305 research outputs found

### 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

### 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.

### 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

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