Related papers: Conceptual Foundations of Diffusion in Magnetic Re…
The Fourier law and the diffusion equation are derived from the Schrodinger equation of a diffusive medium (consisting of a random potential). The theoretical model is backed by numerical simulation. This derivation can easily be…
Discovering a new field is not usually an easy process, especially when you choose magnetic resonance imaging (MRI). MRI is one of the few non-invasive medical procedures, if not the only one, that someone can receive in modern day…
In this paper, we take the slowly rotating black three-brane background and perturb it by introducing a vector gauge field. We find the components of the gauge field through Maxwell equations and Bianchi identities. Using currents and some…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
Fluid approximations to cosmic ray (CR) transport are often preferred to kinetic descriptions in studies of the dynamics of the interstellar medium (ISM) of galaxies, because they allow simpler analytical and numerical treatments.…
Diffusion probabilistic models (DPMs) which employ explicit likelihood characterization and a gradual sampling process to synthesize data, have gained increasing research interest. Despite their huge computational burdens due to the large…
We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation…
In this paper, we review the quantum mechanics of magnetic resonance imaging (MRI). We traverse its hierarchy of scales from the spin and orbital angular momentum of subatomic particles to the ensemble magnetization of tissue. And we review…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are…
We provide some on-off type criteria for recurrence and transience of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion…
Diffusion magnetic resonance imaging is an imaging technology designed to probe anatomical architectures of biological samples in an in vivo and non-invasive manner through measuring water diffusion. The contribution of this paper is…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit…
We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of non-instantaneous correlation functions at finite particle…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
The underlying concepts of collisionless magnetic field reconnection in the vicinity of the diffusion regions are developed qualitatively from first principles. One conclusion of this analysis is that energetic ions and electrons observed…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
The main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical…
We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on…