Binary permutation sequences as subsets of Levenshtein codes,spectral null codes,run-length limited codes and constant weight codes

We investigate binary sequences which can be obtained by concatenating the columns of (0,1)-matrices derived from permutation sequences. We then prove that these binary sequences are subsets of a surprisingly diverse ensemble of codes, namely the Levenshtein codes, capable of correcting insertion/deletion errors; spectral null codes, with spectral nulls at certain frequencies; as well as being subsets of run-length limited codes, Nyquist null codes and constant weight codes. This paper was presented in part at the IEEE Information Theory Workshop, Chengdu, China, October, 2006.     

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Does the strain hardening modulus of glassy polymers scale with the flow stress?

Using a generic coarse‐grained bead‐spring model, Hoy and Robbins reproduced important experimental observations on strain hardening, specifically the generally observed Gaussian strain hardening response and its dependence on network density and temperature. Moreover, their simulation results showed that the strain hardening response at different strain rates collapses to a single curve when scaled to the value of the flow stress, a phenomenon that has not yet been verified experimentally. In the present study, the proposed scaling law is experimentally investigated on a variety of polymer glasses: poly(methyl methacrylate), poly(phenylene ether), polycarbonate, polystyrene, and poly(ethylene terephthalate)‐glycol. For these polymers, true stress–strain curves in uniaxial compression were collected over a range of strain rates and temperatures and scaled to the flow stress. It was found that, generally, the curves do not collapse on a mastercurve. In all cases, the strain hardening modulus is observed to increase linearly, but not proportionally to the flow stress. The experimental data, therefore, unambiguously demonstrate that the proposed scaling law does not apply within the range of temperature and strain rate covered in this study. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2475–2481, 2008     

Polarons in magnesium-doped lithium niobate crystals induced by femtosecond light pulses

Strong light-induced absorption has been observed in lithium niobate crystals doped with magnesium after application of femtosecond illumination. In this material there are no Nb-on-Li-site defects and hence no antisite polarons occur, but small free polarons close to the conduction band can be generated. The light-induced absorption observed is attributed to these polarons. For LiNbO₃:Mg, their decay times are about two orders of magnitude smaller than those of the Nb-on-Li-site polarons in undoped material. The results are relevant for a better understanding of the suppression of the so-called optical damage in these crystals and for their use in femtosecond applications.     

Geometrical and electronic structures of dinuclear complex ions {(mu-bpym)[Cu(EAr3)2]2}2+ with intramolecular "organic sandwich" formation (E = P or As; Ar = Aryl; bpym = 2,2'-bipyrimidine)

The compound {(mu-bpym)[Cu(AsPh3)2]2}(BF4)2 (1) has been prepared and studied in comparison with the triphenylphosphine analogue 2. Qualitatively, the structure of 1 with characteristically distorted copper(I) coordination caused by Ph/bpym/Ph sandwich interactions is similar to that of 2 and is approximately reproduced by DFT calculations for the model complex ions {(mu-bpym)[Cu(EMe2Ph)2]2}2+, E = P or As. In contrast, the dinuclear {(mu-bpym)[Cu(P(3-Me-C6H4)3)2]2}(BF4)2 (3) displays a distinctly less distorted metal coordination geometry due to the steric requirements of the methyl groups in the meta-tolyl substituents. The electrochemical reduction of 1 is less reversible than for the phosphine analogues; the one-electron-reduced form 1*- exhibits a broad, unresolved EPR signal at g = 2.0023. Resonance Raman spectroscopy of 1 shows the typical vibrations of the bpym ligand in agreement with the MLCT assignment of the long-wavelength transitions below 500 nm. All three dinuclear complexes exhibit luminescence at room temperature in the solid and in solution.     

Zur Konstruktion lokal kompakter Dicksonscher Fastkörper

Ohne ZusammenfassungAus dem Nachlaß. Für den Druck vorbereitet von Theo Grundhöfer (Tübingen) und Heinz Lüneburg (Kaiserslautern).     

Topological speed limits to network synchronization

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.