An analytical study of resonant transport of Bose-Einstein condensates

We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the transport properties of the system analytically in terms of ingoing and outgoing waves. Resonances and bound states are obtained analytically. The transmitted flux shows a bistable behaviour. Novel crossing scenarios of eigenstates similar to beak--to--beak structures are observed for a repulsive mean-field interaction. It is proven that resonances transform to bound states due to an attractive nonlinearity and vice versa for a repulsive nonlinearity, and the critical nonlinearity for the transformation is calculated analytically. The bound state wavefunctions of the system satisfy an oscillation theorem as in the case of linear quantum mechanics. Furthermore, the implications of the eigenstates on the dymamics of the system are discussed.Comment: RevTeX4, 16 pages, 19 figure

Optimal time travel in the Godel universe

Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we present a candidate for the minimum total integrated acceleration closed timelike curve in the Godel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament's conjectured value (Malament, 1984), as was already implicit in the work of Manchak (Manchak, 2011); however, Malament's conjecture does seem to hold for periodic closed timelike curves.Comment: 16 pages, 2 figures; v2: lower bound in the velocity and reference adde

On the generalized continuity equation

A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.Comment: 9 Latex pages, no figure

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Realistic Earth escape strategies for solar sailing

With growing interest in solar sailing comes the requirement to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. Previously unexplained seasonal variations in sail escape times from Earth orbit are explained analytically and corroborated within a numerical trajectory model. Blended-sail control algorithms, explicitly independent of time, which providenear-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller, are then presented. These algorithms are investigated from a range of initial conditions and are shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the minimum sail characteristic acceleration required for escape from a polar orbit without traversing the Earth shadow cone increases exponentially as initial altitude is decreased

Stability of non-time-reversible phonobreathers

Non-time reversible phonobreathers are non-linear waves that can transport energy in coupled oscillator chains by means of a phase-torsion mechanism. In this paper, the stability properties of these structures have been considered. It has been performed an analytical study for low-coupling solutions based upon the so called {\em multibreather stability theorem} previously developed by some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms the analytical predictions and gives a detailed picture of the existence and stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010

(G)hosting television: Ghostwatch and its medium

This article’s subject is Ghostwatch (BBC, 1992), a drama broadcast on Halloween night of 1992 which adopted the rhetoric of live non-fiction programming, and attracted controversy and ultimately censure from the Broadcasting Standards Council. In what follows, we argue that Ghostwatch must be understood as a televisually-specific artwork and artefact. We discuss the programme’s ludic relationship with some key features of television during what Ellis (2000) has termed its era of ‘availability’, principally liveness, mass simultaneous viewing, and the flow of the television super-text. We trace the programme’s television-specific historicity whilst acknowledging its allusions and debts to other media (most notably film and radio). We explore the sophisticated ways in which Ghostwatch’s visual grammar and vocabulary and deployment of ‘broadcast talk’ (Scannell 1991) variously ape, comment upon and subvert the rhetoric of factual programming, and the ends to which these strategies are put. We hope that these arguments collectively demonstrate the aesthetic and historical significance of Ghostwatch and identify its relationship to its medium and that medium’s history. We offer the programme as an historically-reflexive artefact, and as an exemplary instance of the work of art in television’s age of broadcasting, liveness and co-presence

Paroxysmal extreme pain disorder M1627K mutation in human Nav1.7 renders DRG neurons hyperexcitable

Background: Paroxysmal extreme pain disorder (PEPD) is an autosomal dominant painful neuropathy with many, but not all, cases linked to gain-of-function mutations in SCN9A which encodes voltage-gated sodium channel Nav1.7. Severe pain episodes and skin flushing start in infancy and are induced by perianal probing or bowl movement, and pain progresses to ocular and mandibular areas with age. Carbamazepine has been effective in relieving symptoms, while other drugs including other anti-epileptics are less effective. Results: Sequencing of SCN9A coding exons from an English patient, diagnosed with PEPD, has identified a methionine 1627 to lysine (M1627K) substitution in the linker joining segments S4 and S5 in domain IV. We confirm that M1627K depolarizes the voltage-dependence of fast-inactivation without substantially altering activation or slow-inactivation, and inactivates from the open state with slower kinetics. We show here that M1627K does not alter development of closed-state inactivation, and that M1627K channels recover from fast-inactivation faster than wild type channels, and produce larger currents in response to a slow ramp stimulus. Using current-clamp recordings, we also show that the M1627K mutant channel reduces the threshold for single action potentials in DRG neurons and increases the number of action potentials in response to graded stimuli. Conclusion: M1627K mutation was previously identified in a sporadic case of PEPD from France, and we now report it in an English family. We confirm the initial characterization of mutant M1627K effect on fast-inactivation of Nav1.7 and extend the analysis to other gating properties of the channel. We also show that M1627K mutant channels render DRG neurons hyperexcitable. Our new data provide a link between altered channel biophysics and pain in PEPD patients

New spin Calogero-Sutherland models related to B_N-type Dunkl operators

We construct several new families of exactly and quasi-exactly solvable BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of two new families of Dunkl operators of B_N type which, together with the original B_N-type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of quadratic combinations involving these three sets of Dunkl operators always yields a spin Calogero-Sutherland model, which is (quasi-)exactly solvable by construction. We show that all the spin Calogero-Sutherland models obtainable within this framework can be expressed in a unified way in terms of a Weierstrass P function with suitable half-periods. This provides a natural spin counterpart of the well-known general formula for a scalar completely integrable potential of BC_N type due to Olshanetsky and Perelomov. As an illustration of our method, we exactly compute several energy levels and their corresponding wavefunctions of an elliptic quasi-exactly solvable potential for two and three particles of spin 1/2.Comment: 18 pages, typeset in LaTeX 2e using revtex 4.0b5 and the amslatex package Minor changes in content, one reference adde

Reduction of Low-Thrust Continuous Controls for Trajectory Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76670/1/AIAA-40619-128.pd