Intersection de sous-groupes et de sous-variétés I

We study the intersection of a subvariety X of an abelian variety A over with the union of all the algebraic subgroups of A of given dimension d. Our main result states that if we remove a suitable exceptional subset from X and if d is small enough then the intersection enjoys a Northcott-like property: the points of bounded height on it form a finite set. The condition on d involves only the dimension of X and the structure of A up to isogenies. We show how it can be weakened if we assume certain conjectures in the direction of an abelian version of Lehmer's problem. The theorem is especially meaningful when X is a curve since it is then possible to bound the height and hence to prove finiteness of the set under consideration. This generalises the result of E. Viada on powers of elliptic curves and is analogous to work of E. Bombieri, D. Masser and U. Zannier on tori, whose general strategy we follow.     

Formation of radicals in the photodestruction of polypropylene

Conclusions In the UV irradiation (wavelength interval 236–800 m) of polypropylene (atactic and isotactic) and polyethylene at temperatures of 77–123°K, a substantial amount (10¹⁸–10¹⁹ g^–1) of radicals of various types are formed. Hydroperoxide groups are among the main sources of radicals in the case of oxidized polypropylene.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 778–783, April, 1967.     

First-principles investigation of the vibrational properties of 3-tert-butylcyclohexene

I present a first-principles investigation of the vibrational properties of the chiral molecule 3-tert-butylcyclohexene. The vibrational density of states (vDOS) of the two existing conformers has been calculated ab initio within the framework of density-functional theory and density-functional perturbation theory, using both the local-density approximation and the generalized-gradient approximation for the exchange-correlation potential. The vDOS of the two conformers are very similar. The vDOS has been investigated with respect to contributions of the cyclohexene ring and the tert-butyl group and also regarding the localization of vibrational modes. Additionally, the eigendisplacements of characteristic modes of 3-tert-butylcyclohexene have been analyzed.     

Coordination ability of trans-cyclohexane-1,2-diamine-N,N,N',N'-tetrakis(methylenephosphonic acid) towards lanthanide(III) ions

The proton and metal complex equilibria of trans-cyclohexane-1,2-diamine-N,N,N',N'-tetrakis(methylenephosphonic acid) (CDTP) with lanthanide(iii) ions, where Ln(III) = La(III), Nd(III), Sm(III), Eu(III), Gd(III), Tb(III), Ho(III) and Lu(III) were studied. The stoichiometry, protonation and complex formation constants were determined by potentiometric titration at 25.0 degrees C and ionic strength of 0.1 mol dm(-3) (KCl). All metal ions form several species: [LnH4L]-, [LnH3L](2-), [LnH2L](3-), [LnHL](4-), [LnL](5-), [LnH(-1)L](6-) and [LnH(-2)L](7-) in the pH range between 2 and 11. The stability constants log beta(LnL) were found to be between 14.7 and 16.7. The studied complexes were also characterized by spectroscopic methods (31P NMR, UV-Vis absorption and emission spectroscopy). These studies allowed to reveal a distinct structural change of the Ln(III)-CDTP complex which occurs between protonated and hydroxy species in solutions at pH around 7.5. The major change is caused by the involvement of both nitrogen donors in the metal ion coordination occurring in ML species. The data obtained from UV-Vis spectroscopy allowed to draw conclusions about complex symmetry and to estimate a number of coordinated water molecules. The hydration number or more precisely the number of two OH oscillators was found to be approximately one in all species formed over the pH range between 5 and 10. The structure of the major hydroxy complex was supported by X-ray crystallographic data. The crystal structures of the Eu(III) and Tb(III) complexes clearly show that the CDTP ligand is coordinated to the Ln(III) ion by two nitrogen and four oxygen atoms in such a way that only one oxygen atom from each phosphonic group is placed in the lanthanide inner sphere. The monomeric complex anion is connected to a symmetry related ion through short hydrogen bonds formed by two hydroxy ions and one water molecule. In this way the two neighbouring anions form a quasi-dimer in which one of the Ln(III) ion is seven-coordinate (two N atoms, four O atoms and one hydroxy ion) and the other is eight-coordinate (two N atoms, four O atoms, one hydroxy ion and one water molecule).     

Bubbling in unbounded coflowing liquids

An investigation of the stability of low density and viscosity fluid jets and spouts in unbounded coflowing liquids is presented. A full parametrical analysis from low to high Weber and Reynolds numbers shows that the presence of any fluid of finite density and viscosity inside the hollow jet elicits a transition from an absolute to a convective instability at a finite value of the Weber number, for any value of the Reynolds number. Below that critical value of the Weber number, the absolute character of the instability leads to local breakup, and consequently to local bubbling. Experimental data support our model.     

Unified description of nonclassical uniaxial ferroelectric materials in order–disorder phase transitions

An equation of state accounting for coupling of the primary order parameter (here the polarization) with a secondary order parameter (here a strain ?) is used to describe the temperature dependences of the spontaneous polarization and of the electric susceptibility on external biasing field. A new scaling invariant and its explicit expression are given. The theory is exemplified by the effective critical behavior of the molecular ferroelectric crystals (CH₃NH₃)₅Bi₂Cl₁₁ (MAPCB) and (CH₃NH₃)₅Bi₂Br₁₁ (MAPBB).     

Continuous-wave far-infrared ESR spectrometer for high-pressure measurements

We present a newly-developed microwave probe for performing sensitive high-field/multi-frequency electron spin resonance (ESR) measurements under high hydrostatic pressures. The system consists of a BeCu-made pressure-resistant vessel, which accommodates the investigated sample and a diamond microwave coupling window. The probe’s interior is completely filled with a pressure-transmitting fluid. The setup operates in reflection mode and can easily be assembled with a standard oversized microwave circuitry. The probe-head withstands hydrostatic pressures up to 1.6 GPa and interfaces with our home-built quasi-optical high-field ESR facility, operating in a millimeter/submillimeter frequency range of 105–420 GHz and in magnetic fields up to 16 T. The overall performance of the probe was tested, while studying the pressure-induced changes in the spin-relaxation mechanisms of a quasi-1D conducting polymer, KC₆₀. The preliminary measurements revealed that the probe yields similar signal-to-noise ratio to that of commercially available low-frequency ESR spectrometers. Moreover, by observing the conduction electron spin resonance (CESR) linewidth broadening for KC₆₀ in an unprecedented microwave frequency range of 210–420 GHz and in the pressure range of up to 1.6 GPa, we demonstrate that a combination of high-pressure ESR probe and high-field/multi-frequency spectrometer allows us to measure the spin relaxation rates in conducting spin systems, like the quasi-1D conductor, KC₆₀.     

Primordial <Superscript>4</Superscript>He Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value

We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial ⁴He abundance (Y _P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial ⁴He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v ₀ denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .     

Transient adaptivity applied to two-phase incompressible flows

An anisotropic adaptation process is applied to a three-dimensional incompressible two-phase flow solver. The solver uses a level set/finite element method on unstructured tetrahedral meshes. We show how the level set function can be used to build an anisotropic mesh with good properties. Some computations with a strong transient character and large densities ratios (1/1000) are presented. We show that the efficiency of the computations can be deeply enhanced by mesh adaptations.     

Narrow-band multiresonant plasmon nanostructure for the coherent control of light: an optical analog of the xylophone

We demonstrate that it is possible to combine several small metallic particles in a very compact geometry without loss of their individual modal properties by adding a gold metallic film underneath. This film essentially acts as a "ground plane" which channels the optical field of each particle and decreases the interparticle coupling. The localization of the electric field can then be controlled temporally by illuminating the chain with a chirped pulse. The sign of the chirp controls the excitation sequence of the particles with great flexibility.