Based on the past twenty-five years of lattice Boltzmann research, we venture into a far-flung prediction for the next twenty-five, with past and future privileged over the present state of affairs. Copyright (C) EPLA, 2015

We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher-order terms on the resulting macroscopic equations.

Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics transport phenomena within a lattice kinetic formalism. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes.

The inverse problem of MEG aims at estimating electromagnetic cerebral activity from measurements of the magnetic fields outside the head. After formulating the problem within the Bayesian framework, a hierarchical conditionally Gaussian prior model is introduced, including a physiologically inspired prior model that takes into account the preferred directions of the source currents. The hyperparameter vector consists of prior variances of the dipole moments, assumed to follow a non-conjugate gamma distribution with variable scaling and shape parameters.

We present a lattice Boltzmann (LB) model for the simulation of hemodynamic flows in the presence of compliant walls. The new scheme is based on the use of a continuous bounce-back boundary condition, as combined with a dynamic constitutive relation between the flow pressure at the wall and the resulting wall deformation. The method is demonstrated for the case of two-dimensional (axisymmetric) pulsatile flows, showing clear evidence of elastic wave propagation of the wall perturbation in response to the fluid pressure.

By tailoring the geometry of the upper boundary in turbulent Rayleigh-Benard convection we manipulate the boundary layer-interior flow interaction, and examine the heat transport using the lattice Boltzmann method. For fixed amplitude and varying boundary wavelength., we find that the exponent beta in the Nusselt-Rayleigh scaling relation, Nu - 1 proportional to Ra-beta, is maximized at lambda =lambda(max) approximate to ( 2 pi)(-1), but decays to the planar value in both the large (lambda >> lambda(max)) and small (lambda << lambda(max)) wavelength limits.

One of the most popular discrete approximating polynomials is the Lagrange interpolation polynomial and the Jacobi zeros provide a particularly convenient choice of the interpolation knots on [?1, 1]. However, it is well known that there is no point system such that the associate sequence of Lagrange polynomials, interpolating an arbitrary function f, would converge to f w.r.t. any weighted uniform or L1 norm.

We establish a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.