Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Exchange transformations reversing orientation

University of Sao Paulo (USP)

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Schrodinger-Poisson equations without Ambrosetti-Rabinowitz condition

We prove the existence of ground state solutions for a stationary Schrodinger-Poisson equation in R(3). The proof is based on the mountain pass theorem and it does not require the Ambrosetti-Rabinowitz condition. (C) 2010 Elsevier Inc. All rights reserved.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Existence of secondary bifurcations or isolas for PDEs

In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines the Global Bifurcation Theorem, knowledge about the non-existence of nontrivial steady state solutions at the zero parameter value and explicit information about the coexistence of multiple nontrivial steady states at a positive parameter value. We apply the method to the two-dimensional Swift-Hohenberg equation. (C) 2011 Elsevier Ltd. All rights reserved.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features. Published by Elsevier Ltd.

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

A geometric mass-preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)-based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE-based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well-suited for the highly stretched curvilinear grids used in CFD simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.

Numerical study of the atmospheric flow over a coastal cliff

This work presents a numerical method suitable for the study of the development of internal boundary layers (IBL) and their characteristics for flows over various types of coastal cliffs. The IBL is an important meteorological occurrence for flows with surface roughness and topographical step changes. A two-dimensional flow program was used for this study. The governing equations were written using the vorticity-velocity formulation. The spatial derivatives were discretized by high-order compact finite differences schemes. The time integration was performed with a low storage fourth-order Runge-Kutta scheme. The coastal cliff (step) was specified through an immersed boundary method. The validation of the code was done by comparison of the results with experimental and observational data. The numerical simulations were carried out for different coastal cliff heights and inclinations. The results show that the predominant factors for the height of the IBL and its characteristics are the upstream velocity, and the height and form (inclination) of the coastal cliff. Copyright (C) 2010 John Wiley & Sons, Ltd.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.