Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations. In an earlier work, this strategy allowed us to develop a regularization method based on a thick interface model in one space variable. In the present paper, we significantly extend this framework and, in addition, encompass equations in several space variables. This new formulation includes the coupling of several distinct conservation laws and allows for a possible covering in space. Our main contributions are, on one hand, the design and analysis of a well-balanced finite volume method on general triangulations and, on the other hand, a proof of convergence of this method toward entropy solutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to a single conservation law without coupling). The core of our analysis is, first, the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and, second, a proof of convergence toward the entropy solution of the coupling problem.Comment: 37 page

Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces

We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between fluid flows. The main technical difficulty to be overcome lies in the possible resonance effect when wave speeds coincide and global hyperbolicity is lost. As a consequence, non-uniqueness of weak solutions is observed for the initial value problem which need to be supplemented with further admissibility conditions. This first paper is devoted to investigating these issues in the setting of self-similar vanishing viscosity approximations to the Riemann problem for general hyperbolic systems. Following earlier works by Joseph, LeFloch, and Tzavaras, we establish an existence theorem for the Riemann problem under fairly general structural assumptions on the nonlinear hyperbolic system and its regularization. Our main contribution consists of nonlinear wave interaction estimates for solutions which apply to resonant wave patterns.Comment: 28 page

Convergent and conservative schemes for nonclassical solutions based on kinetic relations

We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces, contrary to standard finite difference schemes. The main challenge is to achieve, at the discretization level, a consistency property with respect to a prescribed kinetic relation. The latter is required for the selection of physically meaningful nonclassical shocks. Our method is based on a reconstruction technique performed in each computational cell that may contain a nonclassical shock. To validate this approach, we establish several consistency and stability properties, and we perform careful numerical experiments. The convergence of the algorithm toward the physically meaningful solutions selected by a kinetic relation is demonstrated numerically for several test cases, including concave-convex as well as convex-concave flux-functions.Comment: 31 page

Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces

We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called thin interface model and uses an augmented formulation and an additional unknown for the interface location; this framework has the advantage of avoiding any explicit modeling of the interface structure. In the present paper, we pursue our investigation of the augmented formulation and we introduce a new coupling framework which is now based on the so-called thick interface model. For scalar nonlinear hyperbolic equations in one space variable, we observe that the Cauchy problem is well-posed. Then, our main achievement in the present paper is the design of a new well-balanced finite volume scheme which is adapted to the thick interface model, together with a proof of its convergence toward the unique entropy solution (for a broad class of nonlinear hyperbolic equations). Due to the presence of a possibly resonant interface, the standard technique based on a total variation estimate does not apply, and DiPerna's uniqueness theorem must be used. Following a method proposed by Coquel and LeFloch, our proof relies on discrete entropy inequalities for the coupling problem and an estimate of the discrete entropy dissipation in the proposed scheme.Comment: 21 page

The deep-pocket effect of internal capital markets

We provide evidence that incumbent and entrant firms' access to business group deep pockets affects entry patterns in product markets. Relying on a unique French data set on business groups, our paper shows that entry in manufacturing industries is negatively related to the cash hoarded by incumbent-affiliated groups, and positively related to entrant groups' cash. In line with theoretical predictions, we find that the impact on entry of group cash holdings is more important in environments where financial constraints are pronounced and in more financially dependent sectors. The cash holdings of incumbent and entrant groups also affect the survival rate of entrants in the 3 to 5 year post-entry window. Overall, our findings suggest that internal capital markets operate within corporate groups and affect the product market behavior of affiliated firms by mitigating financial constraints

3D-printed system optimizing dissolution of hyperpolarized gaseous species for micro-sized NMR

International audienceDissolution of hyperpolarized species in liquids of interest for NMR is often hampered by the presence of bubbles that degrade the field homogeneity. Here a device constituted by a bubble pump and a miniaturized NMR cell fitting both inside the narrow bore of an NMR magnet is built by 3D printing. 129Xe NMR experiments performed with hyperpolarized xenon reveal high and homogeneous dissolution of the gas in water

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16

Biomass to oil : fast pyrolysis and subcritical hydrothermal liquefaction

International audienceThe present abstract deals with the comparison of two biomass-to-oil processes: fast pyrolysis and subcritical hydrothermal liquefaction. Using the same biomass (beech sawdust), fast pyrolysis was led thanks to the cyclone reactor (wall temperature between 870 and 1040 K) and subcritical hydrothermal liquefaction thanks to a 150-ml-batch-reactor (temperature between 420 and 600 K). Mass balances and analysis (ultimate analysis, HHV, pH, Karl-Fischer, gas chromatographies, H 1 NMR) allow the comparison of both processes and the characterization of the main fractions of pyro-oils (heavy oils, light oils and aerosols) and liq-oils (heavy oils and water soluble organics)

Spin-Exchange optical pumping in a van

International audienceThe advent of spin-hyperpolarization techniques designed to overcome the sensitivity issue of nuclear magnetic resonance owing to polarization transfer from more ordered systems has recently raised great enthusiasm. However, the out-of-equilibrium character of the polarization requires a close proximity between the area of production and the site of use. We present here a mobile spin-exchange optical pumping setup that enables production of laser-polarized noble gases in a standalone mode, in close proximity to hospitals or research laboratories. Only compressed air and mains power need to be supplied by the host laborator