In this paper, we consider the problem of planning collision-free trajectories to navigate a team of labeled robots from a set of start locations to a set of goal locations, where robots have pre-assigned and non-interchangeable goals. We present a solution to this problem for a centralized team operating in an obstaclefree, two-dimensional workspace. Our algorithm allows robots to follow Optim...

Stereotactic body radiation therapy (SBRT) using recently introduced multileaf collimators (MLC) is preferred over circular collimators in the treatment of localized prostate cancer. The objective of this study was to assess the clinical usefulness of MLCs in prostate SBRT by comparing the effectiveness of treatment plans using fixed collimators, variable collimators, and MLCs and by ensuring d...

BACKGROUND Intensity-modulated radiotherapy is useful for cervical oesophageal carcinoma (CEC); however, increasing low-dose exposure to the lung may lead to radiation pneumonitis. Nevertheless, an irradiation technique that avoids the lungs has never been examined due to the high difficulty of dose optimization. In this study, we examined the efficacy of helical tomotherapy that can restrict b...

The initial stages of spinodal decomposition were studied by subjecting a critical blend of model polyolefins to a pressure quench and monitoring the evolution by time-resolved small angle neutron scattering. Contrary to the predictions of the widely accepted Cahn-Hilliard-Cook theory, we demonstrate that coarsening of the phase-separated structure begins immediately after the quench and occurs...

This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved order parameter and resembles the Swift-Hohenberg model. The early-stage growth kinetics is analyzed and compared to the Cahn-Hilliard theory of continuous o...

We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in R, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: partial differentialxG(Hx). We find that the stability of steady states depends on dv/dq , the derivative of the interface velocity on the wave vector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if G is an odd function of Hx. In this case...

Milling is the mechanical process of removing material from a piece of stock through the use of a rapidly spinning circular milling tool in order to form some desired geometric shape. An important problem in computer-aided design and manufacturing is the automated generation of efficient milling plans for computerized numerically controlled (CNC) milling machines. Among the most common milling ...