The Cop Number of the One-Cop-Moves Game on Planar Graphs

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each other's positions. If a cop eventually occupies the same vertex as the robber, then the cops win; the robber wins if she can indefinitely evade capture. Aigner and Frommer established that in every connected planar graph, three cops are sufficient to capture a single robber. In this paper, we consider a recently studied variant of the cops-and-robbers game, alternately called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers game, where at most one cop can move during any round. We show that Aigner and Frommer's result does not generalise to this game variant by constructing a connected planar graph on which a robber can indefinitely evade three cops in the one-cop-moves game. This answers a question recently raised by Sullivan, Townsend and Werzanski.Comment: 32 page

Inverse Diffusion Theory of Photoacoustics

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.Comment: 24 page

Survey of the sea fisheries of India

A preliminary account is given of the design and technique of the sampling method employed for estimating the landings of sea fish at some selected centres along the East and West coasts of India. Statistics of marine fishing villages, fishing populations, boats and nets are presented along with app roximate percentages of the occurrence of important fishes and also the estimated monthly landings of fish during 1949 at some representauve places

Systematic account of the eels of Bombay

Eels form an important fishery in different parts of the world and they have attracted the attention of naturalists since the beginning of this century, when the Danish scientist Johannes Schmidt (1906) made the sensational discovery of the breeding migration of the European eel

Measurement of Magnetization Dynamics in Single-Molecule Magnets Induced by Pulsed Millimeter-Wave Radiation

We describe an experiment aimed at measuring the spin dynamics of the Fe8 single-molecule magnet in the presence of pulsed microwave radiation. In earlier work, heating was observed after a 0.2-ms pulse of intense radiation, indicating that the spin system and the lattice were out of thermal equilibrium at millisecond time scale [Bal et al., Europhys. Lett. 71, 110 (2005)]. In the current work, an inductive pick-up loop is used to probe the photon-induced magnetization dynamics between only two levels of the spin system at much shorter time scales (from ns to us). The relaxation time for the magnetization, induced by a pulse of radiation, is found to be on the order of 10 us.Comment: 3 RevTeX pages, including 3 eps figures. The paper will appear in the Journal of Applied Physics as MMM'05 conference proceeding

Resistance and reconfiguration of natural flexible submerged vegetation in hydrodynamic river modelling

In-stream submerged macrophytes have a complex morphology and several species are not rigid, but are flexible and reconfigure along with the major flow direction to avoid potential damage at high stream velocities. However, in numerical hydrodynamic models, they are often simplified to rigid sticks. In this study hydraulic resistance of vegetation is represented by an adapted bottom friction coefficient and is calculated using an existing two layer formulation for which the input parameters were adjusted to account for (i) the temporary reconfiguration based on an empirical relationship between deflected vegetation height and upstream depth-averaged velocity, and (ii) the complex morphology of natural, flexible, submerged macrophytes. The main advantage of this approach is that it removes the need for calibration of the vegetation resistance coefficient. The calculated hydraulic roughness is an input of the hydrodynamic model Telemac 2D, this model simulates depth-averaged stream velocities in and around individual vegetation patches. Firstly, the model was successfully validated against observed data of a laboratory flume experiment with three macrophyte species at three discharges. Secondly, the effect of reconfiguration was tested by modelling an in situ field flume experiment with, and without, the inclusion of macrophyte reconfiguration. The inclusion of reconfiguration decreased the calculated hydraulic roughness which resulted in smaller spatial variations of simulated stream velocities, as compared to the model scenario without macrophyte reconfiguration. We discuss that including macrophyte reconfiguration in numerical models input, can have significant and extensive effects on the model results of hydrodynamic variables and associated ecological and geomorphological parameters

Kinetic Limit for Wave Propagation in a Random Medium

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon to 0 the disorder averaged Wigner function on the kinetic scale, time and space of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure

Radiation- and Phonon-Bottleneck-Induced Tunneling in the Fe8 Single-Molecule Magnet

We measure magnetization changes in a single crystal of the single-molecule magnet Fe8 when exposed to intense, short (<20 $\mu$s) pulses of microwave radiation resonant with the m = 10 to 9 transition. We find that radiation induces a phonon bottleneck in the system with a time scale of ~5 $\mu$s. The phonon bottleneck, in turn, drives the spin dynamics, allowing observation of thermally assisted resonant tunneling between spin states at the 100-ns time scale. Detailed numerical simulations quantitatively reproduce the data and yield a spin-phonon relaxation time of T1 ~ 40 ns.Comment: 6 RevTeX pages, including 4 EPS figures, version accepted for publicatio