Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Calibration of BAS-TR image plate response to high energy (3-300 MeV) carbon ions

The paper presents the calibration of Fuji BAS-TR image plate (IP) response to high energy carbon ions of different charge states by employing an intense laser-driven ion source, which allowed access to carbon energies up to 270 MeV. The calibration method consists of employing a Thomson parabola spectrometer to separate and spectrally resolve different ion species, and a slotted CR-39 solid state detector overlayed onto an image plate for an absolute calibration of the IP signal. An empirical response function was obtained which can be reasonably extrapolated to higher ion energies. The experimental data also show that the IP response is independent of ion charge states.

On the numerical solution of the 2d wave equation with compact fdtd schemes

This paper discusses compact-stencil finite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and efficiency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also discusses the relevance to digital waveguide mesh modelling, and highlights the optimally efficient explicit scheme.

A Schamel equation for ion acoustic waves in superthermal plasmas

An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u₀. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation. 

Non-linear analysis of composite structures with integrated piezoelectric sensors and actuators

This paper deals with the geometrically non linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuors or sensors layers and/or patches.The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings. the finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of fredom for the generalized displacements and one eçlectrical potential degree of freedom for each piezoelectric layer or patch. An updated Lagrangian formulation associated to Newton-Raphson technique is used to solve incrementally and iteratively the equilibrium equation.The model is applied in the solution of four illustrative cases, and the results are compared and discussedwith alternative solutions when available.

Magnetic studies of the Late Cretaceous magmatism in Portugal : from Iberian plate kinematics to magnetic fabrics

Tese de doutoramento (co-tutela), Ciências Geofísicas e da Geoinformação (Geofísica), Université de Toulouse, Universidade de Lisboa, 2013

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

Trigger and data link system for CMS Resistive Plate Chambers at the LHC accelerator

The purpose of the work was to realize a high-speed digital data transfer system for RPC muon chambers in the CMS experiment on CERN’s new LHC accelerator. This large scale system took many years and many stages of prototyping to develop, and required the participation of tens of people. The system interfaces to Frontend Boards (FEB) at the 200,000-channel detector and to the trigger and readout electronics in the control room of the experiment. The distance between these two is about 80 metres and the speed required for the optic links was pushing the limits of available technology when the project was started. Here, as in many other aspects of the design, it was assumed that the features of readily available commercial components would develop in the course of the design work, just as they did. By choosing a high speed it was possible to multiplex the data from some the chambers into the same fibres to reduce the number of links needed. Further reduction was achieved by employing zero suppression and data compression, and a total of only 660 optical links were needed. Another requirement, which conflicted somewhat with choosing the components a late as possible was that the design needed to be radiation tolerant to an ionizing dose of 100 Gy and to a have a moderate tolerance to Single Event Effects (SEEs). This required some radiation test campaigns, and eventually led to ASICs being chosen for some of the critical parts. The system was made to be as reconfigurable as possible. The reconfiguration needs to be done from a distance as the electronics is not accessible except for some short and rare service breaks once the accelerator starts running. Therefore reconfigurable logic is extensively used, and the firmware development for the FPGAs constituted a sizable part of the work. Some special techniques needed to be used there too, to achieve the required radiation tolerance. The system has been demonstrated to work in several laboratory and beam tests, and now we are waiting to see it in action when the LHC will start running in the autumn 2008.

[1er mai 1920 à Paris, un receveur volontaire encadré par des gendarmes sur la plate-forme d'un autobus] : [photographie de presse] / [Agence Rol]

Référence bibliographique : Rol, 59111