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.

International business cycles, financial markets and household production

This paper investigates the properties of an international real business cycle model with household production. We show that a model with disturbances to both market and household technologies reproduces the main regularities of the data and improves existing models in matching international consumption, investment and output correlations without irrealistic assumptions on the structure of international financial markets. Sensitivity analysis shows the robustness of the results to alternative specifications of the stochastic processes for the disturbances and to variations of unmeasured parameters within a reasonable range.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Surface collective oscillations of metal clusters and spheres: Random-phase-approximation sum-rules approach

Using the once and thrice energy-weighted moments of the random-phase-approximation strength function, we have derived compact expressions for the average energy of surface collective oscillations of clusters and spheres of metal atoms. The L=0 volume mode has also been studied. We have carried out quantal and semiclassical calculations for Na and Ag systems in the spherical-jellium approximation. We present a rather thorough discussion of surface diffuseness and quantal size effects on the resonance energies.

Spectrum of transmitted light in optical bistability: Effects of phase fluctuations of the driving laser

Time-dependent correlation functions and the spectrum of the transmitted light are calculated for absorptive optical bistability taking into account phase fluctuations of the driving laser. These fluctuations are modeled by an extended phase-diffusion model which introduces non-Markovian effects. The spectrum is obtained as a superposition of Lorentzians. It shows qualitative differences with respect to the usual calculation in which phase fluctuations of the driving laser are neglected.

Fission stability diagram of 240Pu

We have used an axially symmetric deformed Thomas-Fermi model to evaluate the fission barrier of 240Pu as a function of the quadrupole moment Q2 for different values of the angular momentum L and temperature T. The fission stability diagram of this nucleus is investigated.

Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Decay of unstable states in the presence of colored noise and random initial conditions. II. Analog experiments and digital simulations

The decay of an unstable state under the influence of external colored noise has been studied by means of analog experiments and digital simulations. For both fixed and random initial conditions, the time evolution of the second moment ¿x2(t)¿ of the system variable was determined and then used to evaluate the nonlinear relaxation time. The results obtained are found to be in excellent agreement with the theoretical predictions of the immediately preceding paper [Casademunt, Jiménez-Aquino, and Sancho, Phys. Rev. A 40, 5905 (1989)].

Spatiotemporal order out of noise

Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

Analysis of the role of mobility-lifetime products in the performance of amorphous silicon p-i-n solar cells

An analytical model of an amorphous silicon p-i-n solar cell is presented to describe its photovoltaic behavior under short-circuit conditions. It has been developed from the analysis of numerical simulation results. These results reproduce the experimental illumination dependence of short-circuit resistance, which is the reciprocal slope of the I(V) curve at the short-circuit point. The recombination rate profiles show that recombination in the regions of charged defects near the p-i and i-n interfaces should not be overlooked. Based on the interpretation of the numerical solutions, we deduce analytical expressions for the recombination current and short-circuit resistance. These expressions are given as a function of an effective ¿¿ product, which depends on the intensity of illumination. We also study the effect of surface recombination with simple expressions that describe its influence on current loss and short-circuit resistance.

Induced quantum metric fluctuations and the validity of semiclassical gravity

We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

Algebraic decay of velocity fluctuations in a confined fluid

Computer simulations of a colloidal particle suspended in a fluid confined by rigid walls show that, at long times, the velocity correlation function decays with a negative algebraic tail. The exponent depends on the confining geometry, rather than the spatial dimensionality. We can account for the tail by using a simple mode-coupling theory which exploits the fact that the sound wave generated by a moving particle becomes diffusive.