Contact geometry of the restricted three‐body problem

We show that the planar circular restricted three‐body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of contact topology to understand this particular dynamical system. © 2011 Wiley Periodicals, Inc.     

Effects of Aromatic Fluorine Substitution on Protonated Neurotransmitters: The Case of 2‐Phenylethylamine

Fluorination of pharmaceutical compounds is a common tool to modulate their physiochemical properties. We determine the effects of site‐specific aromatic fluorine substitution on the geometric, energetic, vibrational, and electronic properties of the protonated neurotransmitter 2‐phenylethylamine (xF‐H⁺PEA, x=ortho, meta, para) by infrared multiphoton photodissociation (IRMPD) in the fingerprint range (600–1750 cm^?1) and quantum chemical calculations at the B3LYP‐D3/aug‐cc‐pVTZ level. The IRMPD spectra of all ions are assigned to their folded gauche conformers stabilized by intramolecular NH⁺???π hydrogen bonds (H‐bonds) between the protonated amino group and the aromatic ring. H→F substitution reduces the symmetry and allows for additional NH⁺???F interactions in oF‐H⁺PEA, leading to three distinct gauche conformers. In comparison to oF‐H⁺PEA, the fluorination effects on the energy landscape (energy ordering and isomerization barriers) in pF‐H⁺PEA and mF‐H⁺PEA with one and two gauche conformers are less pronounced. The strengths of the intramolecular NH⁺???F and NH⁺???π bonds are analyzed by the noncovalent interaction (NCI) method.     

Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws

An entropy solution u of a multi-dimensional scalar conservation law is not necessarily in BV, even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV function in the sense that the shock location is codimension-one rectifiable. This result highlights the regularizing effect of genuine nonlinearity in a qualitative way; it is based on the locally finite rate of entropy dissipation. The proof relies on the geometric classification of blow-ups in the framework of the kinetic formulation.     

Finite Bending of a Rectangular Block of an Elastic Hencky Material

Hencky's elasticity model is an isotropic, finite hyperelastic equation obtained by simply replacing the Cauchy stress tensor and the infinitesimal strain tensor in the classical Hooke's law for isotropic infinitesimal elasticity with the Kirchhoff stress tensor and Hencky's logarithmic strain tensor. A study by Anand in 1979 and 1986 indicates that it is a realistic finite elasticity model that is in good accord with experimental data for a variety of engineering materials for moderate deformations. Most recently, by virtue of well-founded physical grounds and rigorous mathematical procedures it has been demonstrated by these authors that this model may be essential to achieving self-consistent Eulerian rate type theories of finite inelasticity, e.g., the J ₂-flow theory for metal plasticity, etc. Its predictions have been studied for some typical deformation modes, including extension, simple shear and torsion, etc. Here we are concerned with finite bending of a rectangular block. We show that a closed-form solution may be obtained. We present explicit expressions for the bending angle and the bending moment in terms of the maximum or minimum circumferential stretch in a general case of compressible deformations for any assigned stretch normal to the bending plane. In particular, simplified results are derived for the plane strain case and for the case of incompressibility. This revised version was published online in June 2006 with corrections to the Cover Date.     

Relativity symmetries and Lie algebra contractions

We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n)$SO(m,n)$ symmetry as an isometry on an m+n$m+n$ dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n)$G(m,n)$ preserving a symmetry of the same type at dimension m+n−1$m+n-1$, e.g.   a G(m,n−1)$G(m,n-1)$, together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4)$SO(2,4)$, which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3)$G(1,3)$ may be relevant to real physics.     

Continuous‐Flow Synthesis of CdSe Quantum Dots: A Size‐Tunable and Scalable Approach

In recent years, continuous‐flow/microreactor processing for the preparation of colloidal nanocrystals has received considerable attention. The intrinsic advantages of microfluidic reactors have opened new opportunities for the size‐controlled synthesis of nanocrystals either in the laboratory or on a large scale. Herein, an experimentally simple protocol for the size‐tunable continuous‐flow synthesis of rather monodisperse CdSe quantum dots (QDs) is presented. CdSe QDs are manufactured by using cadmium oleate as cadmium source, selenium dioxide as selenium precursor, and 1‐octadecene as solvent. Exploiting selenium dioxide as selenium source and 1‐octadecene as solvent allows execution of the complete process in open air without any requirement for air‐free manipulations using a glove box or Schlenk line. Continuous‐flow processing is performed with a stainless steel coil of 1.0 mm inner diameter pumping the combined precursor solution through the reactor by applying a standard HPLC pump. The effect of different reaction parameters, such as temperature, residence time, and flow rate, on the properties of the resulting CdSe QDs was investigated. A temperature increase from 240 to 260 °C or an extension of the residence time from 2 to 20 min affords larger nanocrystals (range 3–6 nm) whereas the size distribution does not change significantly. Longer reaction times and higher temperatures result in QDs with lower quantum yields (range 11–28 %). The quality of the synthesized CdSe QDs was confirmed by UV/Vis and photoluminescence spectroscopy, small‐angle X‐ray scattering, and high‐resolution transmission electron microscopy. Finally, the potential of this protocol for large‐scale manufacturing was evaluated and by operating the continuous‐flow process for 87 min it was possible to produce 167 mg of CdSe QDs (with a mean diameter of 4 nm) with a quantum yield of 28 %.