The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
N. V. Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
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Matlab Code for lyapunov exponents of fractional order systems
International Journal of Bifurcation and Chaos, 2018Co-Authors: Mariusf Danca, N. V. KuznetsovAbstract:In this paper, the Benettin–Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo’s derivative and the corresponding Matlab Code are presented...
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Matlab Code for lyapunov exponents of fractional order systems
arXiv: Computational Physics, 2018Co-Authors: Mariusf Danca, N. V. KuznetsovAbstract:In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab Code are presented. First it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The Matlab program prints and plots the Lyapunov exponents as function of time. Also, the programs to obtain Lyapunov exponents as function of the bifurcation parameter and as function of the fractional order are described. The Matlab program for Lyapunov exponents is developed from an existing Matlab program for Lyapunov exponents of integer order. To decrease the computing time, a fast Matlab program which implements the Adams-Bashforth-Moulton method, is utilized. Four representative examples are considered.
Jacques Malavieille - One of the best experts on this subject based on the ideXlab platform.
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3d_fault_offsets a Matlab Code to automatically measure lateral and vertical fault offsets in topographic data application to san andreas owens valley and hope faults
Journal of Geophysical Research, 2018Co-Authors: N Stewart, Yves Gaudemer, Isabelle Manighetti, L Serreau, A Vincendeau, Stephane Dominguez, Lionel Matteo, Jacques MalavieilleAbstract:Measuring fault offsets preserved at the ground surface is of primary importance to recover earthquake and long‐term slip distributions and understand fault mechanics. The recent explosion of high‐resolution topographic data, such as Lidar and photogrammetric digital elevation models, offers an unprecedented opportunity to measure dense collections of fault offsets. We have developed a new Matlab Code, 3D_Fault_Offsets, to automate these measurements. In topographic data, 3D_Fault_Offsets mathematically identifies and represents nine of the most prominent geometric characteristics of common sublinear markers along faults (especially strike slip) in 3‐D, such as the streambed (minimum elevation), top, free face and base of channel banks or scarps (minimum Laplacian, maximum gradient, and maximum Laplacian), and ridges (maximum elevation). By calculating best fit lines through the nine point clouds on either side of the fault, the Code computes the lateral and vertical offsets between the piercing points of these lines onto the fault plane, providing nine lateral and nine vertical offset measures per marker. Through a Monte Carlo approach, the Code calculates the total uncertainty on each offset. It then provides tools to statistically analyze the dense collection of measures and to reconstruct the prefaulted marker geometry in the horizontal and vertical planes. We applied 3D_Fault_Offsets to remeasure previously published offsets across 88 markers on the San Andreas, Owens Valley, and Hope faults. We obtained 5,454 lateral and vertical offset measures. These automatic measures compare well to prior ones, field and remote, while their rich record provides new insights on the preservation of fault displacements in the morphology.
Ole Sigmund - One of the best experts on this subject based on the ideXlab platform.
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compact 200 line Matlab Code for inverse design in photonics by topology optimization tutorial
Journal of The Optical Society of America B-optical Physics, 2021Co-Authors: Rasmus E Christiansen, Ole SigmundAbstract:We provide a compact 200 line Matlab Code demonstrating how topology optimization (TopOpt) as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as examples. The physics model is solved using the finite element method, and the Code utilizes Matlab’s fmincon algorithm to solve the optimization problem. In addition to presenting the Code itself, we briefly discuss a number of extensions and provide the Code required to implement some of these. Finally, we demonstrate the superiority of using a gradient-based method compared to a genetic-algorithm-based method (using Matlab’s ga algorithm) for solving inverse design problems in photonics. The Matlab software is freely available in the paper and may be downloaded from https://www.topopt.mek.dtu.dk.
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a 200 line Matlab Code for inverse design in photonics by topology optimization
arXiv: Mathematical Software, 2020Co-Authors: Rasmus E Christiansen, Ole SigmundAbstract:We provide a compact 200 line Matlab Code demonstrating how Topology Optimization (TopOpt) as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as examples. The physics model is solved using the finite element method and the Code utilizes Matlabs fmincon algorithm to solve the optimization problem. In addition to presenting the Code itself, we briefly discuss a number of extensions and provide the Code required to implement some of these. Finally, we demonstrate the superiority of using a gradient-based method compared to a genetic-algorithm-based method (using Matlabs ga algorithm) for solving inverse design problems in photonics. The Matlab software is freely available in the paper and may be downloaded from https://www.topopt.dtu.dk.
Krishnan Suresh - One of the best experts on this subject based on the ideXlab platform.
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A 199-line Matlab Code for Pareto-optimal tracing in topology optimization
Structural and Multidisciplinary Optimization, 2010Co-Authors: Krishnan SureshAbstract:The paper ‘A 99-line topology optimization Code written in Matlab’ by Sigmund (Struct Multidisc Optim 21(2):120–127, 2001 ) demonstrated that SIMP-based topology optimization can be easily implemented in less than hundred lines of Matlab Code. The published method and Code has been used even since by numerous researchers to advance the field of topology optimization. Inspired by the above paper, we demonstrate here that, by exploiting the notion of topological-sensitivity (an alternate to SIMP), one can generate Pareto-optimal topologies in about twice the number of lines of Matlab Code. In other words, optimal topologies for various volume fractions can be generated in a highly efficient manner, by directly tracing the Pareto-optimal curve.
N Stewart - One of the best experts on this subject based on the ideXlab platform.
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3d_fault_offsets a Matlab Code to automatically measure lateral and vertical fault offsets in topographic data application to san andreas owens valley and hope faults
Journal of Geophysical Research, 2018Co-Authors: N Stewart, Yves Gaudemer, Isabelle Manighetti, L Serreau, A Vincendeau, Stephane Dominguez, Lionel Matteo, Jacques MalavieilleAbstract:Measuring fault offsets preserved at the ground surface is of primary importance to recover earthquake and long‐term slip distributions and understand fault mechanics. The recent explosion of high‐resolution topographic data, such as Lidar and photogrammetric digital elevation models, offers an unprecedented opportunity to measure dense collections of fault offsets. We have developed a new Matlab Code, 3D_Fault_Offsets, to automate these measurements. In topographic data, 3D_Fault_Offsets mathematically identifies and represents nine of the most prominent geometric characteristics of common sublinear markers along faults (especially strike slip) in 3‐D, such as the streambed (minimum elevation), top, free face and base of channel banks or scarps (minimum Laplacian, maximum gradient, and maximum Laplacian), and ridges (maximum elevation). By calculating best fit lines through the nine point clouds on either side of the fault, the Code computes the lateral and vertical offsets between the piercing points of these lines onto the fault plane, providing nine lateral and nine vertical offset measures per marker. Through a Monte Carlo approach, the Code calculates the total uncertainty on each offset. It then provides tools to statistically analyze the dense collection of measures and to reconstruct the prefaulted marker geometry in the horizontal and vertical planes. We applied 3D_Fault_Offsets to remeasure previously published offsets across 88 markers on the San Andreas, Owens Valley, and Hope faults. We obtained 5,454 lateral and vertical offset measures. These automatic measures compare well to prior ones, field and remote, while their rich record provides new insights on the preservation of fault displacements in the morphology.