1,128 research outputs found
An Efficient Algorithm for Computing Network Reliability in Small Treewidth
We consider the classic problem of Network Reliability. A network is given
together with a source vertex, one or more target vertices, and probabilities
assigned to each of the edges. Each edge appears in the network with its
associated probability and the problem is to determine the probability of
having at least one source-to-target path. This problem is known to be NP-hard.
We present a linear-time fixed-parameter algorithm based on a parameter
called treewidth, which is a measure of tree-likeness of graphs. Network
Reliability was already known to be solvable in polynomial time for bounded
treewidth, but there were no concrete algorithms and the known methods used
complicated structures and were not easy to implement. We provide a
significantly simpler and more intuitive algorithm that is much easier to
implement.
We also report on an implementation of our algorithm and establish the
applicability of our approach by providing experimental results on the graphs
of subway and transit systems of several major cities, such as London and
Tokyo. To the best of our knowledge, this is the first exact algorithm for
Network Reliability that can scale to handle real-world instances of the
problem.Comment: 14 page
Closed geodesics and holonomies for Kleinian manifolds
For a rank one Lie group G and a Zariski dense and geometrically finite
subgroup of G, we establish equidistribution of holonomy classes about
closed geodesics for the associated locally symmetric space. Our result is
given in a quantitative form for real hyperbolic geometrically finite manifolds
whose critical exponents are big enough. In the case when G=PSL(2, C), our
results can be interpreted as the equidistribution of eigenvalues of
in the complex plane.
When is a lattice, this result was proved by Sarnak and Wakayama in
1999.Comment: 28 pages, Minor corrections in the main term of the effective
versions of Theorem 1.2, 1.3 and 5.1 are made from the printed version
(GAFA,Vol 24 (2014) 1608-1636
A Facile, Fast, and Low-Cost Method for Fabrication of Micro/Nano-Textured Superhydrophobic Surfaces
Background
Alkyl ketene dimer (AKD) is frequently used in paper industry as an inexpensive sizing agent. The formation of a fractal structure after curing the solidified AKD for an extra-long time (4 - 6 days) results in superhydrophobicity. In this study, a facile and low-cost method was utilized to turn AKD’s surface superhydrophobic in a very short period of time.
Method
We fabricated a superhydrophobic layer by dipping glass and paper substrates in molten AKD and then treating them with ethanol after solidification. The samples were characterized by X-ray diffraction, Scanning electron microscopy, Fourier transform-infrared spectroscopy, X-ray photoelectron spectroscopy, Confocal laser scanning microscopy, and dynamic contact angle goniometry.
Results
The results show that briefly treating the coatings, obtained from isothermally heated AKD melt at 40°C for 3 min, with ethanol leads to superhydrophobicity with an advancing and receding contact angle of 158.7±1.4° and 156.8±0.9°, respectively. By increasing the melt temperature to 70°C and heating time to 6 h followed by ethanol treatment, the advancing and receding contact angles increased to 163.7±1.3° and 162.6±1.2°, respectively.
Conclusions
This enhancement in superhydrophobicity is due to the formation of entangled irregular micro/nano textures that create air cushions on the surface resulting in droplet state transition from Wenzel to Cassie. In this method, ethanol can be used several times, and the energy consumption becomes very low. Based on the other techniques in this field, our method has eliminated the complex equipment and procedure applied in the fabrication of a superhydrophobic AKD.https://scholarscompass.vcu.edu/gradposters/1072/thumbnail.jp
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