Moving boulders in flash floods and estimating flow conditions using boulders in ancient deposits

Boulders moving in flash floods cause considerable damage and casualties. More and bigger boulders move in flash floods than predicted from published theory. The interpretation of flow conditions from the size of large particles within flash flood deposits has, until now, generally assumed that the velocity (or discharge) is unchanging in time (i.e. flow is steady), or changes instantaneously between periods of constant conditions. Standard practice is to apply theories developed for steady flow conditions to flash floods, which are however inherently very unsteady flows. This is likely to lead to overestimates of peak flow velocity (or discharge). Flash floods are characterised by extremely rapid variations in flow that generate significant transient forces in addition to the mean-flow drag. These transient forces, generated by rapid velocity changes, are generally ignored in published theories, but they are briefly so large that they could initiate the motion of boulders. This paper develops a theory for the initiation of boulder movement due to the additional impulsive force generated by unsteady flow, and discusses the implications. Keywords

Recent high-magnetic-field studies of unusual groundstates in quasi-two-dimensional crystalline organic metals and superconductors

After a brief introduction to crystalline organic superconductors and metals, we shall describe two recently-observed exotic phases that occur only in high magnetic fields. The first involves measurements of the non-linear electrical resistance of single crystals of the charge-density-wave (CDW) system (Per)$_2$Au(mnt)$_2$ in static magnetic fields of up to 45 T and temperatures as low as 25 mK. The presence of a fully gapped CDW state with typical CDW electrodynamics at fields higher that the Pauli paramagnetic limit of 34 T suggests the existence of a modulated CDW phase analogous to the Fulde-Ferrell-Larkin-Ovchinnikov state. Secondly, measurements of the Hall potential of single crystals of $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$, made using a variant of the Corbino geometry in quasistatic magnetic fields, show persistent current effects that are similar to those observed in conventional superconductors. The longevity of the currents, large Hall angle, flux quantization and confinement of the reactive component of the Hall potential to the edge of the sample are all consistent with the realization of a new state of matter in CDW systems with significant orbital quantization effects in strong magnetic fields.Comment: SNS 2004 Conference presentatio

Antiferromagnetic Domains and Superconductivity in UPt3

We explore the response of an unconventional superconductor to spatially inhomogeneous antiferromagnetism (SIAFM). Symmetry allows the superconducting order parameter in the E-representation models for UPt3 to couple directly to the AFM order parameter. The Ginzburg-Landau equations for coupled superconductivity and SIAFM are solved numerically for two possible SIAFM configurations: (I) abutting antiferromagnetic domains of uniform size, and (II) quenched random disorder of `nanodomains' in a uniform AFM background. We discuss the contributions to the free energy, specific heat, and order parameter for these models. Neither model provides a satisfactory account of experiment, but results from the two models differ significantly. Our results demonstrate that the response of an E_{2u} superconductor to SIAFM is strongly dependent on the spatial dependence of AFM order; no conclusion can be drawn regarding the compatibility of E_{2u} superconductivity with UPt3 that is independent of assumptions on the spatial dependence of AFMComment: 12 pages, 13 figures, to appear in Phys. Rev.

Weak localization of disordered quasiparticles in the mixed superconducting state

Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear sigma model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field H_c1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-T_c experiments by Aubin et al.Comment: RevTex, 8 pages, 1 eps figure, typos correcte

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Evolution of magnetic interactions in a pressure-induced Jahn-Teller driven magnetic dimensionality switch

We present the results of high-field magnetization and muon-spin relaxation measurements on the coordination polymer CuF 2 (H 2 O) 2 (pyrazine) in pressures up to 22.5 kbar. We observe a transition from a quasi-two-dimensional to a quasi-one-dimensional antiferromagnetic phase at 9.1 kbar, driven by a rotation of the Jahn-Teller axis. Long-range antiferromagnetic ordering is seen in both regimes, as well as a phase separation in the critical pressure region. The magnetic dimensionality switching as pressure is increased is accompanied by a halving of the primary magnetic exchange energy J and a fivefold decrease in the ordering temperature T N . J decreases gradually with pressure in the two-dimensional phase, and then increases in the one-dimensional regime. We relate both effects to the changes in the crystal structure with applied pressure

Increasing 3D Supramolecular Order by Decreasing Molecular Order. A Comparative Study of Helical Assemblies of Dendronized Nonchlorinated and Tetrachlorinated Perylene Bisimides

A nonplanar, twisted, and flexible tetrachlorinated perylene bisimide (Cl4PBI) was functionalized with two AB3 minidendrons containing hydrogenated or semifluorinated dodecyl groups. The hydrogenated dendron was attached to the imide groups of Cl4PBI via m = 0, 1, and 2 methylenic units, whereas the dendron containing semifluorinated groups was attached via m = 3 or a di(ethylene oxide) linker (m = 2EO). The supramolecular structures of these compounds, determined by a combination of differential scanning calorimetry, X-ray diffraction, and solid-state NMR, were compared with those of nonchlorinated planar and rigid PBI reported previously, which demonstrated the thermodynamically controlled formation of 2D periodic arrays at high temperatures and 3D arrays at low temperatures. The molecularly less ordered Cl4PBI containing hydrogenated dendrons self-organize into exclusively 3D crystalline periodic arrays under thermodynamic control for m = 0 and 2, while the more highly molecularly ordered PBI produced less stable and ordered 3D crystals and also 2D assemblies. This induction of a higher degree of 3D order in supramolecular assemblies of the less well-ordered molecular building blocks was unanticipated. The semifluorinated dendronized Cl4PBI with m = 3 formed a 2D columnar hexagonal array under kinetic control, whereas the compound with m = 2EO formed an unusual 2D honeycomb-like hexagonal phase under thermodynamic control. These Cl4PBI compounds provide a new route to stable crystalline assemblies via thermodynamic control at lower temperatures than previously obtained with PBI, thus generating 3D order in an accessible range of temperature of interest for structural analysis and for technological applications

Shot noise in normal metal-d-wave superconducting junctions

We present theoretical calculations and predictions for the shot noise in voltage biased junctions of $d_{x^2-y^2}$ superconductors and normal metal counter-electrodes. In the clean limit for the d-wave superconductor the shot noise vanishes at zero voltage because of resonant Andreev reflection by zero-energy surface bound states. We examine the sensitivity of this resonance to impurity scattering. We report theoretical results for the magnetic field dependence of the shot noise, as well the fingerprints of subdominant $s$- and $d_{xy}$ pairing channels.Comment: 15 pages, 8 figures and 3 tables embedde

Effect of controlled disorder on quasiparticle thermal transport in Bi2_2Sr2_2CaCu2_2O8_8

Low temperature thermal conductivity, $\kappa$, of optimally-doped Bi2212 was studied before and after the introduction of point defects by electron irradiation. The amplitude of the linear component of $\kappa$ remains unchanged, confirming the universal nature of heat transport by zero-energy quasiparticles. The induced decrease in the absolute value of $\kappa$ at finite temperatures allows us to resolve a nonuniversal term in $\kappa$ due to conduction by finite-energy quasiparticles. The magnitude of this term provides an estimate of the quasiparticle lifetime at subkelvin temperatures.Comment: 5 pages including 2 .eps figuer

Response, relaxation and transport in unconventional superconductors

We investigate the collision-limited electronic Raman response and the attenuation of ultrasound in spin-singlet d-wave superconductors at low temperatures. The dominating elastic collisions are treated within a t-matrix approximation, which combines the description of weak (Born) and strong (unitary) impurity scattering. In the long wavelength limit a two-fluid description of both response and transport emerges. Collisions are here seen to exclusively dominate the relaxational dynamics of the (Bogoliubov) quasiparticle system and the analysis allows for a clear connection of response and transport phenomena. When applied to quasi-2-d superconductors like the cuprates, it turns out that the transport parameter associated with the Raman scattering intensity for B1g and B2g photon polarization is closely related to the corresponding components of the shear viscosity tensor, which dominates the attenuation of ultrasound. At low temperatures we present analytic solutions of the transport equations, resulting in a non-power-law behavior of the transport parameters on temperature.Comment: 22 pages, 3 figure