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.     

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.     

Predicting dispersion in porous media

We present a fundamental theory of solute dispersion in porous using (i) critical path analysis and cluster statistics of percolation theory far from the percolation threshold and (ii) the tortuosity and structure of large clusters near the percolation threshold. We use the simplest possible model of porous media, with a single length scale of heterogeneity in which the statistics of local conductances are uncorrelated. This combination of percolation‐based techniques allows comprehensive investigation and predictions concerning the process of dispersion. Our predictions, which ignore molecular diffusion and make minimal use of unknown parameters, account for results obtained in a comprehensive set of nearly 1100 experiments performed on systems ranging in size from centimeters to 100 km. The success of our simple treatment overturns many existing notions about transport in porous media, such as (1) multiscale heterogeneity must be accounted for in predictions (single scale is sufficient), (2) geologic correlations are of great importance (the randomness of percolation theory is more appropriate for prediction than the most complicated models in other frameworks), (3) geologic complexity is more important than statistical physics (exactly the reverse), (4) knowledge of the subsurface is more important than knowledge of the initial conditions of the plume (the latter is critical, the former may be virtually irrelevant), (5) diffusion is dominant over advection (diffusion appears seldom to be relevant at all), (6) fracture networks are fundamentally different, and more complex, than porous media (the two are mostly equivalent), (7) the fractal structure of the medium is relevant to power‐law behavior of the dispersion (in fact, at short times it is the heterogeneity of the medium, while at long times it is the fractal structure of the critical paths), and (8) there is a relation between an increase in dispersion with scale and a similar increase in the hydraulic conductivity (in fact the present model is consistent with both a diminishing hydraulic conductivity and a diminishing solute velocity with increasing spatial scale). © 2009 Wiley Periodicals, Inc. Complexity, 16,43–55, 2010     

Linear phase slope in pulse design: application to coherence transfer

Using optimal control methods, robust broadband excitation pulses can be designed with a defined linear phase dispersion. Applications include increased bandwidth for a given pulse length compared to equivalent pulses requiring no phase correction, selective pulses, and pulses that mitigate the effects of relaxation. This also makes it possible to create pulses that are equivalent to ideal hard pulses followed by an effective evolution period. For example, in applications, where the excitation pulse is followed by a constant delay, e.g. for the evolution of heteronuclear couplings, part of the pulse duration can be absorbed in existing delays, significantly reducing the time overhead of long, highly robust pulses. We refer to the class of such excitation pulses with a defined linear phase dispersion as ICEBERG pulses (Inherent Coherence Evolution optimized Broadband Excitation Resulting in constant phase Gradients). A systematic study of the dependence of the excitation efficiency on the phase dispersion of the excitation pulses is presented, which reveals surprising opportunities for improved pulse sequence performance.     

Potentials evoked by the sinusoidal modulation of the amplitude or frequency of a tone

Steady state responses to the sinusoidal modulation of the amplitude or frequency of a tone were recorded from the human scalp. For both amplitude modulation (AM) and frequency modulation (FM), the responses were most consistent at modulation frequencies between 30 and 50 Hz. However, reliable responses could also be recorded at lower frequencies, particularly at 2-5 Hz for AM and at 3-7 Hz for FM. With increasing modulation depth at 40 Hz, both the AM and FM response increased in amplitude, but the AM response tended to saturate at large modulation depths. Neither response showed any significant change in phase with changes in modulation depth. Both responses increased in amplitude and decreased in phase delay with increasing intensity of the carrier tone, the FM response showing some saturation of amplitude at high intensities. Both responses could be recorded at modulation depths close to the subjective threshold for detecting the modulation and at intensities close to the subjective threshold for hearing the stimulus. The responses were variable but did not consistently adapt over periods of 10 min. The 40-Hz AM and FM responses appear to originate in the same generator, this generator being activated by separate auditory systems that detect changes in either amplitude or frequency.     

Observations of four-wave mixing processes in barium vapour

Emission at fifty discrete wavelengths is observed when Ba I is excited by two laser beams, a dye laser tuned to the λ 7911 Å intercombination line, 6s²¹S₀-6s6p ³P₁ and a ruby laser. The wavelengths range from 2312 Å to 8027 Å. Most of the emission lines can be attributed to four-wave mixing processes in barium.     

Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.