Structural properties of the one-dimensional drift-diffusion models for semiconductors

This paper is devoted to the analysis of the one-dimensional current and voltage drift-diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination. We show in the course of this paper, that these models satisfy structural properties, which are due to the particular form of the coupling of the involved systems. These structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current , of the electron and hole current densities and of the electric field at the contacts. We also prove analytic dependence of the solutions on . These results allow us to establish several qualitative properties of the current voltage characteristic. In particular, we give the nature of the (possible) bifurcation points of this curve, we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages. As a consequence, we show that the currents never saturate as the voltage goes to , contrary to what was predicted by numerical simulations by M. S. Mock (Compel. 1 (1982), pp. 165--174). We also analyze the drift-diffusion models under the assumption of quasi-neutral approximation. We show, in particular, that the reduced current driven model has at most one solution, but that it does not always have a solution. Then, we compare the full and the reduced voltage driven models and we show that, in general, the quasi-neutral approximation is not accurate for large voltages, even if no saturation phenomenon occurs. Finally, we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms.

     

Baryon masses in relativistic potential models

We study the spectrum of a semi relativistic three-body hamiltonian. The hyperspherical method proves to be very efficient. We show that the ground states of baryons can be calculated with good accuracy. However, when using the meson potential, together with the colour assumption \(Vqq = \tfrac{1}{2}Vq\bar q\) , baryon Regge slopes come out noticeably too small. We analyze this problem and show that a quarkdiquark structure for baryons cures this defect. Altogether the construction of a global unified potential model for mesons and baryons seems quite hopeful.     

Effect of surfactant and mineral additive on the efficiency of lead-acid battery positive active material

The effect of Sodium tripolyphosphate (STPP) and mineral additive on the performance of the lead-acid battery positive plate has been investigated. The addition of alumina-silicate to the positive paste and STPP to the electrolyte modifies the shape and size of PbO₂ crystals and improves the utilization of the positive active material (PAM). The electrochemical performance of the positive active material was determined using galvanostatic discharge and electrochemical impedance spectroscopy (EIS). The crystal structure and morphology of the PAM (PbO₂) were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The water content of the PAM was calculated using Thermogravimetric analysis (TGA) technique. The results showed that the addition of surfactant and mineral additive changes the morphology and the crystallite size of the PAM. We observe a remarkable improvement of the discharge capacity of the PAM when the surfactant (STPP) is added in the electrolyte. The discharge capacity increases with the decrease of the crystallite size and the charge transfer resistance R_ct of the PAM. This shows that the addition of mineral additive and the surfactant together improves the electrical performance of lead-acid battery.     

Eigenproblem for p-Laplacian and nonlinear elliptic equation with nonlinear boundary conditions

In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalue problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov–Robin.     

Exponential and polynomial stability of a wave equation for boundary memory damping with singular kernels

This work is concerned with stabilization of a wave equation stabilized by a boundary feedback. When the feedback is both frictional and with memory, we prove exponential stability of the solutions. In case of a boundary feedback which is only of memory type, uniform stability is not expected. We prove in this latter case, that the solutions decay polynomially. The method is new and uses the method of higher order energies (see [F. Alabau-Boussouira, J. Prüss, R. Zacher, Exponential and polynomial stabilization of wave equations subjected to boundary-memory dissipation with singular kernels, in preparation; F. Alabau, Stabilisation frontière indirecte de systèmes faiblement couplés, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 1015–1020; F. Alabau, P. Cannarsa, V. Komornik, Indirect internal damping of coupled systems, J. Evolution Equations 2 (2002) 127–150; F. Alabau, Indirect boundary stabilization of weakly coupled systems, SIAM J. Control Optim. 41 (2002) 511–541]), the multiplier method and the properties of a large class of singular kernels. Moreover, our method can be extended to include cases of nonsingular kernels (see [V. Vergara, R. Zacher, Lyapunov functions and convergence to steady state for differential equations of fractional order, Math. Z. 259 (2008) 287–309; R. Zacher, Convergence to equilibrium for second order differential equations with weak damping of memory type, preprint.]). To cite this article: F. Alabau-Boussouira et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

New trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems

We present an approach based on comparison principles for energy and interpolation properties to derive lower energy estimates for nonlinearly either locally damped or boundary damped vibrating systems. We show how the dissipation relation provides strong information on the asymptotic behavior of the energy of solutions. The geometrical situations are either one-dimensional, or radial two-dimensional or three-dimensional for annulus domains. We also consider the case of general domains, but in this case, for solutions with bounded velocities in time and space. In all these cases, the nonlinear damping function is assumed to have arbitrary (strictly sublinear) growth at the origin. We give results for strong solutions and stronger lower estimates for smoother solutions. The results are presented in two forms, either on the side of energy comparison principles, or through time-pointwise lower estimates. Under additional geometric assumptions, we give the resulting lower and upper estimates for four representative examples of damping functions. We further give a “weak” lower estimate (in the sense of a certain lim supt→∞) and an upper estimate of the velocity for smoother solutions in case of general damping functions and for radial, as well as multi-dimensional domains. We also discuss these estimates in the framework of optimality, which is not proved here, and indicate open problems raised by these results.     

On a coupled nonlinear singular thermoelastic system

For a coupled nonlinear singular system of thermoelasticity with one space dimension, we consider its initial boundary value problem on an interval. For one of the unknowns a classical condition is replaced by a nonlocal constraint of integral type. Because of the presence of a memory term in one of the equations and the presence of a weighted boundary integral condition, the solution requires a delicate set of techniques. We first solve a particular case of the given nonlinear problem by using a functional analysis approach. On the basis of the results obtained and an iteration method we establish the well-posedness of solutions in weighted Sobolev spaces.     

Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids

This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.