Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]

O Ensino-aprendizagem de Matemática Através de Projetos Envolvendo Profissões: um Estudo de Caso no Ensino Fundamental

Este projeto teve como objetivo elaborar uma possibilidade de ensino/aprendizagem de alguns conhecimentos de matemática e aplicá-la através de projetos práticos relacionados a uma profissão, visando melhorar o aprendizado dos alunos. Para isto foi feito um estudo de caso com duas turmas de 8ª série (9° ano) do ensino fundamental de uma escola pública municipal da Serra-ES envolvendo as profissões de arquitetura e engenharia, que foram escolhidas junto com as turmas. Os conteúdos trabalhados foram definidos pelo pesquisador, que também era professor da disciplina, com base em sua experiência prévia e nos itens em que os alunos normalmente encontravam maiores dificuldades, a saber: trigonometria no triângulo retângulo e áreas de figuras planas. O projeto ficou definido como: a construção de uma maquete da escola e plantas baixas da escola em escala. Os alunos, organizados em grupos, foram acompanhados e auxiliados pelo professor durante todo o projeto. Os resultados foram positivos: os alunos se mostraram comprometidos e motivados; aumentou sua autoestima, diminuiu a resistência em relação à matemática e a distância entre teoria e prática; estimulou o trabalho em equipe, melhorando as relações professor-aluno e aluno-aluno; melhorou significativamente o desempenho dos alunos nas avaliações comparado a outras turmas ou a essas mesmas turmas em outros conteúdos

Algebro-Geometric Solutions of the Boussinesq Hierarchy

We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function representation of all algebro-geometric quasi-periodic solutions and related quantities of the Bsq hierarchy.Comment: LaTeX, 48 page

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Anomalous Dynamic Scaling in Locally-Conserved Coarsening of Fractal Clusters

We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as functions of time. Analyzing the correlation function dynamics, we identify two different time-dependent length scales that exhibit power laws in time. The exponents of these power laws are independent of D, one of them is apparently the classic exponent 1/3. The solute mass versus time exhibits dynamic scaling with a D-dependent exponent, in agreement with a simple scaling theory.Comment: 5 pages, 4 figure

Perceptions and evaluations of front-line health workers regarding the Brazilian National Program for Improving Access and Quality to Primary Care (PMAQ): a mixed-method approach

Although it is well known that a successful implementation depends on the front-liners’ knowledge and participation, as well as on the organizational capacity of the institutions involved, we still know little about how front-line health workers have been involved in the implementation of the Brazilian National Program for Improving Access and Quality to Primary Care (PMAQ). This paper develops a contingent mixed-method approach to explore the perceptions of front-line health workers - managers, nurses, community health workers, and doctors - regarding the PMAQ (2nd round), and their evaluations concerning health unit organizational capacity. The research is guided by three relevant inter-related concepts from implementation theory: policy knowledge, participation, and organizational capacity. One hundred and twenty-seven health workers from 12 primary health care units in Goiânia, Goiás State, Brazil, answered semi-structured questionnaires, seeking to collect data on reasons for adherence, forms of participation, perceived impact (open-ended questions), and evaluation of organizational capacity (score between 0-10). Content analyses of qualitative data enabled us to categorize the variables “level of perceived impact of PMAQ” and “reasons for adhering to PMAQ”. The calculation and aggregation of the means for the scores given for organizational capacity enabled us to classify distinct levels of organizational capacity. We finally integrated both variables (Perceived-Impact and Organizational-Capacity) through cross-tabulation and the narrative. Results show that nurses are the main type of professional participating. The low organizational capacity and little policy knowledge affected workers participation in and their perceptions of the PMAQ

Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode

An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude $\rho(t)$ decouples from the phase due to the spatial homogeneity of the equilibrium, and the resulting one-dimensional dynamics is analyzed using an expansion in $\rho$. As the linear growth rate $\gamma$ vanishes, the expansion coefficients diverge; a rescaling $\rho(t)\equiv\gamma^2\,r(\gamma t)$ of the mode amplitude absorbs these singularities and reveals that the mode electric field exhibits trapping scaling $|E_1|\sim\gamma^2$ as $\gamma\rightarrow0$. The dynamics for $r(\tau)$ depends only on the phase $e^{i\xi}$ where $d\epsilon_{{k}} /dz=|{\epsilon_{{k}}}|e^{-i\xi/2}$ is the derivative of the dielectric as $\gamma\rightarrow0$.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the Author ([email protected]); paper accepted by Physical Review Letter

Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers

Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by a combination of asymptotic ODE estimates and numerical Evans function computations. Our results indicate stability for gamma in the interval [1, 3] for all compressive boundary-layers, independent of amplitude, save for inflow layers in the characteristic limit (not treated). Expansive inflow boundary-layers have been shown to be stable for all amplitudes by Matsumura and Nishihara using energy estimates. Besides the parameter of amplitude appearing in the shock case, the boundary-layer case features an additional parameter measuring displacement of the background profile, which greatly complicates the resulting case structure. Moreover, inflow boundary layers turn out to have quite delicate stability in both large-displacement and large-amplitude limits, necessitating the additional use of a mod-two stability index studied earlier by Serre and Zumbrun in order to decide stability

Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

We analyze a recent experiment of Sharon \textit{et al.} (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural model for that experiment, belongs to the same universality class as model B of phase ordering. Two series of numerical simulations with model B are performed, with the FVFPs grown in the experiment, and with Diffusion Limited Aggregates, as the initial conditions. We observed Lifshitz-Slyozov scaling $t^{1/3}$ at intermediate distances and very slow convergence to this scaling at small distances. Dynamic scale invariance breaks down at large distances.Comment: 4 pages, 4 eps figures; to appear in Phys. Rev.