Global Behavior of the Douglas-Rachford Method for a Nonconvex Feasibility Problem

In recent times the Douglas-Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems

Noise control by sonic crystal barriers made of recycled materials

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is here reported. The barriers consist of only three rows of perforated metal shells filled with rubber crumb. Measurements of reflectance and transmittance by these barriers are reported. Their attenuation properties result from a combination of sound absorption by the rubber crumb and reflection by the periodic distribution of scatterers. It is concluded that porous cylinders can be used as building blocks whose physical parameters can be optimized in order to design efficient barriers adapted to different noisy environments

Zero-temperature random-field Ising model on a bilayered Bethe lattice

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Degenerate Four Virtual Soliton Resonance for KP-II

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by which, one and two soliton solutions are constructed and the resonance character of their mutual interactions is studied. By our bilinear form, we first time created four virtual soliton resonance solution for KP-II and established relations of it with degenerate four-soliton solution in the Hirota-Satsuma bilinear form for KP-II.Comment: 10 pages, 5 figures, Talk on International Conference Nonlinear Physics. Theory and Experiment. III, 24 June-3 July, 2004, Gallipoli(Lecce), Ital

Is There a Fundamental Line for Disk Galaxies?

We show that there are strong local correlations between metallicity, surface brightness, and dynamical mass-to-light ratio within M33, analogous to the fundamental line of dwarf galaxies identified by Prada & Burkert (2002). Using near-infrared imaging from 2MASS, the published rotation curve of M33, and literature measurements of the metallicities of HII regions and supergiant stars, we demonstrate that these correlations hold for points at radial distances between 140 pc and 6.2 kpc from the center of the galaxy. At a given metallicity or surface brightness, M33 has a mass-to-light ratio approximately four times as large as the Local Group dwarf galaxies; other than this constant offset, we see broad agreement between the M33 and dwarf galaxy data. We use analytical arguments to show that at least two of the three fundamental line correlations are basic properties of disk galaxies that can be derived from very general assumptions. We investigate the effect of supernova feedback on the fundamental line with numerical models and conclude that while feedback clearly controls the scatter in the fundamental line, it is not needed to create the fundamental line itself, in agreement with our analytical calculations. We also compare the M33 data with measurements of a simulated disk galaxy, finding that the simulation reproduces the trends in the data correctly and matches the fundamental line, although the metallicity of the simulated galaxy is too high, and the surface brightness is lower than that of M33.Comment: 14 pages, 14 figures (5 in color). Accepted for publication in Ap

Non-standard quantum so(3,2) and its contractions

A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf structures for the conformal algebras of the 2+1 Galilean and Carroll spacetimes. Relations between the latter and the null-plane quantum Poincar\'e algebra are studied.Comment: 9 pages, LaTe

Global convergence of a non-convex Douglas-Rachford iteration

We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given

Segregation of an intruder in a heated granular dense gas

A recent segregation criterion [V. Garz\'o, Phys. Rev. E \textbf{78}, 020301(R) (2008)] based on the thermal diffusion factor $\Lambda$ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of $\Lambda$ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to get the kinetic diffusion coefficient $D_0$. The comparison between theory and simulation shows that the second Sonine approximation to $D_0$ yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE/RBNE transition, the kinetic theory results for the factor $\Lambda$ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.Comment: 9 figures; to be published in Phys. Rev.

Regulation of durum wheat Na(+)/H (+) exchanger TdSOS1 by phosphorylation

We have identified a plasma membrane Na+/H+ exchanger from durum wheat, designated TdSOS1. Heterologous expression of TdSOS1 in a yeast strain lacking endogenous Na+ efflux proteins showed complementation of the Na+- and Li+-sensitive phenotype by a mechanism involving cation efflux. Salt tolerance conferred by TdSOS1 was maximal when co-expressed with the Arabidopsis protein kinase complex SOS2/SOS3. In vitro phosphorylation of TdSOS1 with a hyperactive form of the Arabidopsis SOS2 kinase (T/DSOS2∆308) showed the importance of two essential serine residues at the C-terminal hydrophilic tail (S1126, S1128). Mutation of these two serine residues to alanine decreased the phosphorylation of TdSOS1 by T/DSOS2∆308 and prevented the activation of TdSOS1. In addition, deletion of the C-terminal domain of TdSOS1 encompassing serine residues at position 1126 and 1128 generated a hyperactive form that had maximal sodium exclusion activity independent from the regulatory SOS2/SOS3 complex. These results are consistent with the presence of an auto-inhibitory domain at the C-terminus of TdSOS1 that mediates the activation of TdSOS1 by the protein kinase SOS2. Expression of TdSOS1 mRNA in young seedlings of the durum wheat variety Om Rabia3, using different abiotic stresses (ionic and oxidative stress) at different times of exposure, was monitored by RT–PCR.Peer Reviewe