Duality in matrix lattice Boltzmann models

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.Comment: 12 pages, 3 figure

Direct effects of CO2 concentration on growth and isotopic composition of marine plankton.

The assessment of direct effects of anthropogenic CO2 increase on the marine biota has received relatively little attention compared to the intense research on CO2-related responses of the terrestrial biosphere. Yet, due to the rapid air–sea gas exchange, the observed past and predicted future rise in atmospheric CO2 causes a corresponding increase in seawater CO2 concentrations, [CO2], in upper ocean waters. Increasing [CO2] leads to considerable changes in the surface ocean carbonate system, resulting in decreases in pH and the carbonate concentration, [CO2−3]. These changes can be shown to have strong impacts on the marine biota. Here we will distinguish between CO2-related responses of the marine biota which (a) potentially affect the ocean's biological carbon pumps and (b) are relevant to the interpretation of diagnostic tools (proxies) used to assess climate change on geological times scales. With regard to the former, three direct effects of increasing [CO2] on marine plankton have been recognized: enhanced phytoplankton growth rate, changing elemental composition of primary produced organic matter, and reduced biogenic calcification. Although quantitative estimates of their impacts on the oceanic carbon cycle are not yet feasible, all three effects increase the ocean's capacity to take up and store atmospheric CO2 and hence, can serve as negative feedbacks to anthropogenic CO2 increase. With respect to proxies used in palaeo-reconstructions, CO2-sensitivity is found in carbon isotope fractionation by phytoplankton and foraminifera. While CO2- dependent isotope fractionation by phytoplankton may be of potential use in reconstructing surface ocean pCO2 at ancient times, CO2-related effects on the isotopic composition of foraminiferal shells confounds the use of the difference in isotopic signals between planktonic and benthic shells as a measure for the strength of marine primary production. The latter effect also offers an alternative explanation for the large negative swings in δ13C of foraminiferal calcite between glacial and interglacial periods. Changes in [CO2−3] affect the δ18O in foraminiferal shells. Taking this into account brings sea surface temperature estimates for the glacial tropics closer to those obtained from other geochemical proxies

Lattice-Gas Cellular Automaton Models for Biology: From Fluids to Cells

Lattice-gas cellular automaton (LGCA) and lattice Boltzmann (LB) models are promising models for studying emergent behaviour of transport and interaction processes in biological systems. In this chapter, we will emphasise the use of LGCA/LB models and the derivation and analysis of LGCA models ranging from the classical example dynamics of fluid flow to clotting phenomena in cerebral aneurysms and the invasion of tumour cell

Exploring performance and power properties of modern multicore chips via simple machine models

Modern multicore chips show complex behavior with respect to performance and power. Starting with the Intel Sandy Bridge processor, it has become possible to directly measure the power dissipation of a CPU chip and correlate this data with the performance properties of the running code. Going beyond a simple bottleneck analysis, we employ the recently published Execution-Cache-Memory (ECM) model to describe the single- and multi-core performance of streaming kernels. The model refines the well-known roofline model, since it can predict the scaling and the saturation behavior of bandwidth-limited loop kernels on a multicore chip. The saturation point is especially relevant for considerations of energy consumption. From power dissipation measurements of benchmark programs with vastly different requirements to the hardware, we derive a simple, phenomenological power model for the Sandy Bridge processor. Together with the ECM model, we are able to explain many peculiarities in the performance and power behavior of multicore processors, and derive guidelines for energy-efficient execution of parallel programs. Finally, we show that the ECM and power models can be successfully used to describe the scaling and power behavior of a lattice-Boltzmann flow solver code.Comment: 23 pages, 10 figures. Typos corrected, DOI adde

Lattice Boltzmann model with hierarchical interactions

We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of the interaction strength, the competition between stable and unstable regions results in a short-ranged disordered fluid pattern with sharp density contrasts. These disordered configurations contrast with phase-separation scenarios typically observed in binary fluids. The present results indicate that frustration can be modelled within the framework of a suitable one-body effective Boltzmann equation. The lattice implementation of such an effective Boltzmann equation may be seen as a preliminary step towards the development of complementary/alternative approaches to truly atomistic methods for the computational study of glassy dynamics.Comment: 14 pages, 5 figure

A lattice mesoscopic model of dynamically heterogeneous fluids

We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann dynamics with self-consistent constraints based on the non-local density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic heterogeneous fluids, such as non-Gaussian density distributions and long-time relaxation. Due to its intrinsically parallel dynamics, and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo and lattice glass models.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Generalized Lattice Boltzmann Method with multi-range pseudo-potential

The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100)

Volumetric formulation of lattice Boltzmann models with energy conservation

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.Comment: 8 figure