Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Determination of the critical coupling for oscillators in a ring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The canonical structure of Podolsky's generalized electrodynamics on the null-plane

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Numerical simulation of a radial diffuser turbulent airflow

In the present work are presented results from numerical simulations performed with the ANSYS-CFX (R) code. We have studied a radial diffuser flow case, which is the main academic problem used to study the flow behavior on flat plate valves. The radial flow inside the diffuser has important behavior such as the turbulence decay downstream and recirculation regions inside the valve flow channel due to boundary layer detachment. These flow structures are present in compressor reed valve configurations, influencing to a greater extent the compressor efficiency. The main target of the present paper was finding the simulation set-up (computational domain, boundary conditions and turbulence model) that better fits with experimental data published by Tabatabai and Pollard. The local flow turbulence and velocity profiles were investigated using four different turbulence models, two different boundary conditions set-up, two different computational domains and three different flow conditions (Re-in - Reynolds number at the diffuser inlet). We used the Reynolds stress (BSL); the k-epsilon; the RNG k-epsilon; and the shear stress transport (SST) k-omega turbulence models. The performed analysis and comparison of the computational results with experimental data show that the choice of the turbulence model, as well as the choice of the other computational conditions, plays an important role in the results physical quality and accuracy. (c) 2007 Elsevier B.V. All rights reserved.

Energy spectrum and eigenfunctions through the Quantum Section Method

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

Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations

For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).

PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Application of a meshless method in electromagnetics

An improved meshless method is presented with an emphasis on the detailed description of this new computational technique and its numerical implementations by investigating the usefulness of a commonly neglected parameter in this paper. Two approaches to enforce essential boundary conditions are also thoroughly investigated. Numerical tests on a mathematical function is carried out as a means of validating the proposed method. It will be seen that the proposed method is more robust than the conventional ones. Applications in solving electromagnetic problems are also presented.

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

The electrochemical behavior of pyrite-pyrrhotite mixtures

To assess the response of common sulfide minerals to oxidizing conditions, a methodology to immobilize mechanically solid particles on carbon surfaces (voltammetry of microparticles, VMP) was employed, to define the influence of the pyrrhotite content in pyrite-pyrrhotite mixtures. The influence of the galvanic interactions and local pH on the oxidation reaction of pyrite was also investigated. With this purpose, artificial two-mineral electrodes were constructed, ranging in weight from 20 to 80% pyrrhotite. The resulting cyclic voltammograms were analyzed and relative quantities of oxidation products were evaluated. The goal of this work was to define the boundary conditions, in terms of pyrrhotite content in the mixture, that determine the SO42-/S ratio obtained and to describe some parameters which influence this ratio: local pH and galvanic interactions. (C) 2003 Elsevier B.V. All rights reserved.

The application of interpolating MLS approximations to the analysis of MHD flows

The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.

A note on the controllability for the wave equation in nonsmooth plane domains

We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved part of the boundary, while in the straight part we impose homogeneous Dirichlet boundary condition. The initial state has finite energy and the control is square integrable. (c) 2005 Elsevier B.V. All rights reserved.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).