In this paper, a nonlinear control volume finite element (CVFE) scheme for a degenerate Keller– Segel model with anisotropic and heterogeneous diffusion tensors is proposed and analyzed. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in finite element methods. The diffusion term which involves an anisotropic and heterogeneous tensor is discretized on...

1. Introduction In brain regions containing numerous parallel fibers, extracellular diffusion is anisotropic, i.e. faster along the fibers than across them, implying a preferential pathway for the transport of molecules in the extracellular space (ECS) [1,2]. To date, anisotropic diffusion in the ECS was measured with real-time iontophoretic method employing the small ion, tetramethylammonium (...

Many sensing techniques and image processing applications are characterized by random noisy, or corrupted, image data. Nonlinear Anisotropic diffusion is a popular, and theoretically well understood, technique for enhancing such images.Diffusion approaches however require the selection of an “edge stopping” function, the definition of which is typically adhoc. Many recent techniques for digital...

Advances in digital imaging techniques have made possible the acquisition of large volumes of Trans-rectal Ultrasound (TRUS) prostate images so that there is considerable demand for automated segmentation of these images. Prostate cancer diagnosis and treatment rely on segmentation of TRUS prostate images. This is a challenging and difficult task due to weak prostate boundaries, speckle noise, ...

Taylor dispersion--shear-induced enhancement of translational diffusion--is an important phenomenon with applications ranging from pharmacology to geology. Through experiments and simulations, we show that rotational diffusion is also enhanced for anisotropic particles in oscillatory shear. This enhancement arises from variations in the particle's rotation (Jeffery orbit) and depends on the str...

Transmittance and reflectance from spruce wood and bovine ligamentum nuchae as two different fibrous media are examined by time-of-flight spectroscopy for varying source detector separations and several orientations of the fibers in the sample. The anisotropic diffusion theory is used to obtain the absorption coefficient and the diffusion coefficients parallel and perpendicular to the fibers. T...

tics are described in this paper. We show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The “edge-~topping~’ function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new “edge-stopping’’ funct...

We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are sharp.

In the ordered phase of 2D XY ferromagnet the dipole force induce a strong interaction between spin-waves in the long wavelength limit. This interaction leads to the transformation of the spin-wave excitation into a new soft-mode excitation in an intermediate range of wavelengths limited in magnitude and direction; and into an anomalous anisotropic diffusion mode excitation at long wavelengths....

A symmetric discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may for instance be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell-centred if no edge unknown is kept. It is sh...