We modeled the landscape dispersal process as a diffusion equation system, which describes the movements of insects around an interior boundary between two habitat types. For quantifying the diffusion parameters, the model with discontinuous diffusion rates within the composite medium, and with the absorbing exterior boundaries need to be solved. Two cases were studied: 1) Rectangular filed. 2)...

We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of scalar parabolic equations of divergence form with discontinuous coefficients. The estimate is very important for many applications. For example, it is impor...

In this work we study the inhomogeneous Muskat problem, \emph{i.e.} evolution of an internal wave between two different fluids in a porous medium with discontinuous permeability. particular, under precise conditions on initial datum and physical quantities our results ensure decay solutions towards equilibrium state Lipschitz norm. addition, establish global existence solutions.

We experimentally investigate the flow field in plane geometry around a slowly moving rigid finger in a dry, randomly packed granular medium. The finger enters the medium vertically from its free surface, in analogy with indentation tests on ductile materials. By developing a particle imaging velocimetry technique, we identify a localized flow around the finger, limited by two nearly symmetric ...

A nonspecific density labeling technique has been employed to monitor the synthesis of intracytoplasmic membrane in synchronously dividing populations of Rhodopseudomonas sphaeroides. The intracytoplasmic membranes of cells synchronized in D2O-based medium were found to undergo discontinuous decreases in specific density during synchronous cell growth following transfer to H2O-based medium. The...