Related papers: Solving the inverse Knudsen problem: gas diffusion…
This thesis presents an experimental study of the inverse energy cascade as it occurs in an electromagnetically forced soap film. It focuses on characterizing important features of the inverse cascade such as it's range, how energy is…
Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a…
We consider random flights of point particles inside $n$-dimensional channels of the form $\mathbb{R}^{k} \times \mathbb{B}^{n-k}$, where $\mathbb{B}^{n-k}$ is a ball of radius $r$ in dimension $n-k$. The particle velocities immediately…
The classical Prats' problem of flow instability in a horizontal porous channel saturated by a fluid subject to a buoyancy force is reconsidered. In the original formulation, the driving buoyancy force results from thermal diffusion. This…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
Single-file systems, in which particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined geometries, such as in zeolites or carbon nanotubes. Twenty years…
Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, and fuel cells and batteries. However, such modeling remains…
Experiments and numerical simulations were conducted to investigate the dispersion of turbulent jets issuing from realistic pipe geometries. The effect of jet densities and Reynolds numbers on vertical buoyant jets were investigated, as…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…
Most of the physically based techniques for rendering translucent objects use the diffusion theory of light scattering in turbid media. The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived…
The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of the surface (a complex surface naturally tailored to the…
In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and…
Simultaneous use of partial differential equations in conjunction with data analysis has proven to be an efficient way to obtain the main parameters of various phenomena in different areas, such as medical, biological, and ecological. In…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
We solve an inverse problem for fluid particle pair-statistics: we show that a time sequence of probability density functions (PDF's) of separations can be exactly reproduced by solving the diffusion equation with a suitable time-dependent…
Moisture diffusion in polymers and bio-based materials frequently exhibits non-Fickian behavior that cannot be described by classical diffusion models. The Langmuir model, which accounts for the coexistence of mobile and bound water…
Mass transport of impurities immersed in a confined quasi-two-dimensional moderately dense granular gas of inelastic hard spheres is studied. The effect of the confinement on granular particles is modeled through a collisional model (the…
The penetration of atomic hydrogen through defect-free graphene was generally predicted to have a barrier of at least several eV, which is much higher than the 1 eV barrier measured for hydrogen-gas permeation through pristine graphene…
We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different…