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Mustansir Barma

Publications and source records attributed to Mustansir Barma.

At least 37 records · Page 2Linked to original sources
arXiv2022

Solution of the random field $XY$ magnet on a fully connected graph

We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude $h$. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the disorder-averaged ordered state reflects the symmetry of the underlying distribution. The phase boundary has a multicritical point which separates a locus of continuous transitions (for small values of $h$) from a locus of first order transitions (for large $h$). The free energy is a function of a single variable in case (a) and a function of two variables in case (b), leading to different characters of the multicritical points in the two cases. We find that the locus of continuous transitions is given by the same equation for a family of quadriperiodic distributions, which includes the distributions (a) and (b). However, the location of the multicritical point and the nature of ordered state depend on the form of the distribution. The disorder-averaged ground state energy is found exactly, and the specific heat is shown to approach a constant as temperature approaches zero.

cond-mat.stat-mech↗
arXiv2020

Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations

We study the early time and coarsening dynamics in the Light-Heavy model, a system consisting of two species of particles ($light$ and $heavy$) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts are coupled through local update rules, and are known to lead to different ordered and disordered steady state phases depending on the microscopic rates. We introduce a generalized balance mechanism in non-equilibrium systems, namely $bunchwise~balance$, in which incoming and outgoing transition currents are balanced between groups of configurations. This allows us to exactly determine the steady state in a subspace of the phase diagram of this model. We introduce the concept of $irreducible~sequences$ of interfaces and bends in this model. These sequences are non-local, and we show that they provide a coarsening length scale in the ordered phases at late times. Finally, we propose a $local$ correlation function ($\mathcal{S}$) that has a direct relation to the number of irreducible sequences, and is able to distinguish between several phases of this system through its coarsening properties. Starting from a totally disordered initial configuration, $\mathcal{S}$ displays an initial linear rise and a broad maximum. As the system evolves towards the ordered steady states, $\mathcal{S}$ further exhibits power law decays at late times that encode coarsening properties of the approach to the ordered phases. Focusing on early time dynamics, we posit coupled mean-field evolution equations governing the particles and tilts, which at short times are well approximated by a set of linearized equations, which we solve analytically. Beyond a timescale set by a lattice cutoff and preceding the onset of coarsening, our linearized theory predicts the existence of an intermediate power-law stretch, which we also find in simulations of the ordered regime of the system.

cond-mat.stat-mech↗
arXiv2020

Size-Stretched Exponential Relaxation in a Model with Arrested States

We study the effect of rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $\exp(-2r/\sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in steady state, while the temporal auto-correlation function follows $\exp(-(t/τ_L)^{1/2})$, where $t$ is the time and $τ_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $\mathcal{L}(t_w) \sim t_w^{1/2}$ and $\mathcal{R}(t_w) \sim t_w^{1/4}$; the spatial correlation function decays as $\exp(-r/ \mathcal{R}(t_w))$. Interestingly, the stretched exponential form of the auto-correlation function of a single typical sample in steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power law decay at large times.

cond-mat.soft↗
arXiv2020

Fixation in Competing Populations: Diffusion and Strategies for Survival

How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though identical at the mean-field level, the three models exhibit drastically different behaviour leading to different optimal strategies for survival, with or without a selective advantage for one species. With conserved total particle number, dispersal has no effect on survival probability. With a fluctuating number, faster dispersal is advantageous if intra-species competition is present, while moving slower is the optimal strategy for the disadvantaged species if there is no intra-species competition: it is imperative to include fluctuations to properly formulate survival strategies.

q-bio.PE↗
arXiv2019

Interface growth driven by a single active particle

We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma membrane, responsible for membrane deformation and cell movement. In our model, the active particle overturns local valleys of the interface into hills, simulating growth, while itself sliding and seeking new valleys. In 1D, this overturn-slide-search dynamics of the active particle causes it to move superdiffusively in the transverse direction while pulling the immobile interface upwards. Using Monte Carlo simulations, we find an emerging tent-like mean profile developing with time, despite large fluctuations. The roughness of the interface follows scaling with the growth, dynamic and roughness exponents, derived using simple arguments as $β=2/3, z=3/2, α=1/2$ respectively, implying a breakdown of the usual scaling law $β= α/z$, owing to very local growth of the interface. The transverse displacement of the puller on the interface scales as $\sim t^{2/3}$ and the probability distribution of its displacement is bimodal, with an unusual linear cusp at the origin. Both the mean interface pattern and probability distribution display scaling. A puller on a static 2D interface also displays aspects of scaling in the mean profile and probability distribution. We also show that a pusher on a fluctuating interface moves subdiffusively leading to a separation of time scale in pusher motion and interface response.

cond-mat.stat-mech↗
arXiv2019

Dynamics of coupled modes for sliding particles on a fluctuating landscape

The recently developed formalism of nonlinear fluctuating hydrodynamics (NLFH) has been instrumental in unraveling many new dynamical universality classes in coupled driven systems with multiple conserved quantities. In principle, this formalism requires knowledge of the exact expression of locally conserved current in terms of local density of the conserved components. However, for most nonequilibrium systems an exact expression is not available and it is important to know what happens to the predictions of NLFH in these cases. We address this question for the first time here in a system with coupled time evolution of sliding particles on a fluctuating energy landscape. In the disordered phase this system shows short-ranged correlations, this system shows short-ranged correlations, the exact form of which is not known, and so the exact expression for current cannot be obtained. We use approximate expressions based on mean-field theory and corrections to it, to test the prediction of NLFH using numerical simulations. In this process we also discover important finite size effects and show how they affect the predictions of NLFH. We find that our system is rich enough to show a large variety of universality classes. From our analytics and simulations we have been able to find parameter values which lead to diffusive, Kardar-Parisi-Zhang (KPZ), $5/3 $ Lévy and modified KPZ universality classes. Interestingly, the scaling function in the modified KPZ case turns out to be close to the Prähofer-Spohn function which is known to describe usual KPZ scaling. Our analytics also predict the golden mean and the $3/2$ Lévy universality classes within our model but our simulations could not verify this, perhaps due to strong finite size effects.

cond-mat.stat-mech↗
arXiv2019

Fluctuation-dominated phase ordering at a mixed order transition

Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

cond-mat.stat-mech↗
arXiv2019

Clustering, intermittency and scaling for passive particles on fluctuating surfaces

We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for passive particles sliding on one-dimensional Edwards-Wilkinson or Kardar-Parisi-Zhang surfaces, with particles moving either along or against the growth direction in the latter case. Extensive numerical simulations are supplemented by analytical results for a sticky slider model in which particles coalesce when they meet. Results for single particle displacement versus time show to what extent particle dynamics is slaved to the surface, while scaling properties of the probability distribution of the separation of two particles have important implications for replica symmetry breaking for a pair of trajectories. For the many-particle system, clustering in steady state is studied via moments of particle number fluctuations in a single stretch, revealing different degrees of spatial multiscaling with different driving. Temporal intermittency in steady state is established by showing that the scaled flatness diverges. Finally we consider the approach to the steady state, and study both the flatness and the evolution of equal-time correlation functions, as in coarsening of phase ordering systems. Our studies give clear evidence for a simple scaling description of the approach to steady state, with a diverging length scale. An investigation of aging properties reveals that flatness is nonmonotonic in time with two distinct branches, and that a scaling description holds for each one.

cond-mat.soft↗
arXiv2018

Reversals in infinite-Prandtl-number Rayleigh-Bénard convection

Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-Bénard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long time scales, while the interval between successive crossings on short time scales shows a power law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and $1/f^2$ power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.

physics.flu-dyn↗
arXiv2018

Time evolution of intermittency in the passive slider problem

How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing length scale which governs scaling properties. A simple model of sticky sliders suggests scaling forms for the time-dependent flatness and hyperflatness, both measures of intermittency and these are confirmed numerically for passive sliders driven by a Kardar-Parisi-Zhang surface. Aging properties are studied via a two-time flatness. We predict and verify numerically that the time-dependent flatness is, remarkably, a non-monotonic function of time, with different scaling forms at short and long times. The scaling description remains valid when clustering is more diffuse as for passive sliders evolving through Edwards-Wilkinson driving or under antiadvection, although exponents and scaling functions differ substantially.

cond-mat.stat-mech↗
arXiv2017

Ordered phases in coupled nonequilibrium systems: static properties

We study a coupled driven system in which two species of particles are advected by a fluctuating potential energy landscape. While the particles follow the potential gradient, each species affects the local shape of the landscape in different ways. As a result of this two-way coupling between the landscape and the particles, the system shows interesting new phases, characterized by different sorts of long ranged order in the particles and in the landscape. In all these ordered phases the two particle species phase separate completely from each other, but the underlying landscape may either show complete ordering, with macroscopic regions with distinct average slopes, or may show coexistence of ordered and disordered regions, depending on the differential nature of effect produced by the particle species on the landscape. We discuss several aspects of static properties of these phases in this paper, and we discuss the dynamics of these phases in the sequel.

cond-mat.stat-mech↗
arXiv2017

Ordered phases in coupled nonequilibrium systems: dynamic properties

We study the dynamical properties of the ordered phases obtained in a coupled nonequilibrium system describing advection of two species of particles by a stochastically evolving landscape. The local dynamics of the landscape also gets affected by the particles. In a companion paper we have presented static properties of different phases that arise as the two-way coupling parameters are varied. In this paper we discuss the dynamics. We show that in the ordered phases macroscopic particle clusters move over an ergodic time-scale growing exponentially with system size but the ordered landscape shows dynamics over a faster time-scale growing as a power of system size. We present a scaling ansatz that describes several dynamical correlation functions of the landscape measured in steady state.

cond-mat.stat-mech↗
arXiv2016

Coarsening in a 1-D system of Orienting Arrowheads: Persistence with $A+B \rightarrow$ 0

We demonstrate the large scale effects of the interplay between shape and hard core interactions in a system with left- and right-pointing arrowheads ~$\textless ~~ \textgreater$~ on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain wall, diffusive ($A$) and static ($B$). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain wall annihilation $A+B\rightarrow 0$, quite different from $A+A \rightarrow 0$ kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially in time, in contrast to the power law decay known for $A+A \rightarrow 0$. In the thermodynamic limit with a finite density of walls, coarsening as a function of time $t$ is studied by simulation. While the number of walls falls as $t^{-\frac{1}{2}}$, the fraction of persistent arrowheads decays as $t^{-θ}$ where $θ$ is close to $\frac{1}{4}$, quite different from the Ising value. The global persistence too has $θ=\frac{1}{4}$, as follows from a heuristic argument. In a generalization where the $B$ walls diffuse slowly, $θ$ varies continuously, increasing with increasing diffusion constant.

cond-mat.stat-mech↗
arXiv2016

Nonequilibrium mechanisms underlying de novo biogenesis of Golgi cisternae

A central issue in cell biology is the physico-chemical basis of organelle biogenesis in intracellular trafficking pathways, its most impressive manifestation being the biogenesis of Golgi cisternae. At a basic level, such morphologically and chemically distinct compartments should arise from an interplay between the molecular transport and chemical maturation. Here, we formulate analytically tractable, minimalist models, that incorporate this interplay between transport and chemical progression in physical space, and explore the conditions for de novo biogenesis of distinct cisternae. We propose new quantitative measures that can discriminate between the various models of transport in a qualitative manner- this includes measures of the dynamics in steady state and the dynamical response to perturbations of the kind amenable to live-cell imaging.

physics.bio-ph↗
arXiv2016

Large compact clusters and fast dynamics in coupled nonequilibrium systems

We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle density and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow algebraically with size, not seen earlier in systems with pure domains.

cond-mat.stat-mech↗
arXiv2015

Order parameter scaling in fluctuation dominated phase ordering

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile. We study both static and dynamic scaling laws obeyed by the Fourier modes $Q_m$ and find that the mean value obeys the static scaling law $\langle Q_m \rangle \sim L^{-ϕ}f(m/L)$ with $ϕ\simeq2/3$ and $ϕ\simeq 3/5$ with Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution respectively. The full probability distribution $P(Q_m)$ exhibits scaling as well. Further, time-dependent correlation functions such as the steady state auto-correlation and cross-correlations of order parameter components are scaling functions of $t/L^z$, where $L$ is the system size and $z$ is the dynamic exponent with $z=2$ for EW and $z=3/2$ for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and a weak divergence of the flatness as the scaled time approaches zero.

cond-mat.stat-mech↗
arXiv2015

Condensate formation in a zero-range process with random site capacities

We study the effect of quenched disorder on the zero-range process (ZRP), a system of interacting particles undergoing biased hopping on a one-dimensional periodic lattice, with the disorder entering through random capacities of sites. In the usual ZRP, sites can accommodate an arbitrary number of particles, and for a class of hopping rates and high enough density, the steady state exhibits a condensate which holds a finite fraction of the total number of particles. The sites of the disordered zero-range process considered here have finite capacities chosen randomly from the Pareto distribution. From the exact steady state measure of the model, we identify the conditions for condensate formation, in terms of parameters that involve both interactions (through the hop rates) and randomness (through the distribution of the site capacities). Our predictions are supported by results obtained from a direct numerical sampling of the steady state and from Monte Carlo simulations. Our study reveals that for a given realization of disorder, the condensate can relocate on the subset of sites with largest capacities. We also study sample-to-sample variation of the critical density required to observe condensation, and show that the corresponding distribution obeys scaling, and has a Gaussian or a Levy-stable form depending on the values of the relevant parameters.

cond-mat.stat-mech↗