arXiv subjects

A. V. Anil Kumar

Publications and source records attributed to A. V. Anil Kumar.

13 recordsLinked to original sources

arXiv2026

Nonreciprocal McKean-Vlasov Equations: From Stationary Instabilities to Travelling Waves

Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species nonreciprocal McKean-Vlasov equation derived from an underlying system of interacting stochastic particles. Combining linear stability analysis, weakly nonlinear arguments, pseudo-spectral simulations, and Langevin particle dynamics, we show that the structure of nonreciprocity controls the onset and nature of collective order. For spatially uniform weak nonreciprocity, asymmetry shifts the critical diffusion threshold but produces only stationary instabilities, indicating that uniform imbalance alone is insufficient to generate sustained time-dependent motion. In contrast, spatially modulated nonreciprocity fundamentally enriches the dynamics: depending on its symmetry and coupling to the interaction potential, the homogeneous state can lose stability through Hopf bifurcations, giving rise to standing and travelling wave states. We identify both subcritical and supercritical Hopf transitions, relate the selected patterns to Landau saturation coefficients, and show that travelling waves can emerge even in the weak-nonreciprocity regime without explicit microscopic run-and-chase rules. Direct Langevin simulations confirm that these oscillatory and travelling states persist at the particle level and are not artefacts of the continuum mean-field description. Our results establish nonreciprocal McKean-Vlasov equations as a minimal framework for understanding how spatially structured asymmetric interactions generate self-organized motion, dynamical phase transitions, and nonequilibrium collective order.

cond-mat.stat-mech↗

arXiv2026

Kinetic Random-Field Nonreciprocal Ising Model

We introduce and analyse the kinetic random-field nonreciprocal Ising model, which incorporates bimodal (double-delta) diffusive disorder along with pairwise nonreciprocal interactions between two different species. Using mean-field and effective-field theory, in combination with kinetic Monte Carlo simulations (3D Glauber dynamics), we identify a nonequilibrium tricritical (Bautin) point separating Hopf-type transitions (continuous) from saddle-node-of-limit-cycle (SNLC) transitions (discontinuous). For a weak random field which is less than a critical value, the onset of collective oscillations (the "swap" phase) occurs via a supercritical Hopf bifurcation, whereas for fields greater than the critical value, the transition is first-order (SNLC), exhibiting hysteresis and Binder-cumulant signatures. The finite-size scaling of the susceptibility is consistent with the distinct critical and discontinuous behaviour shown in the Hopf and SNLC regimes, respectively (effective exponents $\approx1.96$ in the Hopf regime and $\approx3.0$ in the SNLC regime). Additionally, in the first-order regime, the swap phase is sustained only above a threshold nonreciprocity, and this threshold increases monotonically with the disorder strength. We further identify a new droplet-induced swap phase in the larger field-strength region, which cycles eight different metastable states. A dynamical free-energy picture rationalises droplet nucleation as the mechanism for these cyclic jumps. Together, these results demonstrate how disorder and nonreciprocity combined generate rich nonequilibrium criticality, with implications for driven and active systems.

cond-mat.stat-mech↗

arXiv2025

Nonreciprocal Blume-Capel Model with Antisymmetric Single-Ion Anisotropies

We investigate the interplay between nonreciprocal interactions and chemical-potential imbalance in a two-species nonreciprocal Blume-Capel model. Combining a systematic mean-field bifurcation analysis with large-scale Monte Carlo simulations in two and three dimensions, we map the model's dynamical regimes and transitions. Mean-field theory predicts a rich phase structure -- disorder, a time-dependent 'swap' (limit-cycle) phase, and static ordered states -- separated by Hopf, saddle-node on invariant circle, saddle-node of limit cycles, pitchfork and saddle-node bifurcations. In two dimensions, Monte Carlo simulations reveal that spiral defects destabilise global swapping and, unless vacancies are strongly favoured, destroy long-range order. Crucially, a finite single-ion anisotropy $Δ_α= - Δ_β$ promotes vacancy occupation in the $α$ species and suppresses nonreciprocal dynamics, thereby restoring a robust static ordered phase. Finite-size scaling of susceptibility and Binder cumulants places the disorder to static transition firmly in the 2D Ising universality class. Moreover, within the static ordered phase, we observe a crossover that sharpens into a line of first-order phase transitions; these two regimes are separated by a critical point, analogous to the termination of the liquid-gas coexistence curve. In three dimensions, simulations largely mirror mean-field expectations, though swap to static ordering occurs indirectly via a disordered regime. Our results demonstrate that vacancy energetics provide a simple, experimentally relevant control knob that stabilises equilibrium-like order in nonreciprocal systems and that defects can generate novel critical behaviour.

cond-mat.stat-mech↗

arXiv2025

Emergence of rotating clusters in active Brownian particles with visual perception

We examine the group formation and subsequent dynamics of active particles which are equipped with a visual perception using Langevin dynamics simulations. These particles possess an orientational response to the position of the nearest neighbours which are within a vision cone of these particles. We observe the emergence of rotating clusters when the visual perception of the particles are in the intermediate range. We have found that the persistent motion of these active particles are intimately correlated with the emerging structures by analysing the persistence probability as well as the orientational correlation function. For rotating clusters, the persistent probability is found to be very quickly decaying and orientational correlation function shows oscillatory behaviour.

cond-mat.soft↗

arXiv2024

Phase separation in a binary mixture of sticky spheres

We numerically investigate the dependence of range of attractive potential on the phase separation of 2-D binary systems. Through extensive simulations and analysis, we show that when the range of attractive interactions approaches the sticky sphere limit, the system undergoes a phase separation at lower temperature. Further reduction in temperature causes the system to mix again. These mixing-demixing-mixing transitions are of first order. Such phase separation is not observed for systems with larger interaction range. In the phase separated region of the phase diagram, one of the components of the mixture chooses to be in crystalline configuration, while other being in disordered state

physics.comp-ph↗

arXiv2024

Ising model with non-reciprocal interactions

Effective interactions that violate Newton's third law of action-reaction symmetry are common in systems where interactions are mediated by a non-equilibrium environment. Extensive Monte Carlo simulations are carried out on a two-dimensional Ising model, where the interactions are modified non-reciprocally. We demonstrate that the critical temperature decreases as the non-reciprocity increases and this decrease depends only on the magnitude of non-reciprocity. Further, travelling spin waves due to the local fluctuations in magnetisation are observed and these spin waves travel opposite to the non-reciprocity vector.

cond-mat.stat-mech↗

arXiv2021

Depletion induced demixing and crystallization in binary colloids subjected to an external potential barrier

A binary colloidal mixture of unequal sizes, subjected to an external potential barrier, has been investigated using canonical ensemble molecular dynamics simulations. The attractive depletion interaction between the external barrier and larger species in the binary mixture causes the mixture to phase separate. At higher volume fractions, a pure phase of larger particles forms near the potential barrier, and the local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

cond-mat.soft↗

arXiv2021

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

cond-mat.soft↗

arXiv2020

Phase separation in a two-dimensional binary colloidal mixture by quorum sensing activity

We present results from Langevin dynamics simulations of a glassy active-passive mixture of soft-repulsive binary colloidal disks. Activity on the smaller particles is applied according to the quorum sensing scheme, in which a smaller particle will be active for a persistence time if its local nearest neighbors are equal to or greater than a certain threshold value. We start with a passive glassy state of the system and apply activity to the smaller particles, which shows a nonmonotonous glassy character of the active particles with the persistence time of the active force, from its passive limit (zero activity). On the other hand, passive particles of the active-passive mixture phase separate at the intermediate persistence time of the active force, resulting in the hexatic-liquid and solid-liquid phases. Thus, our system shows three regimes as active glass, phase separation, and active liquid, as the persistence time increases from its smaller values. We show that the solidlike and hexatic phases consisting of passive large particles are stable due to the smaller momentum transfer from active to passive particles, compared to the higher persistence time where the positional and orientational ordering vanishes. Our model is relevant to active biological systems, where glassy dynamics is present, e.g., bacterial cytoplasm, biological tissues, dense quorum sensing bacteria, and synthetic smart amorphous glasses.

cond-mat.soft↗

arXiv2020

A Stochastic model for dynamics of FtsZ filaments and the formation of Z-ring

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the $Z$-ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro} observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.

q-bio.SC↗

arXiv2020

Sub-Arrhenius diffusion in a binary colloidal system

The dynamics of binary colloidal mixture subjected to an external potential barrier is investigated using molecular dynamics simulations. The depletion interactions between the potential barrier and larger components of the mixture alters the dynamics of the system significantly. The larger particles undergo sub-Arrhenius diffusion while smaller particles obey normal Arrhenius diffusion. These results show that quantum phenomena such as tunneling is not required to have sub-Arrhenius diffusion, in contrast to the general agreement in the literature. The depletion interactions between the external potential barrier and larger component increases with decreasing temperature which makes the effective activation energy for barrier crossing temperature dependent leading to sub-Arrhenius diffusion.

cond-mat.soft↗

arXiv2017

Dissipation dynamics with two distinct chaotic baths

Dissipation using a finite environment coupled to a single harmonic oscillator have been studied quite extensively. We extend the study by looking at the dynamics of the dissipation when we introduce a second bath of N identical quartic systems different from the 1st bath. We look at the energy flow into the environment as a function of the chaotic parameters of the bath and also try to develop a linear response theory to describe the system. The energy flow is always more to the more chaotic system irrespective of the initial energy of the baths.

nlin.CD↗

arXiv2002

A New Source of Reaction - Diffusion Coupling in Confined Systems due to Temperature Inhomogeneity

Diffusion is often accompanied by a reaction or sorption which can induce temperature inhomogeneities. Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported with a hot zone presumed to be created by a reaction. Our simulations show that localised hot regions can alter both the kinetic and transport properties. Further, enhancement of the diffusion constant is greater for larger barrier height, a surprising result of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot zone in addition to that which normally exists via concentration.

cond-mat.stat-mech↗