Search results for "Applied Mathematic"
showing 10 items of 4398 documents
A compliant visco-plastic particle contact model based on differential variational inequalities
2013
This work describes an approach to simulate contacts between threedimensional shapes with compliance and damping using the framework of the differential variational inequality theory. Within the context of nonsmooth dynamics, we introduce an extension to the classical set-valued model for frictional contacts between rigid bodies, allowing contacts to experience local compliance, viscosity, and plasticization. Different types of yield surfaces can be defined for various types of contact, a versatile approach that contains the classic dry Coulomb friction as a special case. The resulting problem is a differential variational inequality that can be solved, at each integration time step, as a v…
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…
Shock-capturing schemes: high accuracy versus total-variation boundedness
2007
In this reseach work we analyze the total variation growth of some high order accurate reconstruction procedures used for the design of shock capturing schemes. This study allows to measure how oscillatory a high order accurate method is in terms of the basic elementary function chosen to increase the order of accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental determination of mode I fracture parameters in orthotropic materials by means of Digital Image Correlation
2020
Abstract The mode I fracture parameters for an orthotropic body are directly calculated from full-field deformation measurements provided by Digital Image Correlation (DIC). Three complementary and direct approaches are evaluated and compared: (i) the determination of the Stress Intensity Factor (SIF) by fitting the displacement field using the analytical expression proposed by Lekhnitskii; (ii) the determination of the J-Integral by using the Energy Domain Integral (EDI) formulation on the raw DIC data; and (iii) the calculation of the J-Integral using the EDI approach on the displacement data fitted using Lekhnitskii’s formulation. A comparative experimental study is performed by testing …
A Consistent Formulation of the BEM within Elastoplasticity
1988
A symmetric-definite BEM formulation is derived by making alternatively use of two energy principles, i.e. the Hellinger-Reissner principle and a boundary min-max principle ad-hoc formulated. Two kinds of discretization are operated, one by boundary elements to model the system elastic properties, another by cell-elements to model the material plastic behavior. The cell yielding laws are expressed in terms of generalized variables and comply with the features of associated plasticity, due to the maximum plastic work theorem used for their derivation.
Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms
2010
In this work we are concerned with certain numerical difficulties associated to the use of high order Implicit–Explicit Runge–Kutta (IMEX-RK) schemes in a direct discretization of balance laws with stiff source terms. We consider a simple model problem, introduced by LeVeque and Yee in [J. Comput. Phys 86 (1990)], as the basic test case to explore the ability of IMEX-RK schemes to produce and maintain non-oscillatory reaction fronts.
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
2018
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
A probabilistic approach to radiant field modeling in dense particulate systems
2016
Radiant field distribution is an important modeling issue in many systems of practical interest, such as photo-bioreactors for algae growth and heterogeneous photo-catalytic reactors for water detoxification.In this work, a simple radiant field model suitable for dispersed systems showing particle size distributions, is proposed for both dilute and dense two-phase systems. Its main features are: (i) only physical, independently assessable parameters are involved and (ii) its simplicity allows a closed form solution, which makes it suitable for inclusion in a complete photo-reactor model, where also kinetic and fluid dynamic sub-models play a role. A similar model can be derived by making us…
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 …
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.