Droplets and the configurational entropy crisis for random first order transitions

We consider the effect of droplet excitations in the random first order transition theory of glasses on the configurational entropy. The contribution of these excitations is estimated both at and above the ideal glass transition temperature. The temperature range where such excitations could conceivably modify or `round-out' an underlying glass transition temperature is estimated, and found to depend strongly on the surface tension between locally metastable phases in the supercooled liquid. For real structural glasses this temperature range is found to be very narrow, consistent with the quantitative success of the theory. For certain finite-range spin-glass models, however, the surface tension is estimated to be significantly lower leading to much stronger entropy renormalizations, thus providing an explanation for the lack of a strict thermodynamic glass transition in simulations of these models.Comment: 5 page

Multi-beam Energy Moments of Multibeam Particle Velocity Distributions

High resolution electron and ion velocity distributions, f(v), which consist of N effectively disjoint beams, have been measured by NASA's Magnetospheric Multi-Scale Mission (MMS) observatories and in reconnection simulations. Commonly used standard velocity moments generally assume a single mean-flow-velocity for the entire distribution, which can lead to counterintuitive results for a multibeam f(v). An example is the (false) standard thermal energy moment of a pair of equal and opposite cold particle beams, which is nonzero even though each beam has zero thermal energy. By contrast, a multibeam moment of two or more beams has no false thermal energy. A multibeam moment is obtained by taking a standard moment of each beam and then summing over beams. In this paper we will generalize these notions, explore their consequences and apply them to an f(v) which is sum of tri-Maxwellians. Both standard and multibeam energy moments have coherent and incoherent forms. Examples of incoherent moments are the thermal energy density, the pressure and the thermal energy flux (enthalpy flux plus heat flux). Corresponding coherent moments are the bulk kinetic energy density, the RAM pressure and the bulk kinetic energy flux. The false part of an incoherent moment is defined as the difference between the standard incoherent moment and the corresponding multibeam moment. The sum of a pair of corresponding coherent and incoherent moments will be called the undecomposed moment. Undecomposed moments are independent of whether the sum is standard or multibeam and therefore have advantages when studying moments of measured f(v).Comment: 27 single-spaced pages. Three Figure

Analytical and Numerical Treatment of the Mott--Hubbard Insulator in Infinite Dimensions

We calculate the density of states in the half-filled Hubbard model on a Bethe lattice with infinite connectivity. Based on our analytical results to second order in $t/U$, we propose a new `Fixed-Energy Exact Diagonalization' scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated by results from the Random Dispersion Approximation, we find that the gap opens at $U_{\rm c}=4.43 \pm 0.05$. Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent $\alpha=1/2$ in the insulating phase. We critically examine other analytical and numerical approaches and specify their merits and limitations when applied to the Mott--Hubbard insulator.Comment: 22 pages, 16 figures; minor changes (one reference added, included comparison with Falicov-Kimball model

Prolongations of Geometric Overdetermined Systems

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.Comment: 22 pages. In the second version, a comparison with the classical theory of prolongations was added. In this third version more details were added concerning our construction and especially the use of Kostant's computation of Lie algebra cohomolog

Super-Alfv\'enic propagation of reconnection signatures and Poynting flux during substorms

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfv\'en wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfv\'enic (V_parallel ~ 1500 - 5500 km/s) and generates substantial Poynting flux (S ~ 10^-5 - 10^-4 W/m^2) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in the Earth's ionosphere.Comment: Submitted to PRL on 11/1/2010. Resubmitted on 4/5/201

Modelling and simulation of fluid-structure interactions in human snoring

Snoring noise is generated by vibration of the soft tissues of the upper airway, principally those that form the back of the roof of the mouth (the soft palate) and its conical extension (the uvula). In addition to discord with bed partners, snorers are at much greater risk of obstructive sleep apnoea. This sleep-related breathing disorder is characterised by episodic upper airway obstruction with accompanying sleep disruption and consequent excessive daytime sleepiness, as well as an elevated risk of accidents and cardiovascular disease. The instability that leads to flow-induced oscillations characteristic of inspiratory snoring in the human upper airway may be modelled using a cantilevered flexible plate in a mean channel flow. However, the cantilever in existing models strictly only captures the dynamics of the uvula. In a more complete model, these dynamics will be augmented by their interaction with the motions of the soft palate—itself a flexible structure of higher effective stiffness—from which the uvula extends. To investigate how the elasticity of the soft palate affects uvula motion and their combined susceptibility to flow-induced oscillation a modification is made to the standard model. In a one-dimensional cantilevered flexible plate we allow thickness to vary as a function of length, thus effecting local changes in inertia and flexural rigidity.The overall cantilever therefore comprises a section representing the soft palate followed by a section of lower thickness that represents the uvula. The cantilever is attached to a rigid wall (hard palate) separating upper (nasal) and lower (oral) inlets of a rigid-walled channel (pharynx) conveying a viscous flow. This model is formulated using the open-source finite-element software library oomph-lib. A parametric study is performed in which the uvula-to-soft palate length and thickness ratios are varied whilst keeping their combined length constant. Results show that there is a critical uvula-length fraction that determines whether the uvula stabilises or destabilises the system. A relatively ‘short’ uvula swings out of phase with the soft palate and these oscillations are observed to decay; the mode shapes involved are not predicted by a uniform-thickness plate model. By contrast, if the uvula is relatively ‘long’ the flexible plate motion is isolated to the uvular section and the oscillations grow in amplitude, indicating a net energy transfer from fluid to structure. Increasing the thickness, hence inertia and flexural rigidity, of a ‘short’ uvula, e.g., by oedema, makes the fluid-structure system more unstable. In this case if the oedema were aggrevated by the vibratory mechanical insult then it would be self-sustaining and imply a bidirectional relationship between snoring and oedema of the uvula.Anatomical variability is common in the lengths of the soft palate and uvula which may make some people more susceptible than others to uvulopalatal snoring. Palatal surgery for snoring has proved highly variable in its effectiveness. Modelling of palatal motion using this approach may help guide patient selection for and type of soft-palate surgery applied to treat this common and potentially disabling condition

Observations of magnetic flux ropes during magnetic reconnection in the Earth's magnetotail

We present an investigation of magnetic flux ropes observed by the four Cluster spacecraft during periods of magnetic reconnection in the Earth's magnetotail. Using a list of 21 Cluster encounters with the reconnection process in the period 2001–2006 identified in Borg et al. (2012), we present the distribution and characteristics of the flux ropes. We find 27 flux ropes embedded in the reconnection outflows of only 11 of the 21 reconnection encounters. Reconnection processes associated with no flux rope observations were not distinguishable from those where flux ropes were observed. Only 7 of the 27 flux ropes show evidence of enhanced energetic electron flux above 50 keV, and there was no clear signature of the flux rope in the thermal particle measurements. We found no clear correlation between the flux rope core field and the prevailing IMF <I>B</I>_y direction

Electrophoresis of a rod macroion under polyelectrolyte salt: Is mobility reversed for DNA?

By molecular dynamics simulation, we study the charge inversion phenomenon of a rod macroion in the presence of polyelectrolyte counterions. We simulate electrophoresis of the macroion under an applied electric field. When both counterions and coions are polyelectrolytes, charge inversion occurs if the line charge density of the counterions is larger than that of the coions. For the macroion of surface charge density equal to that of the DNA, the reversed mobility is realized either with adsorption of the multivalent counterion polyelectrolyte or the combination of electrostatics and other mechanisms including the short-range attraction potential or the mechanical twining of polyelectrolyte around the rod axis.Comment: 8 pages, 5 figures, Applied Statistical Physics of Molecular Engineering (Mexico, 2003). Journal of Physics: Condensed Matters, in press (2004). Journal of Physics: Condensed Matters, in press (2004