A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems

Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.Comment: 24 pages, 3 figures, submitted to Astronomical Journal; minor errors in equations and one figure correcte

Changing the Ties That Bind? The Emerging Roles and Identities of General Practitioners and Managers in the New Clinical Commissioning Groups in the English NHS

The English National Health Service (NHS) is undergoing significant reorganization following the 2012 Health and Social Care Act. Key to these changes is the shift of responsibility for commissioning services from Primary Care Trusts (PCTs) to general practitioners (GPs) working together in Clinical Commissioning Groups (CCGs). This article is based on an empirical study that examined the development of emerging CCGs in eight case studies across England between September 2011 and June 2012. The findings are based on interviews with GPs and managers, observations of meetings, and reading of related documents. Scott’s notion that institutions are constituted by three pillars—the regulative, normative, and cognitive–cultural—is explored here. This approach helps to understand the changing roles and identities of doctors and managers implicated by the present reforms. This article notes the far reaching changes in the regulative pillar and questions how these changes will affect the normative and cultural–cognitive pillars

Giant electrocaloric effect in thin film Pb Zr_0.95 Ti_0.05 O_3

An applied electric field can reversibly change the temperature of an electrocaloric material under adiabatic conditions, and the effect is strongest near phase transitions. This phenomenon has been largely ignored because only small effects (0.003 K V^-1) have been seen in bulk samples such as Pb0.99Nb0.02(Zr0.75Sn0.20Ti0.05)0.98O3 and there is no consensus on macroscopic models. Here we demonstrate a giant electrocaloric effect (0.48 K V^-1) in 300 nm sol-gel PbZr0.95Ti0.05O3 films near the ferroelectric Curie temperature of 222oC. We also discuss a solid state device concept for electrical refrigeration that has the capacity to outperform Peltier or magnetocaloric coolers. Our results resolve the controversy surrounding macroscopic models of the electrocaloric effect and may inspire ab initio calculations of electrocaloric parameters and thus a targeted search for new materials.Comment: 5 pages, 4 figure

Fast algorithm for detecting community structure in networks

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for detecting such structure. These algorithms however are computationally demanding, which limits their application to small networks. Here we describe a new algorithm which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster than previous algorithms. We give several example applications, including one to a collaboration network of more than 50000 physicists.Comment: 5 pages, 4 figure

Minimum orbit dimension for local unitary action on n-qubit pure states

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.Comment: 19 page

Hybrid phase-space simulation method for interacting Bose fields

We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive-P representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The Hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive-P method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the Hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.Comment: 13 pages; 6 figures; references added; figures correcte

Optimal Moments for the Analysis of Peculiar Velocity Surveys

We present a new method for the analysis of peculiar velocity surveys which removes contributions to velocities from small scale, nonlinear velocity modes while retaining information about large scale motions. Our method utilizes Karhunen--Lo\`eve methods of data compression to construct a set of moments out of the velocities which are minimally sensitive to small scale power. The set of moments are then used in a likelihood analysis. We develop criteria for the selection of moments, as well as a statistic to quantify the overall sensitivity of a set of moments to small scale power. Although we discuss our method in the context of peculiar velocity surveys, it may also prove useful in other situations where data filtering is required.Comment: 25 Pages, 3 figures. Submitted to Ap

Simple theory for spin-lattice relaxation in metallic rare earth ferromagnets

The spin-lattice relaxation time $\tau_{SL}$ is a key quantity both for the dynamical response of ferromagnets excited by laser pulses and as the speed limit of magneto-optical recording. Extending the theory for the electron paramagnetic resonance of magnetic impurities to spin-lattice relaxation in ferromagnetic rare earths we calculate $\tau_{SL}$ for Gd and find a value of 48 ps in very good agreement with time-resolved spin-polarized photoemission experiments. We argue that the time scale for $\tau_{SL}$ in metals is essentially given by the spin-orbit induced magnetocrystalline anisotropy energy.Comment: 18 pages revtex, 5 uuencoded figure

Fast and Slow Rotators in the Densest Environments: a SWIFT IFS study of the Coma Cluster

We present integral-field spectroscopy of 27 galaxies in the Coma cluster observed with the Oxford SWIFT spectrograph, exploring the kinematic morphology-density relationship in a cluster environment richer and denser than any in the ATLAS3D survey. Our new data enables comparison of the kinematic morphology relation in three very different clusters (Virgo, Coma and Abell 1689) as well as to the field/group environment. The Coma sample was selected to match the parent luminosity and ellipticity distributions of the early-type population within a radius 15' (0.43 Mpc) of the cluster centre, and is limited to r' = 16 mag (equivalent to M_K = -21.5 mag), sampling one third of that population. From analysis of the lambda-ellipticity diagram, we find 15+-6% of early-type galaxies are slow rotators; this is identical to the fraction found in the field and the average fraction in the Virgo cluster, based on the ATLAS3D data. It is also identical to the average fraction found recently in Abell 1689 by D'Eugenio et al.. Thus it appears that the average slow rotator fraction of early type galaxies remains remarkably constant across many different environments, spanning five orders of magnitude in galaxy number density. However, within each cluster the slow rotators are generally found in regions of higher projected density, possibly as a result of mass segregation by dynamical friction. These results provide firm constraints on the mechanisms that produce early-type galaxies: they must maintain a fixed ratio between the number of fast rotators and slow rotators while also allowing the total early-type fraction to increase in clusters relative to the field. A complete survey of Coma, sampling hundreds rather than tens of galaxies, could probe a more representative volume of Coma and provide significantly stronger constraints, particularly on how the slow rotator fraction varies at larger radii.Comment: Accepted for publication in MNRA