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

A 3D short-characteristics method for continuum and line scattering problems in the winds of hot stars

Context: Knowledge about hot, massive stars is usually inferred from quantitative spectroscopy. To analyse non-spherical phenomena, the existing 1D codes must be extended to higher dimensions, and corresponding tools need to be developed. Aims: We present a 3D radiative transfer code that is capable of calculating continuum and line scattering problems in the winds of hot stars. By considering spherically symmetric test models, we discuss potential error sources, and indicate advantages and disadvantages by comparing different solution methods. Further, we analyse the UV resonance line formation in the winds of rapidly rotating O stars. Methods: We consider both a (simplified) continuum model including scattering and thermal sources, and a UV resonance line transition approximated by a two-level-atom. We applied the short-characteristics (SC) method, using linear or monotonic B\'ezier interpolations, to solve the equation of radiative transfer on a non-uniform Cartesian grid. To calculate scattering dominated problems, our solution method is supplemented by an accelerated $\Lambda$-iteration scheme. Results: For the spherical test models, the mean relative error of the source function is on the $5-20\,\%$ level, depending on the applied interpolation technique and the complexity of the considered model. All calculated line profiles are in excellent agreement with corresponding 1D solutions. The predicted line profiles from fast rotating stars show a distinct behaviour as a function of rotational speed and inclination. This behaviour is tightly coupled to the wind structure and the description of gravity darkening and stellar surface distortion. Conclusions: Our SC methods are ready to be used for quantitative analyses of UV resonance line profiles. When calculating optically thick continua, both SC methods give reliable results, in contrast to the alternative finite-volume method

Binary-object spectral-synthesis in 3D (BOSS-3D) -- Modelling H-alpha emission in the enigmatic multiple system LB-1

Context: To quantitatively decode the information stored within an observed spectrum, detailed modelling of the physical state and accurate radiative transfer solution schemes are required. In the analysis of stellar spectra, the numerical model often needs to account for binary companions and 3D structures in the stellar envelopes. The enigmatic binary (or multiple) system LB-1 constitutes a perfect example of such a complex multi-D problem. Aims: To improve our understanding of the LB-1 system, we directly modelled the phase-dependent H-alpha line profiles of this system. To this end, we developed a multi-purpose binary-object spectral-synthesis code in 3D (BOSS-3D). Methods: BOSS-3D calculates synthetic line profiles for a given state of the circumstellar material. The standard pz-geometry commonly used for single stars is extended by defining individual coordinate systems for each involved object and by accounting for the appropriate coordinate transformations. The code is then applied to the LB-1 system, considering two main hypotheses, a binary containing a stripped star and Be star, or a B star and a black hole with a disc. Results: Comparing these two scenarios, neither model can reproduce the detailed phase-dependent shape of the H-alpha line profiles. A satisfactory match with the observations, however, is obtained by invoking a disc around the primary object in addition to the Be-star disc or the black-hole accretion disc. Conclusions: The developed code can be used to model synthetic line profiles for a wide variety of binary systems, ranging from transit spectra of planetary atmospheres, to post-asymptotic giant branch binaries including circumstellar and circumbinary discs and massive-star binaries with stellar winds and disc systems. For the LB-1 system, our modelling provides strong evidence that each object in the system contains a disc-like structure

Port Protocols for Deadlock-Freedom of Component Systems

In component-based development, approaches for property verification exist that avoid building the global system behavior of the component model. Typically, these approaches rely on the analysis of the local behavior of fixed sized subsystems of components. In our approach, we want to avoid not only the analysis of the global behavior but also of the local behaviors of the components. Instead, we consider very small parts of the local behaviors called port protocols that suffice to verify properties.Comment: In Proceedings ICE 2010, arXiv:1010.530

Ultraviolet Line Profiles of Slowly Rotating Massive Star Winds Using the "Analytic Dynamical Magnetosphere" Formalism

Recent large-scale spectropolarimetric surveys have established that a small but significant percentage of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense, radiatively driven stellar wind into circumstellar magnetospheres, whose density and velocity structure can be probed using ultraviolet (UV) spectroscopy of wind-sensitive resonance lines. Coupled with appropriate magnetosphere models, UV spectroscopy provides a valuable way to investigate the wind-field interaction, and can yield quantitative estimates of the wind parameters of magnetic massive stars. We report a systematic investigation of the formation of UV resonance lines in slowly rotating magnetic massive stars with dynamical magnetospheres. We pair the Analytic Dynamical Magnetosphere (ADM) formalism with a simplified radiative transfer technique to produce synthetic UV line profiles. Using a grid of models, we examine the effect of magnetosphere size, the line strength parameter, and the cooling parameter on the structure and modulation of the line profile. We find that magnetic massive stars uniquely exhibit redshifted absorption at most viewing angles and magnetosphere sizes, and that significant changes to the shape and variation of the line profile with varying line strengths can be explained by examining the individual wind components described in the ADM formalism. Finally, we show that the cooling parameter has a negligible effect on the line profiles.Comment: 16 pages, 15 figures, accepted to MNRA

Extended ML: Past, present and future

An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development

Verification for Everyone? An Overview of Dynamic Logic

This note, reporting the homonym keynote presented in the International Symposium on Molecular Logic and Computational Synthetic Biology 2018, traces an informal roadmap on Dynamic Logic (DL) field, focusing on its versatility and resilience to be adjusted and adopted in a wide class of application domains and computational paradigms. The exposition argues the room for developments on tagging DL to the analysis of synthetic biologic domain.publishe

Ultraviolet line profiles of slowly rotating massive star winds using the 'analytic dynamical magnetosphere' formalism

peer reviewedRecent large-scale spectropolarimetric surveys have established that a small but significant percentage of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense, radiatively driven stellar wind into circumstellar magnetospheres, whose density and velocity structure can be probed using ultraviolet (UV) spectroscopy of wind-sensitive resonance lines. Coupled with appropriate magnetosphere models, UV spectroscopy provides a valuable way to investigate the wind-field interaction, and can yield quantitative estimates of the wind parameters of magnetic massive stars. We report a systematic investigation of the formation of UV resonance lines in slowly rotating magnetic massive stars with dynamical magnetospheres. We pair the analytic dynamical magnetosphere (ADM) formalism with a simplified radiative transfer technique to produce synthetic UV line profiles. Using a grid of models, we examine the effect of magnetosphere size, the line strength parameter, and the cooling parameter on the structure and modulation of the line profile. We find that magnetic massive stars uniquely exhibit redshifted absorption at most viewing angles and magnetosphere sizes, and that significant changes to the shape and variation of the line profile with varying line strengths can be explained by examining the individual wind components described in the ADM formalism. Finally, we show that the cooling parameter has a negligible effect on the line profiles

Testing data types implementations from algebraic specifications

Algebraic specifications of data types provide a natural basis for testing data types implementations. In this framework, the conformance relation is based on the satisfaction of axioms. This makes it possible to formally state the fundamental concepts of testing: exhaustive test set, testability hypotheses, oracle. Various criteria for selecting finite test sets have been proposed. They depend on the form of the axioms, and on the possibilities of observation of the implementation under test. This last point is related to the well-known oracle problem. As the main interest of algebraic specifications is data type abstraction, testing a concrete implementation raises the issue of the gap between the abstract description and the concrete representation. The observational semantics of algebraic specifications bring solutions on the basis of the so-called observable contexts. After a description of testing methods based on algebraic specifications, the chapter gives a brief presentation of some tools and case studies, and presents some applications to other formal methods involving datatypes