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Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…

The paper develops a new integral micromorphic elastic continuum model, which can describe dispersion properties of band-gap metamaterials, i.e., metamaterials that inhibit propagation of waves in a certain frequency range. The enrichment…

Calculations of propagating quantum trajectories associated to a wave function provide new insight into quantum processes such as particle scattering and diffraction. Here, hydrodynamic calculations of electron beam imaging under conditions…

We determine numerically the parallel, perpendicular, and antisymmetric diffusion coefficients for charged particles propagating in highly turbulent magnetic fields, by means of extensive Monte Carlo simulations. We propose simple…

Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

In modern radio astronomy, one of the key technologies is to widen the frequency coverage of an instrument. The effects of higher-order modes on an instrument associated with wider bandwidths have been reported, which may degrade…

This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…

In its normal mode of operation the Argonne Wakefield Accelerator Facility uses a high charge (10-100 nC), short pulse (3-5 psec) drive bunch to excite high-gradient accelerating fields in various slow-wave structures. To generate this…

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

Electrocardiography (ECG) signals are frequently degraded by noise, limiting their clinical reliability in both conventional and wearable settings. Existing methods for addressing ECG noise, relying on artifact classification or denoising,…

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…

We present a microfluidic method leading to accurate measurements of the mutual diffusion coefficient of a liquid binary mixture over the whole solute concentration range in a single experiment. This method fully exploits solvent…

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…

We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…

This paper provides an analysis of radio wave scattering for frequencies ranging from the microwave to the Terahertz band (e.g., 1 GHz - 1 THz), by studying the scattering power reradiated from various types of materials with different…

Driven by the need for describing and understanding wave propagation in structural materials and components, several analytical, numerical, and experimental techniques have been developed to obtain dispersion curves. Accurate…

Diffusion coefficient measurements are important for many biological and material investigations, such as particle dynamics, kinetics, and size determinations. Amongst current measurement methods, single particle tracking (SPT) offers the…

Diffuse scattering of electromagnetic waves from natural and artificial surfaces has been extensively studied in various disciplines, including radio wave propagation, and several diffuse scattering models based on different approaches have…

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…