We consider the heat equation with a discontinuous diffusion coefficient and give uniqueness and stability results for both the diffusion coefficient and the initial condition from a measurement of the solution on an arbitrary part of the boundary and at some arbitrary positive time. The key ingredient is the derivation of a Carleman-type estimate. The diffusion coefficient is assumed to be dis...

Abstract. We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green-Kubo formula is also studied and its conver...

The transcription factor NF-κB shuttles between the cytoplasm and the nucleus, and nuclear NF-κB is known to oscillate with a cycle of 1.5-2.5 h following the application of external stimuli. Oscillation pattern of NF-κB is implicated in regulation of the gene expression profile. In a previous report, we found that the oscillation pattern of nuclear NF-κB in a computational 3D spherical cell wa...

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an asymptotically efficient estimator of the moment type functional or of a parameter which has a one-to-one correspondence to such a functional. Next, we clarify a higher...

We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow. The simulations are done in a local coordinate frame comoving with the gas in Keplerian rotation. Periodic boundary conditions are used in all directions, and vertical gravity is...

Molecular diffusion in brain extracellular space (ECS) is primarily controlled by interactions with the geometry and the interstitial matrix. Both factors increase λ, the tortuosity, a measure of hindrance to diffusion where λ2 = D/D∗ with D the free diffusion coefficient and D∗ the effective diffusion coefficient in brain [1]. Geometry lengthens diffusion paths or creates holdup in local voids...

Loss of cortical gray matter is accompanied by a commensurate increase in the sulcal and intraventricular cerebrospinal fluid volume. On diffusion-weighted magnetic resonance imaging, this would be reflected as a higher apparent diffusion coefficient in affected brain regions. On the basis of the above premise, we suggest that the apparent diffusion coefficient may be used as a surrogate marker...

The sedimentation and diffusion coefficients have been determined for Hemophilus influenzae transforming activity and DNA using P(32)-labeled DNA. The methods employed the Spinco fixed boundary separation cell for measurements of the sedimentation coefficient and the Northrop-Anson diffusion cell to determine the diffusion coefficient. There was a very close correlation between the amount of DN...

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical...