Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Perturbation-induced radiation by the Ablowitz-Ladik soliton

An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are calculated for linear damping and quintic perturbations.Comment: 13 pages, 4 figures, Phys. Rev. E (in press

Omicron infection enhances Delta antibody immunity in vaccinated persons

The extent to which Omicron infection(1–9), with or without previous vaccination, elicits protection against the previously dominant Delta (B.1.617.2) variant is unclear. Here we measured the neutralization capacity against variants of severe acute respiratory syndrome coronavirus 2 in 39 individuals in South Africa infected with the Omicron sublineage BA.1 starting at a median of 6 (interquartile range 3–9) days post symptom onset and continuing until last follow-up sample available, a median of 23 (interquartile range 19–27) days post symptoms to allow BA.1-elicited neutralizing immunity time to develop. Fifteen participants were vaccinated with Pfizer's BNT162b2 or Johnson & Johnson's Ad26.CoV2.S and had BA.1 breakthrough infections, and 24 were unvaccinated. BA.1 neutralization increased from a geometric mean 50% focus reduction neutralization test titre of 42 at enrolment to 575 at the last follow-up time point (13.6-fold) in vaccinated participants and from 46 to 272 (6.0-fold) in unvaccinated participants. Delta virus neutralization also increased, from 192 to 1,091 (5.7-fold) in vaccinated participants and from 28 to 91 (3.0-fold) in unvaccinated participants. At the last time point, unvaccinated individuals infected with BA.1 had low absolute levels of neutralization for the non-BA.1 viruses and 2.2-fold lower BA.1 neutralization, 12.0-fold lower Delta neutralization, 9.6-fold lower Beta variant neutralization, 17.9-fold lower ancestral virus neutralization and 4.8-fold lower Omicron sublineage BA.2 neutralization relative to vaccinated individuals infected with BA.1. These results indicate that hybrid immunity formed by vaccination and Omicron BA.1 infection should be protective against Delta and other variants. By contrast, infection with Omicron BA.1 alone offers limited cross-protection despite moderate enhancement

A numerical study of the large-period limit of a ZakharovShabat eigenvalue problem with periodic potentials

Deconinck and Kutz (2006 J. Comput. Phys. 219 296321) developed an efficient algorithm for solving the ZakharovShabat eigenvalue problem with periodic potentials numerically. It is natural to use the same algorithm for solving the problem for non-periodic potential (decaying potentials defined over the whole real line) using large periods. In this paper, we propose the use of a specific value of the Floquet exponent. Our numerical results indicate that it can produce accurate results long before the period becomes large enough for the analytical convergence results of Gardner (1997 J. Reine Angew. Math. 491 14981) to be valid. We also illustrate the rather complicated path to convergence of some nonlinear Schrödinger potentials. © 2012 IOP Publishing Ltd

A Field Based, Self-Excited Compulsator Power Supply for A 9 MJ Railgun Demonstrator

Fabrication efforts have begun on a field-based compulsator for firing 9 MJ projectiles from a railgun launcher. The machine is designed to store 200 MJ kinetic energy and fire a salvo of nine rounds in three minutes at velocities between 2.5 and 4.0 km/s. Prime power required to meet this firing schedule is 1.865 kW, and will be supplied by a gas turbine engine. It is also possible to fire a burst of two shots in rapid succession, if desired. Operating speed of the machine is 8250 r/min and it has design ratings of 3.2 MA peak current and 20 GW peak power into a 9 MJ railgun load. A two-pole configuration is used for pulse-length considerations, and selectivity passive compensation is used to produced a relatively flat pulse and limit peak projectile acceleration to about 980000 m/s2. Other distinguishing features include an air core magnetic circuit, separate rotor armature windings for self-excitation and railgun firing, ambient temperature field coils, and excitation field magnetic energy recovery capability. A detailed description of the machine as designed, and its auxiliary and control systems, is provided. Fabrication and assembly methods are reviewed, and the current status of the project is discussedCenter for Electromechanic

Design of a Self-Excited, Air-Core Compulsator for a Skid-Mounted, Repetitive Fire 9 MJ Railgun System

The design of a lightweight, compulsator-driven 9-MJ electromagnetic (EM) launcher has been completed and is in the fabrication phase. Scheduled for initial field testing in early 1989, the system will be capable of firing a salvo of nine rounds in three minutes at muzzle velocities between 2.5 and 4.0 km/s. Prime power for the compulsator is supplied by a 5000-hp gas turbine engine through a gearbox and clutch arrangement, and auxiliary power is provided by a small 750-hp turbine. Electrical power generation and pulse conditioning for the launcher are performed by the compulsator, which features a self-excited, air-core magnetic circuit and selectively passive armature compensation designed to minimize peak projectile acceleration. Peak power from the machine is 27 GW, and a total of 30 MJ is extracted from the rotor during each firing of the gun. System mass, including gun, compulsator, prime power, and auxiliary systems, is less than 22 tons and will be mounted on a 36-ton concrete slab which simulates the mass of an armored vehicle on which the system will eventually be integratedCenter for Electromechanic