Boundedness results of minimizers of fully anisotropic variational problems and of weak solutions to fully anisotropic quasilinear elliptic equations are established.

We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the balance of the momentum of the system influences significantly the numerical solution and is necessary in order to get a better match with the experimental observations. Here an up-to-date list of the most meaningful mathematical models and numerical simulations of this test is discussed and the need is shown of an accurate revision of the numerical simulations of melting/solidification processes of pure materials (e.g. artificial crystal growth) produced in the last thirty years and not accounting for the solid phase mechanics.

In this paper we investigate the permanence of a system and give a sufficient condition for the endemic equilibrium to be globally asymptotically stable, which are the remaining problems in our previous paper (G. Izzo, Y. Muroya, A. Vecchio, A general discrete time model of population dynamics in the presence of an infection, Discrete Dyn. Nat. Soc. (2009), Article ID 143019, 15 pages. doi:10.1155/2009/143019.) (C) 2011 Elsevier Ltd. All rights reserved.

This paper describes a collocation method for solving numerically a singular integral equation with Cauchy and Volterra operators, associated with a proper constraint condition. The numerical method is based on the transformation of the given integral problem into a hypersingular integral equation and then applying a collocation method to solve the latter equation. Convergence of the resulting method is then discussed, and optimal convergence rates for the collocation and discrete collocation methods are given in suitable weighted Sobolev spaces. Numerical examples are solved using the proposed numerical technique.

Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the convection-diffusion equation for the order parameter to a generalized Navier-Stokes equation. The dynamical equations are simulated by implementing a hybrid method based on a lattice Boltzmann algorithm coupled to finite difference schemes. Simulations show that the ordering process occurs with morphologies depending on the speed of the thermal fronts or, equivalently, on the value of the thermal conductivity xi. At large values of xi, as in instantaneous quenching, the system is frozen in entangled configurations at high viscosity while it consists of grains with well-ordered lamellae at low viscosity. By decreasing the value of xi, a regime with very ordered lamellae parallel to the thermal fronts is found. At very low values of xi the preferred orientation is perpendicular to the walls in d = 2, while perpendicular order is lost moving far from the walls in d = 3.

Reactive Rayleigh-Taylor systems are characterized by the competition between the growth of the instability and the rate of reaction between cold (heavy) and hot (light) phases. We present results from state-of-the-art numerical simulations performed at high resolution in 2d by means of a self-consistent lattice Boltzmann (LB) method which evolves the coupled momentum and temperature equations and includes a reactive term. We tune parameters in order to address the competition between turbulent mixing and reaction, ranging from slow-to fast-reaction rates. We also study the mutual feedback between turbulence evolution driven by the Rayleigh-Taylor instability and front propagation against gravitational acceleration. We quantify both the enhancement of "flame" propagation due to turbulent mixing for the case of slow reaction-rate as well as the slowing-down of turbulence growth for the fast-reaction case, when the front quickly burns the gravitationally unstable phase. An increase of intermittency at small scales for temperature characterizes the case of fast reaction, associated to the formation of sharp wrinkled fronts separating pure burnt/unburnt fluids regions.

Purpose - The purpose of this paper is to present numerical results about phase separation of binary fluid mixtures quenched by contact with cold walls. Design/methodology/approach - The thermal phase separation is simulated by using a hybrid lattice Boltzmann method that solves the continuity and the Navier-Stokes equations. The equations for energy and concentration are solved by using a finite-difference scheme. This approach provides a complete description of the thermo-hydrodynamic effects in the mixture. Findings - A rich variety of domain patterns are found depending on the viscosity and on the heat conductivity of the mixture. Ordered lamellar structures are observed at high viscosity while domains rounded in shape dominate the phase separation at low viscosity, where two scales characterize the growth of domains. Research limitations/implications - The present approach provides a numerical method that can be extended to other systems such as liquid-vapor or lamellar systems. Moreover, a three-dimensional study can give a complete picture of thermo-hydrodynamic effects. Originality/value - This paper provides a consistent thermodynamic theoretical framework for a binary fluid mixture and a numerically stable method to simulate them.

The nature of blood as a suspension of red blood cells makes computational haemodynamics a demanding task. Our coarse-grained blood model, which builds on a lattice Boltzmann method for soft particle suspensions, enables the study of the collective behaviour of the order of 10(6) cells in suspension. After demonstrating the viscosity measurement in Kolmogorov flow, we focus on the statistical analysis of the cell orientation and rotation in Couette flow. We quantify the average inclination with respect to the flow and the nematic order as a function of shear rate and haematocrit. We further record the distribution of rotation periods around the vorticity direction and find a pronounced peak in the vicinity of the theoretical value for free model cells, even though cell-cell interactions manifest themselves in a substantial width of the distribution.

We present state-of-the-art numerical simulations of a two-dimensional Rayleigh-Taylor instability for a compressible stratified fluid. We describe the computational algorithm and its implementation on the QPACE supercomputer. High resolution enables the statistical properties of the evolving interface that we characterize in terms of its fractal dimension to be studied.

The parametrization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science, and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density, or both develop highly nonlinear mean profiles due to the interactions between the turbulent boundary layer and the unmixed-stable-flow above or below it. We present a second-order closure able to cope simultaneously with both bulk and boundary layer regions, and we test it against high-resolution state-of-the-art two-dimensional numerical simulations in a convective and stratified belt for values of the Rayleigh number up to Ra similar to 10(10). Data are taken from a Rayleigh-Taylor system confined by the existence of an adiabatic gradient.

High Reynolds numbers Navier-Stokesequations are believed to break self-similarity concerning both spatial and temporal properties: correlation functions of different orders exhibit distinct decorrelation times and anomalous spatial scaling properties. Here, we present a systematic attempt to measure multi-time and multi-scale correlations functions, by using high Reynolds numbers numerical simulations of fully homogeneous and isotropic turbulent flow. The main idea is to set-up an ensemble of probing stations riding the flow, i.e., measuring correlations in a reference frame centered on the trajectory of distinct fluid particles (the quasi-Lagrangian reference frame introduced by Belinicher and L'vov [Sov. Phys. JETP 66, 303 (1987)]). In this way, we reduce the large-scale sweeping and measure the non-trivial temporal dynamics governing the turbulent energy transfer from large to small scales. We present evidences of the existence of the dynamic multiscaling properties of turbulence - first proposed by L'vov et al. [Phys. Rev. E 55, 7030 (1997)] - in which multi-time correlation functions are characterized by an infinite set of characteristic times.

We consider explicit symplectic partitioned Runge-Kutta (ESPRK) methods for the numerical integration of non-autonomous dynamical systems. It is known that, in general, the accuracy of a numerical method can diminish considerably whenever an explicit time dependence enters the differential equations and the order reduction can depend on the way the time is treated. In the present paper, we demonstrate that explicit symplectic partitioned Runge-Kutta-Nyström (ESPRKN) methods specifically designed for second order differential equations , undergo an order reduction when M=M(t), independently of the way the time is approximated. Furthermore, by means of symmetric quadrature formulae of appropriate order, we propose a different but still equivalent formulation of the original non-autonomous problem that treats the time as two added coordinates of an enlarged differential system. In so doing, the order reduction is avoided as confirmed by the presented numerical tests.