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Kevin Zumbrun - One of the best experts on this subject based on the ideXlab platform.
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pointwise nonlinear stability of nonlocalized modulated periodic reaction Diffusion Waves
Journal of Differential Equations, 2016Co-Authors: Soyeun Jung, Kevin ZumbrunAbstract:Abstract In this paper, extending previous results of [2] , we obtain pointwise nonlinear stability of periodic traveling reaction–Diffusion Waves, assuming spectral linearized stability, under nonlocalized perturbations. More precisely, we establish pointwise estimate of nonlocalized modulational perturbation under a small initial perturbation consisting of a nonlocalized modulation plus a localized perturbation decaying algebraically.
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pointwise nonlinear stability of nonlocalized modulated periodic reaction Diffusion Waves
arXiv: Analysis of PDEs, 2016Co-Authors: Soyeun Jung, Kevin ZumbrunAbstract:In this paper, extending previous results of \cite{J1}, we obtain pointwise nonlinear stability of periodic traveling reaction-Diffusion Waves, assuming spectral linearized stability, under nonlocalized perturbations. More precisely, we establish pointwise estimate of nonlocalized modulational perturbation under a small initial perturbation consisting of a nonlocalized modulation plus a localized perturbation decaying algebraically.
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nonlocalized modulation of periodic reaction Diffusion Waves nonlinear stability
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Mathew A Johnson, Pascal Noble, Miguel L Rodrigues, Kevin ZumbrunAbstract:Extending results of Johnson and Zumbrun showing stability under localized (L1) perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction Diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. The main new ingredient is a detailed analysis of linear behavior under modulational data \({\bar{u}^{\prime}(x)h_{0}(x)}\), where \({\bar{u}}\) is the background profile and h0 is the initial modulation.
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nonlocalized modulation of periodic reaction Diffusion Waves the whitham equation
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Mathew A Johnson, Pascal Noble, Miguel L Rodrigues, Kevin ZumbrunAbstract:In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction Diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized (L1) perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist of a leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.
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nonlocalized modulation of periodic reaction Diffusion Waves nonlinear stability
arXiv: Analysis of PDEs, 2011Co-Authors: Mathew A Johnson, Pascal Noble, Miguel L Rodrigues, Kevin ZumbrunAbstract:By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction Diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. The main new ingredient is a detailed analysis of linear behavior under modulational data $\bar u'(x)h_0(x)$, where $\bar u$ is the background profile and $h_0$ is the initial modulation
Lianzhong Zhang - One of the best experts on this subject based on the ideXlab platform.
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Propagation of pore pressure Diffusion Waves in saturated dual-porosity media (II)
Journal of Applied Physics, 2016Co-Authors: Duoxing Yang, Lianzhong ZhangAbstract:A mechanism has been established for pressure Diffusion Waves in dual-porosity media. Pressure Diffusion Waves are heavily damped with relatively low velocities and short wavelengths. The characteristic frequency dominates the attenuation behavior of pressure Diffusions and separates wave fields into two asymptotic regimes: relaxed and unrelaxed. Characteristic delay times control the pressure Diffusion between the matrix and the fractures. The transition zones in wavelength and attenuation peak shift toward high frequencies when the characteristic delay time decreases. In contrast, the transition zones in both phase and group velocity shift toward low frequencies as the characteristic time of the delay increases. In a spatially dependent diffusivity field, the pressure Diffusion Waves in dual-porosity media obey an accumulation-depletion law.
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Propagation of pore pressure Diffusion Waves in saturated porous media
Journal of Applied Physics, 2015Co-Authors: Duoxing Yang, Lianzhong ZhangAbstract:A microscopic 1D analytical model was developed for describing pore pressure Diffusion wave propagation in porous media. The pressure Diffusion Waves, being heavily damped, have relatively slow velocities and short wavelength, and do not exhibit square-law behavior. Investigation on permeability effect on attenuation dispersion and penetration depth indicates that the transition zone in attenuation and penetration depth peak shifts toward low frequency when permeability decreases. Controversially, the transition zone in phase velocity peak shifts toward high frequency when permeability decreases. The high frequency-dependent attenuation of low-frequency Waves was well predicted by the pressure Diffusion mechanism. At a mass interface, pressure Diffusion Waves obey an accumulation–depletion law, rather than the reflection–refraction law. Pressure Diffusion Waves are accelerated and amplified by a space-dependent diffusivity field.
Duoxing Yang - One of the best experts on this subject based on the ideXlab platform.
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Propagation of pore pressure Diffusion Waves in saturated dual-porosity media (II)
Journal of Applied Physics, 2016Co-Authors: Duoxing Yang, Lianzhong ZhangAbstract:A mechanism has been established for pressure Diffusion Waves in dual-porosity media. Pressure Diffusion Waves are heavily damped with relatively low velocities and short wavelengths. The characteristic frequency dominates the attenuation behavior of pressure Diffusions and separates wave fields into two asymptotic regimes: relaxed and unrelaxed. Characteristic delay times control the pressure Diffusion between the matrix and the fractures. The transition zones in wavelength and attenuation peak shift toward high frequencies when the characteristic delay time decreases. In contrast, the transition zones in both phase and group velocity shift toward low frequencies as the characteristic time of the delay increases. In a spatially dependent diffusivity field, the pressure Diffusion Waves in dual-porosity media obey an accumulation-depletion law.
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Propagation of pore pressure Diffusion Waves in saturated porous media
Journal of Applied Physics, 2015Co-Authors: Duoxing Yang, Lianzhong ZhangAbstract:A microscopic 1D analytical model was developed for describing pore pressure Diffusion wave propagation in porous media. The pressure Diffusion Waves, being heavily damped, have relatively slow velocities and short wavelength, and do not exhibit square-law behavior. Investigation on permeability effect on attenuation dispersion and penetration depth indicates that the transition zone in attenuation and penetration depth peak shifts toward low frequency when permeability decreases. Controversially, the transition zone in phase velocity peak shifts toward high frequency when permeability decreases. The high frequency-dependent attenuation of low-frequency Waves was well predicted by the pressure Diffusion mechanism. At a mass interface, pressure Diffusion Waves obey an accumulation–depletion law, rather than the reflection–refraction law. Pressure Diffusion Waves are accelerated and amplified by a space-dependent diffusivity field.
Nazim Fatès - One of the best experts on this subject based on the ideXlab platform.
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Amoebae for clustering: a bio-inspired cellular automata method for data classification
2020Co-Authors: Amaury Saint-jore, Nazim Fatès, Emmanuel JeandelAbstract:We present a bio-inspired mechanism for data clustering. Our method uses amoebae which evolve according to cellular automata rules: they contain the data to be processed and emit reaction-Diffusion Waves at random times. The Waves transmit the information across the lattice and causes other amoebae to react, by being attracted or repulsed. The local reactions produce small homogeneous groups which progressively merge and realise the clustering at a larger scale. Despite the simplicity of the local rules, interesting complex behaviour occur, which make the model robust to various changes of its settings. We evaluate this prototype with a simple task: the separation of two groups of integer values distributed according to Gaussian laws.
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Large-scale Simulations on FPGAs: Finding the Asymptotic Critical Threshold of the Greenberg-Hastings Cellular Automata
Journal of Cellular Automata, 2012Co-Authors: Nikolaos Vlassopoulos, Nazim Fatès, Hugues Berry, Bernard GirauAbstract:The stochastic Greenberg-Hastings cellular automaton is a model that mimics the propagation of reaction-Diffusion Waves in an active medium. Notably, this model undergoes a phase transition from an "alive" state to a "dead" state when the probability of excitation of a cell varies. We develop a specific FPGA design to study the critical behaviour of this model. Using dedicated architectural optimisations, we obtain a significant speed-up with respect to software simulation for lattice sizes of 512 × 512. We exploit this speed-up to obtain improved estimations of the critical threshold. Our results indicate the existence of a non-trivial asymptotic value of this threshold when the number of cell states increases.
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An FPGA Design for the Stochastic Greenberg-Hastings Cellular Automata
2010Co-Authors: Nikolaos Vlassopoulos, Nazim Fatès, Hugues Berry, Bernard GirauAbstract:The stochastic Greenberg-Hastings cellular automaton is a model that mimics the propagation of reaction-Diffusion Waves in active media. Notably, this model undergoes a phase transition when the probability of excitation of a cell varies. We developed a specific FPGA design to study the critical behavior of this model. Using dedicated architectural optimizations, we obtain a significant speed-up with respect to software simulation for lattice sizes of 512×512. We exploited this speed-up to obtain improved estimations of the critical threshold.Our results indicate the existence of an asymptotic value of this threshold when the number of cell states increases.
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Solving the decentralised gathering problem with a reaction–Diffusion–chemotaxis scheme
Swarm Intelligence, 2010Co-Authors: Nazim FatèsAbstract:The decentralised gathering problem consists in grouping in a compact cluster agents that are initially randomly scattered. We propose a bio-inspired algorithm, the Reaction–Diffusion–Chemotaxis aggregation scheme, to group agents that have limited abilities. The agents and their environment are described with a stochastic model inspired by the aggregation of the Dictyostelium discoideum cellular slime mold. The environment is an active lattice, whose cells transmit information according to a reaction–Diffusion mechanism. The agents are virtual amoebae; they trigger excitations randomly and move by following reaction–Diffusion Waves. We demonstrate that despite its simplicity, this model exhibits interesting properties of self-organisation and is efficient for gathering agents. Moreover, observations show that the system is robust to various perturbations, such as the presence of obstacles on the lattice or noise in the movements of the agents.
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How Fast can Virtual Amoebae Aggregate? Analysis for the Optimal Firing Rate in an Instance of the Reaction-Diffusion-Chemotaxis Aggregation Scheme
2010Co-Authors: Nikolaos Vlassopoulos, Nazim FatèsAbstract:Decentralised gathering is a challenging problem in systems involving numerous identical agents. In our current work we analyse the dynamics of a gathering model that is based on virtual amoebae that fire reaction-Diffusion Waves with a given probability. Interestingly, it has been shown that there exists a tuning of this probability that minimises the aggregation time. Our study is aimed at experimentally measuring this optimal value and analysing how it is related to the dynamics of the model.
Andrea Alu - One of the best experts on this subject based on the ideXlab platform.
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corrigendum thermal invisibility based on scattering cancellation and mantle cloaking
Scientific Reports, 2016Co-Authors: Mohamed Farhat, Paiyen Chen, Hakan Bagci, Claude Amra, Sebastien Guenneau, Andrea AluAbstract:Scientific Reports 5: Article number: 987610.1038/srep09876; published online: April302015; updated: January212016 This Article contains errors. In the Results section under subheading ‘Scattering cancellation technique for heat Diffusion Waves: static regime’ “For , , therefore and all the other coefficients are zero.” should read: “For , with the heat generated by unit surface and unit time, in contrast to Q, of Eqs (1)–(2) that represents the heat generated by unit volume and unit time. Therefore and all the other coefficients are zero.” In Equation (6), should read: And lastly, in Equation (7) should read:
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Thermal invisibility based on scattering cancellation and mantle cloaking
Scientific Reports, 2015Co-Authors: Mohamed Farhat, Hakan Bagci, Claude Amra, Sebastien Guenneau, P.-y Chen, Andrea AluAbstract:We theoretically and numerically analyze thermal invisibility based on the concept of scattering cancellation and mantle cloaking. We show that a small object can be made completely invisible to heat Diffusion Waves, by tailoring the heat conductivity of the spherical shell enclosing the object. This means that the thermal scattering from the object is suppressed, and the heat flow outside the object and the cloak made of these spherical shells behaves as if the object is not present. Thermal invisibility may open new vistas in hiding hot spots in infrared thermography, military furtivity, and electronics heating reduction.