Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.Comment: 3 pages, 1 figur

Quantitative Stability and Optimality Conditions in Convex Semi-Infinite and Infinite Programming

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is $l_{\infty}(T)$. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map, which involves only the system data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. On one hand, in this way we extend to the convex setting the results of [4] developed in the linear framework under the boundedness assumption on the system coefficients. On the other hand, in the case when the decision space is reflexive, we succeed to remove this boundedness assumption in the general convex case, establishing therefore results new even for linear infinite and semi-infinite systems. The last part of the paper provides verifiable necessary optimality conditions for infinite and semi-infinite programs with convex inequality constraints and general nonsmooth and nonconvex objectives. In this way we extend the corresponding results of [5] obtained for programs with linear infinite inequality constraints

From Brittle to Ductile Fracture in Disordered Materials

We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility. The dynamics of yielding exhibits avalanches with a power-law distribution

Flow Blurring-Enabled Production of Polymer Filaments from Poly(ethylene oxide) Solutions

Flow blurring (FB) atomizers are relatively simple yet robust devices used for the generation of sprays from solutions of a wide range of viscosities. In this work, we have demonstrated that FB devices may also be applied for massive production of liquid filaments from polymeric solutions. They can later be transformed into solid filaments and fibers, leading to the production of so-called fiber mats. The liquid precursors consisted of poly(ethylene oxide) (PEO) solutions of varying molecular weights (105 [100k] to 4 × 106 g/mol [4M]) and concentrations. The FB device was operated in the gas pressure range of 3−6 bar. Except for solutions of PEO 100k, all solutions exhibited a shear thinning behavior. For massive filament production, a threshold polymer concentration (ct) was identified for each molecular weight. Below such concentration, the atomization resulted in droplets (the classical FB functioning mode). Such a threshold value decreased as the PEO molecular weight increased, and it coincides with the polymer coil overlap concentration, c*. The viscoelastic nature of the solutions was also observed to increase with the molecular weight. A 3.2 dependency of the zero-shear rate viscosity on a so-called Bueche parameter was found for filament production, whereas a nearly linear dependency was found for droplet production. In general, the mean diameter of the filaments decreased as they traveled downstream from the atomization point. Furthermore, at a given distance from the atomizer outlet and gas pressure, the mean filament diameter slightly shifted toward larger sizes with increasing PEO molecular weight. The tendency agrees well with the calculated filaments’ Deborah number, which increases with PEO molecular weight. The approach presented herein describes a highthroughput and efficient method for the massive production of viscous filaments. These may be transformed into fibers by an on-line drying step.Ministerio de Economía y Competitividad DPI2016-78887-C3-1-

Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices

We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review

Absolute Calibration of the Radio Astronomy Flux Density Scale at 22 to 43 GHz Using Planck

The Planck mission detected thousands of extragalactic radio sources at frequencies from 28 to 857 GHz. Planck's calibration is absolute (in the sense that it is based on the satellite's annual motion around the Sun and the temperature of the cosmic microwave background), and its beams are well characterized at sub-percent levels. Thus Planck's flux density measurements of compact sources are absolute in the same sense. We have made coordinated VLA and ATCA observations of 65 strong, unresolved Planck sources in order to transfer Planck's calibration to ground-based instruments at 22, 28, and 43 GHz. The results are compared to microwave flux density scales currently based on planetary observations. Despite the scatter introduced by the variability of many of the sources, the flux density scales are determined to 1-2% accuracy. At 28 GHz, the flux density scale used by the VLA runs 3.6% +- 1.0% below Planck values; at 43 GHz, the discrepancy increases to 6.2% +- 1.4% for both ATCA and the VLA.Comment: 16 pages, 4 figures and 4 table

Revisiting the optical PTPT-symmetric dimer

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.Comment: 25 pages, 12 figure