay of activity, order and flow through a set of coarse-grained equations governing the hydrodynamic velocity, concentration and stress fields in a suspension of active, energy-dissipating particles. We make several predictions for the rheology of such systems, which can be tested on bacterial suspensions, cell extracts with motors and filaments, or artificial machines in a fluid. The phenomena of cytoplasmic streaming, elastotaxis and active mechanosensing find natural explanations within our model.

cond-mat.soft↗

Driven Heisenberg Magnets: Nonequilibrium Criticality, Spatiotemporal Chaos and Control

We drive a $d$-dimensional Heisenberg magnet using an anisotropic current. The continuum Langevin equation is analysed using a dynamical renormalization group and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be `controlled' in a robust manner to target spatially periodic steady states with helical order.

cond-mat.stat-mech↗

Two Modes of Solid State Nucleation - Ferrites, Martensites and Isothermal Transformation Curves

When a crystalline solid such as iron is cooled across a structural transition, its final microstructure depends sensitively on the cooling rate. For instance, an adiabatic cooling across the transition results in an equilibrium `ferrite', while a rapid cooling gives rise to a metastable twinned `martensite'. There exists no theoretical framework to understand the dynamics and conditions under which both these microstructures obtain. Existing theories of martensite dynamics describe this transformation in terms of elastic strain, without any explanation for the occurence of the ferrite. Here we provide evidence for the crucial role played by non-elastic variables, {\it viz.}, dynamically generated interfacial defects. A molecular dynamics (MD) simulation of a model 2-dimensional (2d) solid-state transformation reveals two distinct modes of nucleation depending on the temperature of quench. At high temperatures, defects generated at the nucleation front relax quickly giving rise to an isotropically growing `ferrite'. At low temperatures, the defects relax extremely slowly, forcing a coordinated motion of atoms along specific directions. This results in a twinned critical nucleus which grows rapidly at speeds comparable to that of sound. Based on our MD results, we propose a solid-state nucleation theory involving the elastic strain and non-elastic defects, which successfully describes the transformation to both a ferrite and a martensite. Our work provides useful insights on how to formulate a general dynamics of solid state transformations.

cond-mat.mtrl-sci↗

A model solid-state structural transformation: Tetragonal to Orthorhombic

We study equilibrium properties of a system of particles in two dimensions, interacting with pair and three body potentials, which undergoes a structural transition from a square to a rhombic lattice and thus constitutes a simple model for a generic tetragonal to orthorhombic transition. We aim at an intermediate level of description lying in-between that of coarse grained elastic strain hamiltonians and microscopic ab-initio approaches. Macroscopic thermodynamic properties and phase diagram at zero and finite temperatures as a function of the density and the relative strengths of the pair and three body energies are obtained using lattice sums, an approximate `cell-model' theory and molecular dynamics simulations in the NVT ensemble. We propose that this model solid can be used as a test bed for studies of statics and dynamics of structural transitions.

cond-mat.mtrl-sci↗

Tilt Texture Domains on a Membrane and Chirality induced Budding

We study the equilibrium conformations of a lipid domain on a planar fluid membrane where the domain is decorated by a vector field representing the tilt of the stiff fatty acid chains of the lipid molecules, while the surrounding membrane is fluid and structureless. The inclusion of chirality in the bulk of the domain induces a novel budding of the membrane, which preempts the budding induced by a decrease in interfacial tension.

cond-mat.soft↗

Active Fusion and Fission Processes on a Fluid Membrane

We investigate the steady states and dynamical instabilities resulting from ``particles'' depositing on (fusion) and pinching off (fission) a fluid membrane. These particles could be either small lipid vesicles or isolated proteins. In the stable case, such fusion/fission events suppress long wavelength fluctuations of the membrane. In the unstable case, the membrane shoots out long tubular structures reminiscent of endosomal compartments or folded structures as in internal membranes like the endoplasmic reticulum or Golgi. We argue that these fusion/fission events should be strongly affected by tension.

cond-mat.soft↗

Ordering Dynamics of Heisenberg Spins with Torque: Crossover, Spinwaves and Defects

We study the effect of a torque induced by the local molecular field on the phase ordering dynamics of the Heisenberg model when the total magnetization is conserved. The torque drives the zero-temperature ordering dynamics to a new fixed point, characterized by exponents $z=2$ and $λ\approx 5$. This `torque-driven' fixed point is approached at times such that $g^2 t\gg 1$, where $g$ is the strength of the torque. All physical quantities, like the domain size $L(t)$ and the equal and unequal time correlation functions obey a crossover scaling form over the entire range of $g$. An attempt to understand this crossover behavior from the approximate Gaussian Closure Scheme fails completely, implying that the dynamics at late times cannot be understood from the dynamics of defects alone. We provide convincing arguments that the spin configurations can be decomposed in terms of defects and spin-waves which interact with each other even at late times. In the absence of the torque term, the spin waves decay faster, but even so we find that the Gaussian closure scheme is inconsistent. In the latter case the inconsistency may be remedied by including corrections to a simple gaussian distribution. For completeness we include a discussion of the ordering dynamics at $T_c$, where the torque is shown to be relevant, with exponents $z=4-ε/2$ and $λ= d$ (where $ε= 6-d$). We show to all orders in perturbation theory that $λ=d$ as a consequence of the conservation law.

cond-mat.stat-mech↗

Elastic constants from microscopic strain fluctuations

Fluctuations of the instantaneous local Lagrangian strain $ε_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $<ε_{ij}ε_{kl}>$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of the ``soft'' and the hard disk triangular solids in two dimensions from molecular dynamics and Monte Carlo simulations. We compare our results with those from earlier simulations and density functional theory.

cond-mat↗

Arrested States of Solids

Solids produced as a result of a fast quench across a freezing or a structural transition get stuck in long-lived metastable configurations of distinct morphology, sensitively dependent on the processing history. {\it Martensites} are particularly well studied examples of nonequilibrium solid-solid transformations. Since there are some excellent reviews on the subject, we shall, in this brief article, mainly present a summary of our work on the nonequilibrium statistical mechanics of Martensites.

cond-mat.stat-mech↗

Dynamics of Ordering of Isotropic Magnets

We study the dynamics of ordering of the nonconserved and conserved Heisenberg magnet. The dynamics consists of two parts - an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches both to T=0 and T=T_c, we show that the torque is irrelevant when the dynamics is nonconserved but relevant when the dynamics is conserved and is governed by a new nontrivial fixed point.

cond-mat.stat-mech↗