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 $n$-vertex graph $G$ and a positive integer $k$, we want to decide whether there is a set of at most $k$ vertices whose removal turns $G$ into a graph of linear rankwidth at most $1$ 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 $f(k)\cdot n^3$ for some function $f$, 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 $8^k\cdot n^{\mathcal{O}(1)}$. 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 $2^{\mathcal{O}(k)}\cdot n^4$. We also prove that the running time cannot be improved to $2^{o(k)}\cdot n^{\mathcal{O}(1)}$ 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