Analytical Solution to Transport in Brownian Ratchets via Gambler's Ruin Model

We present an analogy between the classic Gambler's Ruin problem and the thermally-activated dynamics in periodic Brownian ratchets. By considering each periodic unit of the ratchet as a site chain, we calculated the transition probabilities and mean first passage time for transitions between energy minima of adjacent units. We consider the specific case of Brownian ratchets driven by Markov dichotomous noise. The explicit solution for the current is derived for any arbitrary temperature, and is verified numerically by Langevin simulations. The conditions for vanishing current and current reversal in the ratchet are obtained and discussed.Comment: 4 pages, 3 figure

The Nullity of Bicyclic Signed Graphs

Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5

Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

Low relaxation rate in a low-Z alloy of iron

The longest relaxation time and sharpest frequency content in ferromagnetic precession is determined by the intrinsic (Gilbert) relaxation rate \emph{$G$}. For many years, pure iron (Fe) has had the lowest known value of $G=\textrm{57 Mhz}$ for all pure ferromagnetic metals or binary alloys. We show that an epitaxial iron alloy with vanadium (V) possesses values of $G$ which are significantly reduced, to 35$\pm$5 Mhz at 27% V. The result can be understood as the role of spin-orbit coupling in generating relaxation, reduced through the atomic number $Z$.Comment: 14 pages, 4 figure

Su(3) Algebraic Structure of the Cuprate Superconductors Model based on the Analogy with Atomic Nuclei

A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an $su(3)$ structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of $su(3)$ algebra. Using algebraic method, we derive the eigenvalues of the reduced Hamiltonian beyond the subalgebras $u(1)\bigotimes u(2)$ and $so(3)$ of $su(3)$ algebra. In particular, by considering the coherence between s- and d-wave pairs as perturbation, the effects of coherent term upon the energy spectrum are investigated

Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with $m$ arbitrary time-dependent coefficients are obtained possessing symmetries involving $m$ arbitrary functions of time. A particular graded symmetry algebra for the modified KP equations is derived in this connection homomorphic to the Virasoro algebras.Comment: 19 pages, latex, to appear in J. Nonlinear Math. Phy

High-power operation of a K-band second harmonic gyroklystron

Amplification studies of a two-cavity second-harmonic gyroklystron are reported. A magnetron injection gun produces a 440 kV, 200–245 A, 1 μs beam with an average perpendicular-to-parallel velocity ratio slightly less than 1. The TE011 input cavity is driven near 9.88 GHz and the TE021 output cavity resonates near 19.76 GHz. Peak powers exceeding 21 MW are achieved with an efficiency near 21% and a large signal gain above 25 dB. This performance represents the current state of the art for gyroklystrons in terms of the peak power normalized to the output wavelength squared

PF-35 Spider Silk (Nephilia sp.) as Suture Material on Blood Vessel Surgery

Surgical suture is a medical device used to hold body tissues together after an injury or surgery. Application generally involves using a needle with an attached length of thread. Surgical sutures are normally classified into two types, absorbable and non-absorbable. They can also be classified based on their construction, either mono-filament or multi-filament and also whether they are made from natural or synthetic materials. Sutures can also be classified according to their usage e.g. cardiovascular sutures, ophthalmic sutures, general sutures, orthopaedic sutures etc. Common problems associated with the choice of suture material include increased risk of infection, foreign body reactions, and inappropriate mechanical responses, particularly decreases in mechanical properties over time. Improved suture materials are therefore needed. As a high- performance material with excellent tensile strength, spider silk fibres are an extremely promising candidate for use in surgical sutures. However, the biochemical behaviour of individual silk fibres braided together has not been thoroughly investigated. In the present study, we characterise the inflammatory response produced from silk sutures and absorbance time

Parsec-scale jet properties of the gamma-ray quasar 3C 286

The quasar 3C~286 is one of two compact steep spectrum sources detected by the {\it Fermi}/LAT. Here, we investigate the radio properties of the parsec(pc)-scale jet and its (possible) association with the $\gamma$-ray emission in 3C~286. The Very Long Baseline Interferometry (VLBI) images at various frequencies reveal a one-sided core--jet structure extending to the southwest at a projected distance of $\sim$1 kpc. The component at the jet base showing an inverted spectrum is identified as the core, with a mean brightness temperature of $2.8\times 10^{9}$~K. The jet bends at about 600 pc (in projection) away from the core, from a position angle of $-135^\circ$ to $-115^\circ$. Based on the available VLBI data, we inferred the proper motion speed of the inner jet as $0.013 \pm 0.011$ mas yr$^{-1}$ ($\beta_{\rm app} = 0.6 \pm 0.5$), corresponding to a jet speed of about $0.5\,c$ at an inclination angle of $48^\circ$ between the jet and the line of sight of the observer. The brightness temperature, jet speed and Lorentz factor are much lower than those of $\gamma$-ray-emitting blazars, implying that the pc-scale jet in 3C~286 is mildly relativistic. Unlike blazars in which $\gamma$-ray emission is in general thought to originate from the beamed innermost jet, the location and mechanism of $\gamma$-ray emission in 3C~286 may be different as indicated by the current radio data. Multi-band spectrum fitting may offer a complementary diagnostic clue of the $\gamma$-ray production mechanism in this source.Comment: 9 pages, 4 figures, accept for publication in MNRA

Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a conformal transformation of the initial metric g. We prove the existence of the relative determinant of the pair $(\Delta_{h},\Delta_{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov's formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51 page