231 research outputs found
Gradient discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media with discontinuous pressures at the matrix fracture interfaces
We investigate the discretization of Darcy flow through fractured porous
media on general meshes. We consider a hybrid dimensional model, invoking a
complex network of planar fractures. The model accounts for matrix-fracture
interactions and fractures acting either as drains or as barriers, i.e. we have
to deal with pressure discontinuities at matrix-fracture interfaces. The
numerical analysis is performed in the general framework of gradient
discretizations which is extended to the model under consideration. Two
families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the
Hybrid Finite Volume scheme (HFV) are detailed and shown to satisfy the
gradient scheme framework, which yields, in particular, convergence. Numerical
tests confirm the theoretical results. Gradient Discretization; Darcy Flow,
Discrete Fracture Networks, Finite Volum
3D radiative transfer: Continuum and line scattering in non-spherical winds from OB stars
Context: State of the art quantitative spectroscopy of OB-stars compares
synthetic spectra (calculated by means of 1D, spherically symmetric computer
codes) with observations. Certain stellar atmospheres, however, show strong
deviations from spherical symmetry, and need to be treated in 3D. Aims: We
present a newly developed 3D radiative transfer code, tailored to the solution
of the radiation field in rapidly expanding stellar atmospheres. We apply our
code to the continuum transfer in wind-ablation models, and to the UV resonance
line formation in magnetic winds. Methods: We have used a 3D finite-volume
method for the solution of the equation of radiative transfer, to study
continuum- and line-scattering problems. Convergence has been accelerated by a
non-local approximate Lambda-iteration scheme. Particular emphasis has been put
on careful (spherically symmetric) test cases. Results: Typical errors of the
source functions, when compared to 1D solutions, are of the order of 10-20 %,
and increase for optically thick continua. In circumstellar discs, the
radiation temperatures in the (optically thin) transition region from wind to
disc are quite similar to corresponding values in the wind. For MHD simulations
of dynamical magnetospheres, the line profiles, calculated with our 3D code,
agree well with previous solutions using a 3D-SEI method. When compared with
profiles resulting from the `analytic dynamical magnetosphere' (ADM) model,
significant differences become apparent. Conclusions: Due to similar radiation
temperatures in the wind and the transition region to the disc, the same
line-strength distribution can be applied within radiation hydrodynamic
calculations for circumstellar discs in `accreting high-mass stars'. To
properly describe the UV line formation in dynamical magnetospheres, the ADM
model needs to be further developed, at least in a large part of the outer
wind
(Ω, Ξ)-Logic: On the Algebraic Extension of Coalgebraic Specifications
We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications
Behavioural and abstractor specifications
AbstractIn the literature, one can distinguish two main approaches to the definition of observational semantics of algebraic specifications. On one hand, observational semantics is defined using a notion of observational satisfaction for the axioms of the specifications and, on the other hand, one can define observational semantics by abstraction with respect to an observational equivalence relation between algebras. In this paper, we present an analysis and a comparative study of the different approaches in a more general framework which subsumes the observational case. The distinction between the different observational concepts is reflected by our notions of behavioural specification and abstractor specification. We provide necessary and sufficient conditions for the semantical equivalence of both kinds of specifications and we show that behavioural specifications can be characterized by an abstractor construction and, vice versa, abstractor specifications can be characterized in terms of behavioural specifications. Hence, there exists a duality between both concepts which allows to express each one by the other. We also study the relationships to fully abstract algebras which can be used for a further characterization of behavioural semantics. Finally, we provide proof-theoretic results which show that behavioural theories of specifications can be reduced to standard theories of some classes of algebras
Behavioural and abstractor specifications revisited
In the area of algebraic specification there are two main approaches for defining observational abstraction: behavioural specifications use a notion of observational satisfaction for the axioms of a specification, whereas abstractor specifications define an abstraction from the standard semantics of a specification w.r.t. an observational equivalence relation between algebras. Earlier work by Bidoit, Hennicker, Wirsing has shown that in the case of first-order logic specifications both concepts coincide semantically under mild assumptions. Analogous results have been shown by Sannella and Hofmann for higher-order logic specifications and recently, by Hennicker and Madeira, for specifications of reactive systems using a dynamic logic with binders. In this paper, we bring these results into a common setting: we isolate a small set of characteristic principles to express the behaviour/abstractor equivalence and show that all three mentioned specification frameworks satisfy these principles and therefore their behaviour and abstractor specifications coincide semantically (under mild assumptions). As a new case we consider observational modal logic where observational satisfaction of Hennessy–Milner logic formulae is defined “up to” silent transitions and observational abstraction is defined by weak bisimulation. We show that in this case the behaviour/abstractor equivalence can only be obtained, if we restrict models to weakly deterministic labelled transition systems.publishe
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