HYDROSTATIC LIMIT OF THE NAVIER-STOKES-ALPHA MODEL

In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.

Modeling and Numerical Simulation of Heat Transfers in a Metallic Pressure Cooker Isolated with Kapok Wool

In this work, a numerical study of heat transfers in a metallic pressure cooker isolated with kapok wool was carried out. This equipment works like a thermos, allowing finishing cooking meals only thanks to the heat stored at the beginning of cooking, which generates energy savings. Cooked meals are also kept hot for long hours. In our previous work, we have highlighted the performances of the pressure cooker when making common dishes in Burkina Faso. Also, the parameters (thickness and density) of the insulating matrix allowing having such performances as well as the influence of the climatic conditions on the pressure cooker operation were analyzed in detail in this present work. The numerical methodology is based on the nodal method and the transfer equations obtained by making an energy balance on each node have been discretized using an implicit scheme with finite differences and resolved by the Gauss algorithm. Numerical results validated experimentally show that the thickness of the kapok wool as well as its density play an important role in the pressure cooker operation. In addition, equipment performances are very little influenced by the weather conditions of the city of Ouagadougou (Burkina Faso).

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.

Simulating Particle Swarm Optimization Algorithm to Estimate Likelihood Function of ARMA（1, 1） Model

This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent to maximizing its logarithm, so the objective function ＇obj.fun＇ is maximizing log-likelihood function. Monte Carlo method adapted for implementing and designing the experiments of this simulation. This study including a comparison among three versions of PSO algorithm “Constriction coefficient CCPSO, Inertia weight IWPSO, and Fully Informed FIPSO”, the experiments designed by setting different values of model parameters al, bs sample size n, moreover the parameters of PSO algorithms. MSE used as test statistic to measure the efficiency PSO to estimate model. The results show the ability of PSO to estimate ARMA＇ s parameters, and the minimum values of MSE getting for COPSO.

Estimate of an Hypoelliptic Heat-Kernel outside the Cut-Locus in Semi-Group Theory

We give a proof in semi-group theory based on the Malliavin Calculus of Bismut type in semi-group theory and Wentzel-Freidlin estimates in semi-group of our result giving an expansion of an hypoelliptic heat-kernel outside the cut-locus where Bismut’s non-degeneray condition plays a preominent role.

下临界维数情形Stable过程投影相交局部时的上尾估计(英文)

利用其中一个稳定过程将Rd上的p个α稳定过程相交局部时测度投影到其相交点集合上的这种方式,在相交集合点上定义一个自然测度l.在p(d-α)<d且d≥2的条件下,证明了对任意的有界集U,事件l(U)>a的概率随着a的增长将以指数速度衰减.

Complex and p-Adic Meromorphic Functions f′P′( f ),g′P′(g) Sharing a Small Function

Let K be a complete algebraically closed p-adic field of characteristic zero. We apply results in algebraic geometry and a new Nevanlinna theorem for p-adic meromorphic functions in order to prove results of uniqueness in value sharing prob-lems, both on K and on C. Let P be a polynomial of uniqueness for meromorphic functions in K or C or in an open disk. Let f , g be two transcendental meromorphic functions in the whole field K or in C or meromorphic functions in an open disk of K that are not quotients of bounded analytic functions. We show that if f′P′（ f ） and g′P′（g） share a small function α counting multiplicity, then f=g, provided that the multiplicity order of zeros of P′satisfy certain inequalities. A breakthrough in this pa-per consists of replacing inequalities n≥k＋2 or n≥k＋3 used in previous papers by Hypothesis （G）. In the p-adic context, another consists of giving a lower bound for a sum of q counting functions of zeros with （q-1） times the characteristic function of the considered meromorphic function.

Impulse Control Problem of Partially Observed Diffusion Processes

The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.

Pointwise Convergence of a Nonparametric Estimator of Regression in a Measurable Space Used in Contingent Valuation Method

The Contingent Valuation Method is used to evaluate individual preferences for a change concerning a public non-market resource or property. The objective is to build a nonparametric forecasting model of an individual＇s Willingness To Pay according to geographical location. Within this framework, an estimator （of type Nadaraya-Watson） is proposed for the regression of the variable related to geolocation. The specific characteristics of the location variable lead us to a more general regression model than the traditional models. Results are established for convergence of our estimator.

Experimental and Numerical Study of Energy Losses in a Barbecue Oven in Burkina Faso

This work concerns an experimental and numerical study of energy losses in a typical oven usually used in the agro-food craft sector in Burkina Faso. The experimental results were obtained by infrared thermography of the oven and by monitoring the evolution of the wall temperatures using thermocouples connected to a data acquisition system. These results indicate that the energy losses are mainly through the walls of the oven. The numerical study based on the energy balance and corroborated by the experimental study made it possible to quantify these losses of energy which represents almost half of the fuel used. These results will allow us to work on a new, more efficient oven model for the grilling sector in Burkina Faso.

Boundary Conditions for Limited Area Models Based on the Shallow Water Equations

A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions.The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain.The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.

On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river

In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are： （i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.

Forward–Backward SDEs Driven by Levy Process in Stopping Time Duration

As the first part in the present paper,we study a class of backward stochastic differential equation(BSDE,for short)driven by Teugels martingales associated with some Levy processes having moment of all orders and an independent Brownian motion.We obtain an existence and uniqueness result for this type of BSDEs when the final time is allowed to be random.As the second part,we prove,under a monotonicity condition,an existence and uniqueness result for fully coupled forward-backward stochastic differential equation(FBSDE,for short)driven by Teugels martingales in stopping time duration.As an illustration of our theoretical results,we deal with a portfolio selection in Levy-type market.

A Complete Characterization of Multivariate Normal Stable Tweedie Models through a Monge Ampere Property

Extending normal gamma and normal inverse Gaussian models,multivariate normal stable Tweedie(NST)models are composed by a fixed univariate stable Tweedie variable having a positive value domain,and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component.Within the framework of multivariate exponential families,the NST models are recently classified by their covariance matrices V(m)depending on the mean vector m.In this paper,we prove the characterization of all the NST models through their determinants of V(m),also called generalized variance functions,which are power of only one component of m.This result is established under the NST assumptions of Monge-Ampere property and steepness.It completes the two special cases of NST,namely normal Poisson and normal gamma models.As a matter of fact,it provides explicit solutions of particular Monge-Ampere equations in differential geometry.

Strong Consistency and CLT for the Random Decrement Estimator

The random decrement technique （RDT）, introduced in the sixties by Cole [NASA CR- 2005, 1973], is a very performing method of analysis for vibration signature of a structure under ambient loading. But the real nature of the random decrement signature has been misunderstood until now. Moreover, the various interpretations were made in continuous time setting, while real experimental data are obtained in discrete time. In this paper, the really implemental discrete time algorithms are studied. The asymptotic analysis as the number of triggering points go to infinity is achieved, and a Law of Large Numbers as well as a Central Limit Theorem is proved. Moreover, the limit as the discretization time step goes to zero is computed, giving more tractable formulas to approximate the random decrement. This is a new approach of the famous ＂Kac-Slepian paradox＂ [Ann. Math. Star., 30, 1215-1228 （1959）]. The main point might be that the RDT is a very efficient functional estimator of the correlation function of a stationary ergodic Gaussian process. Very fast, it is to classical estimators what Fast Fourier Transform （FFT） is to ordinary Discrete Fourier Transforms.

Fully nonlinear stochastic and rough PDEs:Classical and viscosity solutions

We study fully nonlinear second-order(forward)stochastic PDEs.They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework.For the most general fully nonlinear case,we develop a local theory of classical solutions and then define viscosity solutions through smooth test functions.Our notion of viscosity solutions is equivalent to the alternative using semi-jets.Next,we prove basic properties such as consistency,stability,and a partial comparison principle in the general setting.If the diffusion coefficient is semilinear(i.e,linear in the gradient of the solution and nonlinear in the solution;the drift can still be fully nonlinear),we establish a complete theory,including global existence and a comparison principle.

Simulation and computational heat transfer in the human eye with Dirichlet–Neumann domain decomposition approximation

In this paper,a bioheat model of temperature distribution in the human eye is studied,the mathematical formulation of this model is described using adequate mathematical tools.The existence and the uniqueness of the solution of this problem is proven and four algorithms based on finite element method approximation and domain decomposition methods are presented in details.The validation of all algorithm is done using a numerical application for an example where the analytical solution is known.The properties and parameters reported in the open literature for the human eye are used to approximate numerically the temperature for bioheat model by finite element approximation and nonoverlapping domain decomposition method.The obtained results that are verified using the experimental results recorded in the literature revealed a better accuracy by the use of algorithm proposed.

Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries

In this paper,we study the numerical solution of the Stokes system in deformed axisymmetric geometries.In the azimuthal direction the discretization is carried out by using truncated Fourier series,thus reducing the dimension of the problem.The resulting two-dimensional problems are discretized using the spectral element method which is based on the variational formulation in primitive variables.The meridian domain is subdivided into elements,in each of which the solution is approximated by truncated polynomial series.The results of numerical experiments for several geometries are presented.

NumericalMethods for Balance Laws with Space Dependent Flux:Application to Radiotherapy Dose Calculation

The present work is concerned with the derivation of numerical methods to approximate the radiation dose in external beam radiotherapy.To address this issue,we consider a moment approximation of radiative transfer,closed by an entropy minimization principle.The model under consideration is governed by a system of hyperbolic equations in conservation form supplemented by source terms.The main difficulty coming from the numerical approximation of this system is an explicit space dependence in the flux function.Indeed,this dependence will be seen to be stiff and specific numerical strategiesmust be derived in order to obtain the needed accuracy.A first approach is developed considering the 1D case,where a judicious change of variables allows to eliminate the space dependence in the flux function.This is not possible in multi-D.We therefore reinterpret the 1D scheme as a scheme on two meshes,and generalize this to 2D by alternating transformations between separate meshes.We call this procedure projection method.Several numerical experiments,coming from medical physics,illustrate the potential applicability of the developed method.

High-Order Low Dissipation Conforming Finite-Element Discretization of the Maxwell Equations

In this paper,we study high order discretization methods for solving the Maxwell equations on hybrid triangle-quad meshes.We have developed high order finite edge element methods coupled with different high order time schemes and we compare results and efficiency for several schemes.We introduce in particular a class of simple high order low dissipation time schemes based on a modified Taylor expansion.