13,820 research outputs found
Electrical transport studies of quench condensed Bi films at the initial stage of film growth: Structural transition and the possible formation of electron droplets
The electrical transport properties of amorphous Bi films prepared by
sequential quench deposition have been studied in situ. A
superconductor-insulator (S-I) transition was observed as the film was made
increasingly thicker, consistent with previous studies. Unexpected behavior was
found at the initial stage of film growth, a regime not explored in detail
prior to the present work. As the temperature was lowered, a positive
temperature coefficient of resistance (dR/dT > 0) emerged, with the resistance
reaching a minimum before the dR/dT became negative again. This behavior was
accompanied by a non-linear and asymmetric I-V characteristic. As the film
became thicker, conventional variable-range hopping (VRH) was recovered. We
attribute the observed crossover in the electrical transport properties to an
amorphous to granular structural transition. The positive dR/dT found in the
amorphous phase of Bi formed at the initial stage of film growth was
qualitatively explained by the formation of metallic droplets within the
electron glass.Comment: 7 pages, 6 figure
Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
We investigate the asymptotic properties of inertial modes confined in a
spherical shell when viscosity tends to zero. We first consider the mapping
made by the characteristics of the hyperbolic equation (Poincar\'e's equation)
satisfied by inviscid solutions. Characteristics are straight lines in a
meridional section of the shell, and the mapping shows that, generically, these
lines converge towards a periodic orbit which acts like an attractor.
We then examine the relation between this characteristic path and
eigensolutions of the inviscid problem and show that in a purely
two-dimensional problem, convergence towards an attractor means that the
associated velocity field is not square-integrable. We give arguments which
generalize this result to three dimensions. We then consider the viscous
problem and show how viscosity transforms singularities into internal shear
layers which in general betray an attractor expected at the eigenfrequency of
the mode. We find that there are nested layers, the thinnest and most internal
layer scaling with -scale, being the Ekman number. Using an
inertial wave packet traveling around an attractor, we give a lower bound on
the thickness of shear layers and show how eigenfrequencies can be computed in
principle. Finally, we show that as viscosity decreases, eigenfrequencies tend
towards a set of values which is not dense in , contrary to the
case of the full sphere ( is the angular velocity of the system).
Hence, our geometrical approach opens the possibility of describing the
eigenmodes and eigenvalues for astrophysical/geophysical Ekman numbers
(), which are out of reach numerically, and this for a wide
class of containers.Comment: 42 pages, 20 figures, abstract shortene
Unit Interval Editing is Fixed-Parameter Tractable
Given a graph~ and integers , , and~, the unit interval
editing problem asks whether can be transformed into a unit interval graph
by at most vertex deletions, edge deletions, and edge
additions. We give an algorithm solving this problem in time , where , and denote respectively
the numbers of vertices and edges of . Therefore, it is fixed-parameter
tractable parameterized by the total number of allowed operations.
Our algorithm implies the fixed-parameter tractability of the unit interval
edge deletion problem, for which we also present a more efficient algorithm
running in time . Another result is an -time algorithm for the unit interval vertex deletion problem,
significantly improving the algorithm of van 't Hof and Villanger, which runs
in time .Comment: An extended abstract of this paper has appeared in the proceedings of
ICALP 2015. Update: The proof of Lemma 4.2 has been completely rewritten; an
appendix is provided for a brief overview of related graph classe
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