Abstract We show that solutions for a specifically scaled nonlinear wave equation of elasticity converge to linear Euler–Bernoulli beam system. construct an approximation the solution, using suitable asymptotic expansion ansatz based upon one-dimensional equation. Following this, we derive existence appropriately initial data and can bound difference between analytical solution approximating se...

In this paper, the conditions for which three-dimensional crystalline ion beams were attained in the rf quadrupole storage ring PALLAS at a velocity of around 2800 m/s are presented. The stability of these crystalline beams when subjected to discontinuous cooling is discussed for beams of different linear density and thus of different crystal structure. The survival time seems to only weakly de...

PURPOSE To characterize and quantify the distal edge activity fall off, created in a phantom by a proton therapy beam METHOD AND MATERIALS: A 30×30×10cm polymethylmethacrylate phantom was irradiated with a proton therapy beam using different ranges and beams. The irradiation volume is approximated by a right circular cylinder of diameter 7.6cm and varying lengths. After irradiation, the phantom...

We report two-dimensional simulations of strongly vibrated granular materials in zero gravity. The coefficient of restitution depends on the impact velocity between particles by taking into account both the viscoelastic and plastic deformations of particles, occurring at low and high velocities respectively. Use of this realistic restitution coefficient leads to new unexpected behaviors. When t...

Modern dual photon energy linear accelerators often come with a few megavoltage electron beams. The megavoltage electron beam has limited range and relative sharp distal falloff in its depth dose curve compared to that of megavoltage photon beam. Its radiation dose is often delivered appositionally to cover the target volume to its distal 90% depth dose (d90), while avoiding the normal--sometim...