Search results for "Numerical Analysis"
showing 10 items of 883 documents
Normalizability, Synchronicity, and Relative Exactness for Vector Fields in C2
2004
In this paper, we study the necessary and su.cient condition under which an orbitally normalizable vector field of saddle or saddle-node type in C2 is analytically conjugate to its formal normal form (i.e., normalizable) by a transformation fixing the leaves of the foliation locally. First, we express this condition in terms of the relative exactness of a certain 1-form derived from comparing the time-form of the vector field with the time-form of the normal form. Then we show that this condition is equivalent to a synchronicity condition: the vanishing of the integral of this 1-form along certain asymptotic cycles de.ned by the vector field. This can be seen as a generalization of the clas…
The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two
1997
In previous papers, we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems\(\dot v(t) = X(v(t)) + u(t)Y(v(t))\) with a terminal submanifoldN of codimension one when the trajectories are not tangent toN. We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimensionn≥3, out of a subvariety ofN of codimension there, we have described all the local synthesis.
Ecuaciones en derivadas parciales gobernadas por operadores acretivos
2010
Una teoria que ha resultado ser de gran utilidad en el estudio de muchas ecuaciones en derivadas parciales no lineales es la teoria de semigrupos no lineales generados por operadores acretivos en espacios de Banach. Dicha teoria se basa fundamentalmente en el Teorema de Crandall-Ligget y en las aportaciones de Ph. Benilan. En este articulo, despues de hacer una exposicion esquematica de esta teoria general, veremos como la hemos aplicado a algunas ecuaciones en derivadas parciales no lineales que aparecen en diversos campos de la Ciencia.
CQ *-algebras of measurable operators
2022
Abstract We study, from a quite general point of view, a CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative L 2-spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative L 2-spaces.
Fractional characteristic times and dissipated energy in fractional linear viscoelasticity
2016
Abstract In fractional viscoelasticity the stress–strain relation is a differential equation with non-integer operators (derivative or integral). Such constitutive law is able to describe the mechanical behavior of several materials, but when fractional operators appear, the elastic and the viscous contribution are inseparable and the characteristic times (relaxation and retardation time) cannot be defined. This paper aims to provide an approach to separate the elastic and the viscous phase in the fractional stress–strain relation with the aid of an equivalent classical model (Kelvin–Voigt or Maxwell). For such equivalent model the parameters are selected by an optimization procedure. Once …
High-order Runge–Kutta–Nyström geometric methods with processing
2001
Abstract We present new families of sixth- and eighth-order Runge–Kutta–Nystrom geometric integrators with processing for ordinary differential equations. Both the processor and the kernel are composed of explicitly computable flows associated with non trivial elements belonging to the Lie algebra involved in the problem. Their efficiency is found to be superior to other previously known algorithms of equivalent order, in some case up to four orders of magnitude.
A physical approach to the connection between fractal geometry and fractional calculus
2014
Our goal is to prove the existence of a connection between fractal geometries and fractional calculus. We show that such a connection exists and has to be sought in the physical origins of the power laws ruling the evolution of most of the natural phenomena, and that are the characteristic feature of fractional differential operators. We show, with the aid of a relevant example, that a power law comes up every time we deal with physical phenomena occurring on a underlying fractal geometry. The order of the power law depends on the anomalous dimension of the geometry, and on the mathematical model used to describe the physics. In the assumption of linear regime, by taking advantage of the Bo…
Step-by-step integration for fractional operators
2018
Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and th…
On the Stochastic Response of a Fractionally-damped Duffing Oscillator
2012
A numerical method is presented to compute the response of a viscoelastic Duffing oscillator with fractional derivative damping, subjected to a stochastic input. The key idea involves an appropriate discretization of the fractional derivative, based on a preliminary change of variable, that allows to approximate the original system by an equivalent system with additional degrees of freedom, the number of which depends on the discretization of the fractional derivative. Unlike the original system that, due to the presence of the fractional derivative, is governed by non-ordinary differential equations, the equivalent system is governed by ordinary differential equations that can be readily h…
Incremental elastoplastic analysis for active macro-zones
2012
SUMMARY In this paper a strategy to perform incremental elastoplastic analysis using the symmetric Galerkin boundary element method for multidomain type problems is shown. The discretization of the body is performed through substructures, distinguishing the bem-elements characterizing the so-called active macro-zones, where the plastic consistency condition may be violated, and the macro-elements having elastic behaviour only. Incremental analysis uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The nonlinear analysis does not use updating of the elastic response inside each plas…