cis‐Di­phenyl­bis(1,3,5‐tri­aza‐7‐phospha­adamantane‐κP)platinum(II)

The structure of the title compound, [Pt(C₆H₅)₂(C₆H₁₂N₃P)₂] or [Pt(Ph)₂(PTA)₂] (where Ph is phenyl and PTA is 1,3,5‐tri­aza‐7‐phosphaadamantane), is discussed. Selected geom­etric parameters are: Pt—P = 2.2888 (16) and 2.2944 (17) Å, Pt—C = 2.052 (5) and 2.064 (6) Å, C—Pt—C = 84.6 (2)° and P—Pt—P = 99.28 (6)°. The effective cone angle for the PTA ligands was calculated as 113°.     

[2‐(Anilino­methyl)­phenyl]­di­phenyl­phosphine and {2‐[(N‐methyl­anilino)­methyl]­phenyl}di­phenyl­phosphine

The title compounds, Ph₂PCH₂N(H)Ph or C₂₅H₂₂NP and Ph₂PCH₂N(CH₃)Ph or C₂₆H₂₄NP, respectively, are isomorphous, with calculated theoretical Tolman angles of 174 and 182°.     

Cellulose and the twofold screw axis: modeling and experimental arguments

Crystallography indicates that molecules in crystalline cellulose either have twofold screw-axis (2₁) symmetry or closely approximate it, leading to short distances between H4 and H1′ across the glycosidic linkage. Therefore, modeling studies of cellobiose often show elevated energies for 2₁ structures, and experimental observations are often interpreted in terms of intramolecular strain. Also, some computer models of cellulose crystallites have an overall twist as well as twisted individual chains, again violating 2₁ symmetry. To gain insight on the question of inherent strain in 2₁ structures, modeling was employed and crystal structures of small molecules were surveyed. (Residues in a disaccharide cannot be related by 2₁ symmetry because they are not identical but if their linkage geometry would lead to 2₁ symmetry for an infinite cellulose chain, the disaccharide would have 2₁ pseudo symmetry.) Several initial structures in quantum mechanics (QM) studies of cellobiose minimized to structures having 2₁ pseudo symmetry. Similarly, a number of relevant small molecules in experimental crystal structures have pseudo symmetry. While the QM models of cellobiose with 2₁ pseudo symmetry had inter-residue hydrogen bonding, the experimental studies included cellotriose undecaacetate, a molecule that cannot form conventional hydrogen bonds. Limitations in characterizing symmetry based on the linkage torsion angles ϕ and ψ were also explored. It is concluded that 2₁ structures have little intrinsic strain, despite indications from empirical models.     

The directed genus of the de Bruijn graph

Define the directed genus, Γ(G), of an Eulerian digraph G to be the minimum value of p for which G has a 2-cell embedding in the orientable surface of genus p so that every face of the embedding is bounded by a directed circuit in G. The directed genus of the de Bruijn graph D_n is shown to be

     

Simultaneous determination of particle size and refractive index by time-resolved Mie scattering

With this numerical study we have investigated the pulse-induced and time-resolved Mie scattering with the aim of determining the size and the refractive index of transparent spherical particles simultaneously. The temporal interval between the scattering light signals of two different orders of scattered light allows only particle sizing. But if it is possible to detect three different orders of scattered light, then we have two independent time intervals. This situation is given if the detector has a position about θ=90°. With these scattering angle signals of reflection and refraction of 1st and 3rd order appear with approximately the same intensity. Then the numerical quotient of the two temporal intervals between these scattering orders is a function of the refractive index only. We have calculated these specific quotients by models of geometric optics for 1.1≤m≤1.6 and 75°≤θ≤90° and have seen that there is a very high agreement with the results of time-resolved Mie calculations.     

Difluorotetrakis(2‐oxypyridine)dirhenium(III) – Preparation,Crystallographic Structure,and Electrochemical Properties

The solid‐state‐melt reaction of (NH₄)₂[Re₂F₈] · 2H₂O with 2‐hydroxypyridine (2‐HOpy) produced dark‐red Re₂(2‐Opy)₄F₂ ( 1 ). This air‐stable compound was obtained in crystalline form as 1· CHCl₃. It was characterized in the solid state by single‐crystal X‐ray diffraction and in solution by UV/Vis spectroscopy and cyclic voltammetry. 1· CHCl₃ forms triclinic crystals with α = 8.3254(5) Å, b = 8.5563(5) Å, c = 11.6784(8) Å, α = 82.723(3)°, β = 75.769(3) °, γ = 64.407(2) °. The Re–Re and Re–F distances were 2.2091(7) and 2.115(6) Å, respectively. The molecule is isostructural with the corresponding chloro derivative.     

Finite Intersection Property and Dynamical Compactness

Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800–6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the \(\omega _{{\mathcal {F}}}\)-limit and the \(\omega \)-limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics.     

Magnetic friction in Ising spin systems

A new contribution to friction is predicted to occur in systems with magnetic correlations: Tangential relative motion of two Ising spin systems pumps energy into the magnetic degrees of freedom. This leads to a friction force proportional to the area of contact. The velocity and temperature dependence of this force are investigated. Magnetic friction is strongest near the critical temperature, below which the spin systems order spontaneously. Antiferromagnetic coupling leads to stronger friction than ferromagnetic coupling with the same exchange constant. The basic dissipation mechanism is explained. A surprising effect is observed in the ferromagnetically ordered phase: The relative motion can act like a heat pump cooling the spins in the vicinity of the friction surface.     

Inverted direction of wave propagation (IDWP) in the cochlea

The "classical" view on wave propagation is that propagating waves are possible in both directions along the length of the basilar membrane and that they have identical properties. Results of several recently executed experiments [T. Ren, Nat. Neurosci. 2, 333-334 (2004) and W. X. He, A. L. Nuttall, and T. Ren, Hear. Res., 228, 112-122 (2007)] appear to contradict this view. In the current work measurements were made of the velocity of the guinea-pig basilar membrane (BM). Distortion products (DPs) were produced by presenting two primary tones, with frequencies below the characteristic frequency f(0) of the BM location at which the BM measurements were made, with a constant frequency ratio. In each experiment the phase of the principal DP, with frequency 2f(1)-f(2), was recorded as a function of the DP frequency. The results indicate that the DP wave going from the two-tone interaction region toward the stapes is not everywhere traveling in the reverse direction, but also in the forward direction. The extent of the region in which the forward wave occurs appears larger than is accounted for by classical theory. This property has been termed "inverted direction of wave propagation." The results of this study confirm the wave propagation findings of other authors. The experimental data are compared to theoretical predictions for a classical three-dimensional model of the cochlea that is based on noise-response data of the same animal. Possible physical mechanisms underlying the findings are discussed.     

Resonant Forcing of Chaotic Dynamics

We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.