A continuously differentiable upwinding scheme for the simulation of fluid flow problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Solving MPCC problem with the hyperbolic penalty function

The main goal of this work is to solve mathematical program with complementarity constraints (MPCC) using nonlinear programming techniques (NLP). An hyperbolic penalty function is used to solve MPCC problems by including the complementarity constraints in the penalty term. This penalty function [1] is twice continuously differentiable and combines features of both exterior and interior penalty methods. A set of AMPL problems from MacMPEC [2] are tested and a comparative study is performed.

Aversion Analysis

In this paper : a) the consumer’s problem is studied over two periods, the second one involving S states, and the consumer being endowed with S+1 incomes and having access to N financial assets; b) the consumer is then representable by a continuously differentiable system of demands, commodity demands, asset demands and desirabilities of incomes (the S+1 Lagrange multiplier of the S+1 constraints); c) the multipliers can be transformed into subjective Arrow prices; d) the effects of the various incomes on these Arrow prices decompose into a compensation effect (an Antonelli matrix) and a wealth effect; e) the Antonelli matrix has rank S-N, the dimension of incompleteness, if the consumer can financially adjust himself when facing income shocks; f) the matrix has rank S, if not; g) in the first case, the matrix represents a residual aversion; in the second case, a fundamental aversion; the difference between them is an aversion to illiquidity; this last relation corresponds to the Drèze-Modigliani decomposition (1972); h) the fundamental aversion decomposes also into an aversion to impatience and a risk aversion; i) the above decompositions span a third decomposition; if there exists a sure asset (to be defined, the usual definition being too specific), the fundamental aversion admits a three-component decomposition, an aversion to impatience, a residual aversion and an aversion to the illiquidity of risky assets; j) the formulas of the corresponding financial premiums are also presented.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

Inada conditions imply that production function must be asymptotically Cobb-Douglas

We show that every twice-continuously differentiable and strictly concave function f : R+ → R+ can be bracketed between two C.E.S. functions at each open interval. In particular, for the Inada conditions to hold, a production function must be asymptotically Cobb-Douglas.

A C2-continuous high-resolution upwind convection scheme

A bounded upwinding scheme for numerical solution of hyperbolic conservation laws and Navier-Stokes equations is presented. The scheme is based on convection boundedness criterion and total variation diminishing stability criteria and developed by employing continuously differentiable functions. The accuracy of the scheme is verified by assessing the error and observed convergence rate on 1-D benchmark test cases. A comparative study between the new scheme and conventional total variation diminishing/convection boundedness criterion-based upwind schemes to solve standard nonlinear hyperbolic conservation laws is also accomplished. The scheme is then examined in the simulation of Newtonian and non-Newtonian fluid flows of increasing complexity; a satisfactory agreement has been observed in terms of the overall behavior. Finally, the scheme is used to study the hydrodynamics of a gas-solid flow in a bubbling fluidized bed. © 2013 John Wiley & Sons, Ltd.

Condições de otimidade para problemas de controle ótimo com condições de contorno funcionais

Pós-graduação em Matemática - IBILCE

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Über die Existenz invarianter Tori in Hamiltonschen Systemen, die bis auf eine endlich oft differenzierbare Störung analytisch und integrabel sind

Es wird die Existenz invarianter Tori in Hamiltonschen Systemen bewiesen, die bis auf eine 2n-mal stetig differenzierbare Störung analytisch und integrabel sind, wobei n die Anzahl der Freiheitsgrade bezeichnet. Dabei wird vorausgesetzt, dass die Stetigkeitsmodule der 2n-ten partiellen Ableitungen der Störung einer Endlichkeitsbedingung (Integralbedingung) genügen, welche die Hölderbedingung verallgemeinert. Bisher konnte die Existenz invarianter Tori nur unter der Voraussetzung bewiesen werden, dass die 2n-ten Ableitungen der Störung hölderstetig sind.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

Respiratory Viruses Are Continuously Detected In Children With Chronic Tonsillitis Throughout The Year.

To evaluate the oscillations on the viral detection in adenotonsillar tissues from patients with chronic adenotonsillar diseases as an indicia of the presence of persistent viral infections or acute subclinical infections. Cross-sectional prospective study. Tertiary hospital. The fluctuations of respiratory virus detection were compared to the major climatic variables during a two-year period using adenoids and palatine tonsils from 172 children with adenotonsillar hypertrophy and clinical evidence of obstructive sleep apnoea syndrome or recurrent adenotonsillitis, without symptoms of acute respiratory infection (ARI), by TaqMan real-time PCR. The rate of detection of at least one respiratory virus in adenotonsillar tissue was 87%. The most frequently detected viruses were human adenovirus in 52.8%, human enterovirus in 47.2%, human rhinovirus in 33.8%, human bocavirus in 31.1%, human metapneumovirus in 18.3% and human respiratory syncytial virus in 17.2%. Although increased detection of human enterovirus occurred in summer/autumn months, and there were summer nadirs of human respiratory syncytial virus in both years of the study, there was no obvious viral seasonality in contrast to reports with ARI patients in many regions of the world. Respiratory viruses are continuously highly detected during whole year, and without any clinical symptomatology, indicating that viral genome of some virus can persist in lymphoepithelial tissues of the upper respiratory tract.

Tillering dynamics in palisadegrass swards continuously stocked by cattle

Plant communities on pastures adapt to varying frequencies and severities of defoliation through mechanisms capable of ensuring their longevity and photosynthetic efficiency. The objective of this experiment was to evaluate tiller population density, demographic patterns of tillering and population stability of palisadegrass swards subjected to four grazing intensities. Treatments corresponded to four sward steady state conditions (sward heights of 10, 20, 30 and 40 cm) generated by continuous stocking. Measurements of tiller population density and population dynamics were performed at 4 week intervals and the results were used to calculate tiller appearance, death and survival rates. Tiller appearance and death rate were used to calculate sward stability index. The results indicate that keeping swards low (10 cm or lower) may be prejudicial to persistency and productivity of palisadegrass. The results also indicate that a low tiller population alone should not be considered as an indicator of loss of productive potential and of reduced plant persistency, since swards may be stable even with low population of tillers.

Evaluation of the composition of continuously-cultivated Arthrospira (Spirulina) platensis using ammonium chloride as nitrogen source

This work is focused on the influence of dilution rate (0.08 <= D <= 0.32 d(1)) on the continuous cultivation and biomass composition of Arthrospira (Spirulina) platensis using three different concentrations of ammonium chloride (c(No) = 1.0, 5.0 and 10 mol m (3)) as nitrogen source. At c(No) = 1.0 and 5.0 mol m (3) the biomass protein content was an increasing function of D, whereas, when using c(No) = 10 mol m (3), the highest protein content (72.5%) was obtained at D = 0.12 d (1). An overall evaluation of the process showed that biomass protein content increased with the rate of nitrogen supply (D c(No)) up to 72.5% at D c(No) = 1.20 mol m (3) d (1). Biomass lipid content was an increasing function of D only when the nitrogen source was the limiting factor for the growth (D c(No) <= 0.32 mol m (-3) d (1)), which occurred solely with c(No), = 1.0 mol m (3). Under such conditions, A. platensis reduced its nitrogen reserve in the form of proteins, while maintaining almost unvaried its lipid content. The latter was affected only when the concentration of nitrogen was extremely low (c(No) = 1.0 mol m (3)). The most abundant fatty acids were the palmitic (45.8 +/- 5.20%) and the gamma-linolenic (20.1 +/- 2.00%) ones. No significant alteration in the profiles either of saturated or unsaturated fatty acids was observed with c(No) <= 5.0 mol m (3), prevailing those with 16 and 18 carbons. (C) 2010 Elsevier Ltd. All rights reserved.