Related papers: Reconstructing the gradient source position from s…
We study the two-dimensional motion of an active Brownian particle of speed $v_0$, with intermittent directional reversals in the presence of a harmonic trap of strength $\mu$. The presence of the trap ensures that the position of the…
We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…
We study the recovery of one-dimensional semipermeable barriers for a stochastic process in a planar domain. The considered process acts like Brownian motion when away from the barriers and is reflected upon contact until a sufficient but…
Diffusion models have demonstrated strong generative performance; however, generated samples often fail to fully align with human intent. This paper studies a test-time scaling method that enables sampling from regions with higher…
Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not…
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…
Astrophysical observations originate from matter that interacts with radiation or transported particles. We develop a pragmatic approximation in order to enable multi-dimensional simulations with basic spectral radiative transfer when the…
Active particles, which are self-propelled nonequilibrium systems, are modelled by overdamped Langevin equations with colored noise, emulating the self-propulsion. In this chapter, we present a review of the theoretical results for the…
The spatiotemporal stochastic dynamics of the voltage as well as the upcrossing rate are derived for a model neuron comprising a long dendrite with uniformly distributed filtered excitatory and inhibitory synaptic drive. A cascade of…
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between…
The Fleming-Viot process describes a system of $N$ particles diffusing on a graph with an absorbing site. Whenever one of the particles is absorbed, it is replaced by a new particle at the position of one of the $N-1$ remaining particles.…
Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this non-equilibrium rare-event problem by developing an…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but non-zero Brownian rotations. The equations are based on a multiple time scale approach that allows fast…
We introduce a residence-time approach (RTA) for determining position-dependent diffusivities from biased molecular dynamics simulations. The method is formulated for trajectory segments in which the effective drift along the transport…
Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…
We study the position distribution of an active Brownian particle (ABP) in the presence of stochastic resetting in two spatial dimensions. We consider three different resetting protocols : (I) where both position and orientation of the…