Linear multistep methods for integrating reversible differential equations

This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here, we report on a subset of these methods -- the zero-growth methods -- that evade these instabilities. We provide an algorithm for identifying these rare methods. We find and study all zero-growth, reversible multisteps with six or fewer steps. This select group includes two well-known second-order multisteps (the trapezoidal and explicit midpoint methods), as well as three new fourth-order multisteps -- one of which is explicit. Variable timesteps can be readily implemented without spoiling the reversibility. Tests on Keplerian orbits show that these new reversible multisteps work well on orbits with low or moderate eccentricity, although at least 100 steps/radian are required for stability.Comment: 31 pages, 9 figures, in press at The Astronomical Journa

State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy

We consider a connection-level model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighted $\alpha$-fair bandwidth sharing policy introduced by Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567] [$\alpha\in (0,\infty)$]. Assuming Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. A fluid model (or functional law of large numbers approximation) for this stochastic model was derived and analyzed in a prior work [Ann. Appl. Probab. 14 (2004) 1055--1083] by two of the authors. Here, we use the long-time behavior of the solutions of the fluid model established in that paper to derive a property called multiplicative state space collapse, which, loosely speaking, shows that in diffusion scale, the flow count process for the stochastic model can be approximately recovered as a continuous lifting of the workload process.Comment: Published in at http://dx.doi.org/10.1214/08-AAP591 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

CP violating dimuon charge asymmetry in general left-right models

The recently measured charge asymmetry of like-sign dimuon events by the D0 collaboration at Tevatron shows the 3.9 \sigma\ deviation from the standard model prediction. In order to solve this mismatch, we investigate the right-handed current contributions to $B_s-\bar{B}_s$ and $B_d-\bar{B}_d$ mixings which are the major source of the like-sign dimuon events in $b \bar{b}$ production in general left-right models without imposing manifest or pseudo-manifest left-right symmetry. We find the allowed region of new physics parameters satisfying the current experimental data.Comment: 9 pages, 4 figure

Study of 0-π\pi phase transition in hybrid superconductor-InSb nanowire quantum dot devices

Hybrid superconductor-semiconducting nanowire devices provide an ideal platform to investigating novel intragap bound states, such as the Andreev bound states (ABSs), Yu-Shiba-Rusinov (YSR) states, and the Majorana bound states. The competition between Kondo correlations and superconductivity in Josephson quantum dot (QD) devices results in two different ground states and the occurrence of a 0-$\pi$ quantum phase transition. Here we report on transport measurements on hybrid superconductor-InSb nanowire QD devices with different device geometries. We demonstrate a realization of continuous gate-tunable ABSs with both 0-type levels and $\pi$-type levels. This allow us to manipulate the transition between 0 and $\pi$ junction and explore charge transport and spectrum in the vicinity of the quantum phase transition regime. Furthermore, we find a coexistence of 0-type ABS and $\pi$-type ABS in the same charge state. By measuring temperature and magnetic field evolution of the ABSs, the different natures of the two sets of ABSs are verified, being consistent with the scenario of phase transition between the singlet and doublet ground state. Our study provides insights into Andreev transport properties of hybrid superconductor-QD devices and sheds light on the crossover behavior of the subgap spectrum in the vicinity of 0-$\pi$ transition

Body shape preferences: Associations with rater body shape and sociosexuality

Copyright @ 2013 Price et al.This article has been made available through the Brunel Open Access Publishing Fund.There is accumulating evidence of condition-dependent mate choice in many species, that is, individual preferences varying in strength according to the condition of the chooser. In humans, for example, people with more attractive faces/bodies, and who are higher in sociosexuality, exhibit stronger preferences for attractive traits in opposite-sex faces/bodies. However, previous studies have tended to use only relatively simple, isolated measures of rater attractiveness. Here we use 3D body scanning technology to examine associations between strength of rater preferences for attractive traits in opposite-sex bodies, and raters' body shape, self-perceived attractiveness, and sociosexuality. For 118 raters and 80 stimuli models, we used a 3D scanner to extract body measurements associated with attractiveness (male waist-chest ratio [WCR], female waist-hip ratio [WHR], and volume-height index [VHI] in both sexes) and also measured rater self-perceived attractiveness and sociosexuality. As expected, WHR and VHI were important predictors of female body attractiveness, while WCR and VHI were important predictors of male body attractiveness. Results indicated that male rater sociosexuality scores were positively associated with strength of preference for attractive (low) VHI and attractive (low) WHR in female bodies. Moreover, male rater self-perceived attractiveness was positively associated with strength of preference for low VHI in female bodies. The only evidence of condition-dependent preferences in females was a positive association between attractive VHI in female raters and preferences for attractive (low) WCR in male bodies. No other significant associations were observed in either sex between aspects of rater body shape and strength of preferences for attractive opposite-sex body traits. These results suggest that among male raters, rater self-perceived attractiveness and sociosexuality are important predictors of preference strength for attractive opposite-sex body shapes, and that rater body traits -with the exception of VHI in female raters- may not be good predictors of these preferences in either sex.This study is funded by the Brunel University School of Social Sciences and made available through the Brunel Open Access Publishing Fund

Triple sign reversal of Hall effect in HgBa_{2}CaCu_{2}O_{6} thin films after heavy-ion irradiations

Triple sign reversal in the mixed-state Hall effect has been observed for the first time in ion-irradiated HgBa_{2}CaCu_{2}O_{6} thin films. The negative dip at the third sign reversal is more pronounced for higher fields, which is opposite to the case of the first sign reversal near T_c in most high-T_c superconductors. These observations can be explained by a recent prediction in which the third sign reversal is attributed to the energy derivative of the density of states and to a temperature-dependent function related to the superconducting energy gap. These contributions prominently appear in cases where the mean free path is significantly decreased, such as our case of ion-irradiated thin films.Comment: 4 pages, 3 eps figures, submitted Phys. Rev. Let