3,822 research outputs found
Exact solution of the three-boson problem at vanishing energy
A zero range approach is used to model resonant two-body interactions between
three identical bosons. A dimensionless phase parametrizes the three-body
boundary condition while the scattering length enters the Bethe-Peierls
boundary condition. The model is solved exactly at zero energy for any value of
the scattering length, positive or negative. From this solution, an analytical
expression for the rate of three-body recombination to the universal shallow
dimer is extracted.Comment: 12 page
An FPT algorithm and a polynomial kernel for Linear Rankwidth-1 Vertex Deletion
Linear rankwidth is a linearized variant of rankwidth, introduced by Oum and
Seymour [Approximating clique-width and branch-width. J. Combin. Theory Ser. B,
96(4):514--528, 2006]. Motivated from recent development on graph modification
problems regarding classes of graphs of bounded treewidth or pathwidth, we
study the Linear Rankwidth-1 Vertex Deletion problem (shortly, LRW1-Vertex
Deletion). In the LRW1-Vertex Deletion problem, given an -vertex graph
and a positive integer , we want to decide whether there is a set of at most
vertices whose removal turns into a graph of linear rankwidth at most
and find such a vertex set if one exists. While the meta-theorem of
Courcelle, Makowsky, and Rotics implies that LRW1-Vertex Deletion can be solved
in time for some function , it is not clear whether this
problem allows a running time with a modest exponential function.
We first establish that LRW1-Vertex Deletion can be solved in time . The major obstacle to this end is how to handle a long
induced cycle as an obstruction. To fix this issue, we define necklace graphs
and investigate their structural properties. Later, we reduce the polynomial
factor by refining the trivial branching step based on a cliquewidth expression
of a graph, and obtain an algorithm that runs in time . We also prove that the running time cannot be improved to under the Exponential Time Hypothesis assumption. Lastly,
we show that the LRW1-Vertex Deletion problem admits a polynomial kernel.Comment: 29 pages, 9 figures, An extended abstract appeared in IPEC201
Degradation of AB25 dye in liquid medium by atmospheric pressure non-thermal plasma and plasma combination with photocatalyst TiO2
In this work, degradation of the anthraquinonic dye Acid Blue 25 by non-thermal plasma at atmospheric pressure with and without photocatalyst is investigated. Titanium dioxide (TiO2) is used as a photocatalyst. The dye degradation by plasma in the presence of TiO2 is investigated as a function of TiO2 concentration, dye concentration and pH. The degradation rate is higher in acidic solutions with pH of 2 to 4.3, especially at pH 2, and decreases to 0.38 mg L-1 min(-1) with the increase of pH from 2 to 5.65. A similar effect is observed in basic media, where a higher degradation rate is found at pH = 10.3. The degradation rate increases in the presence of TiO2 compared to the discharge without photocatalysis. The results show that the degradation of the dye increases in the presence of TiO2 until the catalyst load reaches 0.5 g L-1 after which the suppression of AB25 degradation is observed. The results indicate that the tested advanced oxidation processes are very effective for the degradation of AB25 in aqueous solutions
Peeling Bifurcations of Toroidal Chaotic Attractors
Chaotic attractors with toroidal topology (van der Pol attractor) have
counterparts with symmetry that exhibit unfamiliar phenomena. We investigate
double covers of toroidal attractors, discuss changes in their morphology under
correlated peeling bifurcations, describe their topological structures and the
changes undergone as a symmetry axis crosses the original attractor, and
indicate how the symbol name of a trajectory in the original lifts to one in
the cover. Covering orbits are described using a powerful synthesis of kneading
theory with refinements of the circle map. These methods are applied to a
simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review
Eclipses of the inner satellites of Jupiter observed in 2015
During the 2014-2015 campaign of mutual events, we recorded ground-based
photometric observations of eclipses of Amalthea (JV) and, for the first time,
Thebe (JXIV) by the Galilean moons. We focused on estimating whether the
positioning accuracy of the inner satellites determined with photometry is
sufficient for dynamical studies. We observed two eclipses of Amalthea and one
of Thebe with the 1 m telescope at Pic du Midi Observatory using an IR filter
and a mask placed over the planetary image to avoid blooming features. A third
observation of Amalthea was taken at Saint-Sulpice Observatory with a 60 cm
telescope using a methane filter (890 nm) and a deep absorption band to
decrease the contrast between the planet and the satellites. After background
removal, we computed a differential aperture photometry to obtain the light
flux, and followed with an astrometric reduction. We provide astrometric
results with an external precision of 53 mas for the eclipse of Thebe, and 20
mas for that of Amalthea. These observation accuracies largely override
standard astrometric measurements. The (O-C)s for the eclipse of Thebe are 75
mas on the X-axis and 120 mas on the Y-axis. The (O-C)s for the total eclipses
of Amalthea are 95 mas and 22 mas, along the orbit, for two of the three
events. Taking into account the ratio of (O-C) to precision of the astrometric
results, we show a significant discrepancy with the theory established by
Avdyushev and Ban'shikova in 2008, and the JPL JUP 310 ephemeris.Comment: 7 pages, 10 figures, 4 table
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