The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Martin Vallee - One of the best experts on this subject based on the ideXlab platform.
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Source Time Function properties indicate a strain drop independent of earthquake depth and magnitude
Nature Communications, 2013Co-Authors: Martin ValleeAbstract:The movement of tectonic plates leads to strain build-up in the Earth, which can be released during earthquakes when one side of a seismic fault suddenly slips with respect to the other. The amount of seismic strain release (or ‘strain drop’) is thus a direct measurement of a basic earthquake property, that is, the ratio of seismic slip over the dimension of the ruptured fault. Here the analysis of a new global catalogue, containing ~1,700 earthquakes with magnitude larger than 6, suggests that strain drop is independent of earthquake depth and magnitude. This invariance implies that deep earthquakes are even more similar to their shallow counterparts than previously thought, a puzzling finding as shallow and deep earthquakes are believed to originate from different physical mechanisms. More practically, this property contributes to our ability to predict the damaging waves generated by future earthquakes.
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source Time Function properties indicate a strain drop independent of earthquake depth and magnitude
Nature Communications, 2013Co-Authors: Martin ValleeAbstract:Earthquakes occur on a broad range of depths and magnitudes, making their origins and impacts difficult to assess. Here, the analysis of 1,700 earthquakes reveals that strain drop is globally invariant, providing constraints on the rupture process and simplifying the task of earthquake damage predictions.
Ronald J. Stern - One of the best experts on this subject based on the ideXlab platform.
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The state constrained bilateral minimal Time Function
Nonlinear Analysis: Theory Methods & Applications, 2008Co-Authors: Chadi Nour, Ronald J. SternAbstract:Abstract We generalize, to the bilateral case (that is, with variable initial and end points), the main results of Nour and Stern [C. Nour, R.J. Stern, Regularity of the state constrained minimal Time Function, Nonlinear Anal. 66 (1) (2007) 62–72] and Stern [R.J. Stern, Characterization of the state constrained minimal Time Function, SIAM J. Control Optim. 43 (2004) 697–707], where the regularity and Hamilton–Jacobi characterization of the state constrained (unilateral) minimal Time Function were studied.
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Semiconcavity of the bilateral minimal Time Function: The linear case
Systems & Control Letters, 2008Co-Authors: Chadi Nour, Ronald J. SternAbstract:Abstract For a linear control system, we provide conditions under which the bilateral minimal Time Function T ( ⋅ , ⋅ ) is semiconcave near a given point ( α , β ) . A semiconvexity result of Nour [C. Nour, The bilateral minimal Time Function, J. Convex Anal. 13 (1) (2006) 61–80, Theorem 4.7] allows us to deduce that T ( ⋅ , ⋅ ) is then also C 1 , 1 -smooth near ( α , β ) . The nonlinear case, which remains open, is discussed in the concluding remarks.
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Regularity of the state constrained minimal Time Function
Nonlinear Analysis: Theory Methods & Applications, 2007Co-Authors: Chadi Nour, Ronald J. SternAbstract:Abstract The regularity of the state constrained minimal Time Function is studied. We generalize [P. Wolenski, Y. Zhuang, Proximal analysis and the minimal Time Function, SIAM J. Control Optim. 36 (1998) 1048–1072, Theorem 6.1] in which Wolenski and Zhuang give necessary and sufficient conditions for Lipschitz continuity of the unconstrained minimal Time Function, and discuss certain ramifications.
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Characterization of the State Constrained Minimal Time Function
SIAM Journal on Control and Optimization, 2004Co-Authors: Ronald J. SternAbstract:A standard class of finite dimensional control systems is considered, along with a state constraint set S and a target set $\Sigma \subset S$. Under certain geometric assumptions on S and a required S-constrained small Time controllability property, a proximal Hamilton--Jacobi characterization of the S-constrained minimal Time Function to target $\Sigma$ is obtained.
Chadi Nour - One of the best experts on this subject based on the ideXlab platform.
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The state constrained bilateral minimal Time Function
Nonlinear Analysis: Theory Methods & Applications, 2008Co-Authors: Chadi Nour, Ronald J. SternAbstract:Abstract We generalize, to the bilateral case (that is, with variable initial and end points), the main results of Nour and Stern [C. Nour, R.J. Stern, Regularity of the state constrained minimal Time Function, Nonlinear Anal. 66 (1) (2007) 62–72] and Stern [R.J. Stern, Characterization of the state constrained minimal Time Function, SIAM J. Control Optim. 43 (2004) 697–707], where the regularity and Hamilton–Jacobi characterization of the state constrained (unilateral) minimal Time Function were studied.
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Semiconcavity of the bilateral minimal Time Function: The linear case
Systems & Control Letters, 2008Co-Authors: Chadi Nour, Ronald J. SternAbstract:Abstract For a linear control system, we provide conditions under which the bilateral minimal Time Function T ( ⋅ , ⋅ ) is semiconcave near a given point ( α , β ) . A semiconvexity result of Nour [C. Nour, The bilateral minimal Time Function, J. Convex Anal. 13 (1) (2006) 61–80, Theorem 4.7] allows us to deduce that T ( ⋅ , ⋅ ) is then also C 1 , 1 -smooth near ( α , β ) . The nonlinear case, which remains open, is discussed in the concluding remarks.
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Regularity of the state constrained minimal Time Function
Nonlinear Analysis: Theory Methods & Applications, 2007Co-Authors: Chadi Nour, Ronald J. SternAbstract:Abstract The regularity of the state constrained minimal Time Function is studied. We generalize [P. Wolenski, Y. Zhuang, Proximal analysis and the minimal Time Function, SIAM J. Control Optim. 36 (1998) 1048–1072, Theorem 6.1] in which Wolenski and Zhuang give necessary and sufficient conditions for Lipschitz continuity of the unconstrained minimal Time Function, and discuss certain ramifications.
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The Bilateral Minimal Time Function
2006Co-Authors: Chadi NourAbstract:In this paper, we study the minimal Time Function as a Function of two variables (the initial and the terminal points). This Function, called the ’bilateral minimal Time Function‘, plays a central role in the study of the Hamilton-Jacobi equation of minimal control in a domain which contains the target set, as shown in [11]. We study the regularity of the Function, and characterize it as the unique (viscosity) solution of partial Hamilton-Jacobi equations with certain boundary conditions.
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Semigeodesics and the minimal Time Function
ESAIM: Control Optimisation and Calculus of Variations, 2005Co-Authors: Chadi NourAbstract:We study the Hamilton-Jacobi equation of the minimal Time Function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal. , 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.
Yi Jiang - One of the best experts on this subject based on the ideXlab platform.
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Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems
Journal of Optimization Theory and Applications, 2015Co-Authors: Yi Jiang, Jie SunAbstract:The minimal Time Function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal Time Functions of the Yosida approximation equations converge to the minimal Time Function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal Time Function satisfying the Hamilton---Jacobi---Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems.
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subdifferentials of a perturbed minimal Time Function in normed spaces
Optimization Letters, 2014Co-Authors: Yongle Zhang, Yiran He, Yi JiangAbstract:In a general normed vector space, we study the perturbed minimal Time Function determined by a bounded closed convex set \(U\) and a proper lower semicontinuous Function \(f(\cdot )\). In particular, we show that the Frechet subdifferential and proximal subdifferential of a perturbed minimal Time Function are representable by virtue of corresponding subdifferential of \(f(\cdot )\) and level sets of the support Function of \(U\). Some known results is a special case of these results.
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Subdifferential properties of the minimal Time Function of linear control systems
Journal of Global Optimization, 2010Co-Authors: Yi Jiang, Jie SunAbstract:Minimal Time Function, Linear control system, Subdifferentials, Normal cones,
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Subdifferential properties of the minimal Time Function of linear control systems
Journal of Global Optimization, 2010Co-Authors: Yi Jiang, Jie SunAbstract:We present several formulae for the proximal and Frechet subdifferentials of the minimal Time Function defined by a linear control system and a target set. At every point inside the target set, the proximal/Frechet subdifferential is the intersection of the proximal/Frechet normal cone of the target set and an upper level set of a so-called Hamiltonian Function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Frechet subdifferential is the intersection of the proximal/Frechet normal cone of an enlargement of the target set and a level set of the Hamiltonian Function.
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subdifferentials of a minimal Time Function in normed spaces
Journal of Mathematical Analysis and Applications, 2009Co-Authors: Yi Jiang, Yiran HeAbstract:Abstract In a general normed vector space, we study the minimal Time Function determined by a differential inclusion where the set-valued mapping involved has constant values of a bounded closed convex set U and by a closed target set S. We show that proximal and Frechet subdifferentials of a minimal Time Function are representable by virtue of corresponding normal cones of sublevel sets of the Function and level or suplevel sets of the support Function of U. The known results in the literature require the set U to have the origin as an interior point or U be compact. (In particular, if the set U is the unit closed ball, the results obtained reduce to the subdifferential of the distance Function defined by S.)
J. Guilbert - One of the best experts on this subject based on the ideXlab platform.
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Single station estimation of seismic source Time Function from coda waves: The Kursk disaster.
Geophysical Research Letters, 2005Co-Authors: O. Sebe, Pierre-yves Bard, J. GuilbertAbstract:We propose a high-resolution technique for estimating the source Time Function of a seismic event from only one record. This technique is based on the spectral factorization of the minimum phase wavelet from the most random part of a seismogram: its coda. As the coda non-stationarity is inconsistent with the classical spectral factorization theory, we develop a two-step algorithm: first, the diffuse coda field is whitened to remove the non-stationary attenuation effect; second, the minimum phase wavelet equivalent of the seismic source Time Function is estimated. Applied to the recordings of the Kursk's wreck, this method gives a source wavelet strikingly similar to the general shape of an underwater explosion, allowing us to infer its depth and yield. Based on the fundamental “random” character of diffusive waves, this approach opens up promising applications for new blind deconvolution methods.
