Monte Carlo Calculations on Electron Backscattering in Amorphous or Polycrystalline Targets

We propose an application of the Monte Carlo method in the field of backscattering. The results obtained for incident electron energies ranging from 0.3 to 3 MeV and for targets of Al, Cu, Ag and Au are compared with experimental values from several sources. An electron travelling through matter undergoes successive collisions between which it is assumed to travel in a straight line. In our case, we consider the elementary process of interaction electron-nucleus; we have used analytical models for the scattering cross-sections. In order to follow the electron through the specimen, we divide the real trajectory into elements of length much smaller than the mean free path. Pseudo-random number process permits us to determine whether or not an interaction occurs, also the type of interaction. For the energy losses, we introduced a relation derived from Landau\u27s theory. We then followed the electron until it is emerged from the material or halted. The backscattering coefficients obtained for thin and thick targets as a function of the incident electron energy are in good agreement with the experimental data. We have introduced the depth distribution function of the backscattered electrons, which allows us to test the predictions of various theoretical models proposed by other authors

Verdier specialization via weak factorization

Let X in V be a closed embedding, with V - X nonsingular. We define a constructible function on X, agreeing with Verdier's specialization of the constant function 1 when X is the zero-locus of a function on V. Our definition is given in terms of an embedded resolution of X; the independence on the choice of resolution is obtained as a consequence of the weak factorization theorem of Abramovich et al. The main property of the specialization function is a compatibility with the specialization of the Chern class of the complement V-X. With the definition adopted here, this is an easy consequence of standard intersection theory. It recovers Verdier's result when X is the zero-locus of a function on V. Our definition has a straightforward counterpart in a motivic group. The specialization function and the corresponding Chern class and motivic aspect all have natural `monodromy' decompositions, for for any X in V as above. The definition also yields an expression for Kai Behrend's constructible function when applied to (the singularity subscheme of) the zero-locus of a function on V.Comment: Minor revision. To appear in Arkiv f\"or Matemati

Peculiar scaling of self-avoiding walk contacts

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N going to infinity they are strictly finite in number but their radius of gyration Rc is power law distributed, ~ Rc^{-\tau}, where \tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging lengths scales is associated to the Rc distribution. A possibly super-universal \tau=2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.Comment: 4 pages, 5 Postscript figures, uses psfig.sty; some sentences clarifie

Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in FCC Metals

We develop a finite element based dislocation dynamics model to simulate the structure and strength of dislocation junctions in FCC crystals. The model is based on anisotropic elasticity theory supplemented by the explicit inclusion of the separation of perfect dislocations into partial dislocations bounding a stacking fault. We demonstrate that the model reproduces in precise detail the structure of the Lomer-Cottrell lock already obtained from atomistic simulations. In light of this success, we also examine the strength of junctions culminating in a stress-strength diagram which is the locus of points in stress space corresponding to dissolution of the junction.Comment: 9 Pages + 4 Figure

Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts

Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.Comment: 9 pages, 7 figures, accepted for publication in EPJ

Interface relaxation in electrophoretic deposition of polymer chains: Effects of segmental dynamics, molecular weight, and field

Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation. Incorporation of faster modes such as crankshaft and reptation movements along with the relatively slow kink-jump dynamics seems crucial in relaxing the interface width. As the continuously released polymer chains are driven (via segmental movements) and deposited, the interface width $W$ grows with the number of time steps $t$, $W \propto t^{\beta},$ ($\beta \sim 0.4$--$0.8)$, which is followed by its saturation to a steady-state value $W_s$. Stopping the release of additional chains after saturation while continuing the segmental movements relaxes the saturated width to an equilibrium value ($W_s \to W_r$). Scaling of the relaxed interface width $W_r$ with the driving field $E$, $W_r \propto E^{-1/2}$ remains similar to that of the steady-state $W_s$ width. In contrast to monotonic increase of the steady-state width $W_s$, the relaxed interface width $W_r$ is found to decay (possibly as a stretched exponential) with the molecular weight.Comment: 5 pages, 7 figure

Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling

This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of fascinating phenomena can be observed. In particular, the interaction may result in the actuation of the droplet system, i.e. its displacement over a finite length. In order to control this displacement, we consider droplets confined on a hydrophilic stripe created by plasma-treating a PDMS substrate. This controlled actuation opens up unexplored opportunities in the field of microfluidics. In order to explain the observed actuation phenomenon, we propose a simple phenomenological model based on Newton's second law and a simple balance between the driving force arising from surface energy gradients and the viscous resistive force. This simple model is able to reproduce qualitatively and quantitatively the observed droplet dynamics

The effects of LHC civil engineering on the SPS and LEP machines

The LHC will utilise much of the existing LEP infrastructure but will require many new surface buildings and several smaller underground structures, two new transfer tunnels from the SPS to the LHC an d two huge cavern complexes to house the ATLAS and CMS experiments. Excavation for the underground structures will start while LEP and SPS are running, causig the existing tunnels in close proximity t o move. The predicted movements are of sufficient amplitude to prevent machine oepration if no precautions are taken

Adsorption-like Collapse of Diblock Copolymers

A linear copolymer made of two reciprocally attracting N-monomer blocks collapses to a compact phase through a novel transition, whose exponents are determined with extensive MC simulations in two and three dimensions. In the former case, an identification with the statistical geometry of suitable percolation paths allows to predict that the number of contacts between the blocks grows like $N^{9/16}$. In the compact phase the blocks are mixed and, in two dimensions, also zipped, in such a way to form a spiral, double chain structure.Comment: 4 pages, 5 Postscript figure