Search results for "Numerical"
showing 10 items of 2002 documents
A few remarks about the computer implementation and the verification of some hyperelastic constitutive laws and an illustration with the mechanical r…
2022
In this short technical note, we are interested in the constitutive equations used to model macroscopically the mechanical function of soft tissues under mechanical loading. Soft tissues have the ability to undergo large elastic reversible deformations under quasi-static loading and are usually modelled using hyperelastic constitutive laws. Several constitutive equations have been defined in the literature by means of strain components or strain invariants isotropic hyperelastic models. This short technical note recalls how to derive the weak form for hyperelasticity equations, and how this weak form can be linearized. It also presents a semi-analytical solution for a simplified geometry re…
Expansion dynamics of the plasma plume formed by the impact of a nanosecond Nd : YAG laser beam on metallic surface under atmospheric conditions : ex…
2010
Laser ablation in the air at atmospheric pressure is nowadays frequently applied in industry, chemical analysis, surgery… For a further development of laser ablation based technologies, it is necessary to better understand the laser – matter interaction. During the impact of a laser pulse on the surface of the treated material, a plasma plume forms above the target surface. This plume contains particles (electrons, ions, atoms) of ablated matter, as well as of ambient gas, if present. During the laser pulse, this plume absorbs a large amount of the laser beam energy, thus reducing the quantity of the laser radiation arriving to the target surface. Dimensions, as well as parameters of this p…
Optimisation d’un capteur solaire double passe à air et estimation des échanges de chaleur paroi-fluide.
2018
In this work, we present a study of the performance of a double pass flat solar collector for the production of hot air to supply and improve drying techniques. The cases of an absorber with and without fins are analyzed.Theoretical models for the double pass solar collector with and without fins have been established and solved numerically using codes developed in Fortran to obtain a global approach. Comsol Multi-physics code is used for a more local study. An experimental device has been designed to validate the results obtained numerically. One of the particularities of the solar collector developed in the laboratory is its insulation system. For this, a local bio-sourced material compos…
A Numerical Optimisation of a Stirling Engine
2011
International audience; A zero dimensional finite-time thermodynamic, three zones model of a generic Stirling engine has been developed and experimentally validated. Taking into account time-dependant heat transfers and losses, the model calculates the evolution of gas temperature, mass and pressure in each zone.
On a posteriori error bounds for approximations of the generalized Stokes problem generated by the Uzawa algorithm
2012
In this paper, we derive computable a posteriori error bounds for approximations computed by the Uzawa algorithm for the generalized Stokes problem. We show that for each Uzawa iteration both the velocity error and the pressure error are bounded from above by a constant multiplied by the L2-norm of the divergence of the velocity. The derivation of the estimates essentially uses a posteriori estimates of the functional type for the Stokes problem. peerReviewed
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
Mutual inductance for an explicitly finite number of turns
2011
Published version of an article published in Progress In Electromagnetics Research B, 28, 273-287. Also available from the publisher at http://www.jpier.org/pierb/pier.php?paper=10110103 Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an…
Optimal recovery of a radiating source with multiple frequencies along one line
2020
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.
Comparison between simulated and observed LHC beam backgrounds in the ATLAS experiment at E beam =4 TeV
2018
Results of dedicated Monte Carlo simulations of beam-induced background (BIB) in the ATLAS experiment at the Large Hadron Collider (LHC) are presented and compared with data recorded in 2012. During normal physics operation this background arises mainly from scattering of the 4 TeV protons on residual gas in the beam pipe. Methods of reconstructing the BIB signals in the ATLAS detector, developed and implemented in the simulation chain based on the FLUKA Monte Carlo simulation package, are described. The interaction rates are determined from the residual gas pressure distribution in the LHC ring in order to set an absolute scale on the predicted rates of BIB so that they can be compared qua…
A simulation function approach for best proximity point and variational inequality problems
2017
We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.