Performance evaluation of computer software or hardware architectures may rely on the analysis of a complex stochastic model whose specification is usually given in terms of a high level formalism such as queueing networks, stochastic Petri nets, stochastic automata or Markovian process algebras. Compositionality is a key-feature of many of these formalisms and allows the modeller to combine se...

We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the Ericksen’s energy for liquid crystals, the Cahn-Hilliard energy representing the interfacial energy of the droplet, and a weak anchoring energy representing the interaction of the liquid crystal molecules with the su...

The algebraic flux correction (AFC) paradigm is extended to finite element discretizations with a consistent mass matrix. A nonoscillatory low-order scheme is constructed by resorting to mass lumping and conservative elimination of negative off-diagonal coefficients from the discrete transport operator. In order to recover the high accuracy of the original Galerkin scheme, a limited amount of c...

The assumption that a name uniquely identifies an entity introduces two types of errors: splitting treats one entity as two or more (because of name variants); lumping treats multiple entities as if they were one (because of shared names). Here we investigate the extent to which splitting and lumping affect commonly-used measures of large-scale named-entity networks within two disambiguated bib...

This paper is devoted to constructing approximate solutions for the classical Keller–Segel model governing chemotaxis . It consists of a system nonlinear parabolic equations, where unknowns are average density cells (or organisms), which conserved variable, and chemoattractant. The numerical proposal made up crude finite element method together with mass lumping technique semi-implicit Euler ti...

A parallel composition is defined for Markov reward chains with stochastic discontinuity, and with fast and silent transitions. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are τ -lumping and τ -reduction. Discontinuous Markov reward chains are ‘limits’ of Markov reward chains wi...