Reports on Mathematical Physics | Year: 2014
The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the potential free case fulfills the conservation of momentum. © 2014 Polish Scientific Publishers.
Pereira P.J.S.,Polytechnic Institute of Lisbon |
Pereira P.J.S.,New University of Lisbon |
Lopes N.D.,Polytechnic Institute of Lisbon |
Trabucho L.,CMAF |
Trabucho L.,FCT Inc.
Nonlinear Dynamics | Year: 2015
An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations. © 2015, Springer Science+Business Media Dordrecht.
Barbarosie C.,CMAF |
Mechanics of Advanced Materials and Structures | Year: 2012
This article describes a numerical study of the optimization of elastic bodies featuring a locally periodic microscopic pattern. The authors approach makes the link between the microscopic level and the macroscopic one. Two-dimensional linearly elastic bodies are considered; the same techniques can be applied to three-dimensional bodies. Homogenization theory is used to describe the macroscopic (effective) elastic properties of the body. The macroscopic domain is divided in (rectangular) finite elements and in each of them the microstructure is supposed to be periodic; the periodic pattern is allowed to vary from element to element. Each periodic microstructure is discretized using a finite element mesh on the periodicity cell, by identifying the opposite sides of the cell in order to handle the periodicity conditions in the cellular problem. Shape optimization and topology optimization are used at the microscopic level, following an alternate directions algorithm. Numerical examples are presented, in which a cantilever is optimized for different load cases, one of them being multi-load. The problem is numerically heavy, since the optimization of the macroscopic problem is performed by optimizing in simultaneous hundreds or even thousands of periodic structures, each one using its own finite element mesh on the periodicity cell. Parallel computation is used in order to alleviate the computational burden. Copyright © Taylor & Francis Group, LLC.
Barbarosie C.,CMAF |
Structural and Multidisciplinary Optimization | Year: 2010
In the present paper we deduce formulae for the shape and topological derivatives for elliptic problems in unbounded domains subject to periodicity conditions. Note that the known formulae of shape and topological derivatives for elliptic problems in bounded domains do not apply to the periodic framework. We consider a general notion of periodicity, allowing for an arbitrary parallelepiped as periodicity cell. Our calculations are useful for optimizing periodic composite materials by gradient type methods using the topological derivative jointly with the shape derivative for periodic problems. Important particular cases of functionals to minimize/maximize are presented. A numerical algorithm for optimizing periodic composites using the topological and shape derivatives is the subject of a second paper (Barbarosie and Toader, Struct Multidiscipl Optim, 2009). © 2009 Springer-Verlag.
Aguirre C.,Autonomous University of Madrid |
Mendes R.V.,CMAF |
Mendes R.V.,University of Lisbon
IET Signal Processing | Year: 2014
Tomogram, a generalisation of the Radon transform to arbitrary pairs of non-commuting operators, is a positive bilinear transforms with a rigorous probabilistic interpretation which provides a full characterisation of the signal and is robust in the presence of noise. Tomograms based on the time-frequency operator pair, were used in the past for component separation and denoising. Here the authors show that, even for noisy signals, meaningful time-resolved information may be obtained by the construction of an operator pair adapted to the signal. © The Institution of Engineering and Technology 2014.