Related papers: Drift-diffusion on a Cayley tree with stochastic r…
We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…
Spatial spread of minority carriers produced by optical excitation in semiconductors is usually well described by a diffusion equation. The classical diffusion process can be viewed as a result of a random walk of particles in which every…
In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…
The Rayleigh-Taylor (RT) instability is ubiquitously observed, yet has traditionally been studied using ideal fluid models. Collisionality can vary strongly across the fluid interface, and previous work demonstrates the necessity of kinetic…
In this paper we analyze the effects of stochastic resetting on an encounter-based model of an unbiased run-and-tumble particle (RTP) confined to the half-line $[0,\infty)$ with a partially absorbing wall at $x=0$. The RTP tumbles at a…
We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent $\alpha$. We…
The stationary distribution of the diffusion limit of the 2-island, 2-allele Wright-Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for…
We consider a drift-diffusion model, with an unknown function depending on the spatial variable and an additional structural variable, the amount of ingested lipid. The diffusion coefficient depends on this additional variable. The drift…
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to…
The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…
We investigate fluctuations in the average speed or current of a self-interacting diffusion (SID) on a ring, mimicking the non-Markovian behaviour of an agent influenced by its own path. We derive the SID's phase diagram, showing a…
We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability…
Cross-modal image translation remains brittle and inefficient. Standard diffusion approaches often rely on a single, global linear transfer between domains. We find that this shortcut forces the sampler to traverse off-manifold, high-cost…
We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…
We study a one-dimensional (1d) XXZ spin-chain in a random field on the metallic side of the many-body localization transition by level statistics. For a fixed interaction, and intermediate disorder below the many-body localization…
We propose and analyse a boundary-preserving numerical scheme for the weak approximation for some stochastic partial differential equations (SPDEs) with bounded state-space. We impose regularity assumptions on the drift and diffusion…
Reentrant localization transitions, that is, the transitions of a portion of the eigenspectrum from localized to critical and then again to localized as the disorder strength is increased, have been recently unveiled in various…
We derive generalized charge energy rate equations for organic solids and biomolecular aggregates, even when these are dynamically disordered. These equations suggest that the transport in such cases rely on both drift and diffusion…