Linear System Solutions of the Navier-Stokes Equations with Application to Flow over a Backward-Facing Step

Many applications in fluid mechanics require the numerical solution of sequences of linear systems typically issued from finite element discretization of the Navier-Stokes equations. The resulting matrices then exhibit a saddle point structure. To achieve this task, a Newton-based root-finding algorithm is usually employed which in turn necessitates to solve a saddle point system at every Newton iteration. The involved linear systems being large scale and ill-conditioned, effective linear solvers must be implemented. Here, we develop and test several methods for solving the saddle point systems, considering in particular the LU factorization, as direct approach, and the preconditioned generalized minimal residual (ΡGMRES) solver, an iterative approach. We apply the various solvers within the root-finding algorithm for Flow over backward facing step systems. The particularity of Flow over backward facing step system is an interesting case for studying the performance and solution strategy of a turbulence model. In this case, the flow is subjected to a sudden increase of cross-sectional area, resulting in a separation of flow starting at the point of expansion, making the system of differential equations particularly stiff. We assess the performance of the direct and iterative solvers in terms of computational time, numbers of Newton iterations and time steps.

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.

Structure and Properties of Polyamide 11 Nanocomposites Filled with Fibrous Palygorskite Clay

Various amounts(up to 10 wt%)of palygorskite nanofibers functionalized by 3-aminopropyltriethoxysilane(APTES)coupling agent were used to reinforce polyamide 11 nanocomposites prepared by melt compounding.The covalent bonding of the silane on the palygorskite surface was confirmed by infrared spectroscopy and thermogravimetric analysis.X-ray diffraction revealed the retention of theα-form of polyamide crystals upon the addition of both natural and silane treated palygorskite nanorods.All the investigated nanocomposites showed an improvement of the thermal stability,especially when surface treated palygorskite nanofibers were considered.Tensile tests and dynamic mechanical thermal analyses on the prepared materials evidenced how the incorporation of palygorskite nanofibers significantly increased the elastic and the storage moduli of polyamide,and this enhancement was more evident when natural palygorskite nanorods were used.

Morphological Analysis of the Cleft Palate in Dogs(Canis lupus familiaris)

The cleft palate is a defect of longitudinal fusion that affects the bone and the mucosa in the midline of the hard palate.This defect in the fusion of the palatal lateral shelves from the maxillary processes results in an open cleft between the oral and nasal cavities,also known as secondary palatine cleft.The objective of this work is to report the morphological characteristics of palatine clefts observed in stillborn dogs and neonates submitted to euthanasia.Six dogs were evaluated,from each animal the following data were obtained:clinical history,weight and morphometric data.Externally,data regarding to:sex,fur color,malformations,and evaluations of natural openings were evaluated.Every evaluated animal was delivered by caesarean section,50%of stillborn infants had cleft lip associated with secondary cleft palate,50%were female and only one stillborn was a mongrel dog.All others were from the brachycephalic races.It was observed that the cleft palate was found,in great majority,in females,proving the association of sex with this congenital anomaly.In this sense,clinical inspection,including physical examination and anamnesis should be part of the assessment of the neonate patient as parameters to reach a diagnosis and,when it is possible,to be associated with a radiographic image as a complementary method,being the radiography an important auxiliary exam in this context.

The Effects of Gamma Irradiation on Molecular Weight, Morphology and Physical Properties of PHBV/Cloisite 30B Bionanocomposites

In this paper,the effects of gamma irradiation on Cast poly(3-hydroxybutyrate-co-3-hydroxyvalerate)(PHBV)and PHBV/Cloisite 30B(C30B)(3 wt%)bionanocomposite prepared by melt compounding,were evaluated at various doses,i.e.,5,15,20,50 and 100 kGy at room temperature in air.Changes in molecular weight,morphology and physical properties were investigated.The study showed that the main degradation mechanism occurring in gamma irradiation in both Cast PHBV and C-PHBV/3C30B bionanocomposite is chain scission,responsible for the decrease of molecular weight.Differential scanning calorimetry(DSC)data indicated a regular decrease in crystallization temperature,melting temperature and crystallinity index for all irradiated samples with increasing the dose.Further,DSC thermograms of both Cast PHBV and PHBV bionanocomposite exhibited double melting peaks due probably to changes in the PHBV crystal structure.Tensile and DMA data showed a reduction in Young’s modulus,strength,elongation at break and storage modulus with the radiation dose;the decrease was however more pronounced for Cast PHBV.The morphological damages were much less pronounced for the PHBV bionanocomposite sample compared to Cast PHBV,for which some irregularities and defects were observed at 100 kGy.This study highlighted the ability of C30B to counterbalance the detrimental effect of radiolytic degradation on the functional properties of PHBV up to 100 kGy,thus acting as a potential anti-rad.

Recurrence properties of sequences of integers

In order to study the recurrence of sequences of integers, we investigate their L2-exactness and Θ-Hartman property (Θ being a set of rational numbers). Two classes of sequences of integers are well studied, which are return times relative to a weakly mixing system and Bernoulli random sequences.

Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems

In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.

On the General Stability of a Viscoelastic Wave Equation with an Integral Condition

We consider a nonlocal boundary value problem for a viscoelastic equation with a Bessel operator and a weighted integral condition and we prove a general decay result.We also give an example to show that our general result gives the optimal decay rate for ceratin polynomially decaying relaxation functions.This result improves some other results in the literature.