Jordan Areas and Grids

AbstractJordan curves can be used to represent special subsets of the Euclidean plane, either the (open) interior of the curve or the (compact) union of the interior and the curve itself. We compare the latter with other representations of compact sets using grids of points and we are able to show that knowing the length of a rectifiable curve is sufficient to translate from the grid representation to the Jordan curve

Polarization retention loss in PbTiO3 ferroelectric films due to leakage currents

The relationship between retention loss in single crystal PbTiO3 ferroelectric thin films and leakage currents is demonstrated by piezoresponse and conductive atomic force microscopy measurements. It was found that the polarization reversal in the absence of an electric field followed a stretched exponential behavior 1−exp[−(t/k)^d] with exponent d>1, which is distinct from a dispersive random walk process with d<1. The latter has been observed in polycrystalline films for which retention loss was associated with grain boundaries. The leakage current indicates power law scaling at short length scales, which strongly depends on the applied electric field. Additional information of the microstructure, which contributes to an explanation of the presence of leakage currents, is presented with high resolution transmission electron microscopy analysis.

Coupling between gamma-band power and cerebral blood volume during recurrent acute neocortical seizures

Characterization of neural and hemodynamic biomarkers of epileptic activity that can be measured using non-invasive techniques is fundamental to the accurate identification of the epileptogenic zone (EZ) in the clinical setting. Recently, oscillations at gamma-band frequencies and above (>30 Hz) have been suggested to provide valuable localizing information of the EZ and track cortical activation associated with epileptogenic processes. Although a tight coupling between gamma-band activity and hemodynamic-based signals has been consistently demonstrated in non-pathological conditions, very little is known about whether such a relationship is maintained in epilepsy and the laminar etiology of these signals. Confirmation of this relationship may elucidate the underpinnings of perfusion-based signals in epilepsy and the potential value of localizing the EZ using hemodynamic correlates of pathological rhythms. Here, we use concurrent multi-depth electrophysiology and 2-dimensional optical imaging spectroscopy to examine the coupling between multi-band neural activity and cerebral blood volume (CBV) during recurrent acute focal neocortical seizures in the urethane-anesthetized rat. We show a powerful correlation between gamma-band power (25-90 Hz) and CBV across cortical laminae, in particular layer 5, and a close association between gamma measures and multi-unit activity (MUA). Our findings provide insights into the laminar electrophysiological basis of perfusion-based imaging signals in the epileptic state and may have implications for further research using non-invasive multi-modal techniques to localize epileptogenic tissue

Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: the role of multipole effects

We investigate theoretically the effects of interaction between an optical dipole (semiconductor quantum dot or molecule) and metal nanoparticles. The calculated absorption spectra of hybrid structures demonstrate strong effects of interference coming from the exciton-plasmon coupling. In particular, the absorption spectra acquire characteristic asymmetric lineshapes and strong anti-resonances. We present here an exact solution of the problem beyond the dipole approximation and find that the multipole treatment of the interaction is crucial for the understanding of strongly-interacting exciton-plasmon nano-systems. Interestingly, the visibility of the exciton resonance becomes greatly enhanced for small inter-particle distances due to the interference phenomenon, multipole effects, and electromagnetic enhancement. We find that the destructive interference is particularly strong. Using our exact theory, we show that the interference effects can be observed experimentally even in the exciting systems at room temperature.Comment: 9 page

Comb-calibrated solar spectroscopy through a multiplexed single-mode fiber channel

We investigate a new scheme for astronomical spectrograph calibration using the laser frequency comb at the Solar Vacuum Tower Telescope on Tenerife. Our concept is based upon a single-mode fiber channel, that simultaneously feeds the spectrograph with comb light and sunlight. This yields nearly perfect spatial mode matching between the two sources. In combination with the absolute calibration provided by the frequency comb, this method enables extremely robust and accurate spectroscopic measurements. The performance of this scheme is compared to a sequence of alternating comb and sunlight, and to absorption lines from Earth's atmosphere. We also show how the method can be used for radial-velocity detection by measuring the well-explored 5-minute oscillations averaged over the full solar disk. Our method is currently restricted to solar spectroscopy, but with further evolving fiber-injection techniques it could become an option even for faint astronomical targets.Comment: 21 pages, 11 figures. A video abstract for this paper is available on youtube. For watching the video, please follow https://www.youtube.com/watch?v=oshdZgrt89I . The video abstract is also available for streaming and download on the related article website of New Journal of Physic

Approximate Analytical Equations for the Stirrer Angular Correlation in a Reverberation Chamber

IEEE In a reverberation chamber (RC), the angular correlation coefficient of a stirrer is an important parameter. It has been used to evaluate the performance of a stirrer or to estimate the number of independent samples in a measurement. In the previous work, the angular correlation coefficient (ACC) was evaluated numerically and no analytical equation was proposed. In this study, we propose an approximate analytical equation to fit the measured angular correlation that shows good agreements with measurement results. General properties of ACC are explored with physical insights; the equivalency of the mean value of the angular correlation and the $K$-factor is revealed. This study provides further understandings on the control of the stirrer angular correlation and the $K$-factor in an RC

Multisymplectic Geometry and Multisymplectic Preissman Scheme for the KP Equation

The multisymplectic structure of the KP equation is obtained directly from the variational principal. Using the covariant De Donder-Weyl Hamilton function theories, we reformulate the KP equation to the multisymplectic form which proposed by Bridges. From the multisymplectic equation, we can derive a multisymplectic numerical scheme of the KP equation which can be simplified to multisymplectic forty-five points scheme.Comment: 17 papges, 8 figure

Milky Way potentials in CDM and MOND. Is the Large Magellanic Cloud on a bound orbit?

We compute the Milky Way potential in different cold dark matter (CDM) based models, and compare these with the modified Newtonian dynamics (MOND) framework. We calculate the axis ratio of the potential in various models, and find that isopotentials are less spherical in MOND than in CDM potentials. As an application of these models, we predict the escape velocity as a function of the position in the Galaxy. This could be useful in comparing with future data from planned or already-underway kinematic surveys (RAVE, SDSS, SEGUE, SIM, GAIA or the hypervelocity stars survey). In addition, the predicted escape velocity is compared with the recently measured high proper motion velocity of the Large Magellanic Cloud (LMC). To bind the LMC to the Galaxy in a MOND model, while still being compatible with the RAVE-measured local escape speed at the Sun's position, we show that an external field modulus of less than $0.03 a_0$ is needed.Comment: Accepted for publication in MNRAS, 13 pages, 7 figures, 3 table