Effects of physics change in Monte Carlo code on electron pencil beam dose distributions

Pencil beam algorithms used in computerized electron beam dose planning are usually described using the small angle multiple scattering theory. Alternatively, the pencil beams can be generated by Monte Carlo simulation of electron transport. In a previous work, the 4th version of the Electron Gamma Shower (EGS) Monte Carlo code was used to obtain dose distributions from monoenergetic electron pencil beam, with incident energy between 1 MeV and 50 MeV, interacting at the surface of a large cylindrical homogeneous water phantom. In 2000, a new version of this Monte Carlo code has been made available by the National Research Council of Canada (NRC), which includes various improvements in its electron-transport algorithms. In the present work, we were interested to see if the new physics in this version produces pencil beam dose distributions very different from those calculated with oldest one. The purpose of this study is to quantify as well as to understand these differences. We have compared a series of pencil beam dose distributions scored in cylindrical geometry, for electron energies between 1 MeV and 50 MeV calculated with two versions of the Electron Gamma Shower Monte Carlo Code. Data calculated and compared include isodose distributions, radial dose distributions and fractions of energy deposition. Our results for radial dose distributions show agreement within 10% between doses calculated by the two codes for voxels closer to the pencil beam central axis, while the differences are up to 30% for longer distances. For fractions of energy deposition, the results of the EGS4 are in good agreement (within 2%) with those calculated by EGSnrc at shallow depths for all energies, whereas a slightly worse agreement (15%) is observed at deeper distances. These differences may be mainly attributed to the different multiple scattering for electron transport adopted in these two codes and the inclusion of spin effect, which produces an increase of the effective range of electrons.     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Cyano terminated tolane compounds for polymer dispersed liquid crystal application: relationship between cyano terminated tolane based molecular structures and electro-optical properties

ABSTRACT

The structures of the liquid crystal (LC) molecules have a key role in impacting the electro-optical performance of a polymer dispersed liquid crystal (PDLC) film. In this paper, the relationship between the LC molecular structures and the electro-optical properties of PDLC films is investigated based on an unexplored cyano-terminated tolane compounds (CTTCs) doped E8 LCs/UV polymers system. Due to the high polarity of CTTCs, LCs doped with the cyano-terminated tolane (CTT) molecules exhibit high birefringence and large positive dielectric anisotropy. On the whole, PDLC films doped with the CTT molecules exhibit a lower driving voltage than that doped with the pure E8. More excitingly, PDLC films based on CTT molecules with larger length-to-width ratio and longer conjugated system show higher contrast ratio (CR) and faster response time. Eventually, the mechanism of the effects of CTT-based molecular structures and the relationship between the electro-optical performance of PDLC films and CTT molecules are illustrated. This work paves a new way for optimising the electro-optical properties of PDLC films.     

Sur les Transformations Simultanées de Deux Équations Différentielles Linéaires du Deuxième Ordre dans Elles-mêmes

AMS (MOS) Classification 34C20     

POSITIVE SOLUTIONS TO(k,n-k) NONHOMOGENEOUS BOUNDARYVALUE PROBLEM

By the Schauder fixed point theory,this paper establishes the existence of positive solutions to a(k,n k) m-point boundary value problem.We show that there exists a positive constant b such that the problem has at least one positive solution when the homogeneous boundary parameter is smaller than b,and no positive solution when this parameter is greater than b.     

On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.     

Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations

A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well‐known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein–Gordon equation and generalized Boussinesq equation is proven. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being. Copyright © 2015 John Wiley & Sons, Ltd.