Adaptive radiation therapy (ART) is the incorporation of daily images in the radiotherapy treatment process so that the treatment plan can be evaluated and modified to maximize the amount of radiation dose to the tumor while minimizing the amount of radiation delivered to healthy tissue. Registration of planning images with daily images is thus an important component of ART. In this article, th...

The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow up for some initial configurations. This paper strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional weakly restricted Euler-Poisson (WREP) system. This system can be viewed as an im...

The Tadmor type of entropy conservation formulation for the Euler equations and various skewsymmetric splittings of the inviscid flux derivatives are discussed. Numerical stability of high order central and Padé type (centered compact) spatial discretization is enhanced through the application of these formulations. Numerical test on a 2-D vortex convection problem indicates that the stability ...

This work provides a description of the critical threshold phenomenon in multi-dimensional restricted Euler–Poisson (REP) equations, introduced in [H. Liu, E. Tadmor. Spectral dynamics of the velocity gradient field in restricted fluid flows, Comm. Math. Phys. 228 (2002) 435–466]. For three-dimensional REP equations, we identified both upper thresholds for the finite-time blow up of solutions a...

We study the large-time behaviour of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g. Cucker & Smale (2007 IEEE Trans. Autom. Control 52, 852-862. (doi:10.1109/TAC.2007.895842)) and Motsch & Tadmor (2011 J. Stat. Phys. 144, 923-947. (doi:10.1007/s10955-011-0285-9)) models. We prove that, ...

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations.A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two nonstandard formulations, that numerous F...

A. Motivated by the hierarchical multiscale image representation of Tadmor et. al., [25], we propose a novel integro-differential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale space a succession of refined, recursive ‘slices’ of the image, which are balanced by a typical curvature term at the finer scale. Although the original motivati...

We study the behavior of oscillatory solutions to convection-diiusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W ?1;1 to the 'expected' averages and obtain a sharp W ?1;1-convergence rate of order O(") { the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this wea...

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind di erencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the eld-byeld decomposition which is required in order to identify the \direction of the wind." Instead, we propose to use as a building block the more robu...