Treatment Of Energy Loss Research Articles

Aspects of Impact of Planar Deformable Bodies as Linear Complementarity Problems

This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in [7]. Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach.

On the treatment of energy loss in track fitting

As the energy loss of electrons in matter is described by a strongly non-Gaussian distribution, the Kalman filter is not necessarily the optimal procedure for the fitting of electron tracks. We show that the momentum resolution can be improved by using nonlinear methods, such as the Gaussian-sum filter and the Metropolis—Hastings algorithm. We report results of a simple simulation experiment and comment on the respective merits of these methods.

Track fitting with energy loss

This note deals with the treatment of energy loss in track fitting. After reviewing the basic physics of energy loss, we describe the stochastic model and the implementation in the framework of the Kalman filter algorithm. The method is illustrated with results from electron tracks in the DELPHI detector.

Monte Carlo electron trajectory simulation of x-ray emission from films supported on substrates

Monte Carlo electron trajectory simulation provides a powerful tool for theoretical studies of electron/x-ray interactions in solid targets. The great power of a Monte Carlo technique arises from the stepwise treatment of the electron trajectory in the target, which provides the capability of dealing with unusual geometric boundary conditions which differ from the ideal of a flat, polished, semiinfinite slab. Special targets, such as randomly tilted surfaces, particles, thin foils, and films supported on substrates, can be simulated by a Monte Carlo procedure.It is proper to speak of “a” rather than “the” Monte Carlo procedure because there is no single formulation of the simulation in universal use. A variety of choices exists for the treatment of the scattering and energy loss processes. In particular, the approach to simulating inelastic scattering varies widely. While most calculations consider inelastic scattering by means of a continuous energy loss approximation rather than by modeling the discrete inelastic processes, there are now several different choices proposed for the treatment of energy loss in the low energy range (<3 keV) where the Bethe model proves inadequate.