Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients

In this paper the exact solution of the non-symmetric matrixRiccati equation with analytic coefficients is approximatedby a rational matrix function with a prefixed accuracy. Thisrational matrix function is locally defined as the exact solutionof a Riccati problem with matrix polynomial coefficients obtainedby truncation of the Taylor expansions of the matrix coefficientsof the original problem.     

Further experiments on pyrolysis of 2,2-dimethylpropane behind shock waves

Pyrolysis of a dilute mixture of neopentane (2,2-dimethylpropane) has been studied behind incident shock waves at an average pressure of 0.35 atm; the reaction was followed by absorption spectroscopy for H atoms. In the temperature range 1230–1455 K, the rate constant for dissociation of neopentane to t-butyl and methyl radicals is 1.1 E 13 exp(?62 kcal/RT) s^?1. These data and some of the literature results, between 1000 and 1450 K, can be fitted by an RRKM model of the hindered Gorin type, with five active internal rotors in the complex. To match our data with other literature data down to 800 K, a vibrational model was more satisfactory, but this did not fit very low pressure pyrolysis data in the 1000–1100 K range. Apparently, the VLPP data are too high because of heterogeneous processes or chain reactions.     

Surface of liquid water: three-body interactions and vibrational sum-frequency spectroscopy

Phase-sensitive vibrational sum-frequency experiments on the water surface, using isotopic mixtures of water and heavy water, have recently been performed. The experiments show a positive feature at low frequency in the imaginary part of the susceptibility, which has been difficult to interpret, and impossible to reproduce using two-body (pairwise-additive) water simulation models. We have reparameterized a new three-body simulation model for liquid water, and with this model we calculate the imaginary part of the sum-frequency susceptibility, finding good agreement with experiment for dilute HOD in D(2)O. Theoretical analysis provides a molecular-level structural interpretation of these new and exciting experiments. In particular, we do not find evidence of any special ice-like ordering at the surface of liquid water.     

Continuous improvement of H-mode discharge performance with progressively increasing lithium coatings in the National Spherical Torus Experiment

Lithium wall coatings have been shown to reduce recycling, improve energy confinement, and suppress edge localized modes in the National Spherical Torus Experiment. Here, we show that these effects depend continuously on the amount of predischarge lithium evaporation. We observed a nearly monotonic reduction in recycling, decrease in electron transport, and modification of the edge profiles and stability with increasing lithium. These correlations challenge basic expectations, given that even the smallest coatings exceeded that needed for a nominal thickness of the order of the implantation range.     

Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.     

Dispersion of solutes in porous media

A recently introduced theory of solute transport in porous media is tested by comparison with experiment. The solute transport is predicted using an adaptation of the cluster statistics of percolation theory to critical path analysis together with knowledge of how the structure of such percolation clusters affects the time of transport across them. Only the effects of a single scale of medium heterogeneity are incorporated, and a minimal amount of information regarding the structure of the medium is required. This framework is used to find effectively the distributions of solute velocities and travel distances and thus generate arrival time distributions. The comparison with experiment focuses on the dispersivity (the ratio of the second to the first moment of the spatial solute distribution). The predictions of the theory in the absence of diffusion are verified by comparing with over 2200 experiments over length scales from a few microns to 100 km. At larger length scales (centimeters on up) about 95% of the data lie within our predicted bounds. At smaller length scales approximately 99.8% of the data lie where we predict. These comparisons are not trivial as the typical values of the dispersivity increase by ten orders of magnitude over ten orders of magnitude of length scale. Noteworthy is that the classical advection-dispersion (ADE) equation predicts that the dispersivity should be independent of length scale! This agreement with experiment requires rethinking of the relevance of diffusion and multi-scale heterogeneity and would also appear to signal the complete inappropriateness of using the classical ADE or any of its derivatives to model solute transport.     

Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

Approaches for the calculation of vibrational frequencies in liquids: comparison to benchmarks for azide/water clusters

Ultrafast vibrational spectroscopy experiments, together with molecular-level theoretical interpretation, can provide important information about the structure and dynamics of complex condensed phase systems, including liquids. The theoretical challenge is to calculate the instantaneous vibrational frequencies of a molecule in contact with a molecular environment, accurately and quickly, and to this end a number of different methods have been developed. In this paper we critically analyze these different methods by comparing their results to accurate benchmark calculations on azide/water clusters. We also propose an optimized quantum mechanics/molecular mechanics method, which for this problem is superior to the other methods.     

Using delta15N values to characterise the nitrogen nutrient pathways from intensive animal units

Previous studies on foliar delta15N values, in certain bryophytes, have indicated signature similarities to source pollutants. The object of this study was to investigate the effect further, by examining the mechanisms whereby isotopic fractionation occurs in systems such as atmospheric ammonia (NH3), throughfall, vegetation and soil. Measurements taken in and around point emission sources will then be used to characterise the various fractionation effects associated with these N transformations, as well as to demonstrate some of the issues associated with using delta15N values as pollution indicators. The atmospheric dispersion model UK-ADMS has also been used to model atmospheric delta15NH3 emissions, with signatures exhibiting marked negative shifts immediately downwind of an agricultural NH3 source. Similar dispersion patterns were mapped for NH3 concentration data illustrating the link between these two forms of measurement.