Search results for "Linear system"
showing 10 items of 1558 documents
An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology
2016
The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the i…
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …
Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange
2021
Abstract We propose a model for studying several nonlinear waves for heat transport along a cylindrical system with lateral non-linear heat transfer to the environment. We consider relaxational equations, each with its own relaxation time, for longitudinal heat transfer and for lateral heat transfer across the wall. We consider two kinds of nonlinear lateral heat transport: radiative heat transport, and flux-limited heat transport. This work generalizes our previous studies in which the relaxation time for the lateral heat transfer was considered equal to that of the longitudinal heat flux. We explore the influence of both relaxation times on the propagation speed of linear and nonlinear wa…
A non-linear Ritz method for the analysis of low velocity impact induced dynamics in variable angle tow composite laminates
2021
Abstract Variable angle tow (VAT) laminates feature composite layers reinforced by fibres following continuous curved paths and offer a wide structural design space for the manufacturing of composite components. In this work, a formulation for the analysis of the impact-induced dynamics in VAT laminated plates is proposed, implemented and tested in this work. The method is based on the adoption of first order shear deformation kinematics and includes von Karman non-linear strains. The discrete system is obtained by employing a pb-2 Ritz series expansion into the Hamilton’s variational statement, while the impact loading is modelled through Hertzian contact law. The resulting non-linear gove…
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…
Potentialities of microfibers for non linear optics
2010
Micro- and nanofibers present attractive optical properties and may be used in a variety of structures and devices. We report in this work the first global study on the non linear properties of these microfibers: an adequate source is built and its characteristics are described, our first results with a silica loop resonator are presented. Third harmonic generation is obtained in these conditions, however, the low intrinsic non linear index prevents the generation of large non linear effects. The use of highly non linear materials, such as soft glasses, is therefore discussed, with their potentialities and the challenges their integration with standard microfibers represent.
Nonlinear virtues of multimode fibre
2015
The finding that multimode optical fibres support a rich and complex mix of spatial and temporal nonlinear phenomena could yield a plethora of promising applications.
Reaction-Diffusion Network For Geometric Multiscale High Speed Image Processing
2010
International audience; In the framework of heavy mid-level processing for high speed imaging, a nonlinear bi-dimensional network is proposed, allowing the implementation of active curve algorithms. Usually this efficient type of algorithm is prohibitive for real-time image processing due to its calculus charge and the inadequate structure for the use of serial or parallel architectures. Another kind of implementation philosophy is proposed here, by considering the active curve generated by a propagation phenomenon inspired from biological modeling. A programmable nonlinear reaction-diffusion system is proposed under front control and technological constraints. Geometric multiscale processin…
A nonlinear oscillators network devoted to image processing
2004
A contrast enhancement and image inverting tool using a lattice of uncoupled nonlinear oscillators is proposed. We show theoretically and numerically that the gray scale picture contrast is strongly enhanced even if this one is initially very small. An image inversion can be also obtained in real time with the same Cellular Nonlinear Network (CNN) without reconfiguration of the network. A possible electronic implementation of this CNN is finally discussed.
Analysis of an Experimental Model of In Vitro Cardiac Tissue Using Phase Space Reconstruction
2014
International audience; The in vitro cultures of cardiac cells represent valuable models to study the mechanism of the arrhythmias at the cellular level. But the dynamics of these experimental models cannot be characterized precisely, as they include a lot of parameters that depend on experimental conditions. This paper is devoted to the investigation of the dynamics of an in vitro model using a phase space reconstruction. Our model, based on the heart cells of new born rats, generates electrical field potentials acquired using a microelectrode technology, which are analyzed in normal and under external stimulation conditions. Phase space reconstructions of electrical field potential signal…