Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

Multi-vehicle Control in a Strong Flowfield with Application to Hurricane Sampling

A major obstacle to path-planning and formation-control algorithms in multi-vehicle systems are strong flows in which the ambient flow speed is greater than the vehicle speed relative to the flow. This challenge is espe-cially pertinent in the application of unmanned aircraft used for collecting targeted observations in a hurricane. The presence of such a flowfield may inhibit a vehicle from making forward progress relative to a ground-fixed frame, thus limiting the directions in which it can travel. Using a self-propelled particle model in which each particle moves at constant speed relative to the flow, this paper presents results for motion coordination in a strong, known flowfield. We present the particle model with respect to inertial and rotating reference frames and provide for each case a set of con-ditions on the flowfield that ensure trajectory feasibility. Results from the Lyapunov-based design of decentralized control algorithms are presented for circular, folium, and spirograph trajectories, which are selected for their potential use as hurricane sampling trajectories. The theoretical results are illustrated using numerical simulations in an idealized hurricane model. Nomenclature N Number of particles in the system k Particle index k = 1,..., N rk Position of k th particle with respect to inertial frame r̃k Position of k th particle with respect to rotating fram

Kinetic Studies on Photodeposition of Polydiacetylene Thin Film from Solution: Preliminary Determination of the Rate Law

Preliminary kinetic studies were undertaken on the photodeposition of thin films of a polydiacetylene derivative of 2-methyl-4-nitroaniline from monomer solutions onto quartz substrates. Solutions of the monomer, DAMNA, in 1,2-dichloroethane at various concentrations were irradiated at 364 nm using an argon-ion laser at several intensities. It was found that the rate of polydiacetylene (PDAMNA) film photodeposition varies linearly with UV light intensity and as the square root of monomer concentration

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Photon wave mechanics and position eigenvectors

One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin and orbital angular momentum. While only the Landau-Peierls wave function defines a positive definite photon density, a similarity transformation to a biorthogonal field-potential pair of positive frequency solutions of Maxwell's equations preserves eigenvalues and expectation values. We show that this real space description of photons is compatible with all of the usual rules of quantum mechanics and provides a framework for understanding the relationships amongst different forms of the photon wave function in the literature. It also gives a quantum picture of the optical angular momentum of beams that applies to both one photon and coherent states. According to the rules of qunatum mechanics, this wave function gives the probability to count a photon at any position in space.Comment: 14 pages, to be published in Phys. Rev.

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199

Zentrale Zugseilsysteme – vollautomatische, kontinuierliche Kallusdistraktion zur Behandlung langstreckiger Knochendefekte

Distraction osteogenesis involving bone transport enables the reconstruction of large bone defects. The main bone fragments are usually stablilised externally, an intermediate bone segment is separated and moved through the defect at a rate of about 1 mm/day. New high-quality bone is built up in the constantly enlarging osteotomy gap. A major problem associated with the method is the fact that the fixation pins are also moved over the same distance, and cut through the soft tissue, often resulting in painful pin tract infections and ugly scars. An automatic motorized bone transport system employing a single central cable now eliminates this problem. The system can be combined with any external fixateur, since the relevant implanted parts for bone transport are independent of the external stabilizer. The surgical procedure, which is easy on the patient, consists of bone segment separation, central cable fixation, and stabilisation of the main fragments, and requires the use of numerous special tools. The distraction itself results in significantly less soft tissue irritation and pain. Pin tract infections are rare, so that changeover to internal fixation after completion of bone transport carries little risk of infection. This article details the technical features of the stabilizing system and the transport and the control systems, and describes the clinical application in a patient

Search for Lorentz and CPT Violation Effects in Muon Spin Precession

The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero $\Delta\omega_{a}$ (=$\omega_{a}^{\mu^{+}}-\omega_{a}^{\mu^{-}}$); and a sidereal variation of $\omega_{a}^{\mu^{\pm}}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_{Z} =-(1.0 \pm 1.1)\times 10^{-23}$ GeV; $(m_{\mu}d_{Z0}+H_{XY}) = (1.8 \pm 6.0 \times 10^{-23})$ GeV; and the 95% confidence level limits $\check{b}_{\perp}^{\mu^{+}}< 1.4 \times 10^{-24}$ GeV and $\check{b}_{\perp}^{\mu^{-}} < 2.6 \times 10^{-24}$ GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to answer the referees suggestion

Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a_mu = (g-2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a_mu(Expt) = 11 659 208.0(5.4)(3.3) x 10^-10, where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a_mu includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ~0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e+e- hadronic cross sections, lie 2.2 - 2.7 standard deviations below the experimental result.Comment: Summary paper of E821 Collaboration measurements of the muon anomalous magnetic moment, each reported earlier in Letters or Brief Reports; 96 pages, 41 figures, 16 tables. Revised version submitted to PR