A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differe...

We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, “viscous” Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of appropriate “periodizations” of the equations. We also obtain an error estimate, when there is a rate of convergence for the stochastic homogenization.

In this paper we obtain Meyers type regularity estimates for approximate solutions of nonlinear elliptic equations. These estimates are used in the analysis of a numerical scheme obtained from a numerical homogenization of nonlinear elliptic equations. Numerical homogenization of nonlinear elliptic equations results in discretization schemes that require additional integrability of the approxim...

Homogenization is a collection of methods for extracting or constructing equations for the coarse-scale behavior of solutions to equations which incorporate many scales. This paper compares the classical method of homogenization with the recently developed multiresolution strategy for a particular class of onedimensional second-order elliptic equations. We also examine several physical examples...

We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homogenization by Blanc, Le Bris and P.-L. Lions. An application of the abstract result is given for Maxwell’s equations in random dissipative bianisotr...

1. Historically, biogeographic barriers to the movement of aquatic organisms existed at multiple spatial scales and contributed to the development of unique regional faunas. At increasing spatial scales, these barriers consisted of waterfalls and cascades; catchment divides; major mountain ranges and oceans. This hierarchy of movement barriers produced increasingly distinct aquatic biotas at la...

We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell’s partial differential equations. Key wordsMaxwell’s equations, Homogenization, two-scale convergence, oscillating test functions. (MSC)-2000: 35Q60, 35B27 [email protected] hassan.taha@labo...

Chronic pruritus is a debilitating condition with numerous etiologies. Many patients suffer from nocturnal pruritus, which can decrease quality of life and affect mortality in hemodialysis patients. Nocturnal pruritus may occur in all sleep stages but is most prevalent in stages N1 and N2. Further research is needed to elucidate the pathophysiology of nocturnal itch, which will aid in the devel...

A system for computer-assisted encoding, tabulation and analysis of visually scored sleep data is presented. The main features of the system are: (1) The use of computer-readable optical scan sheets for direct encoding of the sleep data. This eliminates the need for a separate transcription and/or key-punching operation. (2) The development of a visually scored data base, organized by NREM and ...