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In porous material research, one main interest of nuclear magnetic resonance diffusion (NMR) experiments is the determination of the shape of pores. While it has been a longstanding question if this is in principle achievable, it has been…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…
The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for…
Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique with exquisite sensitivity to the microstructural properties of heterogeneous media. The conventionally adopted acquisition schemes involving single pulsed field gradients…
Diamond-based quantum sensors have enabled high-resolution NMR spectroscopy at the microscale in scenarios where fast molecular motion averages out dipolar interactions among target nuclei. However, in samples with low-diffusion, ubiquitous…
This work presents a novel diffusion based dual-phase molecular communication system where the source leverages multiple cooperating nanomachines to improve the end-to-end reliability of communication. The Neyman-Pearson Likelihood Ratio…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
Nuclear spin optical rotation (NSOR) is a recently developed technique for detection of nuclear magnetic resonance via rotation of light polarization, instead of the usual long-range magnetic fields. NSOR signals depend on hyperfine…
Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time…
Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…