Recursos de colección

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É um repositório para instituições de ensino e investigação produtoras de literatura científica cuja dimensão ainda não justifica a criação de um repositório próprio. Permite integrar instituições, grupos ou indivíduos na infra-estrutura do projecto, nomeadamente através das pesquisas do Portal RCAAP e da B-On.

Mostrando recursos 1 - 7 de 7

  1. Numerical modelling of operational risks for the banking industry

    Barreira, Raquel; Pryer, Tristan; Tang, Q.

  2. Cross-Diffusion in Reaction-Diffusion Models:Analysis, Numerics, and Applications

    Madzvamuse, Anotida; Barreira, Raquel; Gerisch, Alf

  3. A practical approach to model banking risks using Loss Distribution Approach (LDA) in Basel II framework

    Barreira, Raquel; Pryer, Tristan; Tang, Qi
    In Basel II Capital Accord, the Advanced Measurement Approaches (AMA) is stated as one of the pillar stone methods for calculating corporate risk reserves. One of the common yet cumbersome methods is the one known as loss distribution approach (cf. [3]). In this article, we present an easy to implement scheme through electronic means and discuss some of the mathematical problems we encountered in the process together with proposed solution methods and further sought on the issues.

  4. The surface finite element method for pattern formation on evolving biological surfaces

    Barreira, Raquel; Elliott, C. M.; Madzvamuse, Anotida
    In this article we propose models and a numerical method for patternformation on evolving curved surfaces. We formulate reaction-diffusion equations onevolving surfaces using the material transport formula, surface gradients and diffusiveconservation laws. The evolution of the surface is defined by a material surface veloc-ity. The numerical method is based on the evolving surface finite element method. Thekey idea is based on the approximation of by a triangulated surface hconsistingof a union of triangles with vertices on . A finite element space of functions is thendefined by taking the continuous functions on hwhich are linear affine on each sim-plex of the...

  5. Exhibiting cross-diffusion-induced patterns for reaction-diffusionsystems on evolving domains and surfaces

    Madzvamuse, Anotida; Barreira, Raquel
    The aim of this manuscript is to present for the first time the application of the finite element method for solvingreaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore wepresent pattern formation generated by the reaction-diffusion system with cross-diffusion on evolving domains andsurfaces. A two-component reaction-diffusion system with linear cross-diffusion in bothuandvis presented. Thefinite element method is based on the approximation of the domain or surface by a triangulated domain or surfaceconsisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. Afinite element space of functions is then defined by...

  6. Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations

    Madzvamuse, Anotida; Ndakwo, Hussaini; Barreira, Raquel
    By introducing linear cross-diffusion for a two-component reaction-diffusion system withactivator-depletedreaction kinetics (Gierer and Meinhardt,Kybernetik 12:30–39,1972;PrigogineandLefever,JChemPhys48:1695–1700,1968;Schnakenberg, J Theor Biol 81:389–400,1979), we derivecross-diffusion-driveninstability conditions and show that they are a generalisation of the classical diffusion-driveninstabilityconditionsintheabsenceofcross-diffusion.Ourmostrevealingresultis that, in contrast to the classical reaction-diffusion systems without cross-diffusion,it is no longer necessary to enforce that one of the species diffuse much faster than theother.Furthermore,it is no longer necessary to have an activator–inhibitor mecha-nism as premises for pattern formation, activator–activator,inhibitor–inhibitorreac-tion kinetics as well asshort-range inhibitionandlong-range activationall have thepotential of giving rise to cross-diffusion-driven instability. To support our theoreti-cal findings, we compute cross-diffusion induced parameter spaces and...

  7. Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion

    Madzvamuse, Anotida; Ndakwo, Hussaini; Barreira, Raquel
    This article presents stability analytical results of a two compo-nent reaction-diffusion system with linear cross-diffusion posed on continuouslyevolving domains. First the model system is mapped from a continuously evolv-ing domain to a reference stationary frame resulting in a system of partialdifferential equations with time-dependent coefficients. Second, by employingappropriately asymptotic theory, we derive and prove cross-diffusion-driven in-stability conditions for the model system for the case of slow, isotropic domaingrowth. Our analytical results reveal that unlike the restrictive diffusion-driveninstability conditions on stationary domains, in the presence of cross-diffusioncoupled with domain evolution, it is no longer necessary to enforce cross norpure kinetic conditions....

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