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Projeto de investigação
Center for Computational and Stochastic Mathematics
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Publicações
An adapted plane waves method for heat conduction problems
Publication . Martins, Nuno F. M.; Mota, Pedro; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; Elsevier
In this paper we construct a new set of basis functions for the numerical solution of nonhomogeneous heat conduction problems with Dirichlet boundary conditions and null initial data. These functions can be seen as Newtonian potentials of plane waves for the heat equation and satisfy a null initial condition. Density results for adapted waves will be established and several numerical simulations will be presented in order to discuss the accuracy and feasibility of the proposed method. An application of the method for heat problems with non null initial temperature will also be discussed.
Tropical representations and identities of the stylic monoid
Publication . Aird, Thomas; Ribeiro, Duarte; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; Springer
We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic monoid of finite rank n generates the pseudovariety Jn, which corresponds to the class of all piecewise testable languages of height n, in the framework of Eilenberg’s correspondence. From this, we obtain the equational theory of the stylic monoids of finite rank, show that they are finitely based if and only if n≤ 3 , and that their identity checking problem is decidable in linearithmic time. We also establish connections between the stylic monoids and other plactic-like monoids, and solve the finite basis problem for the stylic monoid with involution.
Analytical study of the annular flow of a generalised Phan-Thien–Tanner fluid
Publication . Ribau, A. M.; Ferrás, L. L.; Morgado, M. L.; Rebelo, M.; Pinho, F. T.; Afonso, A. M.; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; Springer-Verlag Wien
The annular flow of complex viscoelastic fluids, described by the generalised Phan-Thien–Tanner model, is studied. This model considers the Mittag-Leffler function instead of the usual linear or exponential functions of the trace of the stress tensor, and includes two new parameters that provide additional fitting flexibility. We derive a semi-analytical solution that provides a better understanding of the behaviour of this type of fluid in annular flows and also helps to improve the modelling of complex materials.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
6817 - DCRRNI ID
Número da atribuição
UIDP/04621/2020