Global branches of periodic solutions for forced delay differential equations on compact manifolds

We prove a global bifurcation result for T-periodic solutions of the T-periodic delay differential equation x^′(t)=λf(t,x(t),x(t−1)) depending on a real parameter λ?0. The approach is based on the fixed point index theory for maps on ANRs.     

Thermodynamic Limit for Spin Glasses. Beyond the Annealed Bound

Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for finite-dimensional spin glasses, without the assumption of the annealed bound. Using this method we can weaken the hypotheses for this result beyond what exists in the literature.     

Double-peak droplet mass distribution observed during sub-ps laser ablation of Si targets

The angular distribution of the ablated material was studied during sub-ps Si laser ablation deposition using a special hemicylindrical substrate holder and different laser fluences ranging between 0.4 and 1.7 J/cm². Scanning electron microscopy analysis of the deposited films showed that, independent of the fluence, the distribution of the deposited droplets presents two maxima. The first maximum corresponds to the average plume deflection angle value due to the local surface orientation produced by the preferential etching process. The second maximum is observed approximately at 45° with respect to the normal of the target surface, and is related to the phase explosion products that expand along the incident laser beam direction. The investigation of the twofold distribution of the sub-μm size deposited droplets is important to improve the quality of the deposited coatings. PACS 81.15.Fg; 68.55.Jk; 79.20.Ds     

A new analytical model for the elastic–plastic behaviour of spot welded joints subjected to orthogonal load

An analytical procedure for the evaluation of the elastic–plastic stiffness behaviour of spot welded joints is presented. The procedure is based on a new model of spot weld region: a circular plate having variable thickness with a central rigid nugget, which is resolved using an original analytical method.The closed-form solution allows to describe the displacement of a rigid nugget when an axial orthogonal load is applied on the plate while plasticity and large deflections are present. The goal is to reach a reliable spot weld region model which can be used as the basis to develop a spot weld element in FE analysis even when plasticity and large deflections are in effect.The procedure is as completely original as no other can be found in the technical literature, and it has been applied to some examples of plates usually employed for spot weld analysis. The analytical results obtained by using the new general relations precisely match those obtained modelling spot weld area by FEA.     

Rotational Raman scattering dependence on pump polarization

The influence of the ellipticity degree of the pump radiation polarization on threshold energies and energy conversion efficiencies of stimulated rotational Raman scattering (SRRS) are investigated in H₂ with a XeCl excimer laser, by using different focusing geometries. For the first time, it is shown that the dependence of SRRS on pump radiation polarization is also affected by the focusing geometry, i.e. whether low- or high-angle focusing is applied. The experimentally determined threshold energies as a function of the pump radiation polarization are in accordance with theory mainly at high-angle focusing geometries. It is also shown for the first time that gain suppression effects on vibrational Raman scattering have to be considered in understanding the experimental results. Received: 5 January 1999 / Final version: 10 September 1999 / Published online: 8 March 2000     

Hydrogenation of arenes over silica-supported catalysts that combine a grafted rhodium complex and palladium nanoparticles: evidence for substrate activation on Rh(single-site)-Pd(metal) moieties

The complex Rh(cod)(sulfos) (Rh(I); sulfos = (-)O(3)S(C(6)H(4))CH(2)C(CH(2)PPh(2))(3); cod = cycloocta-1,5-diene), either free or supported on silica, does not catalyze the hydrogenation of benzene in either homogeneous or heterogeneous phase. However, when silica contains supported Pd metal nanoparticles (Pd(0)/SiO(2)), a hybrid catalyst (Rh(I)-Pd(0)/SiO(2)) is formed that hydrogenates benzene 4 times faster than does Pd(0)/SiO(2) alone. EXAFS and DRIFT measurements of in situ and ex situ prepared samples, batch catalytic reactions under different conditions, deuterium labeling experiments, and model organometallic studies, taken together, have shown that the rhodium single sites and the palladium nanoparticles cooperate with each other in promoting the hydrogenation of benzene through the formation of a unique entity throughout the catalytic cycle. Besides decreasing the extent of cyclohexa-1,3-diene disproportionation at palladium, the combined action of the two metals activates the arene so as to allow the rhodium sites to enter the catalytic cycle and speed up the overall hydrogenation process by rapidly reducing benzene to cyclohexa-1,3-diene.     

Luminescent hydrido-carbonyl clusters of rhenium containing bridging 1,2-diazine ligands

The reaction of the electronically unsaturated (56 valence electrons, ve) tetrahedral cluster [Re4(mu3-H)4(CO)12] (1) with pyridazine (pydz) gives as the main initial product the tetranuclear cluster [Re4(mu-H)4(mu-pydz)(pydz)2(CO)12] (2a), with 64 ve and four hydrogen-bridged metal-metal interactions, with a spiked-triangle geometry. One of the three pydz ligands bridges, in a cis configuration, the cluster edge opposite to the vertex bearing the spike, as indicated by the X-ray single-crystal analysis. This species slowly decomposes, affording the dinuclear unsaturated (32 ve) complex [Re2(mu-H)2(mu-pydz)(CO)6] (3a) and two isomers of the tetranuclear cluster [Re4(mu-H)4(mu-pydz)2(CO)12] (64 ve), sharing an unusual square cluster geometry and differing in the trans (major, 85%, 4a) or cis (4a') configuration of the bridging pydz ligands. The structures of 3a and 4a have been ascertained by X-ray analysis, while the characterization of 4a' was hampered by its instability (slowly transforming into 3a in THF solution). Both the dimer and the square cluster 4a are also formed directly (and quickly) from 1, being present in solution since the beginning of the reaction. Cluster 4a is the main final reaction product. The reaction with phthalazine follows a similar course, with some differences in the relative amount of the final products 3b and 4b. Most of the novel complexes are able to emit light in solution at room temperature, and photophysical measurements were performed in CH2Cl2 solution on the main stable reaction products (i.e., the dinuclear species 3a and 3b and the trans square clusters 4a and 4b). The emission was in the range of 580-645 nm, from MLCT excited states, with lifetimes on the order of a hundred nanoseconds (50-473 ns). The quantum yields were 1 order of magnitude higher for the squares (1.7 and 1.3% for 4a and 4b, respectively, in CH2Cl2) than for the dinuclear complexes ( approximately 0.1%). In the case of 4a, a blue shift and an increase of the emission intensity were observed upon decreasing the solvent polarity.     

Time Scales in Polymer Modified Asphalts

Historically, Maxwell was probably the first one who recognized the importance of time scales for understanding the mechanical response of asphalt. In instantaneous response asphalt behaves as an elastic, solid-like material, on the other hand its long time response is that of a viscous, fluid-like material. In the linear viscoelastic region asphalt behaves as a low molecular weight polymer. However, in the nonlinear region of high strains or rates of strain the behavior of some asphaltic systems can be rather complicated. In asphalts, asphaltenes, resins and alkanes compose a complex colloidal system, in which alkanes act as a solvent, asphaltenes as micelles and the polar resins as stabilizers. In order to enhance the mechanical properties of asphalts they are frequently modified by blending them with appropriate polymers. Changes in the impermanent network that can be formed in some of these blends can lead to an unexpected behavior of the steady shear viscosity function. Several different time scales emerge from this behavior. A possible relation of these “nonlinear” time scales to the linear viscoelastic time scales is discussed and examples of anomalous behavior of polymer-modified asphalts are given.