A global existence result for the anisotropic magnetohydrodynamical systems

We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size $\epsilon$$\alpha$ with 0 \textless{} $\alpha$ $\le$ $\alpha$0, for some $\alpha$0 \textgreater{} 0). We prove the local existence and uniqueness of a strong solution and then, using Strichartz-type estimates, we prove that this solution globally exists in time for large initial data, when the rotation is fast enough

Formal Verification of Probabilistic SystemC Models with Statistical Model Checking

Transaction-level modeling with SystemC has been very successful in describing the behavior of embedded systems by providing high-level executable models, in which many of them have inherent probabilistic behaviors, e.g., random data and unreliable components. It thus is crucial to have both quantitative and qualitative analysis of the probabilities of system properties. Such analysis can be conducted by constructing a formal model of the system under verification and using Probabilistic Model Checking (PMC). However, this method is infeasible for large systems, due to the state space explosion. In this article, we demonstrate the successful use of Statistical Model Checking (SMC) to carry out such analysis directly from large SystemC models and allow designers to express a wide range of useful properties. The first contribution of this work is a framework to verify properties expressed in Bounded Linear Temporal Logic (BLTL) for SystemC models with both timed and probabilistic characteristics. Second, the framework allows users to expose a rich set of user-code primitives as atomic propositions in BLTL. Moreover, users can define their own fine-grained time resolution rather than the boundary of clock cycles in the SystemC simulation. The third contribution is an implementation of a statistical model checker. It contains an automatic monitor generation for producing execution traces of the model-under-verification (MUV), the mechanism for automatically instrumenting the MUV, and the interaction with statistical model checking algorithms.Comment: Journal of Software: Evolution and Process. Wiley, 2017. arXiv admin note: substantial text overlap with arXiv:1507.0818

Dependability Analysis of Control Systems using SystemC and Statistical Model Checking

Stochastic Petri nets are commonly used for modeling distributed systems in order to study their performance and dependability. This paper proposes a realization of stochastic Petri nets in SystemC for modeling large embedded control systems. Then statistical model checking is used to analyze the dependability of the constructed model. Our verification framework allows users to express a wide range of useful properties to be verified which is illustrated through a case study

Dispersive effects of weakly compressible and fast rotating inviscid fluids

We consider a system describing the motion of an isentropic, inviscid, weakly com-pressible, fast rotating fluid in the whole space R^3 , with initial data belonging to H^s(R^3) , s \textgreater{} 5/2. We prove that the system admits a unique local strong solution in L^$\infty$([0, T ]; H^s(R^3)) , where T is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove that the solution is almost global, i.e. its lifespan is of the order of $\epsilon$^(--$\alpha$) , $\alpha$ \textgreater{} 0, without any smallness assumption on the initial data (the initial data can even go to infinity in some sense), provided that the rotation is fast enough.Comment: Revised versio

Voluntary Contributions to a Public Good: Non-neutrality Results / Contributions volontaires, biens publics

We show that the famous neutrality result in the theory of public good contributions (Warr, Kemp, Bergstrom, Blume and Varian) depends crucially on the assumption that agents do not take into account the effect of their public good contribution decisions on the relative price of the private goods. Thus, the scope of applicability of their result is not as large as one might at first think. Our non-neutrality results hold even if all countries are identical in technology, preferences, and endowments. Nous démontrons que le théorème sur l’invariance du stock total d’un bien public par rapport à la distribution de revenus n’est valable que si les contributeurs ignorent l’impact de leurs contributions sur le prix relatif des biens privés. Par conséquent, le résultat de Warr, Kemp, Bergstrom, Blume et Varian n’a qu’une sphère d’application limitée. Nos résultats sur le manque de neutralité sont valables même si les préférences, les technologies, et les dotations de ressources de tous les pays sont identiques.public goods, voluntary contributions,