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Register a new userSharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect
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We consider the geometry relaxation of an isolated point defect embedded in a homogeneous crystalline solid, within an atomistic description. We prove a sharp convergence rate for a periodic supercell approximation with respect to uniform convergence of the discrete strains.
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We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two stable configurations converge as the cell size tends to infinity. We characterise the limits and establish sharp convergence rates. Both cases can be reduced to a careful renormalisation analysis of the vibrational entropy difference, which is achieved by identifying an underlying spatial decomposition.
We consider the dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles (the stops). We model the contact with Signorinis complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented.
This article studies the problem of approximating functions belonging to a Hilbert space $H_d$ with an isotropic or anisotropic Gaussian reproducing kernel, $$ K_d(bx,bt) = expleft(-sum_{ell=1}^dgamma_ell^2(x_ell-t_ell)^2right) mbox{for all} bx,btinreals^d. $$ The isotropic case corresponds to using the same shape parameters for all coordinates, namely $gamma_ell=gamma>0$ for all $ell$, whereas the anisotropic case corresponds to varying shape parameters $gamma_ell$. We are especially interested in moderate to large $d$.
A new set of nonlocal boundary conditions are proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
Numerical causal derivative estimators from noisy data are essential for real time applications especially for control applications or fluid simulation so as to address the new paradigms in solid modeling and video compression. By using an analytical point of view due to Lanczos cite{C. Lanczos} to this causal case, we revisit $n^{th}$ order derivative estimators originally introduced within an algebraic framework by Mboup, Fliess and Join in cite{num,num0}. Thanks to a given noise level $delta$ and a well-suitable integration length window, we show that the derivative estimator error can be $mathcal{O}(delta ^{frac{q+1}{n+1+q}})$ where $q$ is the order of truncation of the Jacobi polynomial series expansion used. This so obtained bound helps us to choose the values of our parameter estimators. We show the efficiency of our method on some examples.
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