We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an L function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the BV theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equa...

The segmentation of cytoplast and nucleus from a cervical cell image is one of important techniques for automatically detecting abnormal cervical cells. Noise on an image often makes segmentation inaccurate. This paper presents two new techniques, named trimming-mean filter and bi-grouping enhancer, to effectively eliminate noise and make the object boundaries more discernible. In this paper, t...

We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow, except in cases where the underlying manifold is topologically simple (i.e., a graphmanifold). Furthermore, there are strong restrictions on the types of gr...

We present a simple approach to the topological analysis of divergencefree 2D vector fields using discrete Morse theory. We make use of the fact that the point-wise perpendicular vector field can be interpreted as the gradient of the stream function. The topology of the divergence-free vector field is thereby encoded in the topology of a gradient vector field. We can therefore apply a formulati...

A new use of smoothed particle hydrodynamics (SPH) in fluid simulation is presented: an algorithm solving the Helmholtz-Hodge decomposition using SPH in order to find the null divergence velocity field for incompressible flow simulation. Accordingly, a new version of the Laplacian for a vector field is proposed here. In order to improve the accuracy of the SPH technique, the paper also presents...

We analyze dynamical systems of general form possessing gradient (symmetric) and Hamiltonian (antisymmetric) flow parts. The relevance of such systems to self-organizing processes is discussed. Coherent structure formation and related gradient flows on matrix Grassmann type manifolds are considered. The corresponding graph model associated with the partition swap neighborhood problem is studied...

Title of thesis: DISTRIBUTED FLOW OPTIMIZATION IN DENSE WIRELESS NETWORKS Sina Zahedpour Anaraki, Master of Science, 2011 Thesis directed by: Dr. Mehdi Kalantari Department of Electrical and Computer Engineering Due to large number of variables, optimizing information flow in a dense wireless network using discrete methods can be computationally prohibitive. Instead of treating the nodes as dis...

An analytical investigation is conducted to study the unsteady free convection heat and mass transfer flow through a non-homogeneous porous medium with variable permeability bounded by an infinite porous vertical plate in slip flow regime while taking into account the thermal radiation, chemical reaction, the Soret number, and temperature gradient dependent heat source. The flow is considered u...