Langmuir-Maxwell and Langmuir-Smoluchowski boundary conditions for thermal gas flow simulations in hypersonic aerodynamics

The simulation of nonequilibrium thermal gas flow is important for the aerothermodynamic design of re-entry and other high-altitude vehicles. In computational fluid dynamics, the accuracy of the solution to the Navier–Stokes–Fourier (N–S–F) equations depends on the accuracy of the surface boundary conditions. We propose new boundary conditions (called the Langmuir–Maxwell and the Langmuir–Smoluchowski conditions), for use with the N–S–F equations, which combine the Langmuir surface adsorption isotherm with the Maxwell/Smoluchowski slip/jump conditions in order to capture some of the physical processes involved in gas flow over a surface. These new conditions are validated for flat plate flow, circular cylinder in cross-flow, and the flow over a sharp wedge for Mach numbers ranging from 6 to 24, and for argon and nitrogen as the working gases. Our simulation results show that the new boundary conditions give better predictions for the surface pressures, compared with published experimental and DSMC data

Anti-phase Signature of Flare Generated Transverse Loop Oscillation

Copyright © 2013 American Astronomical Society / IOP PublishingTransverse loop oscillations observed by the Atmospheric Imaging Assembly instrument on the Solar Dynamics Observatory spacecraft are studied after an impulsive solar flare eruption on 2012 May 8. We have found that a transversely oscillating coronal loop seen in the 171 Å bandpass oscillates in anti-phase with respect to adjacent larger loops seen in the 193 Å and 211 Å bandpasses. These unusual oscillations are analyzed to investigate the excitation mechanism responsible for their initial inwardly directed anti-phase behavior. The transverse oscillations are analyzed by constructing space-time diagrams from cuts made parallel to the projected loop displacements. The displacement time oscillation profiles are background subtracted and fitted with a damped cosine curve that includes a linear change in the period with time. The local magnetic topology of the active region is modeled using potential field source surface extrapolation. It reveals that the loops are anchored in different topological regions with foot point locations identified on either side of the EUV flare peak emission source. In this context, the oscillation characteristics indicate that the excitation mechanism is closely linked to the local magnetic field topology and the reconnection generated wave dynamics in the active region rather than following an external flare blast wave. We discuss how observations such as these may serve to identify reconnection processes in similar quadrupolar active regions

The seismic response to Faroe basalts from integrated borehole and wide-angle seismic data

We study the seismic response of layered basalts in the Faroe Islands using borehole data and\ud vertical seismic profiles from the Vestmanna borehole, combined with reflection and wideangle\ud seismic data recorded into arrays of both borehole and land multicomponent receivers.\ud Imaging through the basalt cover in the Faroe-Shetland Basin is a challenge for conventional\ud seismic surveys: scattering caused by the high reflectivity of the basalt as well as intra-basalt\ud multiples and high attenuation from the layered sequence make it difficult to image within\ud and beneath the basalts. This project allows us to correlate ultrasonic-scale velocity and\ud density measurements from the borehole together with ground-truthing from borehole logs\ud and core samples with the seismic-scale velocities and reflection images derived from VSP\ud and surface data. We find a good match of observed travel-times of borehole and wide-angle\ud P-wave data with those predicted from the borehole measurements, suggesting lateral\ud homogeneity over horizontal distances on the kilometre scale, and restricted transverse\ud anisotropy of the layered basalts. A pronounced intra-basalt reflector identified on the\ud multichannel surface seismic can be correlated with lithostratigraphic interpretation of the\ud borehole logs as caused by thick flows near the top of the Lower Basalt formation

Particle motion and stain removal during simulated abrasive tooth cleaning

Stain removal from teeth is important both to prevent decay and for appearance. This is usually achieved using a filament-based toothbrush with a toothpaste consisting of abrasive particles in a carrier fluid. This work has been carried out to examine how these abrasive particles interact with the filaments and cause material removal from a stain layer on the surface of a tooth. It is important to understand this mechanism as while maximum cleaning efficiency is required, this must not be accompanied by damage to the enamel or dentine substrate. In this work simple abrasive scratch tests were used to investigate stain removal mechanism of two abrasive particles commonly used in tooth cleaning, silica and perlite. Silica particles are granular in shape and very different to perlite particles, which are flat and have thicknesses many times smaller than their width. Initially visualisation studies were carried out with perlite particles to study how they are entrained into a filament/counterface contact. Results were compared with previous studies using silica. Reciprocating scratch tests were then run to study how many filaments have a particle trapped at one moment and are involved in the cleaning process. Stain removal tests were then carried out in a similar manner to establish cleaning rates with the two particle types. Perlite particles were found to be less abrasive than silica. This was because of their shape and how they were entrained into the filament contacts and loaded against a counterface. With both particles subsurface damage during stain removal was found to be minimal. A simple model was built to predict stain removal rates with silica particles, which gave results that correlated well with the experimental data

Pinned Balseiro-Falicov Model of Tunneling and Photoemission in the Cuprates

The smooth evolution of the tunneling gap of Bi_2Sr_2CaCu_2O_8 with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping, has been interpreted as evidence that the pseudogap must be due to precursor pairing. We suggest an alternative explanation, that the smoothness reflects a hidden SO(N) symmetry near the (pi,0) points of the Brillouin zone (with N = 3, 4, 5, or 6). Because of this symmetry, the pseudogap could actually be due to any of a number of nesting instabilities, including charge or spin density waves or more exotic phases. We present a detailed analysis of this competition for one particular model: the pinned Balseiro-Falicov model of competing charge density wave and (s-wave) superconductivity. We show that most of the anomalous features of both tunneling and photoemission follow naturally from the model, including the smooth crossover, the general shape of the pseudogap phase diagram, the shrinking Fermi surface of the pseudogap phase, and the asymmetry of the tunneling gap away from optimal doping. Below T_c, the sharp peak at Delta_1 and the dip seen in the tunneling and photoemission near 2Delta_1 cannot be described in detail by this model, but we suggest a simple generalization to account for inhomogeneity, which does provide an adequate description. We show that it should be possible, with a combination of photoemission and tunneling, to demonstrate the extent of pinning of the Fermi level to the Van Hove singularity. A preliminary analysis of the data suggests pinning in the underdoped, but not in the overdoped regime.Comment: 18 pages LaTeX, 26 ps. figure

Stripes, Pseudogaps, and Van Hove Nesting in the Three-band tJ Model

Slave boson calculations have been carried out in the three-band tJ model for the high-T_c cuprates, with the inclusion of coupling to oxygen breathing mode phonons. Phonon-induced Van Hove nesting leads to a phase separation between a hole-doped domain and a (magnetic) domain near half filling, with long-range Coulomb forces limiting the separation to a nanoscopic scale. Strong correlation effects pin the Fermi level close to, but not precisely at the Van Hove singularity (VHS), which can enhance the tendency to phase separation. The resulting dispersions have been calculated, both in the uniform phases and in the phase separated regime. In the latter case, distinctly different dispersions are found for large, random domains and for regular (static) striped arrays, and a hypothetical form is presented for dynamic striped arrays. The doping dependence of the latter is found to provide an excellent description of photoemission and thermodynamic experiments on pseudogap formation in underdoped cuprates. In particular, the multiplicity of observed gaps is explained as a combination of flux phase plus charge density wave (CDW) gaps along with a superconducting gap. The largest gap is associated with VHS nesting. The apparent smooth evolution of this gap with doping masks a crossover from CDW-like effects near optimal doping to magnetic effects (flux phase) near half filling. A crossover from large Fermi surface to hole pockets with increased underdoping is found. In the weakly overdoped regime, the CDW undergoes a quantum phase transition ($T_{CDW}\to 0$), which could be obscured by phase separation.Comment: 15 pages, Latex, 18 PS figures Corrects a sign error: major changes, esp. in Sect. 3, Figs 1-4,6 replace

Dynamical Properties of Two Coupled Hubbard Chains at Half-filling

Using grand canonical Quantum Monte Carlo (QMC) simulations combined with Maximum Entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, $A({\bf k},\omega)$, undergoes a qualitative change with interchain hopping $t_\perp$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large $t_\perp$. For smaller $t_\perp$, $A({\bf k}, \omega)$ is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange $J$ reasonably well-described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral $t$, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large $t_\perp$ and to the results of spin-wave theory for small $t_\perp$.Comment: 9 pages + 10 postscript figures, submitted to Phys.Rev.B, revised version with isotropic t_perp=t data include

Dispersion of Ordered Stripe Phases in the Cuprates

A phase separation model is presented for the stripe phase of the cuprates, which allows the doping dependence of the photoemission spectra to be calculated. The idealized limit of a well-ordered array of magnetic and charged stripes is analyzed, including effects of long-range Coulomb repulsion. Remarkably, down to the limit of two-cell wide stripes, the dispersion can be interpreted as essentially a superposition of the two end-phase dispersions, with superposed minigaps associated with the lattice periodicity. The largest minigap falls near the Fermi level; it can be enhanced by proximity to a (bulk) Van Hove singularity. The calculated spectra are dominated by two features -- this charge stripe minigap plus the magnetic stripe Hubbard gap. There is a strong correlation between these two features and the experimental photoemission results of a two-peak dispersion in La$_{2-x}$Sr$_x$CuO$_4$, and the peak-dip-hump spectra in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The differences are suggestive of the role of increasing stripe fluctuations. The 1/8 anomaly is associated with a quantum critical point, here expressed as a percolation-like crossover. A model is proposed for the limiting minority magnetic phase as an isolated two-leg ladder.Comment: 24 pages, 26 PS figure

Modelling the response of phytoplankton in a shallow lake (Loch Leven, UK) to changes in lake retention time and water temperature.

The phytoplankton community of Loch Leven in 2005 was modelled and subjected to a combination of different flushing rates and water temperatures in order to assess the lake’s sensitivity to these two climatic drivers. Whilst the simulated annual mean total chlorophyll a proved relatively insensitive to these changes, at the species level marked changes were recorded. Some species responded positively to increased temperature (e.g. Aulacoseira), some negatively (e.g. Asterionella), whilst others were negatively affected by increased flow (e.g. Aphanocapsa) and others enhanced (e.g. Stephanodiscus). However, this relationship with flow was season dependent with, for example, a simulated increase in summer inflows actually benefiting some species through increased nutrient supply, whereas an equivalent increase in flow in wetter seasons would have negatively affected those species (i.e. through flushing loss). Overall, the simulations showed that the range of species types simulated in the community was sufficient for one species to always benefit from the changing niches created by the multiple climatic drivers applied in this study. The level of exploitation by such a species was only constrained by the nutrient carrying capacity of the system, which led to the overall dampened response in the total chlorophyll a measure, both at the annual and season scale. Thus, whilst overall biomass showed relatively little reaction to the two climatic drivers tested, the phytoplankton community composition responded markedly