The Stokes-Einstein Relation at Moderate Schmidt Number

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently-developed minimally-resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The numerical data is in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.Comment: Submitte

Lattice Boltzmann - Langevin simulations of binary mixtures

We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: a mesoscale simulation study

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k , the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k − 4 for wave vectors along the flow direction and as k − 2 for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k − 2 dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure

Preserved Flora and Organics in Impact Melt Breccias

At least seven glass-bearing strata of varying ages occur at different horizons in the Pampean sediments of Argentina dating back to the Miocene. In a strict sense, these impact glasses are melt-matrix breccias composed of partially digested minerals clasts and basement fragments indicative of crater excavation. Ar-40/Ar-39 dating yield ages (+/- 2 sigma) of 6 +/- 2 Ka, 114 +/- 26 Ka, 230 +/- 30 Ka, 445 +/- 21 Ka, 3.27 +/- 0.08 Ma (near Mar del Plata = MdP), 5.28 +/- 0.04 Ma, and 9.21 +/- 0.08 Ma (near Chasico = CH) Where found in place (not reworked), these ages are consistent with the local stratigraphy and faunal assemblages. A striking property of some of these impact glasses is the encapsulation of preserved fragments of floral (and even soft-tissue faunal remains). Here we identify retained organics and describe a likely process of encapsulation and preservation

Boltzmann equation and hydrodynamic fluctuations

We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.Comment: This is a more detailed version of a related paper: I.V. Karlin, M. Colangeli, M. Kroger, PRL 100 (2008) 214503, arXiv:0801.2932. It contains comparison between predictions and experiment, in particular. 11 pages, 6 figures, 2 table

An evaluation of management strategies for Atlantic tuna stocks

International agreements for the International Commission for the Conservation of Atlantic Tunas (ICCAT) convention area imply that Atlantic tuna stocks should be managed by strategies based on maximum sustainable yield (MSY); however, there is concern whether this will actually ensure sustainability with sufficiently high probability consistent with the principals of the precautionary approach. Therefore, the performance of MSY management strategies based on current assessment procedures was evaluated using a computer simulation framework. The framework includes the data collection, assessment, prediction, and management processes, as well as the implementation of management regulations. It therefore provides an integrated way to evaluate the relative importance of and the interactions between each component of the system with regard to the overall success of the management strategy. The study elucidates guidelines about assessment and management that are general enough to be applied to all tunas in the Atlantic Ocean. It does so by comparing different hypotheses about management and assessment for three stocks (North Atlantic albacore, Atlantic bigeye and East Atlantic skipjack), which are representative of the variety encountered (i.e. from data rich to poor and tropical to temperate waters) in ICCAT stocks. Management performance was especially sensitive to the carrying capacity of the stock. The type of proxy used for MSY was more important to the success of the procedure than the frequency of assessment or the number of indices used in the assessment. Whilst the procedure was successful at achieving the management objectives for albacore, it was only partially successful for bigeye and was too conservative for skipjack.No disponibl

Unreported resistance in the charge transport limits the photoconversion efficiency of aqueous dye-sensitised solar cells: An electrochemical impedance spectroscopy study

In this work, a thorough electrochemical impedance spectroscopy study is performed of both liquid and polymeric aqueous dye-sensitized solar cells (a-DSSCs), which are also compared with conventional organic solvent-based devices. The main purpose is unveiling phenomena limiting the efficiency of water-based photovoltaics. Indeed, electrochemical impedance spectroscopy spectra of a-DSSCs show two peculiar (and unreported) features that are not observed in organic-based DSSCs. The higher frequency one (R45°) is likely associated with a slowdown of the diffusion kinetics of the redox mediator: it is due to the breakdown of the hydrogen-bond network of the aqueous environment, which was also supported by density functional theory calculations. The lower-frequency feature is associated with the additional amount of energy required for the breakdown at the semiconductor/FTO interface of the adducts between protons (coming from the solvent) and electrons localized in the TiO2 surface trap-states. This ‘disruption energy’ results in a resistive element (RIC) that inversely correlates with the device efficiency. Very interestingly, RIC depends on the applied potential and becomes negligible only at much more positive values than VOC. Tailored equivalent circuits implementing simultaneously R45° and RIC are currently under investigation

Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm

Long range correlations and phase transition in non-equilibrium diffusive systems

We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the occurrence of a phase transition as they become singular when the system approaches the transition