The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Bruno Denet - One of the best experts on this subject based on the ideXlab platform.
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Sivashinsky equation in a Rectangular Domain.
Physical Review E, 2007Co-Authors: Bruno DenetAbstract:The (Michelson) Sivashinsky equation of premixed flames is studied in a Rectangular Domain in two dimensions. A huge number of two-dimensional (2D) stationary solutions are trivially obtained by the addition of two 1D solutions. With Neumann boundary conditions, it is shown numerically that adding two stable 1D solutions leads to a 2D stable solution. This type of solution is shown to play an important role in the dynamics of the equation with additive noise.
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Sivashinsky equation in a Rectangular Domain
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2007Co-Authors: Bruno DenetAbstract:The (Michelson) Sivashinsky equation of premixed flames is studied in a Rectangular Domain in two dimensions. A huge number of 2D stationary solutions are trivially obtained by addition of two 1D solutions. With Neumann boundary conditions, it is shown numerically that adding two stable 1D solutions leads to a 2D stable solution. This type of solution is shown to play an important role in the dynamics of the equation with additive noise.
George Weiss - One of the best experts on this subject based on the ideXlab platform.
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stabilizability properties of a linearized water waves system
Systems & Control Letters, 2020Co-Authors: Marius Tucsnak, George WeissAbstract:Abstract We consider the strong stabilization of small amplitude gravity water waves in a two dimensional Rectangular Domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a multiple of a scalar input function u , times a given function h of the height along the active boundary. The state z of the system consists of two functions: the water level ζ along the top boundary, and its time derivative ζ . We prove that for suitable functions h , there exists a bounded feedback functional F such that the feedback u = F z renders the closed-loop system strongly stable. Moreover, for initial states in the Domain of the semigroup generator, the norm of the solution decays like ( 1 + t ) − 1 6 . Our approach uses a detailed analysis of the partial Dirichlet to Neumann and Neumann to Neumann operators associated to certain edges of the Rectangular Domain, as well as recent abstract non-uniform stabilization results by Chill et al. (2019).
Paul Sablonnière - One of the best experts on this subject based on the ideXlab platform.
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error bounds on the approximation of functions and partial derivatives by quadratic spline quasi interpolants on non uniform criss cross triangulations of a Rectangular Domain
Bit Numerical Mathematics, 2013Co-Authors: Catterina Dagnino, Sara Remogna, Paul SablonnièreAbstract:Given a non-uniform criss-cross triangulation of a Rectangular Domain Ω, we consider the approximation of a function f and its partial derivatives, by general C1 quadratic spline quasi-interpolants and their derivatives. We give error bounds in terms of the smoothness of f and the characteristics of the triangulation. Then, the preceding theoretical results are compared with similar results in the literature. Finally, several examples are proposed for illustrating various applications of the quasi-interpolants studied in the paper.
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Error bounds on the approximation of functions and partial derivatives by quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of a Rectangular Domain
BIT Numerical Mathematics, 2013Co-Authors: Dagnino Catterina, Sara Remogna, Paul SablonnièreAbstract:Given a non-uniform criss-cross triangulation of a Rectangular Domain $\Omega$, we consider the approximation of a function f and its partial derivatives, by general $C^1$ quadratic spline quasi-interpolants and their derivatives. We give error bounds in terms of the smoothness of f and the characteristics of the triangulation. Then, the preceding theoretical results are compared with similar results in the literature. Finally, several examples are proposed for illustrating various applications of the quasi-interpolants studied in the paper.
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approximating partial derivatives of first and second order by quadratic spline quasi interpolants on uniform meshes
Mathematics and Computers in Simulation, 2008Co-Authors: Françoise Foucher, Paul SablonnièreAbstract:Given a bivariate function f defined in a Rectangular Domain @W, we approximate it by a C^1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example.
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Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants
Mathematics and Computers in Simulation, 2008Co-Authors: Françoise Foucher, Paul SablonnièreAbstract:Given a bivariate function $f$ defined in a Rectangular Domain $\omega$, we approximate it by a $C^1$ quadratic spline quasi-interpolant (abbr. QI) and we take partial derivatives of this QI as approximations to those of $f$. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example.
Marius Tucsnak - One of the best experts on this subject based on the ideXlab platform.
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stabilizability properties of a linearized water waves system
Systems & Control Letters, 2020Co-Authors: Marius Tucsnak, George WeissAbstract:Abstract We consider the strong stabilization of small amplitude gravity water waves in a two dimensional Rectangular Domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a multiple of a scalar input function u , times a given function h of the height along the active boundary. The state z of the system consists of two functions: the water level ζ along the top boundary, and its time derivative ζ . We prove that for suitable functions h , there exists a bounded feedback functional F such that the feedback u = F z renders the closed-loop system strongly stable. Moreover, for initial states in the Domain of the semigroup generator, the norm of the solution decays like ( 1 + t ) − 1 6 . Our approach uses a detailed analysis of the partial Dirichlet to Neumann and Neumann to Neumann operators associated to certain edges of the Rectangular Domain, as well as recent abstract non-uniform stabilization results by Chill et al. (2019).
Gregor Skok - One of the best experts on this subject based on the ideXlab platform.
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analysis of fraction skill score properties for a displaced rainy grid point in a Rectangular Domain
Atmospheric Research, 2016Co-Authors: Gregor SkokAbstract:Abstract The Fraction Skill Score (FSS) is a recently developed and popular metric used for precipitation verification. A compact analytical expression for FSS is derived for a case with a single displaced rainy grid point in a Rectangular Domain. The existence of an analytical solution is used to determine some properties of FSS, which might also be applicable in other cases since the rain areas of any shape will asymptote towards this solution if the displacement is sufficiently large. The use of the simple square shape of the neighborhood causes the FSS value to be dependent on the direction of the displacements (not only on the displacement size). The effect is limited in scope but can increase or decrease the FSS value by 0.1. Moving a nearby border closer to the rainy points can either increase or decrease the FSS value, depending on the location of the border. The FSS value near a border can be at most 33% larger than the FSS value in the infinite Domain, assuming the same neighborhood size and displacement. The effect of the nearby corner is similar to the effect of the nearby border but is stronger. The useful forecast criteria (FSS useful ) is defined as a value of FSS for a precipitation feature with a displacement half the neighborhood size. FSS useful for a displaced rainy grid point depends on the orientation of the displacement being the largest for displacements that are parallel to the borders and the smallest for a diagonal displacement for which the value can be as low as 0.42. An analysis of a real dataset was also performed, which showed that the border effect is usually small, but in some cases the effect becomes large (an increase of FSS value up to 70% was identified). The likelihood of a strong border effect in real datasets increases significantly if the neighborhood size at FSS = 0.5 is comparable or larger than the Domain size.
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Analysis of Fraction Skill Score properties for a displaced rainband in a Rectangular Domain
Meteorological Applications, 2014Co-Authors: Gregor SkokAbstract:A compact analytical expression of the Fraction Skill Score (FSS) is derived for a case with a single displaced rainband in a Rectangular Domain. The rainband is oriented parallel to the border and displaced perpendicularly to its orientation. An analytical solution is used to determine some of the properties of the FSS which might also be applicable in other cases. The solution is independent of the length of the rainband (it is valid also for a displaced rainy grid point). The position of the borders perpendicular to the rainband orientation does not influence the FSS value. The position of the other two borders does however influence the FSS value in a complex way; moving a border closer to the rainbands can either increase or decrease the FSS value depending on the location of the borders. FSS is shown to be a monotonically increasing function of the neighbourhood size (regardless of the position of the borders). If the FSS value for a displacement that is half the neighbourhood size is used to define a ‘useful’ FSS value then the usefulness criterion is somewhat different than presented in the original FSS paper (there is no dependence on the frequency of the observations/forecasts). ‘Useful’ FSS values are always >1/2 but depend on the position of the borders and the size of the displacement.
