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

Primary Exposure to SARS-CoV-2 via Infection or Vaccination Determines Mucosal Antibody-Dependent ACE2 Binding Inhibition

Background: Mucosal antibodies play a critical role in preventing SARS-CoV-2 infections or reinfections by blocking the interaction of the receptor-binding domain (RBD) with the angiotensin-converting enzyme 2 (ACE2) receptor on the cell surface. In this study, we investigated the difference between the mucosal antibody response after primary infection and vaccination. Methods: We assessed longitudinal changes in the quantity and capacity of nasal antibodies to neutralize the interaction of RBD with the ACE2 receptor using the spike protein and RBD from ancestral SARS-CoV-2 (Wuhan-Hu-1), as well as the RBD from the Delta and Omicron variants. Results: Significantly higher mucosal IgA concentrations were detected postinfection vs postvaccination, while vaccination induced higher IgG concentrations. However, ACE2-inhibiting activity did not differ between the cohorts. Regarding whether IgA or IgG drove ACE2 inhibition, infection-induced binding inhibition was driven by both isotypes, while postvaccination binding inhibition was mainly driven by IgG. Conclusions: Our study provides new insights into the relationship between antibody isotypes and neutralization by using a sensitive and high-Throughput ACE2 binding inhibition assay. Key differences are highlighted between vaccination and infection at the mucosal level, showing that despite differences in the response quantity, postinfection and postvaccination ACE2 binding inhibition capacity did not differ.</p

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