Search results for "Mathematica"
showing 10 items of 7971 documents
Localized potentials in electrical impedance tomography
2008
In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L ∞ -conductivities in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to con- struct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical imp…
Exact 3D solution for static and damped harmonic response of simply supported general laminates
2014
International audience; The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each …
Experimental determination of mode I fracture parameters in orthotropic materials by means of Digital Image Correlation
2020
Abstract The mode I fracture parameters for an orthotropic body are directly calculated from full-field deformation measurements provided by Digital Image Correlation (DIC). Three complementary and direct approaches are evaluated and compared: (i) the determination of the Stress Intensity Factor (SIF) by fitting the displacement field using the analytical expression proposed by Lekhnitskii; (ii) the determination of the J-Integral by using the Energy Domain Integral (EDI) formulation on the raw DIC data; and (iii) the calculation of the J-Integral using the EDI approach on the displacement data fitted using Lekhnitskii’s formulation. A comparative experimental study is performed by testing …
Modelling heat transfer-controlled cooling and freezing times: a comparison between computational values and experimental results
2013
Modelling of heat transfer-controlled cooling and freezing time predictions are very important for a good preservation of foodstuffs. In that regard, we used a computer code based on the finite-element method that allowed us to analyse the phase-change of various foodstuffs during their freezing. The model was exercised to predict process times. The results can be used to design high efficiency plants. In this work, the results predicted by the FEM program are compared with the experimental values given in technical literature.
Simplified Modeling of Radiant Fields in Heterogeneous Photoreactors. 2. Limiting “Two-Flux” Model for the Case of Reflectance Greater Than Zero
1997
In the first part of this work a simple model for the description of the radiant field in heterogeneous photoreactors was developed, based on the assumption of zero reflectance of the particles. In this second part of the investigation a limiting model is developed in which the above hypothesis is removed. In this last model, scattering phenomena are dealt with in a very simple “two-flux” way, so that analytical solutions are obtained again. The case here developed is the same as in part 1, namely slab geometry with orthogonal parallel irradiation, giving special reference to the important case of semi-infinite reactor thickness. Both cases of solid catalysts with single particle size and w…
Scenery Flow, Conical Densities, and Rectifiability
2015
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials
1998
In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system us…
A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates
2020
Abstract In this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a per-layer, high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layer-level description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on a discontinuous representation of the unknown fields over the mesh elements and on the introduction of boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order mesh elements and provide …