A Frequency-Domain Approach to Optimal Fractional-Order Damping

In this paper, we will consider the single term optimal fractional-order damper for an otherwise undamped oscillator. First, we will find the single term damper that minimizes the time domain integral of the squared step error (2-norm) and the integral of the time-weighted squared error (Hilbert–Schmidt–Hankel norm). Next we will consider a more intuitive frequency domain approach that insures the maximally flat magnitude response. Time and frequency domain plots are given for comparison with the integer-order solutions. Further improvements in performance are shown to be possible using multiple active fractional-order dampers.     

Fractional Trigonometry and the Spiral Functions

This paper develops two related fractional trigonometries based on the multi-valued fractional generalization of the exponential function, the R-function. The trigonometries contain the traditional trigonometric functions as proper subsets. Also developed are relationships between the R-function and the new fractional trigonometric functions. Laplace transforms are derived for the new functions and are used to generate solution sets for various classes of fractional differential equations. Because of the fractional character of the R-function, several new trigonometric functions are required to augment the traditional sine, cosine, etc. functions. Fractional generalizations of the Euler equation are derived. As a result of the fractional trigonometry a new set of phase plane functions, the Spiral functions, that contain the circular functions as a subset, is identified. These Spiral functions display many new symmetries.     

Direct Numerical Simulation and Experimental Investigation on Suppression of Vortex Induced Vibrations of Circular Cylinders by Radial Water Jets

The present paper deals with suppression of vortex induced vibrations (VIV) by introducing radial water jets from circular openings in the wall of the oscillating cylinder. Overpressure within the water-filled cylinder propels water jets blowing out into the ambient flow as a means to alter the vortex shedding process. This flow will introduce a disturbance that is expected to yield reduced VIV amplitudes. Results are presented from experiments in a towing tank testing a spring-supported cylinder with two straight rows of radial water jets along the the cylinder, located at positions +120° and?120° on the cylinder circumference. A smooth cylinder with no openings is tested for comparison. Direct Numerical Simulations (DNS) have been performed using the Spectral/hp element code Nεκταr. Outflow through openings in the cylinder wall is modeled, and a parameter study is performed where number of jets as well as jet location on the cylinder circumference and jet flow rate are varied.     

Vibration Induced Sliding: Theory and Experiment for a Beam with a Spring-Loaded Mass

The study sets up a simple model for predicting vibration induced sliding of mass, and provides quantitative experimental evidence for the validity of the model. The results lend confidence to recent theoretical developments on using vibration induced sliding for passive vibration damping, and contributes to a further understanding of this nonlinear phenomenon. A mathematical model is set up to describe vibration induced sliding for a base-excited cantilever beam with a spring-loaded pointmass. Approximations simplify the model into two nonlinear ordinary differential equations, describing motions of the system at near-resonant excitation of a single beam mode. This simplified model is studied numerically and analytically, and tested against laboratory experiments. The experiments provide evidence that the simplified mathematical model retains those features of the real system that are necessary for making useful predictions of transient and stationary first-mode response.     

An Invitation to Infinitary Computability

In the last two decades, various machine models of computability have been generalized to work in the transfinite. I will give an overview of these models, some of the main results concerning them and some reasons why studying them is of interest outside of foundational considerations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametric Representation of 3D Grain Ensembles in Polycrystalline Microstructures

As a straightforward generalization of the well-known Voronoi construction, Laguerre tessellations have long found application in the modelling, analysis and simulation of polycrystalline microstructures. The application of Laguerre tessellations to real (as opposed to computed) microstructures—such as those obtained by modern 3D characterization techniques like X-ray microtomography or focused-ion-beam serial sectioning—is hindered by the mathematical difficulty of determining the correct seed location and weighting factor for each of the grains in the measured volume. In this paper, we propose an alternative to the Laguerre approach, representing grain ensembles with convex cells parametrized by orthogonal regression with respect to 3D image data. Applying our algorithm to artificial microstructures and to microtomographic data sets of an Al-5 wt% Cu alloy, we demonstrate that the new approach represents statistical features of the underlying data—like distributions of grain sizes and coordination numbers—as well as or better than a recently introduced approximation method based on the Laguerre tessellation; furthermore, our method reproduces the local arrangement of grains (i.e., grain shapes and connectivities) much more accurately. The additional computational cost associated with orthogonal regression is marginal.     

Solvent-mediated charge redistribution in photodissociation of IBr(-) and IBr(-)(CO2)

A combined experimental and theoretical investigation of photodissociation dynamics of IBr(-) and IBr(-)(CO(2)) on the B ((2)Σ(1/2)(+)) excited electronic state is presented. Time-resolved photoelectron spectroscopy reveals that in bare IBr(-) prompt dissociation forms exclusively I? + Br(-). Compared to earlier dissociation studies of IBr(-) excited to the A' ((2)Π(1∕2)) state, the signal rise is delayed by 200 ± 20 fs. In the case of IBr(-)(CO(2)), the product distribution shows the existence of a second major (～40%) dissociation pathway, Br? + I(-). In contrast to the primary product channel, the signal rise associated with this pathway shows only a 50 ± 20 fs delay. The altered product branching ratio indicates that the presence of one solvent-like CO(2) molecule dramatically affects the electronic structure of the dissociating IBr(-). We explore the origins of this phenomenon with classical trajectories, quantum wave packet studies, and MR-SO-CISD calculations of the six lowest-energy electronic states of IBr(-) and 36 lowest-energy states of IBr. We find that the CO(2) molecule provides sufficient solvation energy to bring the initially excited state close in energy to a lower-lying state. The splitting between these states and the time at which the crossing takes place depend on the location of the solvating CO(2) molecule.     

Photoelectron spectroscopy of HC4N-

We report the 364-nm photoelectron spectrum of HC(4)N(-). We observe electron photodetachment from the bent X(2)A" state of HC(4)N(-) to both the near-linear X(3)A" and the bent ? (1)A' states of neutral HC(4)N. We observe an extended, unresolved vibrational progression corresponding to X(3)A" ← X(2)A" photodetachment, and we measure the electron affinity (EA) of the X(3)A" state of HC(4)N to be 2.05(8) eV. Photodetachment to the bent ? (1)A' state results in a single intense origin peak at a binding energy of 2.809(4) eV, from which we determine the singlet-triplet splitting (ΔE(ST)) of HC(4)N: 0.76(8) eV. For comparison and to aid in the interpretation of the HC(4)N(-) spectrum, we also report the 364-nm photoelectron spectra of HCCN(-) and DCCN(-). Improved signal-to-noise over the previous HCCN(-) and DCCN(-) photoelectron spectra allows for a more precise determination of the EAs and ΔE(ST)s of HCCN and DCCN. The EAs of HCCN and DCCN are measured to be 2.001(15) eV and 1.998(15) eV, respectively; ΔE(ST)(HCCN) is 0.510(15) eV and ΔE(ST)(DCCN) is 0.508(15) eV. These results are discussed in the context of other organic carbene chains.     

Mutation-induced fold switching among lattice proteins

Recent experiments uncovered a mutational pathway between two proteins, along which a single mutation causes a switch in fold. Searching for such paths between real proteins remains, despite this achievement, a true challenge. Here, we analyze fold switching in the minimalistic hydrophobic/polar model on a square lattice. For this analysis, we generate a comprehensive sequence-structure database for chains of length ≤ 30, which exceeds previous work by five units. Single-mutation-induced fold switching turns out to be quite common in the model. The switches define a fold network, whose topology is roughly similar to what one would expect for a set of randomly connected nodes. In the combinatorially challenging search for fold switches between two proteins, a tempting strategy is to only consider paths containing the minimum number of mutations. Such a restricted search fails to correctly identify 40% of the single-mutation-linked fold pairs that we observe. The thermodynamic stability is correlated with mutational stability and is, on average, markedly reduced at the observed fold switches.     

Copper(I) and Silver(I) Bis(trifluoromethanesulfonyl)imide and Their Interaction with an Arene,Diverse Olefins,and an NTf2−‐Based Ionic Liquid

The chemistry of coinage metal bis(triflyl)imides of technological interest, CuNTf₂ and AgNTf₂, their synthesis and complexes with excess of comparatively weakly coordinating NTf₂^? as well as with ether, olefins, and the arene mesitylene are described. The existence of the solvent‐free pure phase [CuNTf₂]_∞ has not been evidenced so far. Contrary to the literature, in which the preparation of [CuNTf₂]_∞ is supposed to be carried out by reacting mesityl copper, [Cu(Mes)]₅, and HNTf₂, we found that in fact this reaction leads reproducibly to the interesting copper diarene sandwich complex [Cu(η³‐MesH)₂][Cu(NTf₂)₂] ( 1 ) (MesH=1,3,5‐trimethylbenzene). The unexpectedly stable molecular etherate [Cu(Et₂O)(NTf₂)] ( 2 ) turned out to be the best precursor for CuNTf₂ having only an inert and easily exchangeable solvent ligand. The coordination mode of NTf₂^? in 1 and 2 as well as in the hitherto unknown crystalline phase of [AgNTf₂]_∞ ( 3 ) is described. The complex formation, which takes place when dissolving 2 or 3 in the room temperature ionic liquid (RTIL) [emim]NTf₂ ([emim]⁺=1‐ethyl‐3‐methylimidazolium), has been studied. Furthermore, the reaction of 1 – 3 towards the diolefins 1,5‐cyclooctadiene (COD), 2,5‐norbornadiene (NBD) and isoprene (2‐methylbuta‐1,3‐diene) and towards ethylene has been investigated. The products 4 – 13 of these conversions have been isolated and fully characterized by NMR‐ and IR spectroscopies, mass spectrometry, and elemental‐ and XRD analyses. The potential of [Cu(η³‐MesH)₂][Cu(NTf₂)₂] ( 1 ), [Cu(Et₂O)(NTf₂)] ( 2 ) and [AgNTf₂]_∞ ( 3 ) as well as of [emim][M(NTf₂)₂] (M=Cu 4 , Ag 5 ) as chemisorbers for ethylene was studied by NMR spectroscopy.