Fluctuating lattice Boltzmann

The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wavevectors $k$. Unlike previous work, which recovers FDT only as $k\to 0$, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.Comment: 7 pages, 3 figures, to appear in Europhysics Letter

The properties of tagged lattice fluids: II. Velocity correlation functions

We report preliminary measurements of the velocity autocorrelation function for a tagged particle in a lattice gas. These measurements agree with the Boltzmann-level theory. The Green-Kubo integration of these measurements agrees with theoretical predictions for the diffusion coefficient. To within the error bars of the simulations (3 /times/ 10/sup /minus/3/) we observe no long-time tails. 9 refs., 1 fig., 1 tab

Rheology of Lamellar Liquid Crystals in Two and Three Dimensions: A Simulation Study

We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10-100), in both two and three dimensions. In two dimensions we find that modest shear rates align the system and stabilise an almost regular lamellar phase, but high shear rates induce the nucleation and proliferation of defects, which in steady state is balanced by the annihilation of defects of opposite sign. The critical shear rate at onset of this second regime is controlled by thermodynamic and kinetic parameters; we offer a scaling analysis that relates the critical shear rate to a critical "capillary number" involving those variables. Within the defect proliferation regime, the defects may be partially annealed by slowly decreasing the applied shear rate; this causes marked memory effects, and history-dependent rheology. Simulations in three dimensions show instead shear-induced ordering even at the highest shear rates studied here. This suggests that the critical shear rate shifts markedly upward on increasing dimensionality. This may in part reflect the reduced constraints on defect motion, allowing them to find and annihilate each other more easily. Residual edge defects in the 3D aligned state mostly point along the flow velocity, an orientation impossible in two dimensions.Comment: 18 pages, 12 figure

Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field

We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency.Comment: 8 pages, Revtex, 3 Postscript figure

Detailed characterization of a laboratory magnetized supercritical collisionless shock and of the associated proton energization

Collisionless shocks are ubiquitous in the Universe and are held responsible for the production of nonthermal particles and high-energy radiation. In the absence of particle collisions in the system, theory shows that the interaction of an expanding plasma with a pre-existing electromagnetic structure (as in our case) is able to induce energy dissipation and allow shock formation. Shock formation can alternatively take place when two plasmas interact, through microscopic instabilities inducing electromagnetic fields that are able in turn to mediate energy dissipation and shock formation. Using our platform in which we couple a rapidly expanding plasma induced by high-power lasers (JLF/Titan at LLNL and LULI2000) with high-strength magnetic fields, we have investigated the generation of a magnetized collisionless shock and the associated particle energization. We have characterized the shock as being collisionless and supercritical. We report here on measurements of the plasma density and temperature, the electromagnetic field structures, and the particle energization in the experiments, under various conditions of ambient plasma and magnetic field. We have also modeled the formation of the shocks using macroscopic hydrodynamic simulations and the associated particle acceleration using kinetic particle-in-cell simulations. As a companion paper to Yao et al. [Nat. Phys. 17, 1177-1182 (2021)], here we show additional results of the experiments and simulations, providing more information to allow their reproduction and to demonstrate the robustness of our interpretation of the proton energization mechanism as being shock surfing acceleration

Laboratory evidence for proton energization by collisionless shock surfing

Charged particles can be accelerated to high energies by collisionless shock waves in astrophysical environments, such as supernova remnants. By interacting with the magnetized ambient medium, these shocks can transfer energy to particles. Despite increasing efforts in the characterization of these shocks from satellite measurements at Earth’s bow shock as well as powerful numerical simulations, the underlying acceleration mechanism or a combination thereof is still widely debated. Here we show that astrophysically relevant super-critical quasi-perpendicular magnetized collisionless shocks can be produced and characterized in the laboratory. We observe the characteristics of super-criticality in the shock profile as well as the energization of protons picked up from the ambient gas to hundreds of kiloelectronvolts. Kinetic simulations modelling the laboratory experiment identified shock surfing as the proton acceleration mechanism. Our observations not only provide direct evidence of early-stage ion energization by collisionless shocks but also highlight the role played by this particular mechanism in energizing ambient ions to feed further stages of acceleration. Furthermore, our results open the door to future laboratory experiments investigating the possible transition to other mechanisms, when increasing the magnetic field strength, or the effect that induced shock front ripples could have on acceleration processes

Two-dimensional lattice-Boltzmann model of hydrosol depth filtration

International audienceA two-dimensional mathematical model of the initial stage of depth filtration is developed. This model describes the fluid flow and the particle transport and capture in a representative elementary volume of the filter. A typical simulation can be outlined as follows: as a first stage, the flow field is computed in the whole complex void space of the filter using a lattice-Boltzmann method. As a second stage, the trajectory analysis is derived by applying Newton's second law to suspended particles in the flowing fluid. The capture or the reentrainment of the particles encountering the filter surface is determined from a force balance that takes into account the drag force and the solid friction force. This approach, which provides both microscopic data such as the initial capture probability density and macroscopic data such as the filter coefficient, is validated on a model experiment of deep-bed filtration

Lattice gas hydrodynamics in two and three dimensions

Hydrodynamical phenomena can be simulated by discrete lattice gas models obeing cellular automata rules (U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505, (1986); D. d'Humieres, P. Lallemand, and U. Frisch, Europhys. Lett. 2, 291, (1986)). It is here shown for a class of D-dimensional lattice gas models how the macrodynamical (large-scale) equations for the densities of microscopically conserved quantities can be systematically derived from the underlying exact ''microdynamical'' Boolean equations. With suitable restrictions on the crystallographic symmetries of the lattice and after proper limits are taken, various standard fluid dynamical equations are obtained, including the incompressible Navier-Stokes equations in two and three dimensions. The transport coefficients appearing in the macrodynamical equations are obtained using variants of fluctuation-dissipation and Boltzmann formalisms adapted to fully discrete situations