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

The impact of cell shape and chain formation on nutrient acquisition of marine diatoms

Diatoms have evolved a multitude of morphologics, including highly elongated cells and cell chains. Elongation and chain formation have many possible functions, such as grazing protecticn or effects on sinking. Here, a model of diffusive and advective nutrient transport is used to predict impacts of cell shape and chain length on potential nutrient supply and uptake in a turbulent environment. Rigid, contiguous, prolate spheroids thereby represent the shapes of simple chains and solitary cells. At scales larger than a few centimeters, turbulent water motions produce a more or less homogeneous nutrient distribution. At the much smaller stall: of diatom cells, however, turbulence drcates a roughly linear shear and nutrients can locally become strongly dl=pleted because of nutrient uptake by phytoplankton cells. The potential diffusive nutrient supply is greater for elongated than for spherically shaped cells of similar volume but lower for chains than for solitary cells. Although the relative increase in nutrient transport due to turbulence is greater for chains, single cells still enjoy a greater total nutrient supply in turbulent cnvironmerits. Only chains with specialized structures, such as spaces between the cells, can overcome this disadvantage and even obtain a higher nutrient supply than do solitary cells. The mod=1 results are compared to laboratory measurements of nutrient uptake under turbulent conditions and to effects ol’ sinkin

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

Herschel-Bulkley rheology from lattice kinetic theory of soft-glassy materials

We provide a clear evidence that a two species mesoscopic Lattice Boltzmann (LB) model with competing short-range attractive and mid-range repulsive interactions supports emergent Herschel-Bulkley (HB) rheology, i.e. a power-law dependence of the shear-stress as a function of the strain rate, beyond a given yield-stress threshold. This kinetic formulation supports a seamless transition from flowing to non-flowing behaviour, through a smooth tuning of the parameters governing the mesoscopic interactions between the two species. The present model may become a valuable computational tool for the investigation of the rheology of soft-glassy materials on scales of experimental interest.Comment: 5 figure

Carbon, nitrogen and O(2) fluxes associated with the cyanobacterium Nodularia spumigena in the Baltic Sea

Photosynthesis, respiration, N2 fixation and ammonium release were studied directly in Nodularia spumigena during a bloom in the Baltic Sea using a combination of microsensors, stable isotope tracer experiments combined with nanoscale secondary ion mass spectrometry (nanoSIMS) and fluorometry. Cell-specific net C- and N2-fixation rates by N. spumigena were 81.6±6.7 and 11.4±0.9 fmol N per cell per h, respectively. During light, the net C:N fixation ratio was 8.0±0.8. During darkness, carbon fixation was not detectable, but N2 fixation was 5.4±0.4 fmol N per cell per h. Net photosynthesis varied between 0.34 and 250 nmol O2 h−1 in colonies with diameters ranging between 0.13 and 5.0 mm, and it reached the theoretical upper limit set by diffusion of dissolved inorganic carbon to colonies (>1 mm). Dark respiration of the same colonies varied between 0.038 and 87 nmol O2 h−1, and it reached the limit set by O2 diffusion from the surrounding water to colonies (>1 mm). N2 fixation associated with N. spumigena colonies (>1 mm) comprised on average 18% of the total N2 fixation in the bulk water. Net NH4+ release in colonies equaled 8–33% of the estimated gross N2 fixation during photosynthesis. NH4+ concentrations within light-exposed colonies, modeled from measured net NH4+ release rates, were 60-fold higher than that of the bulk. Hence, N. spumigena colonies comprise highly productive microenvironments and an attractive NH4+ microenvironment to be utilized by other (micro)organisms in the Baltic Sea where dissolved inorganic nitrogen is limiting growth

Diel variations in cell division and biomass production of Emiliania huxleyi — Consequences for the calculation of physiological cell parameters

Cell division of the coccolithophore Emiliania huxleyi and other phytoplankton typically becomes entrained to diel light/dark cycles under laboratory conditions, with division occurring primarily during dark phases and production occurring during light phases. Under these conditions, increases in cell and biomass concentrations deviate from exponential functions on time scales < 24 h. These deviations lead to significant diel variations in common measurements of phytoplankton physiology such as cellular quotas of particulate organic and inorganic carbon (POC, PIC) and their production rates. Being time-dependent, only the temporal mean of the various values during the day are comparable between experiments. Deviations from exponential growth furthermore imply that increases in cell and biomass concentrations cannot be expressed by the daily growth rate μ24 h (typically determined from daily increments in cell concentrations). Consequently, conventional calculations of production as the product of a cellular quota (e.g., POC quota) and μ24 h are mathematically incorrect. To account for this, we here describe short-term changes in cell and biomass concentrations of fast -dividing, dilute-batch cultures of E. huxleyi grown under a diel light/dark cycle using linear regression. Based on the derived models, we present calculations for daily means of cellular quotas and production rates. Conventional (time-specific) measurements of cellular quotas and production differ from daily means by up to 65% in our example and, under some circumstances, cause false “effects” of treatments. Intending to reduce errors in ecophysiological studies, we recommend determining daily means—mathematically or by adjusting the experimental setup or sampling times appropriately