3,207 research outputs found
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 internal data for well-chosen
boundary conditions are available, where 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
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
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
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 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 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
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