Free Vibration Analysis of Rotating Nonlinearly Elastic Structures with Symmetry: An Efficient Group-Equivariance Approach

A study is made of the dynamics of oscillating systems with a slowly varying parameter. A slowly varying forcing periodically crosses a critical value corresponding to a pitchfork bifurcation. The instantaneous phase portrait exhibits a centre when the forcing does not exceed the critical value, and a saddle and two centres with an associated double homoclinic loop separatrix beyond this value. The aim of this study is to construct a Poincaré map in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. For that purpose averaging methods and asymptotic matching techniques connecting local solutions are applied. Given the initial state and the values of the parameters the properties of the Poincaré map can be studied. Both sensitive dependence on initial conditions and (quasi) periodicity are observed. Moreover, Lyapunov exponents are computed. The asymptotic expressions for the Poincaré map are compared with numerical solutions of the full system that includes small damping.     

Probabilistic Predictions with Federated Learning

Probabilistic predictions with machine learning are important in many applications. These are commonly done with Bayesian learning algorithms. However, Bayesian learning methods are computationally expensive in comparison with non-Bayesian methods. Furthermore, the data used to train these algorithms are often distributed over a large group of end devices. Federated learning can be applied in this setting in a communication-efficient and privacy-preserving manner but does not include predictive uncertainty. To represent predictive uncertainty in federated learning, our suggestion is to introduce uncertainty in the aggregation step of the algorithm by treating the set of local weights as a posterior distribution for the weights of the global model. We compare our approach to state-of-the-art Bayesian and non-Bayesian probabilistic learning algorithms. By applying proper scoring rules to evaluate the predictive distributions, we show that our approach can achieve similar performance as the benchmark would achieve in a non-distributed setting.     

The Quantum Double Model with Boundary: Condensations and Symmetries

Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to the boundary. We then consider two phases of the quantum double model corresponding to two groups with a domain wall between them, and study the tunneling of anyons from one phase to the other. Using this framework we discuss the necessary and sufficient conditions when two different groups give the same anyon types. As an application we show that in the quantum double model for S ₃ (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. This group is indeed a special case of groups of the form of the semidirect product of the additive and multiplicative groups of a finite field, for all of which we prove a similar symmetry.     

Microwave assisted fluorination: an improved method for side chain fluorination of substituted 1-arylethanones

A two-step, one-pot microwave (MW) assisted fluorination of 1-arylethanones to their corresponding 1-aryl-2-fluoroethanones has been developed. The first step utilises Selectfluor™ as a fluorinating agent in methanol forming 1-aryl-2-fluoroethanones and their corresponding dimethyl acetals. In the second step, water is added and Selectfluor™ acts as a Lewis acid in the hydrolytic cleavage of the dimethyl acetals. Compared to the thermal synthesis, the MW assisted method leads to a reduction in reaction time both in the fluorination and for the dimethyl acetal cleavage. Moreover, the one-pot procedure reduces reagent and solvent consumption. The method is best suited for the preparation of 1-aryl-2-fluoroethanones containing substituents that deactivates electrophilic aromatic substitution, however highly electron deficient ketones such as 1-(3,5-dinitrophenyl)ethanone reacts more slowly. Reactions using electron rich aromatic ketones had a low regioselectivity, and also produced fluoroaromatic products.     

On H-Linked Graphs

For a fixed multigraph H, possibly containing loops, with V(H)={h₁, . . . , h_k}, we say a graph G is H-linked if for every choice of k vertices v₁, . . . , v_k in G, there exists a subdivision of H in G such that v_i represents h_i (for all i). This notion clearly generalizes the concept of k-linked graphs (as well as other properties). In this paper we determine, for a connected multigraph H and for any sufficiently large graph G, a sharp lower bound on δ(G) (depending upon H) such that G is H-linked.     

Subdivision Extendibility

Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V(G) (the ground set) the image of V(H) under the isomorphism. We consider connectivity and minimum degree or degree sum conditions sufficient to imply there is a spanning subgraph of G isomorphic to a subdivision of H on the same ground set S. These results generalize a number of theorems in the literature.     

Die thermodynamischen Eizenschaften von Wasser, das an Quarz adsorbiert ist

Ohne Zusammenfassung     

Effect of finite extensibility on the viscoelastic properties of a styrene–butadiene rubber vulcanizate in simple tensile deformations up to rupture

Stress–strain and rupture data were determined on an unfilled styrene–butadiene vulcanizate at temperatures from ?45 to 35°C and at extension rates from 0.0096 to 9.6 min^?1. The data were represented by four functions: (1) the well-known temperature function (shift factor) a_T; (2) the constant strain rate modulus, F(t,T), reduced to temperature T₀ and time t/a_T, i.e., T₀F(t/a_T)/T; (3) the time-dependent maximum extensibility, λ_m(t/a_T); and (4) a function Ω(χ) where χ = (λ ? 1)λ_m⁰/λ_m, in which λ is the extension ratio and λ_m⁰ is the maximum extensibility under equilibrium conditions. The constant strain rate modulus characterizes the stress–time response to a constant extension rate at small strains, within the range of linear response; λ_m is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress–strain curve of the material in a reference state of unit modulus and λ_m = λ_m. The shift factor a_T was found to be sensibly independent of extension. At all values of t/a_T for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λ_m⁰ = 8.6 and that the largest extension ratio at break, (λ_b)_max, is 7.3. Thus, rupture always occurs before the network is fully extended.     

Fast-neutron total and scattering cross sections of58Ni

Neutron total cross sections of⁵⁸Ni were measured at 25 keV intervals from 0.9 to 4.5 MeV with 50–100 keV resolutions. Attention was given to self-shielding corrections to the observed total cross sections. Differential elastic- and inelastic-scattering cross sections were measured at 50 keV intervals from 1.35 to 4.0 MeV with 50–100 keV resolutions. Inelastic excitation of levels at 1.458±0.009, 2.462+-0.010, 2.791±0.015, 2.927+-0.012 and 3.059+-0.025 MeV was observed. The experimental results were interpreted in terms of optical-statistical and coupled-channels models.     

Hydrogen bonding incis-2,3-epoxycyclooctanol

Hydrogen bonding and the electron-withdrawing or electron-donating characteristics of substituent groups that are neighboring to epoxide groups can affect the reactivity of the epoxide ring. The crystal structure ofcis-2,3-epoxycyclooctanol has been determined as a saturated eight-membered ring compound in which a hydroxyl group is attached to the C(1) atom that is adjacent to a 2,3-fused epoxy ring. The findings are that the longer epoxide C-O bond (and hence the one expected to be more readily broken) is the one farther from the hydroxyl group [1.462(1) å versus 1.447(1) å] and that the optimal hydrogen bonding is to an adjacent molecule radier than within the molecule. The shortest C-C bond is that of the epoxide group; the bond adjacent to it (on the side farther from the hydroxyl group) is the next shortest.