Existence,nonexistence and multiplicity results for nonlocal Dirichlet problems

In this paper we establish various existence, nonexistence and multiplicity results for fully nonlinear Dirichlet problems associated to nonlocal Hamilton–Jacobi equations. This study is accomplished by a careful analysis of the principal eigenvalues of the elliptic operator. Resonance phenomena and anti maximum principles are also established.     

Computational modelling of multi-material energetic materials and systems

ABSTRACT

In this paper, we present a systematic roadmap for developing a robust and parallel multi-material reactive hydrodynamic solver that integrates historically stable algorithms with new and current modern methods to solve explosive system design problems. The Ghost Fluid Method and Riemann solvers were used to enforce appropriate interface boundary conditions. Improved performance in terms of computational work and convergence properties was achieved by modifying a local node sorting strategy that decouples ghost nodes, allowing us to set material boundary conditions via an explicit procedure, removing the need to solve a coupled system of equations numerically. The locality and explicit nature of the node sorting concept allows for greater levels of parallelism and lower computational cost when populating ghost nodes. Non-linear numerical issues endemic to the use of real Equations of State in hydro-codes were resolved by using more thermodynamically consistent forms allowing us to accurately resolve large density gradients associated with high energy detonation problems at material interfaces. Pre-computed volume tables were implemented adding to the robustness of the solver base.     

On Current Developments in Partial Differential Equations

The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The second part is a supplement of various details provided by several outstanding researchers on subjects.     

Geometrical methods for analyzing the optimal management of tipping point dynamics

Natural resources are not infinitely resilient and should not be modeled as being such. Finitely resilient resources feature tipping points and history dependence. This paper provides a didactical discussion of mathematical methods that are needed to understand the optimal management of such resources: viscosity solutions of Hamilton–Jacobi–Bellman equations, the costate equation and the associated canonical equations, exact root counting, and geometrical methods to analyze the geometry of the invariant manifolds of the canonical equations. Recommendations for Resource Managers

• Management of natural resources has to take into account the possible breakdown of resilience and induced regime shifts.
• Depending on the characteristics of the resource and on its present and future economic importance, either for all initial states the same kind of management policy is optimal, or the type of the optimal management policy depends on the initial state.
• Modeling should reflect the finiteness of the data.

     

强耦合腔-QED系统中原子的纳秒脉冲激发光谱研究

本文在多原子强耦合腔-QED系统中,利用脉冲宽度为5 ns的强脉冲光在垂直于腔轴方向直接激发原子,脉冲的峰值功率为40 mW,通过光学腔观测激发原子辐射到腔中的光子获得相应的激发光谱。我们发现当光场频率和原子跃迁失谐±80 MHz时原子激发率达到最大,而在共振时原子激发被抑制。我们建立了脉冲光与三能级原子相互作用的模型,通过缀饰态能够解释此现象。