arXiv subjects

K. Vijay Kumar

Publications and source records attributed to K. Vijay Kumar.

14 recordsLinked to original sources

arXiv2026

Growth phases of an active tissue: determinate, indeterminate, and proportionate

Growth may cease at a target size or continue throughout life: the determinate and indeterminate phenotypes. We develop an active viscoelastic continuum model of a tissue growing along one axis, in which cell division and death generate active stresses. We find two asymptotic states: one in which the tissue reaches a relative size fixed by its material parameters, and one in which it elongates linearly without bound. Which state is realised is set by the ratio of active stress to elastic modulus. The transition originates in a bound on the elastic stress the tissue can support: a sufficiently large activity can never be balanced. In a tissue made of parts with different material properties, the growing phase settles into fixed length proportions, set by the mechanical impedances of the parts rather than inherited; matching impedances to initial lengths preserves the proportions the tissue began with. Determinate, indeterminate and proportionate growth thus appear as regimes of one continuum mechanical framework.

physics.bio-ph↗

arXiv2026

Forces at the scale of the cell

The importance of molecular-scale forces in sculpting biological form and function has been acknowledged for more than a century. Accounting for forces in biology is a problem that lies at the intersection of soft condensed matter physics, statistical mechanics, and experimental methods, all adapted to a cellular context. This review surveys how forces arise within the cell. We provide a summary of the relevant background in cell biophysics, of soft-matter systems in and out of thermodynamic equilibrium, and of various force measurement methods. These ideas are then deployed to describe how forces are generated, transmitted, and sensed in specific cell-scale processes. We emphasize active matter descriptions, methodological tools that provide ways of incorporating non-equilibrium effects in a systematic manner into conceptual as well as quantitative descriptions. Our examples include polymerization forces, the motion of molecular motors, the properties of the actomyosin cortex, the mechanics of cell division, and shape changes in tissues. We suggest that a deeper understanding of cell function will necessarily require integrating the action of cell-scale physical forces with the assimilation and processing of information.

cond-mat.soft↗

arXiv2026

Superdiffusion and antidiffusion in an aligned active suspension

We show theoretically that an imposed uniaxial anisotropy leads to new universality classes for the dynamics of active particles suspended in a viscous fluid. In the homogeneous state, their concentration relaxes superdiffusively, stirred by the long-ranged flows generated by its own fluctuations, as confirmed by our numerical simulations. Increasing activity leads to an anisotropic diffusive instability, and thus an original phase-separation mechanism, driven by the interplay of active stresses with a particle current proportional to the local curvature of the suspension velocity profile.

cond-mat.soft↗

arXiv2025

Active waves from non-reciprocity and cytoplasmic exchange

Pattern formation in active biological matter typically arises from the feedback between chemical concentration fields and mechanical stresses. The actomyosin cortex of cells is an archetypal example of an active thin film that displays such patterns. Here, we show how pulsatory patterns emerge in a minimal model of the actomyosin cortex with a single stress-regulating chemical species that exchanges material with the cytoplasm via a linear turnover reaction. Deriving a low-dimensional amplitude-phase model, valid for a one-dimensional periodic domain and a spherical surface, we show that nonlinear waves arise from a secondary parity-breaking bifurcation that originates from the nonreciprocal interaction between spatial modes of the concentration field. Numerical analysis confirms these analytical predictions, and also reveals analogous pulsatory patterns on impermeable domains. Our study provides a generic route to the emergence of nonreciprocity-driven pulsatory patterns that can be controlled by both the strength of activity and the turnover rate.

physics.bio-ph↗

arXiv2023

Shape-dependent motility of polar inclusions in active baths

Collections of persistently moving active particles are an example of a nonequilibrium heat bath. One way to study the nature of nonequilibrium fluctuations in such systems is to follow the dynamics of an embedded probe particle. With this aim, we study the dynamics of an anisotropic inclusion embedded in a bath of active particles. By studying various statistical correlation functions of the dynamics, we show that the emergent motility of this inclusion depends on its shape as well as the properties of the active bath. We demonstrate that both the decorrelation time of the net force on the inclusion and the dwell time of bath particles in a geometrical trap on the inclusion have a non-monotonic dependence on its shape. We also find that the motility of the inclusion is optimal when the volume fraction of the active bath is close to the value for the onset of motility induced phase separation.

cond-mat.stat-mech↗

arXiv2021

Harnessing confinement and driving to tune active particle dynamics

A distinguishing feature of active particles is the nature of the non-equilibrium noise driving their dynamics. Control of these noise properties is, therefore, of both fundamental and applied interest. We demonstrate emergent tuning of the active noise of a granular self-propelled particle by confining it to a quasi one-dimensional channel. We find that this particle, moving like an active Brownian particle (ABP) in two-dimensions, displays run-and-tumble (RTP) characteristics in confinement. We show that the dynamics of the relative orientation co-ordinate of the particle maps to that of a Brownian particle in a periodic potential subject to a constant force, in analogy to the dynamics of a molecular motor. This mapping captures the essential statistical characteristics of the one-dimensional RTP motion. Specifically, our theoretical analysis is in agreement with the empirical distributions of the relative orientation co-ordinate and the run-times (tumble-rates) of the particle. Finally, we explicitly control these emergent run-and-tumble like noise parameters by external driving. Altogether, our work illustrates geometry-induced tuning of the active dynamics of self-propelled units thus suggesting an independent route to harness their internal dynamics.

cond-mat.soft↗

arXiv2020

Universal scaling in active single-file dynamics

We study the single-file dynamics of three classes of active particles: run-and-tumble particles, active Brownian particles and active Ornstein-Uhlenbeck particles. At high activity values, the particles, interacting via purely repulsive and short-ranged forces, aggregate into several motile and dynamical clusters of comparable size, and do not display bulk phase-segregation. In this dynamical steady-state, we find that the cluster size distribution of these aggregates is a scaled function of the density and activity parameters across the three models of active particles with the same scaling function. The velocity distribution of these motile clusters is non-Gaussian. We show that the effective dynamics of these clusters can explain the observed emergent scaling of the mean-squared displacement of tagged particles for all the three models with identical scaling exponents and functions. Concomitant with the clustering seen at high activities, we observe that the static density correlation function displays rich structures, including multiple peaks that are reminiscent of particle clustering induced by effective attractive interactions, while the dynamical variant shows non-diffusive scaling. Our study reveals a universal scaling behavior in the single-file dynamics of interacting active particles.

cond-mat.stat-mech↗

arXiv2020

Steady State of an Active Brownian Particle in Two-Dimensional Harmonic Trap

We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently explore the behavior of the system in different parameter regimes. Identifying "active" and "passive" regimes, we predict a surprising re-entrant active-to-passive transition with increasing trap stiffness. Our numerical simulations validate this finding. We discuss various interesting limiting cases wherein closed form expressions for the distributions can be obtained.

cond-mat.stat-mech↗

arXiv2019

Minimal model of cellular symmetry breaking

The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechano-chemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities.

physics.bio-ph↗

arXiv2018

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

cond-mat.stat-mech↗

arXiv2010

A note on the possibility of classical orbital diamagnetism for an unbounded system --the Bohr-van Leeuwen Theorem

Recently [EPL, 86, (2009) 17001], we had simulated the classical Langevin dynamics of a charged particle on the surface of a sphere in the presence of an externally applied magnetic field, and found a finite value for the orbital diamagnetic moment in the long-time limit. This result is surprising in that it seems to violate the classic Bohr-van Leeuwen Theorem on the absence of classical diamagnetism. It was indeed questioned by some workers [EPL, 89, (2010) 37001] who verified that the Fokker-Planck (FP) equation derived from our Langevin equation, was satisfied by the classical canonical density in the steady state, obtained by setting d/dt=0 in the FP equation. Inasmuch as the canonical density does not contain the magnetic field, they concluded that the diamagnetic moment must be zero. The purpose of this note is to show that this argument and the conclusion are invalid -- instead of setting d/dt=0 one must first obtain the fundamental time-dependent solution for the FP equation, and then calculate the expectation value of the diamagnetic moment, and finally consider its long-time limit (i.e., $t \to \infty$). This would indeed correspond to our numerical simulation of the dynamics. That this is indeed so is shown by considering the simpler analytically solvable problem, namely that for an unbounded plane for which the above procedure can be carried out exactly. We then find that the limiting value for the expectation of the diamagnetic moment is indeed non-zero, and yet the steady-state FP equation obtained by setting d/dt=0 is satisfied by the canonical density. Admittedly, the exact analytical solution for the sphere is not available. But, the exact solution obtained for the case of the unbounded 2D-plane illustrates our point all right. We also present some further new results for other finite but unbounded surfaces such the ellipsoids of revolution.

cond-mat.stat-mech↗

arXiv2009

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero -- the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial, but subtle role of the boundary, we have simulated here the case of a finite but \emph{unbounded} system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment which now indeed turns out to be non-zero, and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

physics.class-ph↗

arXiv2009

Exact solution of a Brownian inchworm model for self-propulsion

We present the exact solution of a Brownian inchworm model of a self-propelled elastic dimer which has recently been proposed in [K. V. Kumar \textit{et al}, Phys. Rev. E \textbf{77}, 020102(R) (2008)] as a unifying model for the propulsion mechanisms of DNA helicase, polar rods on a vibrated surface, crawling keratocytes, and Myosin VI.

cond-mat.stat-mech↗

arXiv2007

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↗