Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Weak approximations. A Malliavin calculus approach

We introduce a variation of the proof for weak approximations that issuitable for studying the densities of stochastic processes which areevaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations fordensities and distributions can also be achieved. We apply theseideas to the case of stochastic differential equations with boundaryconditions and the composition of two diffusions.

Monte Carlo simulation of kilovolt electron transport in solids

A Monte Carlo procedure to simulate the penetration and energy loss of low¿energy electron beams through solids is presented. Elastic collisions are described by using the method of partial waves for the screened Coulomb field of the nucleus. The atomic charge density is approximated by an analytical expression with parameters determined from the Dirac¿Hartree¿Fock¿Slater self¿consistent density obtained under Wigner¿Seitz boundary conditions in order to account for solid¿state effects; exchange effects are also accounted for by an energy¿dependent local correction. Elastic differential cross sections are then easily computed by combining the WKB and Born approximations to evaluate the phase shifts. Inelastic collisions are treated on the basis of a generalized oscillator strength model which gives inelastic mean free paths and stopping powers in good agreement with experimental data. This scattering model is accurate in the energy range from a few hundred eV up to about 50 keV. The reliability of the simulation method is analyzed by comparing simulation results and experimental data from backscattering and transmission measurements.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Properties of resonant activation phenomena

The phenomenon of resonant activation of a Brownian particle over a fluctuating barrier is revisited. We discuss the important distinctions between barriers that can fluctuate among up and down configurations, and barriers that are always up but that can fluctuate among different heights. A resonance as a function of the barrier fluctuation rate is found in both cases, but the nature and physical description of these resonances is quite distinct. The nature of the resonances, the physical basis for the resonant behavior, and the importance of boundary conditions are discussed in some detail. We obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate, and show that our analytic results are in excellent agreement with numerical results.

Monte Carlo study of the finite-size effects on the magnetization of maghemite small particles

Monte Carlo simulations of a model for gamma-Fe2O3 (maghemite) single particle of spherical shape are presented aiming at the elucidation of the specific role played by the finite size and the surface on the anomalous magnetic behavior observed in small particle systems at low temperature. The influence of the finite-size effects on the equilibrium properties of extensive magnitudes, field coolings, and hysteresis loops is studied and compared to the results for periodic boundaries. It is shown that for the smallest sizes the thermal demagnetization of the surface completely dominates the magnetization while the behavior of the core is similar to that of the periodic boundary case, independently of D. The change in shape of the hysteresis loops with D demonstrates that the reversal mode is strongly influenced by the presence of broken links and disorder at the surface

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Spectral analysis and limit behaviours in a spring-mass system

We consider a model for a damped spring-mass system that is a strongly damped wave equation with dynamic boundary conditions. In a previous paper we showed that for some values of the parameters of the model, the large time behaviour of the solutions is the same as for a classical spring-mass damper ODE. Here we use spectral analysis to show that for other values of the parameters, still of physical relevance and related to the effect of the spring inner viscosity, the limit behaviours are very different from that classical ODE

Cosmic censorship in two-dimensional gravity

A weak version of the cosmic censorship hypothesis is implemented as a set of boundary conditions on exact semiclassical solutions of two-dimensional dilaton gravity. These boundary conditions reflect low-energy matter from the strong coupling region and they also serve to stabilize the vacuum of the theory against decay into negative energy states. Information about low-energy incoming matter can be recovered in the final state but at high energy black holes are formed and inevitably lead to information loss at the semiclassical level.

End point of Hawking radiation

The formation and semiclassical evaporation of two-dimensional black holes is studied in an exactly solvable model. Above a certain threshold energy flux, collapsing matter forms a singularity inside an apparent horizon. As the black hole evaporates the apparent horizon recedes and meets the singularity in a finite proper time. The singularity emerges naked, and future evolution of the geometry requires boundary conditions to be imposed there. There is a natural choice of boundary conditions which matches the evaporated black hole solution onto the linear dilaton vacuum. Below the threshold energy flux no horizon forms and boundary conditions can be imposed where infalling matter is reflected from a timelike boundary. All information is recovered at spatial infinity in this case.

Model of black hole evolution

We investigate a model where the quantum dynamics of black hole evaporation is determined by imposing a boundary on the apparent horizon with suitable boundary conditions. An unconventional scenario for the evolution emerges: only an insignificant fraction of energy of order (mG)-1 is radiated out; the outgoing wave carries a very small part of the quantum-mechanical information of the collapsed body, the bulk of the information remaining in the final stable black hole geometry.

Modelo de comportamiento en sevicio para estructuras reticulares de hormigón. Parte I: Descripción del modelo y ejemplos de aplicación

A general method for instantaneous and time-dependent serviceability analysis of plane concrete frames is presented. The methodology is based in an extension of the classic matrix formulation for bars. The main aspects influencing the behaviour of the structural concrete are considered: cracking, creep, shrinkage or prestress losses. To simulate the effect of cracking a smeared model (developed in Part II) based on the modification of the tensile branch of the concrete stress-strain relationship is adopted. The general approach considered permits the application to different materials and constitutive laws. Sequential construction (sectional and structural), incorporation of reinforcement, consideration of the loads history; placing and removing shores, and restraining or releasing in boundary conditions are considered. Some examples are included to highlight the capabilities of the model

Leaving the Dark ages with AMIGA

We present an Analytic Model of Intergalactic-medium and GAlaxy (AMIGA) evolution since the dark ages. AMIGA is in the spirit of the popular semi-analytic models of galaxy formation, although it does not use halo merger trees but interpolates halo properties in grids that are progressively built. This strategy is less memory-demanding and allows one to start modeling at sufficiently high redshifts and low halo masses to have trivial boundary conditions. The number of free parameters is minimized by making a causal connection between physical processes usually treated as independent of each other, which leads to more reliable predictions. However, the strongest points of AMIGA are the following: (1) the inclusion of molecular cooling and metal-poor, population III (Pop III) stars with the most dramatic feedback and (2) accurate follow up of the temperature and volume filling factor of neutral, singly ionized, and doubly ionized regions, taking into account the distinct halo mass functions in those environments. We find the following general results. Massive Pop III stars determine the intergalactic medium metallicity and temperature, and the growth of spheroids and disks is self-regulated by that of massive black holes (MBHs) developed from the remnants of those stars. However, the properties of normal galaxies and active galactic nuclei appear to be quite insensitive to Pop III star properties due to the much higher yield of ordinary stars compared to Pop III stars and the dramatic growth of MBHs when normal galaxies begin to develop, which cause the memory loss of the initial conditions.