On the calibration of the 3/2 model

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Accurate Evaluation of Charge Asymmetry in Aqueous Solvation

Charge hydration asymmetry (CHA)--a characteristic dependence of hydration free energy on the sign of the solute charge--quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K+/F- pair--a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, ~50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule

We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope function approach in the current scheme and also the merits of various quantum chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent field method, the molecular orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic field control, and error correction.Comment: 22 2-column pages, 11 figures. Published versio

On inferring isoprene emission surface flux from atmospheric boundary layer concentration measurements

We examine the dependence of the inferred isoprene surface emission flux from atmospheric concentration on the diurnal variability of the convective boundary layer (CBL). A series of systematic numerical experiments carried out using the mixed-layer technique enabled us to study the sensitivity of isoprene fluxes to the entrainment process, the partition of surface fluxes, the horizontal advection of warm/cold air masses and subsidence. Our findings demonstrate the key role played by the evolution of boundary layer height in modulating the retrieved isoprene flux. More specifically, inaccurate values of the potential temperature lapse rate lead to changes in the dilution capacity of the CBL and as a result the isoprene flux may be overestimated or underestimated by as much as 20%. The inferred emission flux estimated in the early morning hours is highly dependent on the accurate estimation of the discontinuity of the thermodynamic values between the residual layer and the rapidly forming CBL. Uncertainties associated with the partition of the sensible and latent heat flux also yield large deviations in the calculation of the isoprene surface flux. Similar results are obtained if we neglect the influence of warm or cold advection in the development of the CBL.We show that all the above-mentioned processes are non-linear, for which reason the dynamic and chemical evolutions of the CBL must be solved simultaneously. Based on the discussion of our results, we suggest the measurements needed to correctly apply the mixed-layer technique in order to minimize the uncertainties associated with the diurnal variability of the convective boundary layer

The Likelihood of Mixed Hitting Times

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent L\'evy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of L\'evy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.Comment: 35 page