On the Controllability of the Hydrostatic Stokes Equations

This paper is devoted to present some results on the controllability of the hydrostatic Stokes equations. The first main result of this paper states that the approximate null controllability of this system holds. This is proved whatever the boundary conditions are. Then, we extend this result to an exact null controllability result when the boundary conditions are ∂ _z u = 0 (the vertical derivative of the horizontal velocity) at the bottom.      

Chemically deposited copper oxide thin films: structural, optical and electrical characteristics

Thin films of copper oxide with thickness ranging from 0.05–0.45 μm were deposited on microscope glass slides by successively dipping them for 20 s each in a solution of 1 M NaOH and then in a solution of copper complex. Temperature of the NaOH solution was varied from 50–90°C, while that of the copper solution was maintained at room temperature. X-ray diffraction patterns showed that the films, as prepared, are of cuprite structure with composition Cu₂O. Annealing the films in air at 350°C converts these films to CuO. This conversion is accompanied by a shift in the optical band gap from 2.1 eV (direct) to 1.75 eV (direct). The films show p-type conductivity, 5×10⁻⁴ Ω⁻¹ cm⁻¹ for a film of thickness 0.15 μm. Electrical conductivity of this film increases by a factor of 3 when illuminated with 1 kW m⁻² tungsten halogen radiation. Annealing in a nitrogen atmosphere at temperatures up to 400°C does not change the composition of the films. However, the conductivity in the dark as well as the photoconductivity of the film increases by an order of magnitude. The electrical conductivity of the CuO thin films produced by air annealing at 400°C, is high, 7×10⁻³ Ω⁻¹ cm⁻¹. These films are also photoconductive.     

Imino‐Bridged Bisphosphaalkenes (2,4‐Diphospha‐3‐azapentadienes)

Deprotonation of aminophosphaalkenes (RMe₂Si)₂C?PN(H)(R′) (R=Me, iPr; R′=tBu, 1‐adamantyl (1‐Ada), 2,4,6‐tBu₃C₆H₂ (Mes*)) followed by reactions of the corresponding Li salts Li[(RMe₂Si)₂C?P(M)(R′)] with one equivalent of the corresponding P‐chlorophosphaalkenes (RMe₂Si)₂C?PCl provides bisphosphaalkenes (2,4‐diphospha‐3‐azapentadienes) [(RMe₂Si)₂C?P]₂NR′. The thermally unstable tert‐butyliminobisphosphaalkene [(Me₃Si)₂C?P]₂NtBu ( 4 a ) undergoes isomerisation reactions by Me₃Si‐group migration that lead to mixtures of four‐membered heterocyles, but in the presence of an excess amount of (Me₃Si)₂C?PCl, 4 a furnishes an azatriphosphabicyclohexene C₃(SiMe₃)₅P₃NtBu ( 5 ) that gave red single crystals. Compound 5 contains a diphosphirane ring condensed with an azatriphospholene system that exhibits an endocylic P?C double bond and an exocyclic ylidic P⁽⁺⁾? C^(?)(SiMe₃)₂ unit. Using the bulkier iPrMe₂Si substituents at three‐coordinated carbon leads to slightly enhanced thermal stability of 2,4‐diphospha‐3‐azapentadienes [(iPrMe₂Si)₂C?P]₂NR′ (R′=tBu: 4 b ; R′=1‐Ada: 8 ). According to a low‐temperature crystal‐structure determination, 8 adopts a non‐planar structure with two distinctly differently oriented P?C sites, but ³¹P NMR spectra in solution exhibit singlet signals. ³¹P NMR spectra also reveal that bulky Mes* groups (Mes*=2,4,6‐tBu₃C₆H₂) at the central imino function lead to mixtures of symmetric and unsymmetric rotamers, thus implying hindered rotation around the P? N bonds in persistent compounds [(RMe₂Si)₂C?P]₂NMes* ( 11 a , 11 b ). DFT calculations for the parent molecule [(H₃Si)₂C?P]₂NCH₃ suggest that the non‐planar distortion of compound 8 will have steric grounds.     

Quantitative study of hydration of C<Subscript>3</Subscript>S and C<Subscript>2</Subscript>S by thermal analysis

This research is part of a European project (namely, CODICE project), main objective of which is modelling, at a multi-scale, the evolution of the mechanical performance of non-degraded and degraded cementitious matrices. For that, a series of experiments were planned with pure synthetic tri-calcium silicate (C₃S) and bi-calcium silicate (C₂S) (main components of the Portland cement clinker) to obtain different calcium–silicate–hydrate (C–S–H) gel structures during their hydration. The characterization of those C–S–H gels and matrices will provide experimental parameters for the validation of the multi-scale modelling scheme proposed. In this article, a quantitative method, based on thermal analyses, has been used for the determination of the chemical composition of the C–S–H gel together with the degree of hydration and quantitative evolution of all the components of the pastes. Besides, the microstructure and type of silicate tetrahedron and mean chain length (MCL) were studied by scanning electron microscopy (SEM) and ²⁹Si magic-angle-spinning (MAS) NMR, respectively. The main results showed that the chemical compositions for the C–S–H gels have a CaO/SiO₂ M ratio almost constant of 1.7 for both C₃S and C₂S compounds. Small differences were found in the gel water content: the H₂O/SiO₂ M ratio ranged from 2.9 ± 0.2 to 2.6 ± 0.2 for the C₃S (decrease) and from 2.4 ± 0.2 to 3.2 ± 0.2 for the C₂S (increase). The MCL values of the C–S–H gels, determined from ²⁹Si MAS NMR, were 3.5 and 4 silicate tetrahedron, for the hydrated C₃S and C₂S, respectively, remaining almost constant at all hydration periods.     

Uniform null controllability of a linear KdV equation using two controls

In this paper we consider a linear KdV equation posed on a bounded interval. We study the behavior of the cost of null controllability when two boundary controls are employed. By means of suitable Carleman inequalities and a new exponential dissipation estimate, we prove that uniform null controllability with respect to the dispersion coefficient holds, contrary to the case when one control is used at the left end-point of the interval.     

Recent progress on nanovehicles

Nanovehicles are a new class of molecular machines consisting of a molecular scale chassis, axles, and wheels, that can roll across solid surfaces with structurally defined directions making them of interest to synthetic chemists, surface scientists, chemical engineers, and the general car enthusiast. In this tutorial review, following a brief introduction to the development of nanomachines, our recent progress on the nanovehicle project is presented including the design, synthesis, and testing of a series of nanocars, nanotrucks, and motorized nanocars.     

Updating preconditioners for modified least squares problems

In this paper, we analyze how to update incomplete Cholesky preconditioners to solve least squares problems using iterative methods when the set of linear relations is updated with some new information, a new variable is added or, contrarily, some information or variable is removed from the set. Our proposed method computes a low-rank update of the preconditioner using a bordering method which is inexpensive compared with the cost of computing a new preconditioner. Moreover, the numerical experiments presented show that this strategy gives, in many cases, a better preconditioner than other choices, including the computation of a new preconditioner from scratch or reusing an existing one.     

Fluorescent Pyrene‐Based Bis‐azole Compounds: Synthesis and Photophysical Analysis

A rational synthetic procedure for the preparation of a series of pyrene‐based neutral and dicationic bis‐azole compounds is reported. The method allows the tailored design of pyrene‐based azoles with different substituents at the nitrogen atoms of the heterocycles, for which the relative conformation of the resulting bis‐azoles can be easily controlled. The bis‐azoliums were used for the preparation of the related diplatinum complexes by reaction with [{Pt(ppy)(μ‐Cl)₂}₂] (ppy=2‐phenylpyridinate). The X‐ray molecular structure of one of the resulting compounds, a diplatinum(II) bis(N‐heterocyclic carbene) complex, is described. Studies on the photophysical properties of all new species are described. The emission of the bis‐azole‐based compounds seems to be independent of their substitution patterns, which basically indicates that physical properties such as solubility, melting point, and viscosity can be fine‐tuned while maintaining the luminescence properties. Finally, the energies associated with the HOMO and LUMO levels suggest that this family provides versatility to match the energy levels of a wide range of host materials, which is important for the preparation of organic light‐emitting devices.     

Dissociation of energy selected Sn(CH3)4(+), Sn(CH3)3Cl+, and Sn(CH3)3Br+ ions: evidence for isolated excited state dynamics

The dissociation dynamics of Sn(CH(3))(4)(+), Sn(CH(3))(3)Cl(+), and Sn(CH(3))(3)Br(+) were investigated by threshold photoelectron photoion spectrometry using an electron imaging apparatus (iPEPICO) at the Swiss Light Source. The tetramethyltin ion was found to dissociate via Sn(CH(3))(4)(+) → Sn(CH(3))(3)(+) + CH(3) → Sn(CH(3))(2)(+) + 2CH(3), while the trimethyltin halide ions dissociated via methyl loss at low energies, and a competitive halogen loss at somewhat higher energies. The 0 K methyl loss onset for the three ions was found to be 9.410 ± 0.020 eV, 10.058 ± 0.020 eV, and 9.961 ± 0.020 eV, respectively. Statistical theory could not reproduce the observed onsets for the halogen loss steps in the halotrimethyltin ions. The halide loss signal as a function energy mimicked the excited state threshold photoelectron spectrum, from which we conclude that the halide loss from these ions takes place on an isolated excited state potential energy surface, which we describe by time dependent density functional calculations. The sequential loss of a second methyl group in the Sn(CH(3))(4)(+) ion, observed at about 3 eV higher energies than the first one, is also partially non-statistical. The derived product energy distribution resulting from the loss of the first methyl group is two-component with about 50% being statistical and the remainder associated with high translational energy products that peak at 2 eV. Time dependent DFT calculations show that a dissociative ?B state lies in the vicinity of the experimental measurements. We thus propose that 50% of the Sn(CH(3))(4)(+) ions produced in this energy range internally convert to the ?X state, on which they dissociate statistically, while the remainder dissociate directly from the repulsive ?B state leading to high kinetic energy products.