Space-time paths and prisms are time geographic concepts delimiting the actual and potential mobility pattern of an object in space and time, respectively. While there is a range of similarity measures for space-time paths, it is only recently that researchers started to develop similarity measures for the space-time prism (STP). This paper proposes a new methodology for measuring the similarit...

For the Boussinesq and Charny nonlinear diffusion equations we employ the known similarity solutions and derive new ones using the Adomian decomposition method and separation of variables. For a periodic water-drive regime with a heavier fluid sweeping a lighter one from a porous formation we arrive at an explicit analytical expression for the interface and describe the phenomena of “superpropa...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate swee...

Fixed-point iterative sweeping methods were developed in the literature to efficiently solve static Hamilton-Jacobi equations. This class of methods utilizes the Gauss-Seidel iterations and alternating sweeping strategy to achieve fast convergence rate. They take advantage of the properties of hyperbolic partial differential equations (PDEs) and try to cover a family of characteristics of the c...

This paper is devoted to weaken “classical” assumptions and give new arguments to prove existence of sweeping process (associated to the proximal normal cone of sets). Mainly we define the concept of a “directional prox-regularity” and give assumptions about a Banach space to insure the existence of such sweeping process (which permit to generalize the existing results requiring a Hilbertian st...

We have studied numerically steady and unsteady flow in a straight and a helically stented common carotid artery, in order to model porcine experimental results that show reduced intimal hyperplasia (IH) in the helical case. The combination of flow pulsatility and three-dimensionality generates a sweeping motion of the Dean vortices, which overall reduced extremes of both oxygen flux to the ves...

Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider the following slanted variant of sweeping recently introduced in [1]: In a single sweep, the sweep-line is placed at a start position somewhere in the plane,...

The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to v...

The focus of this project was to provide baseline PM10 emission factor data for almond sweeping operations as well as to move forward on quantification of a possible conservation management practice (CMP) for almond sweeping. In conjunction with the emission factor development work, continued quantification of sampler bias was conducted. This report provides an assessment of the progress and up...