Magnetic Fields and Non-Local Transport in Laser Plasmas

The first Vlasov-Fokker-Planck simulations of nanosecond laser-plasma interactions – including the effects of self-consistent magnetic fields and hydrodynamic plasma expansion – will be presented. The coupling between non-locality and magnetic field advection is elucidated. For the largest (initially uniform) magnetic fields externally imposed in recent long-pulse laser gas-jet plasma experiments (12T) a significant degree of cavitation of the B-field will be shown to occur (> 40%) in under 500ps. This is due to the Nernst effect and leads to the re-emergence of non-locality even if the initial value of the magnetic field strength is sufficient to localize transport. Classical transport theory may also break down in such interactions as a result of inverse bremsstrahlung heating. Although non-locality may be suppressed by a large B-field, inverse bremsstrahlung still leads to a highly distorted distribution. Indeed the best fit for a 12T applied field (after 440ps of laser heating) is found to be a super- Gaussian distribution – f0 α e−vm – with m = 3.4. The effects of such a distribution on the transport properties under the influence of magnetic fields are elucidated in the context of laser-plasmas for the first time. In long pulse laser-plasma interactions magnetic fields generated by the thermoelectric (‘∇ne × ∇Te’) mechanism are generally considered dominant. The strength of B-fields generated by this mechanism are affected, and new generation mechanisms are expected, when non-locality is important. Non-local B-field generation is found to be dominant in the interaction of an elliptical laser spot with a nitrogen gas-jet

Optimal control-based inverse determination of electrode distribution for electroosmotic micromixer

This paper presents an optimal control-based inverse method used to determine the distribution of the electrodes for the electroosmotic micromixers with external driven flow from the inlet. Based on the optimal control method, one Dirichlet boundary control problem is constructed to inversely find the optimal distribution of the electrodes on the sidewalls of electroosmotic micromixers and achieve the acceptable mixing performance. After solving the boundary control problem, the step-shaped distribution of the external electric potential imposed on the sidewalls can be obtained and the distribution of electrodes can be inversely determined according to the obtained external electric potential. Numerical results are also provided to demonstrate the effectivity of the proposed method

Level Set Jet Schemes for Stiff Advection Equations: The SemiJet Method

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided

Stirring up trouble: Multi-scale mixing measures for steady scalar sources

The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence of stirring. These variances can be weighted at various spatial scales, leading to a family of multi-scale mixing measures and efficiencies. We derive a priori estimates on these efficiencies from the advection--diffusion partial differential equation, focusing on a broad class of statistically homogeneous and isotropic incompressible flows. The analysis produces bounds on the mixing efficiencies in terms of the Peclet number, a measure the strength of the stirring relative to molecular diffusion. We show by example that the estimates are sharp for particular source, sink and flow combinations. In general the high-Peclet number behavior of the bounds (scaling exponents as well as prefactors) depends on the structure and smoothness properties of, and length scales in, the scalar source and sink distribution. The fundamental model of the stirring of a monochromatic source/sink combination by the random sine flow is investigated in detail via direct numerical simulation and analysis. The large-scale mixing efficiency follows the upper bound scaling (within a logarithm) at high Peclet number but the intermediate and small-scale efficiencies are qualitatively less than optimal. The Peclet number scaling exponents of the efficiencies observed in the simulations are deduced theoretically from the asymptotic solution of an internal layer problem arising in a quasi-static model.Comment: 37 pages, 7 figures. Latex with RevTeX4. Corrigendum to published version added as appendix

Time evolution of intrinsic alignments of galaxies

Intrinsic alignments (IA), correlations between the intrinsic shapes and orientations of galaxies on the sky, are both a significant systematic in weak lensing and a probe of the effect of large-scale structure on galactic structure and angular momentum. In the era of precision cosmology, it is thus especially important to model IA with high accuracy. Efforts to use cosmological perturbation theory to model the dependence of IA on the large-scale structure have thus far been relatively successful; however, extant models do not consistently account for time evolution. In particular, advection of galaxies due to peculiar velocities alters the impact of IA, because galaxy positions when observed are generally different from their positions at the epoch when IA is believed to be set. In this work, we evolve the galaxy IA from the time of galaxy formation to the time at which they are observed, including the effects of this advection, and show how this process naturally leads to a dependence of IA on the velocity shear. We calculate the galaxy-galaxy-IA bispectrum to tree level (in the linear matter density) in terms of the evolved IA coefficients. We then discuss the implications for weak lensing systematics as well as for studies of galaxy formation and evolution. We find that considering advection introduces nonlocality into the bispectrum, and that the degree of nonlocality represents the memory of a galaxy's path from the time of its formation to the time of observation. We discuss how this result can be used to constrain the redshift at which IA is determined and provide Fisher estimation for the relevant measurements using the example of SDSS-BOSS.Comment: 30 pages, 5 figures, 2 table

Self-diffusion in sheared suspensions

Self-diffusion in a suspension of spherical particles in steady linear shear flow is investigated by following the time evolution of the correlation of number density fluctuations. Expressions are presented for the evaluation of the self-diffusivity in a suspension which is either raacroscopically quiescent or in linear flow at arbitrary Peclet number Pe = ẏa^2/2D, where ẏ is the shear rate, a is the particle radius, and D = k_BT/6πηa is the diffusion coefficient of an isolated particle. Here, k_B is Boltzmann's constant, T is the absolute temperature, and η is the viscosity of the suspending fluid. The short-time self-diffusion tensor is given by k_BT times the microstructural average of the hydrodynamic mobility of a particle, and depends on the volume fraction ø = 4/3πa^3n and Pe only when hydrodynamic interactions are considered. As a tagged particle moves through the suspension, it perturbs the average microstructure, and the long-time self-diffusion tensor, D_∞^s, is given by the sum of D_0^s and the correlation of the flux of a tagged particle with this perturbation. In a flowing suspension both D_0^s and D_∞^s are anisotropic, in general, with the anisotropy of D_0^s due solely to that of the steady microstructure. The influence of flow upon D_∞^s is more involved, having three parts: the first is due to the non-equilibrium microstructure, the second is due to the perturbation to the microstructure caused by the motion of a tagged particle, and the third is by providing a mechanism for diffusion that is absent in a quiescent suspension through correlation of hydrodynamic velocity fluctuations. The self-diffusivity in a simply sheared suspension of identical hard spheres is determined to O(φPe^(3/2)) for Pe « 1 and ø « 1, both with and without hydro-dynamic interactions between the particles. The leading dependence upon flow of D_0^s is 0.22DøPeÊ, where Ê is the rate-of-strain tensor made dimensionless with ẏ. Regardless of whether or not the particles interact hydrodynamically, flow influences D_∞^s at O(øPe) and O(øPe^(3/2)). In the absence of hydrodynamics, the leading correction is proportional to øPeDÊ. The correction of O(øPe^(3/2)), which results from a singular advection-diffusion problem, is proportional, in the absence of hydrodynamic interactions, to øPe^(3/2)DI; when hydrodynamics are included, the correction is given by two terms, one proportional to Ê, and the second a non-isotropic tensor. At high ø a scaling theory based on the approach of Brady (1994) is used to approximate D_∞^s. For weak flows the long-time self-diffusivity factors into the product of the long-time self-diffusivity in the absence of flow and a non-dimensional function of Pe = ẏa^2/2D^s_0(φ)$. At small Pe the dependence on Pe is the same as at low ø