Related papers: Stochastic Aspect of the Tomographic Reconstructio…
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low light…
We consider the statics and dynamics of a single particle trapped in a one-dimensional harmonic potential, and subjected to a driving noise with memory, that is represented by a resetting stochastic process. The finite memory of this…
Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory…
In this paper we address the one-dimensional problem of stochastic renewal in different damping environments. An ensemble of particles with some specified initial distribution in phase space are allowed to evolve stochastically till a…
Conventional rendering techniques are primarily designed and optimized for single-frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
We study the effect of stochastic resetting on a run and tumble particle (RTP) in two spatial dimensions. We consider a resetting protocol which affects both the position and orientation of the RTP: with a constant rate the particle…
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration,…
In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…
To recover the three dimensional (3D) volumetric distribution of matter in an object, images of the object are captured from multiple directions and locations. Using these images tomographic computations extract the distribution. In highly…
Stochastic resonance describes the utility of noise in improving the detectability of weak signals in certain types of systems. It has been observed widely in natural and engineered settings, but its utility in image classification with…
Inspired by applications, we consider reaction-diffusion equations on $\mathbb{R}$ that are stochastically forced by a small multiplicative noise term that is white in time, coloured in space and invariant under translations. We show how…
Computed tomography is a widely used imaging modality with applications ranging from medical imaging to material analysis. One major challenge arises from the lack of scanning information at certain angles, resulting in distortion or…
Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating…
The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase.…
We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by $x$ and $v$ respectively, we consider two different resetting protocols - (i) complete…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…