Stephy Jose

Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive a fluctuating hydrodynamic description of this model from microscopic rules, which we then use to demonstrate that diffusive noise significantly alters early-time genetic demixing, which we characterize through heterozygosity, a key measure of diversity. Combining macroscopic fluctuation theory and microscopic simulations, we demonstrate that the scaling of allele-number fluctuations in a spatial domain displays an early-time behavior dominated by diffusive noise. Our results underscore the need for additional terms in existing continuum theories and highlight the necessity of including diffusive noise in models of spatially structured populations.

We introduce jerky chiral active Brownian particles (ABP), a generalization of conventional chiral ABPs subjected to jerk, the time derivative of acceleration, and analytically derive their mean displacement and mean squared displacement. Our results show that jerk induces anomalous fluctuations and oscillatory behavior on the standard circular swimming of chiral active particles. The interplay of jerk, chirality and persistence produces a family of mean trajectories including damped and exploding Lissajous patterns alongside the well-known spira mirabilis (logarithmic spirals). Our work on jerky chiral active particles opens a new route to explore rich dynamical effects in active matter.

We introduce jerky chiral active Brownian particles (jcABPs), a generalization of conventional chiral active Brownian particles (cABPs) subjected to jerk, the time derivative of acceleration, and analytically derive their mean displacement and mean squared displacement (MSD). Our results show that jerk induces anomalous fluctuations and oscillatory behavior on the standard circular swimming of chiral active particles. The interplay of jerk, chirality and persistence produces a family of mean trajectories including damped and exploding Lissajous patterns alongside the well-known spira mirabilis (logarithmic spirals). Our work on jerky chiral active particles opens a new route to explore rich dynamical effects in active matter.

We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size L. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles (RTPs), respectively. We derive analytic results for the fluctuations in the number of particles exiting the boundaries of the finite confining box. The statistical properties of this quantity crucially depend on how the system is prepared initially. Two common types of averages employed to understand the impact of initial conditions in stochastic systems are annealed and quenched averages. It is well known that for an infinitely extended system, these different initial conditions produce quantitatively different fluctuations, even in the infinite time limit. We demonstrate explicitly that in finite systems, annealed and quenched fluctuations become equal beyond a system-size dependent timescale, t ∼ L 2 . For diffusing particles, the fluctuations exhibit a t growth at short times and decay as 1 / t for time scales, t ≫ L 2 / D , where D is the diffusion constant. Meanwhile, for RTPs, the fluctuations grow linearly at short times and then decay as 1 / t for time scales, t ≫ L 2 / D eff , where D _eff represents the effective diffusive constant for RTPs. To study the effect of confinement in detail, we also analyze two different setups (i) with one reflecting boundary and (ii) with both boundaries open.

We investigate the effect of initial conditions on the fluctuations of the integrated density current across the origin (x = 0) up to a given time t in a one-dimensional system of non-interacting run-and-tumble particles. Each particle has initial probabilities f + and f − to move with an initial velocity +v and −v respectively, where v > 0. We derive exact results for the variance (second cumulant) of the current for quenched and annealed averages over the initial conditions for the magnetization and the density fields associated with the particles. We show that at large times, the variance displays a t behavior, with a prefactor contingent on the specific density initial conditions used. However, at short times, the variance displays either linear t or quadratic t ² behavior, which depends on the combination of magnetization and density initial conditions, along with the fraction f + of particles in the positive velocity state at t = 0. Intriguingly, if f + = 0 , the variance displays a short time t ² behavior with the same prefactor irrespective of the initial conditions for both fields.

We study the fluctuations of the integrated density current across the origin up to time T in a lattice model of active particles with hard-core interactions. This model is amenable to an exact description within a fluctuating hydrodynamics framework. We focus on quenched initial conditions for both the density and the magnetization fields and derive expressions for the cumulants of the density current, which can be matched with direct numerical simulations of the microscopic lattice model. For the case of uniform initial profiles, we show that the variance of the integrated current displays three regimes: an initial T rise with a coefficient given by the symmetric simple exclusion process, a cross-over regime where the effects of activity increase the fluctuations, and a large-time T behavior with a prefactor that depends on the initial conditions, the Péclet number, and the mean density of particles. Additionally, we study the limit of zero diffusion, where the fluctuations intriguingly exhibit a T ² behavior at short times. However, at large times, the fluctuations still grow as T , with a coefficient that can be calculated explicitly. For low densities, we show that this coefficient can be expressed in terms of the effective diffusion constant D _eff for non-interacting active particles.