We introduce new versions of lattice Boltzmann methods (LBM) for incompressible binary mixtures where fluctuations of total density are inhibited. As a test for the improved algorithms we consider the problem of phase separation of two-dimensional binary mixtures quenched from a disordered state into the coexistence region. We find that the stability properties of LBM are greatly improved. The control of density fluctuations and the possibility of running longer simulations allow a more precise evaluation of the growth exponent.

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.

Using an algorithm for simulating equilibrium configurations, we study a fluctuating helical polymer either (i) contained in a cylindrical pore or (ii) wound around a cylindrical rod. We work in the regime where both the contour length and the persistence length of the helical polymer are much larger than the diameter of the cylinder. In case (i) we calculate the free energy of confinement and interpret it in terms of a wormlike chain in a pore with an effective diameter that depends on the parameters of the helix. In case (ii) we consider the possibility that one end of the helical polymer escapes from the rod and wanders away. The average numbers of turns at which the helix escapes or intersects the rod are measured in the simulations, as a function of the pitch p(o). The behavior for large and small p(o) is explained with simple scaling arguments.

Periodicity of the solutions of whole line difference equations is investigated. The considered equations is linear and of convolution type. The expression of the solution by means of a periodic resolvent kernel is given.

We consider the problem of testing for additivity and joint effects in multivariate nonparametric regression when the data are modelled as observations of an unknown response function observed on a d-dimensional lattice and contaminated with additive Gaussian noise. We propose tests for additivity and joint effects, appropriate for both homogeneous and inhomogeneous response functions, using the particular structure of the data expanded in tensor product Fourier or wavelet bases studied recently by Amato & Antoniadis (2001) and Amato, Antoniadis & De Feis (2002). The corresponding tests are constructed by applying the adaptive Neyman truncation and wavelet thresholding procedures of Fan (1996), for testing a high-dimensional Gaussian mean, to the resulting empirical Fourier and wavelet coefficients. As a consequence, asymptotic normality of the proposed test statistics under the null hypothesis and lower bounds of the corresponding powers under a specific alternative are derived.

Objective: The aim of this study was to develop a computational model of HIV infection able to simulate the natural history of the disease and to test predictive parameters of disease progression. Design: We describe the results of a numerical simulation of the cellular and humoral immune response to the HIV-1 infection as an adaptive pathway in a “bit-string” space. Methods: A total of 650 simulations of the HIV-1 dynamics were performed with a modified version of the Celada-Seiden immune system model . Results: Statistics are in agreement with epidemiological studies showing a lognormal distribution for the time span between the infection and AIDS development. As predictive parameters of disease progression we found that HIV-1 accumulates “bit”-mutations mainly in the peptide sequences recognized by cytotoxic CD8 T cells, indicating that cell-mediated immunity plays a major role in viral control. The viral load set-point was closely correlated with the time from the infection to AIDS development. Viral divergence from the viral quasispecies that was present at the beginning of the infection in long-term non-progressors (LTNP) was found to be similar to that found in rapid progressors at the time CD4 T cells drop below the critical value of 200 cells per ml. In contrast, the diversity indicated by the number of HIV strains present at the same time was higher for rapid and normal progressors compared to LTNP, suggesting that the early immune response can make the difference. Conclusion: This computational model may help to define the predictive parameters of HIV dynamics and disease progression, with potential applications in therapeutic and vaccines simulations.

Using importance sampling we give an asymptotic efficient simulation law for risk processes with delayed claims

We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov–Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.

The achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High-purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties. After an introductory overview on dilute quantum gases, both in the homogeneus state and under harmonic or periodic confinement, the article is organized in three main sections. The first concerns Bose-condensed gases at zero temperature, with main regard to the properties of the ground state in different confinements and to collective excitations and transport in the condensate. Bose-Einstein-condensed gases at finite temperature are addressed in the next section, the main emphasis being on equilibrium properties and phase transitions and on dynamical and transport properties associated with the presence of the thermal cloud. Finally, the last section is focused on theoretical and computational issues that have emerged from the efforts to drive gases of fermionic atoms and boson-fermion mixtures deep into the quantum degeneracy regime, with the aim of realizing novel superfluids from fermion pairing. The attention given in this article to methods beyond standard mean-field approaches should make it a useful reference point for future advances in these areas.

We present a numerical study of the micro-dynamical roots of dissipation in two colliding mesoscopic clouds of point-like fermions as a function of the scattering length and of temperature approaching full quantum degeneracy. This study, which is motivated by current experiments on ultracold gaseous mixtures of fermionic atoms inside magnetic traps, combines the solution of the coupled Vlasov-Landau equations for the Wigner distribution functions with a locally adaptive importance-sampling technique for handling collisional interactions. The results illustrate the consequences of genuinely quantum collisional phenomena, and in particular the role of Pauli blocking in the transition to hydrodynamic behaviour. We also compare the computed quantum collision rate as a function of temperature in the weak-coupling case with theoretical results assuming that equilibrium distributions determine the quantum collision integral.

Several studies highlight the need for appropriate statistical and probabilistic tools to analyze the data provided by the participants in an interlaboratory comparison. In some temperature comparisons, where the measurand is a physical state, independent realizations of the same physical state are acquired in each participating institute, which should be considered as belonging to a single super-population. This paper introduces the use of a probabilistic tool, a mixture of probability distributions, to represent the overall population in such a temperature comparison. This super-population is defined by combining the local populations in given proportions. The mixture density function identifies the total data variability, and the key comparison reference value has a natural definition as the expectation value of this probability density.

A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high-order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same timescale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer timescale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non-hydrodynamic fields.

In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime moving obstacles. Fluid motion is described by a lattice Boltzmann equation and obstacles are randomly distributed semi-permeable barriers which constrain the motion of the fluid particles. After a lifetime delay, obstacles move to new random positions. It is found that the non-linearly coupled dynamics of the fluid and obstacles produces heterogeneous patterns in fluid density and non-exponential relaxation of two-time autocorrelation function.