Equation of state of hot, dense stellar matter. Finite temperature nuclear Thomas-Fermi approach

The properties of hot, dense stellar matter are investigated with a finite temperature nuclear Thomas-Fermi model.

Particle in an electromagnetic field: The Lorentz-Dirac equation

A new method to solve the Lorentz-Dirac equation in the presence of an external electromagnetic field is presented. The validity of the approximation is discussed, and the method is applied to a particle in the presence of a constant magnetic field.

Pseudoclassical description for a nonrelativistic spinning particle. I. The Levy-Leblond equation

A pseudoclassical model for a spinning nonrelativistic particle is presented. The model contains two first-class constraints which after quantization give rise to the Levy-Leblond equation for a spin-1/2 particle.

Effects of external noise on the Swift-Hohenberg Equation

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Bnard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution.

Probing elastic anisotropy from defect dynamics in Langmuir monolayers

We study the dynamics of annihilation of point defects in Langmuir monolayers. The absence of hydrodynamic effects allows us to quantitatively relate the asymmetry in defect mobility to the elastic anisotropy of the material, which in turn can be varied through the control of the surface pressure applied to the monolayer. Using the proposed theoretical analysis, we are able to obtain rather elusive equilibrium properties out of relatively simple dynamical measurements. In particular, we measure the elastic constants and their pressure dependence.

State equation for shape-memory alloys. Aplication to Cu-Zn-Al

We deal with the hysteretic behavior of partial cycles in the two¿phase region associated with the martensitic transformation of shape¿memory alloys. We consider the problem from a thermodynamic point of view and adopt a local equilibrium formalism, based on the idea of thermoelastic balance, from which a formal writing follows a state equation for the material in terms of its temperature T, external applied stress ¿, and transformed volume fraction x. To describe the striking memory properties exhibited by partial transformation cycles, state variables (x,¿,T) corresponding to the current state of the system have to be supplemented with variables (x,¿,T) corresponding to points where the transformation control parameter (¿¿ and/or T) had reached a maximum or a minimum in the previous thermodynamic history of the system. We restrict our study to simple partial cycles resulting from a single maximum or minimum of the control parameter. Several common features displayed by such partial cycles and repeatedly observed in experiments lead to a set of analytic restrictions, listed explicitly in the paper, to be verified by the dissipative term of the state equation, responsible for hysteresis. Finally, using calorimetric data of thermally induced partial cycles through the martensitic transformation in a Cu¿Zn¿Al alloy, we have fitted a given functional form of the dissipative term consistent with the analytic restrictions mentioned above.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Dark energy equation of state and anthropic selection

We explore the possibility that the dark energy is due to a potential of a scalar field and that the magnitude and the slope of this potential in our part of the Universe are largely determined by anthropic selection effects. We find that, in some models, the most probable values of the slope are very small, implying that the dark energy density stays constant to very high accuracy throughout cosmological evolution. In other models, however, the most probable values of the slope are such that the slow roll condition is only marginally satisfied, leading to a recollapse of the local universe on a time scale comparable to the lifetime of the Sun. In the latter case, the effective equation of state varies appreciably with the redshift, leading to a number of testable predictions.

Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

Capacidade máxima de adsorção de fósforo e constante de energia em Latossolo Bruno em razão de diferentes ajustes do modelo Langmuir

A capacidade máxima de adsorção de fósforo (CMAP) é um parâmetro bastante útil para caracterizar a capacidade de adsorção de fósforo (P) do solo e, por isso, o modelo de Langmuir, que possibilita essa estimativa, é bastante difundido. Porém, se o ajuste da equação for realizado por modelos não lineares ou linearizados, ou se forem escolhidos modelos de região única ou múltiplas, nem sempre os valores estimados da CMAP e da constante de energia de ligação (k) são semelhantes. O objetivo deste trabalho foi avaliar o efeito do uso de diferentes métodos de ajuste do modelo de Langmuir sobre os valores estimados de CMAP e k. Para isso, utilizouse um único solo de alta capacidade de adsorção de P, o qual foi misturado a quantidades crescentes de areia lavada, construindo-se sistemas com capacidades de sorção crescentes, mas com a fase sólida constituída da mesma mineralogia. Foi utilizado solo do horizonte B de um Latossolo Bruno com 800 g kg-1 de argila, o qual foi misturado com areia em quantidades para obterem-se solos artificiais com 0, 200, 400, 600 e 800 g kg-1 de argila. Esses solos artificiais foram incubados por 30 dias com calcário para elevar o pH(H2O) até 6,0 e, após, foram secos em estufa e peneirados. Foram realizadas as isotermas de adsorção e os dados ajustados pelo modelo de Langmuir, usando os seguintes métodos: NLin - não linear com região única; L-1R - linearização com região única; L-2RG - linearização com duas regiões, ajuste gráfico; L-3RG - linearização com três regiões, ajuste gráfico; L-2RE linerização com duas regiões, ajuste estatístico. Os resultados evidenciaram que todos os métodos utilizados estimaram valores de CMAP proporcionais ao teor de argila dos solos e poderiam ser usados para caracterizar os solos. Contudo, quando utilizados ajustes com mais de uma região de adsorção, os valores da CMAP para a última região foram sensivelmente superiores àqueles observados após a incubação do solo com doses de P em um teste adicional. Isso indica que a CMAP da última região deve ser evitada como caracterizadora da capacidade de adsorção do solo. Conforme era esperado, os valores de k foram proporcionais aos teores de argila do solo na primeira (ou única) região dos modelos linearizados; contudo, não seguiram essa tendência no modelo não linear, recomendando-se cautela na interpretação da constante k ajustada por modelos não lineares.

Solutions of the telegrapher's equation in the presence of traps

Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher¿s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher¿s equation represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinuities even in the presence of traps.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.