The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions

We consider nonholonomic systems with linear, time-independent constraints subject to positional conservative active forces. We identify a distribution on the configuration manifold, that we call the reaction-annihilator distribution ℜ°, the fibers of which are the annihilators of the set of all values taken by the reaction forces on the fibers of the constraint distribution. We show that this distribution, which can be effectively computed in specific cases, plays a central role in the study of first integrals linear in the velocities of this class of nonholonomic systems. In particular we prove that, if the Lagrangian is invariant under (the lift of) a group action in the configuration manifold, then an infinitesimal generator of this action has a conserved momentum if and only if it is a section of the distribution ℜ°. Since the fibers of ℜ° contain those of the constraint distribution, this version of the nonholonomic Noether theorem accounts for more conserved momenta than what was known so far. Some examples are given.      

Ab initio and DFT Study on 2H-Isoxazol-5-one: Consequences of Strong Intermolecular Hydrogen-Bond Formation in Supramolecular Structures

Ab initio and density-functional-theory (DFT) calculations on 2H-isoxazol-5-one (A), its linear dimer (LD), cyclic dimer (CD), and cyclic trimer (CT), have been performed with several basis sets in the gas phase, including electron correlation by second-order Møller-Plesset perturbation theory. The calculated complexation energy for the intermolecular H-bonded trimer as well as the corresponding geometric changes are in good agreement with the notion of resonance-assisted intermolecular H-bond formation. Bond distances and angles of the optimized geometry of CT are in accordance with the X-ray-diffraction data found on a trimeric supramolecular complex of parent compound 4-(2-methoxybenzyl)-3-phenyl-4H-isoxazol-5-one. Ab initio and DFT geometry optimizations are also reproducing exactly the large asymmetry in bond angles around the CO group that is systematically present in all literature available X-ray data for analogous heterocyclic penta-atomic compounds.     

Thermo-elastic solutions for multilayered wide plates and beams with interfacial imperfections through the transfer matrix method

A matrix technique is formulated to efficiently solve stationary two-dimensional thermo-elasticity problems in simply supported multilayered beams and plates with an arbitrary number of layers which may be in imperfect mechanical and thermal contact. The method uses local transfer matrices and continuity conditions at the layer interfaces to establish explicit relationships between the unknown integration constants in the solution of a generic layer and those of the first layer. Explicit expressions are then derived for temperature, displacements and stresses through the imposition of the boundary conditions at the top and bottom surfaces of the plate. The dimensionless expressions allow to easily generate exact solutions, also for plates with many layers and interfacial thermal and mechanical imperfections. The solutions can be used for parametric analyses, to investigate the influence of the inhomogeneous material structure and interfacial imperfections on local fields or to verify the accuracy of approximate theories and numerical models.     

Numerical stability analysis of submerged slopes subject to rapid sedimentation processes

In this paper, the stability of infinitely long submerged slopes subject to rapid sedimentation processes is theoretically/numerically investigated. In particular, rapid deposition is considered as a potential triggering factor for static liquefaction in inclined loose sand layers. The corresponding initial boundary value problem is numerically analysed by employing a one-dimensional finite difference scheme in conjunction with two distinct versions of the same constitutive model—elasto-plastic and elasto-viscoplastic (EV). The EV approach is shown to be the most suitable for describing the onset of liquefaction phenomena, since its mathematical well-posedness and numerical stability are never lost. The results of parametric analyses for both homogeneous and inhomogeneous strata are critically discussed in the light of some case history data concerning natural and anthropic sedimentation processes.     

φ production in In–In collisions at 158 A GeV

The NA60 experiment has measured muon pair production in In–In collisions at 158 AGeV at the CERN SPS. This paper presents a high statistics measurement of φ→μ μ meson production. Differential spectra, yields, mass and width are measured as a function of centrality and compared to previous measurements in other colliding systems at the same energy. The width of the rapidity distribution is found to be constant as a function of centrality, compatible with previous results. The decay muon polar angle distribution is measured in several reference frames. No evidence of polarization is found as a function of transverse momentum and centrality. The analysis of the p _T spectra shows that the φ has a small radial flow, implying a weak coupling to the medium. The T _eff parameter measured in In–In collisions suggests that the high value observed in Pb–Pb in the kaon channel is difficult to reconcile with radial flow alone. The absolute yield is compared to results in Pb–Pb collisions: though significantly smaller than measured by NA50 in the muon channel, it is found to exceed the NA49 and CERES data in the kaon channel at any centrality. The mass and width are found to be compatible with the PDG values at any centrality and at any p _T : no evidence for in-medium modifications is observed.     

Features of electrical discharges in air triggered by laser

A numerical study of laser-triggered discharges in air at atmospheric pressure is presented for an ultraviolet laser in small gaps. Two models, one for the ionization of the air by the laser pulse and the second for the streamer evolution have been computed. From results of numerical simulations the influence of the laser parameters such as energy, pulse duration and beam radius is analyzed and electron distributions are obtained for different small gaps. Electric field, streamer velocity and evolution of the ionized volume are calculated by means of streamer simulations. This paper shows the main features of the laser-triggered discharges and also the importance of using numerical simulations in a laser-triggered experiment.     

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.     

Alkanethiols on platinum: multicomponent self-assembled monolayers

We have studied the formation of self-assembled monolayers (SAMs) of n-alkanethiols on platinum thin films using X-ray photoelectron spectroscopy (XPS), reflection-absorption infrared spectroscopy (RAIRS), spectroscopic ellipsometry (SE), and contact angle (CA) measurements. Specifically, SAMs of 1-hexanethiol, 1-dodecanethiol, and 1-octadecanethiol were grown on polycrystalline Pt films, and the effects of Pt surface preparation, deposition conditions, and solvent treatments on the initial quality and stability of the monolayer in air were investigated. The SAMs prepared under ambient conditions on piranha-cleaned and UV/ozone-cleaned substrates were compared to monolayers formed on template-stripped Pt in an inert atmosphere. We found that alkanethiols deposited from 1 mM ethanolic solutions on piranha-cleaned Pt formed densely packed monolayers in which alkyl chains were oriented close to the surface normal. Stored in the laboratory ambient, these monolayers were unchanged over about 1 week but were largely oxidized in about 1 month. No evidence was found of molecules being weakly bound within the monolayer or having undergone C-S bond scission; however, three distinct sulfur states were observed for all samples in the XPS of the S 2p region. The lowest- and highest-binding-energy components are assigned to alkylthiolate and partially oxidized alkylthiolate species, respectively. The remaining S 2p component (approximately one-third of the sulfur layer), intermediate in binding energy between the other two components, is attributed to a chemisorbed species with a S binding configuration distinct from the majority alkylthiolate: for example, S bound to Pt bound to O, S with a different Pt coordination number, or S in an adsorbed disulfide.