Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.     

Fermi field and Dirac oscillator in a Som–Raychaudhuri space-time

We investigate the relativistic dynamics of a Dirac field in the Som–Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som–Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov–Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som–Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.     

Crystal Structure of the Radical-Cation Salt (<Emphasis Type="Italic">o</Emphasis>-Me<Subscript>2</Subscript>TTF)I<Subscript>3</Subscript> with Close Intermolecular Sulfur Contacts

Abstract  The synthesis and crystal structure of the organic radical-cation salt (o-Me₂TTF)I₃ is described. The salt crystallizes in the monoclinic space group P2 ₁ /n with a = 10.927(2) ?, b = 11.904(2) ?, c = 12.660(2) ?, β = 115.174(5)°. The bond length of the central C=C bond in o-Me₂TTF is 1.401(1) ?, indicating an approximate oxidation state of +1 for the o-Me₂TTF radical cation. Graphical Abstract  The X-ray crystallographic structure of the radical cation salt (o-Me₂TTF)I₃ has been determined and its structural properties and synthetic preparation are discussed.      

Synthesis and characterization of a biphenyl perfluorocyclobutyl (BP‐PFCB) polyethylene glycol (PEG) blend compatibilizer

Polyethylene glycol (PEG) end‐capped trifluorovinyl ether (TFVE) telechelomer was synthesized in one step via esterification of 4‐(trifluorovinyloxy) benzoic acid. The new telechelomer was characterized by attenuated total reflectance Fourier transform infrared (ATR‐FTIR), elemental analysis, and by ¹⁹F and ¹H nuclear magnetic resonance (NMR) spectroscopy. The telechelomer and 4,4′‐bis(4‐trifluorovinyloxy)biphenyl (BPVE) were thermally copolymerized via step‐growth [2 + 2] cycloaddition at 160°C. The polymerization afforded PEG enchained biphenyl perfluorocyclobutyl (BP‐PFCB) copolymers that are solution processable and film forming. These copolymers were characterized by ATR‐FTIR, ¹⁹F NMR, and ¹H NMR. Gel permeation chromatography (GPC) gave number‐average molecular weight (M_n) ranging 11,000 to 12,000. Compatibilization of PEG and a commercial polymer BP‐PFCB was achieved utilizing the new PEG BP‐PFCB copolymer, 3‐co2‐4 . It was found that 5 wt% of 3 ‐ co2 ‐ 4 was ideal to reduce interfacial tension by scanning electron microscope (SEM). In addition, phase homogeneity was studied by differential scanning calorimetry (DSC). Copyright © 2016 John Wiley & Sons, Ltd.     

Supply networks: Instabilities without overload

Supply and transport networks support much of our technical infrastructure as well as many biological processes. Their reliable function is thus essential for all aspects of life. Transport processes involving quantities beyond the pure loads exhibit alternative collective dynamical options compared to processes exclusively characterized by loads. Here we analyze the stability and bifurcations in oscillator models describing electric power grids and demonstrate that these networks exhibit instabilities without overloads. This phenomenon may well emerge also in other sufficiently complex supply or transport networks, including biological transport processes.     

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of panels with localized geometric defects, the case of a notch serving to exemplify the analysis. It is first demonstrated that the reduced order model of the notched panel does indeed provide a close match of the displacement and stress fields obtained from full finite element analyses for moderately large static and dynamic responses (peak displacement of 2 and 4 thicknesses). As might be expected, the reduced order model of the virgin panel would also yield a close approximation of the displacement field but not of the stress one. These observations then lead to two “enrichment” techniques seeking to superpose the notch effects on the virgin panel stress field so that a reduced order model of the latter can be used. A very good prediction of the full finite element stresses, for both static and dynamic analyses, is achieved with both enrichments.     

Experimental evidence of simultaneous multi-resonance noise reduction using an absorber with essential nonlinearity under two excitation frequencies

The addition of an essentially nonlinear membrane absorber to a linear vibroacoustic system with multiple resonances is studied experimentally, using quasiperiodic excitation. An extended experimental dataset of the system response is analyzed under steady-state excitation at two frequencies. Thresholds between low and high damping states within the system and associated noise reduction are observed and quantified thanks to frequency conversion and RMS efficiency indicators. Following previous numerical results, it is shown that the membrane NES (Nonlinear Energy Sink) acts simultaneously and efficiently on two acoustic resonances. In all cases, the introduction of energy at a second excitation frequency appears favorable to lower the frequency conversion threshold and to lower the noise within the system. In particular, a simultaneous control of two one-to-one resonances by the NES is observed. Exploration of energy conversion in the two excitation amplitudes plane advocates for a linear dependence of the frequency conversion thresholds on the two excitation amplitudes.     

Fast wavefront sensing using a hardware parallel classifier chip

In most applications of laser technology and optics the beam quality, the ability to focus a laser beam and the achievement of a good optical resolution play an important role. The compensation of distortions using adaptive optics requires fast wavefront measurement. Classical wavefront analysis schemes use matrix operations, which show a nonlinear computation time dependence with matrix size, making it difficult to achieve high-speed control loops at a high resolution. A novel wavefront sensor system is presented using a massively parallel k-nearest neighbor classifier chip in an embedded hardware setup. Our miniaturized sensor is able to detect one optical distortion within about 80 μs allowing its use for high-speed adaptive optics applications.     

Temperature dependence of Raman scattering and anharmonic properties in LiNbO_3

The temperature dependence of the Raman spectrum in LiNbO \(_3\) is investigated from 100 to 700 K. The various sources of asymmetry of Raman bands and artefacts are discussed before analyzing the temperature dependence of A \(_1\) and E first-order phonon lines. The phonon frequency downshift and damping increase on heating are interpreted in terms of normal volume expansion and third- and fourth-order anharmonic potentials. Anharmonic contributions are highly anisotropic and mainly explain the temperature dependences of both frequency and damping of A \(_1\) optical vibrational modes along the ferroelectric axis. Results are consistent with Caciuc et al. (Phys Rev B 61:8806, 2000) predictions.