Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

Seasonal changes in brain serotonin transporter binding in short 5-HTTLPR-allele carriers but not in long-allele homozygotes

Several findings suggest seasonal variations in the serotonin (5-HT) system. We sought evidence for seasonal variation in the serotonin transporter (5-HTT). We found that length of daylight time in minutes correlates negatively with 5-HTT binding in the putamen and the caudate, with a similar tendency in the thalamus, but no such association in the midbrain. In the putamen, an anatomical region with a dense serotonin innervation that is implicated in processing of aversive stimuli, we found a significant gene*daylight effect with a negative correlation between the 5-HTT binding and daylight time in carriers of the short 5-HTTLPR allele, but not in carriers of the long allele. The neurobiological endophenotype identified here directly links activation studies, showing responses on the neural circuit level, with dynamic changes in transporter expression measured in vivo

Nonlinear resonant behavior of the dispersive readout scheme for a superconducting flux qubit

A nonlinear resonant circuit comprising a SQUID magnetometer and a parallel capacitor is studied as a readout scheme for a persistent-current (PC) qubit. The flux state of the qubit is detected as a change in the Josephson inductance of the SQUID magnetometer, which in turn mediates a shift in the resonance frequency of the readout circuit. The nonlinearity and resulting hysteresis in the resonant behavior are characterized as a function of the power of both the input drive and the associated resonance peak response. Numerical simulations based on a phenomenological circuit model are presented which display the features of the observed nonlinearity.Comment: 9 pages, 9 figure

Yang-Mills analogues of the Immirzi ambiguity

We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories.Comment: 5 pages, revtex, no figure

Charge Transport Processes in a Superconducting Single-Electron Transistor Coupled to a Microstrip Transmission Line

We have investigated charge transport processes in a superconducting single-electron transistor (S-SET) fabricated in close proximity to a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. The macroscopic bonding pads of the S-SET along with the 2DEG form a microstrip transmission line. We observe a variety of current-carrying cycles in the S-SET which we attribute to simultaneous tunneling of Cooper pairs and emission of photons into the microstrip. We find good agreement between these experimental results and simulations including both photon emission and photon-assisted tunneling due to the electromagnetic environment.Comment: 4 pages, 4 figures, REVTeX

Zero-order filter for diffractive focusing of de Broglie matter waves

The manipulation of neutral atoms and molecules via their de Broglie wave properties, also referred to as de Broglie matter wave optics, is relevant for several fields ranging from fundamental quantum mechanics tests and quantum metrology to measurements of interaction potentials and new imaging techniques. However, there are several challenges. For example, for diffractive focusing elements, the zero-order beam provides a challenge because it decreases the signal contrast. Here we present the experimental realization of a zero-order filter, also referred to as an order-sorting aperture for de Broglie matter wave diffractive focusing elements. The zero-order filter makes it possible to measure even at low beam intensities. We present measurements of zero-order filtered, focused, neutral helium beams generated at source stagnation pressures between 11 and 81 bars. We show that for certain conditions the atom focusing at lower source stagnation pressures (broader velocity distributions) is better than what has previously been predicted. We present simulations with the software ray-tracing simulation package mcstas using a realistic helium source configuration, which gives very good agreement with our measurements

Performance of a novel wafer scale CMOS active pixel sensor for bio-medical imaging

Recently CMOS Active Pixels Sensors (APSs) have become a valuable alternative to amorphous Silicon and Selenium Flat Panel Imagers (FPIs) in bio-medical imaging applications. CMOS APSs can now be scaled up to the standard 20 cm diameter wafer size by means of a reticle stitching block process. However despite wafer scale CMOS APS being monolithic, sources of non-uniformity of response and regional variations can persist representing a significant challenge for wafer scale sensor response. Non-uniformity of stitched sensors can arise from a number of factors related to the manufacturing process, including variation of amplification, variation between readout components, wafer defects and process variations across the wafer due to manufacturing processes. This paper reports on an investigation into the spatial non-uniformity and regional variations of a wafer scale stitched CMOS APS. For the first time a per-pixel analysis of the electro-optical performance of a wafer CMOS APS is presented, to address inhomogeneity issues arising from the stitching techniques used to manufacture wafer scale sensors. A complete model of the signal generation in the pixel array has been provided and proved capable of accounting for noise and gain variations across the pixel array. This novel analysis leads to readout noise and conversion gain being evaluated at pixel level, stitching block level and in regions of interest, resulting in a coefficient of variation ≤ 1.9%. The uniformity of the image quality performance has been further investigated in a typical X-ray application, i.e. mammography, showing a uniformity in terms of CNR among the highest when compared with mammography detectors commonly used in clinical practise. Finally, in order to compare the detection capability of this novel APS with the currently used technology (i.e. FPIs), theoretical evaluation of the Detection Quantum Efficiency (DQE) at zero-frequency has been performed, resulting in a higher DQE for this detector compared to FPIs. Optical characterization, X-ray contrast measurements and theoretical DQE evaluation suggest that a trade off can be found between the need of a large imaging area and the requirement of a uniform imaging performance, making the DynAMITe large area CMOS APS suitable for a range of bio-medical applications

Deflection of coronal rays by remote CMEs: shock wave or magnetic pressure?

We analyze five events of the interaction of coronal mass ejections (CMEs) with the remote coronal rays located up to 90^\circ away from the CME as observed by the SOHO/LASCO C2 coronagraph. Using sequences of SOHO/LASCO C2 images, we estimate the kink propagation in the coronal rays during their interaction with the corresponding CMEs ranging from 180 to 920 km/s within the interval of radial distances form 3 R. to 6 R. . We conclude that all studied events do not correspond to the expected pattern of shock wave propagation in the corona. Coronal ray deflection can be interpreted as the influence of the magnetic field of a moving flux rope related to a CME. The motion of a large-scale flux rope away from the Sun creates changes in the structure of surrounding field lines, which are similar to the kink propagation along coronal rays. The retardation of the potential should be taken into account since the flux rope moves at high speed comparable with the Alfven speed.Comment: Accepted for Publication in Solar Physic

Global MHD simulations of Mercury's magnetosphere with coupled planetary interior: Induction effect of the planetary conducting core on the global interaction

Mercury's comparatively weak intrinsic magnetic field and its close proximity to the Sun lead to a magnetosphere that undergoes more direct space‐weathering interactions than other planets. A unique aspect of Mercury's interaction system arises from the large ratio of the scale of the planet to the scale of the magnetosphere and the presence of a large‐size core composed of highly conducting material. Consequently, there is strong feedback between the planetary interior and the magnetosphere, especially under conditions of strong external forcing. Understanding the coupled solar wind‐magnetosphere‐interior interaction at Mercury requires not only analysis of observations but also a modeling framework that is both comprehensive and inclusive. We have developed a new global MHD model for Mercury in which the planetary interior is modeled as layers of different electrical conductivities that electromagnetically couple to the surrounding plasma environment. This new modeling capability allows us to characterize the dynamical response of Mercury to time‐varying external conditions in a self‐consistent manner. Comparison of our model results with observations by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft shows that the model provides a reasonably good representation of the global magnetosphere. To demonstrate the capability to model induction effects, we have performed idealized simulations in which Mercury's magnetosphere is impacted by a solar wind pressure enhancement. Our results show that due to the induction effect, Mercury's core exerts strong global influences on the way Mercury responds to changes in the external environment, including modifying the global magnetospheric structure and affecting the extent to which the solar wind directly impacts the surface. The global MHD model presented here represents a crucial step toward establishing a modeling framework that enables self‐consistent characterization of Mercury's tightly coupled planetary interior‐magnetosphere system.Key PointsDeveloped global MHD model of Mercury's magnetosphere with coupled interiorThe global model is able to self‐consistently model induction effect at the coreInduction effect is shown to have significant effects on the global interactionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112187/1/jgra51879.pd