Cubic Nonlinear Schrödinger Equation on Three Dimensional Balls with Radial Data

We prove wellposedness of the Cauchy problem for the cubic nonlinear Schrödinger equation with Dirichlet boundary conditions and radial data on 3D balls. The main argument is based on a bilinear eigenfunction estimate and the use of X ^{s, b} spaces. The last part presents a first attempt to study the non radial case. We prove bilinear estimates for the linear Schrödinger flow with particular initial data.     

Endurance Tests on a Colloidal Damper Destined to Vehicle Suspension

Endurance tests on a colloidal damper destined to vehicle suspension are performed. Such absorber represents an ecological application of nano-damping; it employs the hysteresis which occurs when water is forced to penetrate and then naturally exudes from a nanoporous silica gel matrix, modified to become liquid-repellent. Damping performances decrease at the increasing of the number of working cycles, partially since the silica gel grains that undergo gradual fatigue fracture are able to escape at the packing used to seal the test chamber, and partially due to the fatigue fracture alone, which is accompanied by an enhancement of the hydrophilic silanol groups on the silica gel surface and a pore size redistribution. In order to augment damper’s life, silica gel is introduced inside of a tank that is separated by a filter from the main cylinder, in which only water is supplied. One discusses the influence of filtration on the colloidal damper performances and the variation of damper’s life versus the ratio of filter pore’s diameter to the mean size of the silica gel particles.     

Chemoselective coupling of sugar oximes and α-ketoacids to glycosyl amides and N-glycopeptides

The reaction of unprotected sugar hydroxylamines and oximes with α-ketoacids leads to the chemoselective formation of glycosyl amides following the decarboxylative condensation pathway of Bode’s ketoacid hydroxylamine (KAHA) ligation. Sugar oximes with gluco configuration stereoselectively form β-linked products. This method can be used for the convergent synthesis of N-acylated sugars and oligosaccharides bearing small labels, spacers, or peptides in the acyl part.     

Acylsilanes in Rhodium(III)‐Catalyzed Directed Aromatic C–H Alkenylations and Siloxycarbene Reactions with C?C Double Bonds

Acylsilanes are known to undergo a 1,2‐silicon‐to‐oxygen migration under thermal or photochemical conditions to form siloxycarbenes. However, there are few reports regarding the application of siloxycarbenes in organic synthesis and surprisingly, their reaction with C C double or triple bonds remains virtually unexplored. To facilitate such a study, previously inaccessible aromatic acylsilanes containing an ortho‐tethered C C double bond were identified as suitable substrates. To access these key intermediates, we developed a new synthetic method utilizing a rhodium‐catalyzed oxidative Heck‐type olefination involving the application of an acylsilane moiety as a directing group. When exposed to visible‐light irradiation, the ortho‐olefinated acylsilanes underwent a smooth intramolecular cyclization process to afford valuable indanone derivatives in quantitative yields. This result paves the way for the development of new transformations involving siloxycarbene intermediates.     

Long-range response to transmission line disturbances in DC electricity grids

We consider a DC electricity grid composed of transmission lines connecting power generators and consumers at its nodes. The DC grid is described by nonlinear equations derived from Kirchhoff's law. For an initial distribution of consumed and generated power, and given transmission line conductances, we determine the geographical distribution of voltages at the nodes. Adjusting the generated power for the Joule heating losses, we then calculate the electrical power flow through the transmission lines. Next, we study the response of the grid to an additional transmission line between two sites of the grid and calculate the resulting change in the power flow distribution. This change is found to decay slowly in space, with a power of the distance from the additional line. We find the geographical distribution of the power transmission, when a link is added. With a finite probability the maximal load in the grid becomes larger when a transmission line is added, a phenomenon that is known as Braess’ paradox. We find that this phenomenon is more pronounced in a DC grid described by the nonlinear equations derived from Kirchhoff's law than in a linearised flow model studied previously in Ref. [1]. We observe furthermore that the increase in the load of the transmission lines due to an added line is of the same order of magnitude as Joule heating. Interestingly, for a fixed system size the load of the lines increases with the degree of disorder in the geographical distribution of consumers and producers.     

Thermal behaviour of some Al(III)-Mg(II) polynuclear coordination compounds with polycarboxylic acid anions as ligands,precursors of aluminates

A TG, DTG and DTA study of three polynuclear coordination compounds,containing Al(III)-Mg(II), namely (NH₄)₄[Al₂Mg(C₄O₅H₄)₄(OH)₄]?2H₂O,(NH₄)₄[MgAl₂(C₄H₄O₆)₄(OH)₄]?3H₂Oand (NH₄)₂[Al₂Mg(C₆O₇H₁₁)₅(OH)₅]?3H₂O,has been reported together with the associated thermal decomposition mechanismrationalized in terms of intermediate products. As decomposition end-product,magnesium-aluminum spinel is obtained. The values of MgAl₂O₄mean crystallite size depend on the anionic ligand contained by the precursorcompound, varying in the order: malate (143 Å) ligand contained by theprecursor compound, varying in the order: malate (143 Å)     

Effect of bromide on the interfacial structure of aqueous tetrabutylammonium iodide: Photoelectron spectroscopy and molecular dynamics simulations

Solvation of surface-active tetrabutylammonium iodide (TBAI) in liquid water and in sodium bromide aqueous solution was investigated by VUV photoelectron spectroscopy and by molecular dynamics simulations. The observed signal intensity changes in the photoemission spectra are consistent with the varying propensities of the different ions for the solution interface. While the cations are surface-bound due to hydrophobic interactions, the anions are driven to the vacuum/solution interface by their large polarizability and size. Iodide is more polarizable, and hence more surface-active than bromide, which explains the relatively small decrease of the iodide photoemission signal when TBAI is dissolved in bromide solution.     

Kinetic of decomposition of some complexes under non-isothermal conditions

Kinetics of thermal decomposition of three structurally similar complexes Co₂Cu(C₂O₄)₃ (R-diam)₂, where R is ethyl, 1,2-propyl or 1,3-propyl, was studied under non-isothermal conditions and nitrogen dynamic atmosphere at heating rates of 5, 7, 10, 12 and 15 K min⁻¹. For data processing the Flynn-Wall-Ozawa and a modified non-parametric kinetic methods were used. By both methods the activation energy are in the range of 97–102 kJ mol⁻¹. The formal kinetic is r=kα(1−α)². Also a compensation effect between lnA and E was evidenced. The kinetic analysis lead to the conclusion of an identic decomposition mechanism by a single step process.