An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

Macroscopic and Microscopic Structures of Cesium Lead Iodide Perovskite from Atomistic Simulations

A first‐principles‐based effective Hamiltonian is developed and employed to investigate finite‐temperature structural properties of a prototype of perovskite halides, that is CsPbI₃. Such simulations, when using first‐principles‐extracted coefficients, successfully reproduce the existence of an orthorhombic Pnma state and its iodine octahedral tilting angles around room temperature. However, they also yield a direct transformation from Pnma to cubic $Pm\overline{3}m$ upon heating, unlike measurements that reported the occurrence of an intermediate long‐range‐tilted tetragonal P4/mbm phase in‐between the orthorhombic and cubic phases. Such disagreement, which may cast some doubts about the extent to which first‐principle methods can be trusted to mimic hybrid perovskites, can be resolved by “only” changing one short‐range tilting parameter in the whole set of effective Hamiltonian coefficients. In such a case, some reasonable values of this specific parameter result in the predictions that i) the intermediate P4/mbm state originates from fluctuations over many different tilted states; and ii) the cubic $Pm\overline{3}m$ phase is highly locally distorted and develops strong transverse antiphase correlation between first‐nearest neighbor iodine octahedral tiltings, before undergoing a phase transition to P4/mbm under cooling.     

Hedging Entry and Exit Decisions: Activating and Deactivating Barrier Options

Investment projects and businesses can be entered or exited at a cost, and the theory of real option teaches us how to find optimal activity levels that should trigger entry or exit. However, in practice, different managers or owners operate under different constraints and might apply different thresholds to the same business. We are interested in the hedging of the risk related to the cost of sub-optimal entry or exit. We introduce a new class of derivative products that can hedge this risk. The pricing of these derivatives involves the joint law of a Brownian excursion and its supremum, which is calculated thanks to Bessel processes-related distribution laws.     

Wavelet Collocation Methods for a First Kind Boundary Integral Equation in Acoustic Scattering

In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively.     

Self and mutual admittance of slot antennas on a dielectric half-space

In this paper, an efficient implementation of the spectral domain moment technique is presented for computing the self and mutual coupling between slot antennas on a dielectric half-space. It is demonstrated that by the proper selection of the weighting functions in the method of moments, the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The method is then utilized in order to provide design data for the self and mutual admittances between two slot antennas on a dielectric substrate lens in the case of fused quartz (∈ _r =3.80), crystal quartz (∈ _r =4.53), silicon (∈ _r =11.9) and GaAs (∈ _r =12.8). The presented technique and associated results are useful when designing twin slot quasi-optical receivers, imaging arrays, phased arrays or power-combining arrays of slot elements at millimeter-wave frequencies.     

Effect of absorbed pump power on the quality of output beam from monolithic microchip lasers

The dependence of the beam propagation factor (M ² parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively studied. Our investigations show that the M ₂ parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration associated with the thermal lens induced by the pump beam. Such dependency of M ² parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd³⁺ -doped GdVO₄ crystal and the values of α and β parameters were estimated from the experimentally measured data points.     

Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottementFinite element method with Lagrange multipliers for contact problems with friction

In this Note, we propose a finite element method with Lagrange multipliers in order to approximate contact problems with friction. The discretized normal and tangential constraints at the candidate contact interface are expressed by using continuous piecewise linear Lagrange multipliers in the saddle-point formulation. An optimal error estimate is established and several numerical studies corresponding to this choice of the discretized normal and tangential constraints are achieved. To cite this article: L. Baillet, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 917–922.     

Localization effects and measure source terms in numerical schemes for balance laws

This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

     

Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.