Modulation theory of quantum tunneling into a Calogero-Sutherland fluid

Quantum hydrodynamics of interacting electrons with a parabolic single particle spectrum is studied using the Calogero-Sutherland model. The effective action and modulation equations, describing evolution of periodic excitations in the fluid, are derived. Applications to the problem of a single electron tunneling into the FQHE edge state are discussed

Background light measurements at the DUMAND site

Ambient light intensities at the DUMAND site, west of the island of Hawaii were measured around the one photoelectron level. Throughout the water column between 1,500m and 4,700m, a substantial amount of stimulateable bioluminescence is observed with a ship suspended detector. But non-stimulated bioluminescence level is comparable, or less than, K sup 40 background, when measured with a bottom tethered detector typical of a DUMAND optical module

Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model

Collective field theory for Calogero model represents particles with fractional statistics in terms of hydrodynamic modes -- density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field -- quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.Comment: 5 pages, 1 figur

Analysis of signalling pathways using continuous time Markov chains

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and remarks added) To appear in Inventione

Topology Change of Coalescing Black Holes on Eguchi-Hanson Space

We construct multi-black hole solutions in the five-dimensional Einstein-Maxwell theory with a positive cosmological constant on the Eguchi-Hanson space, which is an asymptotically locally Euclidean space. The solutions describe the physical process such that two black holes with the topology of S^3 coalesce into a single black hole with the topology of the lens space L(2;1)=S^3/Z_2. We discuss how the area of the single black hole after the coalescence depends on the topology of the horizon.Comment: 10 pages, Some comments are added. to be published as a letter in Classical and Quantum Gravit

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.Comment: 20 pages, 13 figure

Robust magnetotelluric inversion

Author Posting. © The Author(s), 2014. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 196 (2014): 1365-1374, doi:10.1093/gji/ggt484.A robust magnetotelluric (MT) inversion algorithm has been developed on the basis of quantile-quantile (q-q) plotting with confidence band and statistical modelling of inversion residuals for the MT response function (apparent resistivity and phase). Once outliers in the inversion residuals are detected in the q-q plot with the confidence band and the statistical modelling with the Akaike information criterion, they are excluded from the inversion data set and a subsequent inversion is implemented with the culled data set. The exclusion of outliers and the subsequent inversion is repeated until the q-q plot is substantially linear within the confidence band, outliers predicted by the statistical modelling are unchanged from the prior inversion, and the misfit statistic is unchanged at a target level. The robust inversion algorithm was applied to synthetic data generated from a simple 2-D model and observational data from a 2-D transect in southern Africa. Outliers in the synthetic data, which come from extreme values added to the synthetic responses, produced spurious features in inversion models, but were detected by the robust algorithm and excluded to retrieve the true model. An application of the robust inversion algorithm to the field data demonstrates that the method is useful for data clean-up of outliers, which could include model as well as data inconsistency (for example, inability to fit a 2-D model to a 3-D data set), during inversion and for objectively obtaining a robust and optimal model. The present statistical method is available irrespective of the dimensionality of target structures (hence 2-D and 3-D structures) and of isotropy or anisotropy, and can operate as an external process to any inversion algorithm without modifications to the inversion program.TM was supported by the scientific program of TAIGA (trans-crustal advection and in-situ reaction of global sub-seafloor aquifer) sponsored by the MEXT of Japan, and is supported by the NIPR project KP-7. ADC is supported by US National Science Foundation (NSF) grant EAR1015185