Using the Uncharged Kerr Black Hole as a Gravitational Mirror

We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem concerning the conditions the impact parameter has to satisfy if there shall exist boomerang photons. We derive an equation for these boomerang photons and an equation for the emission angle. Finally, the radial null geodesic equation is integrated numerically in order to illustrate boomerang photons.Comment: 11 pages Latex, 3 Postscript figures, uufiles to compres

Imaging a 1-electron InAs quantum dot in an InAs/InP nanowire

Nanowire heterostructures define high-quality few-electron quantum dots for nanoelectronics, spintronics and quantum information processing. We use a cooled scanning probe microscope (SPM) to image and control an InAs quantum dot in an InAs/InP nanowire, using the tip as a movable gate. Images of dot conductance vs. tip position at T = 4.2 K show concentric rings as electrons are added, starting with the first electron. The SPM can locate a dot along a nanowire and individually tune its charge, abilities that will be very useful for the control of coupled nanowire dots

Analyzing capacitance-voltage measurements of vertical wrapped-gated nanowires

The capacitance of arrays of vertical wrapped-gate InAs nanowires are analyzed. With the help of a Poisson-Schr"odinger solver, information about the doping density can be obtained directly. Further features in the measured capacitance-voltage characteristics can be attributed to the presence of surface states as well as the coexistence of electrons and holes in the wire. For both scenarios, quantitative estimates are provided. It is furthermore shown that the difference between the actual capacitance and the geometrical limit is quite large, and depends strongly on the nanowire material.Comment: 15 pages, 6 Figures included, to appear in Nanotechnolog

State transition of a non-Ohmic damping system in a corrugated plane

Anomalous transport of a particle subjected to non-Ohmic damping of the power $\delta$ in a tilted periodic potential is investigated via Monte Carlo simulation of generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locking state and the running state. Under the surrounding of sub-Ohmic damping ($0<\delta<1$), the particle should transfer into a running state from a locking state only when local minima of the potential vanish; hence the particle occurs a synchronization oscillation in its mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping ($1<\delta<2$) for moderate driving forces, namely, where exists double centers in the velocity distribution. This induces the particle having faster diffusion, i.e., its MSD reads $= 2D^{(\delta)}_{eff} t^{\delta_{eff}}$. Our result shows that the effective power index $\delta_{\textmd{eff}}$ can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture effect of the two motion modes also leads to a breakdown of hysteresis loop of the mobility.Comment: 7 pages,7 figure

On the ubiquity of trivial torsion on elliptic curves

The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Growth of Inclined GaAs Nanowires by Molecular Beam Epitaxy: Theory and Experiment

The growth of inclined GaAs nanowires (NWs) during molecular beam epitaxy (MBE) on the rotating substrates is studied. The growth model provides explicitly the NW length as a function of radius, supersaturations, diffusion lengths and the tilt angle. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found that 20° inclined NWs are two times longer in average, which is explained by a larger impingement rate on their sidewalls. We find that the effective diffusion length at 550°C amounts to 12 nm for the surface adatoms and is more than 5,000 nm for the sidewall adatoms. Supersaturations of surface and sidewall adatoms are also estimated. The obtained results show the importance of sidewall adatoms in the MBE growth of NWs, neglected in a number of earlier studies

Comparison of three radiolabelled peptide analogues for CCK-2 receptor scintigraphy in medullary thyroid carcinoma

Purpose: Cholecystokinin 2 (CCK-2) receptor overexpression has been demonstrated in a high percentage of medullary thyroid carcinomas (MTC). Analogous to somatostatin receptors, CCK-2 receptors might be viable targets for radionuclide scintigraphy and/or radionuclide therapy. Several CCK-2 receptor-binding radiopeptides have been developed, and some have been carried through into clinical studies. However, these studies are mostly limited and difficult to compare. The aim of this study was to evaluate the diagnostic and therapeutic potential of three promising CCK-2 receptor-binding radiopeptides in patients with MTC. Methods: 111In-DOTA-(D)Asp-Tyr-Nle-Gly-Trp-Nle- Asp-Phe-NH2 (111In-DOTA-CCK), a CCK analogue, and the gastrin-based ligands 99mTc-N4-Gly-(D)Glu-(Glu) 5-Ala-Tyr-Gly-Trp-Met-Asp-Phe-NH2 (99mTc- demogastrin 2) and 111In-DOTA-(D)Glu-Ala-Tyr-Gly-Trp-Met-Asp-Phe- NH2 (111In-DOTA-MG11) were each administered to the same group of six patients. Planar images made at 3-5, 7 and 24 h p.i. were used for comparison of tumour visualisation and renal uptake. Results: 99mTc-demogastrin 2 scintigraphy visualised all known lesions and new lesions in four of six patients. 111In-DOTA-CCK and 111In-DOTA-MG11 on the other hand missed several lesions; tumour uptake of these two radiopharmaceuticals was quite low. Comparison of retention of renal activity showed no major differences between the three radiopeptides. Conclusion: 99mTc-demogastrin 2 scintigraphy appeared most promising as a diagnostic tool in patients with MTC. Further studies are required to evaluate its value in patient management. Direct comparisons of the compounds studied strongly suggests that 111In-DOTA-CCK and 111In-DOTA-MG11 have less potential as imaging agents than 99mTc-demogastrin 2. These DOTA-linked compounds are considered unlikely to be useful for radionuclide therapy because of low tumour uptake