Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Multivariate Methods Based Soft Measurement for Wine Quality Evaluation
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/740754 Open Access Soft measurement is a new, developing, and promising industry technology and has been widely used in the industry nowadays. This technology plays a significant role especially in the case where some key variables are difficult to be measured by traditional measurement methods. In this paper, the quality of the wine is evaluated given the wine physicochemical indexes according to multivariate methods based soft measurement. The multivariate methods used in this paper include ordinary least squares regression (OLSR), principal c…
Richard von Mises’ work for ZAMM until his emigration in 1933 and glimpses of the later history of ZAMM
2020
Towards Stable Radial Basis Function Methods for Linear Advection Problems
2021
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoret…
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.