Linear System

Attention is here focused on the implementation of a coupled BEM–FEM procedure employing the BE method for the modelling of the near-crack region and the FEM for the far-field, where no singularities in the stress field are expected to arise. The symmetric variational version of the BE method is utilized, allowing to obtain a final linear system endowed with a symmetric matrix. With respect to 3D linear elastic fracture mechanics, the code developed is used to evaluate stress intensity factors for some benchmarks and simulate fracture propagation.

This work proposes a methodology of identifying linear parameter varying (LPV) models for nonlinear systems. First, linear local models in some operating points, by applying standard identifications procedures for linear systems in time domain, are obtained. Next, a LPV model with linear fractional dependence (LFR) with respect to measured variables is fitted with the condition of containing all the linear models identified in previous step (differential inclusion). The fit is carried out using nonlinear least squares algorithms. Finally, this identification methodology will then be applied to a nonlinear turbocharged diesel engine.

This note describes some of the recent methods and eective results in the study of pluricanonical and adjoint linear systems on higher- dimensional varieties. We describe an algebraic construction for the multi- plier ideals and we use it to give a simple proof for the Reider theorem. x1. The purpose of this note is to survey some of the recent results on pluri- canonical and adjoint linear systems on algebraic varieties. Let A be a nef and big divisor on a smooth projective variety X. We would like to study the linear system jKX + Aj .F orX a curve, it is well known that if deg A 2, the linear system jKX + Aj is free, and if deg A 3, then KX + A is very ample. The canonical linear system jKXj is very ample if and only if X is not a hyperelliptic curve. From the theory of curves, we know that the properties of these linear systems are closely related to the geometry of the curve. It is natural that one would like to obtain similar numerical criteria for freeness and very ampleness f...

Résumé/Abstract En utilisant la technique développée dans [7], nous donnons une estimation d'erreur, d'ordre 1/2 par rapport à la taille du maillage, pour une approximation volumes finis explicite en temps, pour la résolution des systèmes hyperboliques linéaires ...

Many problems in Biology and Engineering are governed by anisotropic reaction–diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction–diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

This paper investigates typical behaviors like damped oscillations in fractional order (FO) dynamical systems. Such response occurs due to the presence of, what is conceived as, pseudo-damping and meta-damping in some special class of FO systems. Here, approximation of such damped oscillation in FO systems with the conventional notion of integer order damping and time constant has been carried out using Genetic Algorithm (GA). Next, a multilayer feed-forward Artificial Neural Network (ANN) has been trained using the GA based results to predict the optimal pseudo and meta-damping from knowledge of the maximum order or number of terms in the FO dynamical system.

A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In prior work considering speckle size, others have shown that its spatial variation is functionally dependent primarily on the autocorrelation function of the system's impulse response, but effects of varying the wavelength were largely ignored. In the present paper we treat the general problem in which a diffuse object, illuminated by a collimated, monochromatic beam, is imaged by a system whose amplitude impulse response isz(x, η), wherex and η are space and normalized (temporal) frequency coordinates, respectively. An expression is derived for the multidimensional autocorrelation functionR u (Δx,η 1,η 2) of the intensityu(x,η) in the image plane. Functionally, it depends upon a convolution of the system autocorrelation functionR u (Δx,η 1,η 2) with the characteristic function of the distribution function for heights, which is used to model the input object's surface. Examples are presented; and, it is shown that one can infer valuable information about the variation of heights for points on the surface of the input diffuse object, which are separated by much less than the classical resolution limit.

Optimizing parallel compilers need to be able to analyze nested loop programs with parametric affine loop bounds, in order to derive efficient parallel programs. The iteration spaces of nested loop programs can be modeled by polyhedra and systems of linear constraints. Using this model, important program analyses such as computing the number of flops executed by a loop, computing the number of memory locations or cache lines touched by a loop, and computing the amount of processor to processor communication needed during the execution of a loop--- all reduce to the same mathematical problem: finding the formula for number of integer solutions to a system of parameterized linear constraints, as a function of the parameters. In this paper, we present a method for deriving a closed-form symbolic formula for the number of integer points contained in a polyhedral region in terms of size parameters. If the set of integer points to be counted lies inside a union of rational convex polytope...

ABSTRACT We consider the interior Dirichlet problem for Laplace’s equation on a non-simply connected two-dimensional regions with smooth boundaries. The solution is sought as the real part of a holomorphic function on the region, given as Cauchy-type integral. The approximate double layer density function is found by solving a system of Fredholm integral equations of second kind. Because of the non-uniqueness of the solution of the system we solve it using a technique based on the solution of the “modified Dirichlet problem”. The Nyström’s method coupled with the trapezoidal rule is used as numerical integration scheme. The linear system derived from the integral equation is solved using the conjugate gradient method applied to the normqal equation. Theoretical and computational details of the method are presented.

1. Introduction 2. Integrable dynamical systems 3. Synopsis of integrable systems 4. Algebraic methods 5. Analytical methods 6. The closed Toda chain 7. The Calogero-Moser model 8. Isomonodromic deformations 9. Grassmannian and integrable hierarchies 10. The KP hierarchy 11. The KdV hierarchy 12. The Toda field theories 13. Classical inverse scattering method 14. Symplectic geometry 15. Riemann surfaces 16. Lie algebras Index.

In this paper we deal with the problem of estimating the marking of a labeled Petri net system based on the observation of transitions labels. In particular, we assume that a certain number of transitions are labeled with the empty string ε, while a different label taken from a given alphabet is assigned to all the other transitions. Transitions labeled with the empty string are called silent because their firing cannot be observed. Under some technical assumptions on the structure of the Tε -induced subnet, where Tε denotes the set of silent transitions, we formally prove that the set of markings consistent with the observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

The technique of quasi-symmetrizer has been applied to the well-posedness of the Cauchy problem for scalar operators [10], [13] and linear systems [5], [15], [4], and to the propagation of analitycity for solutions to semi-linear systems [6]. In all these works, it is assumed that the principal symbol depends only on the time variable. In this note we illustrate, in some special cases, a new property of the quasisymmetrizer which allows us to generalize the result in [6] to semi-linear systems with coefficients depending also on the space variables [21]. Such a property is closely connected with some interesting inequalities on the eigenvalues of a hyperbolic matrix. We expect that this technique applies also to other problems. Keywords: First order hyperbolic systems, Quasi-symmetrizer, Glaeser inequality