A unilateral contact problem with the heavy elastica

A heavy inextensible elastic beam of infinite length and lying on a rigid foundation, is loaded by a concentrated force directed opposite to the gravity field. As a result a region of non-contact develops. This contact problem, in which finite deflections are considered, leads to a free boundary value problem for a system of non-linear ordinary differential equations. This system is discretized by means of finite-differences, and a Newton-Raphson method is applied to solve the nonlinear equations. In this type of problems the matrix has not a band structure and this hampers the use of available fast numerical procedures. However, through the use of an artificial devise this difficulty could be circumvented. Numerical results are given and their accuracy is discussed, in particular for large values of the external force.     

CaO as Drop‐In Colloidal Catalysts for the Synthesis of Higher Polyglycerols

Glycerol is an attractive renewable building block for the synthesis of polyglycerols, which find application in the cosmetic and pharmaceutical industries. The selective etherification of glycerol to higher oligomers was studied in the presence of CaO colloids and the data are compared with those obtained from NaOH and CaO. The materials were prepared by dispersing CaO, CaCO₃, or Ca(OH)₂ onto a carbon nanofiber (CNF) support. Colloidal nanoparticles were subsequently dispensed from the CNF into the reaction mixture to give CaO colloids that have a higher activity than equimolar amounts of bulk CaO and NaOH. Optimization of the reaction conditions allowed us to obtain a product with Gardner color number <2, containing no acrolein and minimal cyclic byproducts. The differences in the CaO colloids originating from CNF and bulk CaO were probed using light scattering and conductivity measurements. The results confirmed that the higher activity of the colloids originating from CaO/CNF was due to their more rapid formation and smaller size compared with colloids from bulk CaO. We thus have developed a practical method for the synthesis of polyglycerols containing low amounts of Ca.     

COMPUTATIONAL FLUID DYNAMICS FOR DENSE GAS-SOLID FLUIDIZED BEDS: A MULTI-SCALE MODELING STRATEGY

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissipative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1 ) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow,and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

Die Ultramikroskopie der Asphalte und verwandter Produkte

Zusammenfassung Frühere ultramikroskopische Untersuchungen über Asphalt- und Steinkohlenteerl?sungen wurden wiederholt und erweitert, wobei L?sungen bestimmter Konzentration genommen wurden. Die Resultate sind wesentlich dieselben wie früher. Die Behauptung anderer Forscher, da? L?sungen künstlicher Asphalte keine Ultramikronen zeigen, ist unzutreffend. Nur hat sich herausgestellt, da? die natürlichen Asphalte in st?rkerer Verdünnung ein besseres Bild zeigen als die künstlichen. Eine Mischung eines künstlichen Asphaltes mit feinen anorganischen Pulvern gibt dasselbe ultramikroskopische Bild wie natürliche Asphalte. Mit Ru? gemischt geben Asphaltl?sungen das ultramikroskopische und mikroskopische Bild einer Steinkohlenteerl?sung in Nitrobenzol, Anilin usw.     

Sharing costs in highways: A game theoretic approach

This paper introduces a new class of games, highway games, which arise from situations where there is a common resource that agents will jointly use. That resource is an ordered set of several indivisible sections, where each section has an associated fixed cost and each agent requires some consecutive sections. We present an easy formula to calculate the Shapley value, and we present an efficient procedure to calculate the nucleolus for this class of games.     

Ultrafast tilting of the dispersion of a photonic crystal and adiabatic spectral compression of light pulses

We demonstrate, by theory and experiment, the ultrafast tilting of the dispersion curve of a photonic-crystal waveguide following the absorption of a femtosecond pump pulse. By shaping the pump-beam cross section with a nanometric shadow mask, different waveguide eigenmodes acquire different spatial overlap with the perturbing pump, leading to a local flattening of the dispersion by up to 11%. We find that such partial mode perturbation can be used to adiabatically compress the spectrum of a light pulse traveling through the waveguide.     

Plasmon scattering from single subwavelength holes

We map the complex electric fields associated with the scattering of surface plasmon polaritons by single subwavelength holes of different sizes in thick gold films. We identify and quantify the different modes associated with this event, including a radial surface wave with an angularly isotropic amplitude. This wave is shown to arise from the out-of-plane electric dipole induced in the hole, and we quantify the corresponding polarizability, which is in excellent agreement with electromagnetic theory. Time-resolved measurements reveal a time delay of 38±18 fs between the surface plasmon polariton and the radial wave, which we attribute to the interaction with a broad hole resonance.     

Minimum cost forest games

In this paper we consider a generalization of the minimum cost spanning tree game. The generalized model allows for more than one supplier, where each supplier offers a different type of service to the customers and each customer specifies a non-empty subset of these suppliers to which he wishes to be connected. We show that the core of such a game may be empty, but that it is always non-empty if there is at least one customer who wants to be connected to all suppliers. Furthermore, the core is always non-empty if there are at most two suppliers.     

A molecular-beam investigation of the scattering,adsorption and absorption of H2 and D2 from/on/in Pd(111)

H₂ and D₂ are scattered from clean Pd(111) and a saturated chemisorption layer in a highly specular distribution. Evidence for an ordering of the adiayer with increasing coverage is seen. The hydrogen-deuterium exchange occurs via a Langmuir-Hinshelwood mechanism, and the temperature dependence of the rate of HD production can be understood without assuming an activation energy for equilibration. Lock-in and wave-form analyses of scattered H₂ + D₂ mixed beams show that equilibrium between adsorbed hydrogen and deuterium and that dissolved just below the surface is reached rapidly at temperatures above 300 K.     

Jump to contact and neck formation between Pb surfaces and a STM tip

We present a study of the interaction of a W STM tip and the (110) and (111) surfaces of Pb. Atomic resolution has been obtained at room temperature on Pb(110) and up to 330 K on Pb(111). At higher temperatures the surfaces can jump to mechanical contact with the STM tip, resulting in the formation of a connecting neck of Pb between tip and surface. As the tip is retracted, the neck elongates and finally breaks. The dependence of the maximum neck size on the temperature and the tip retraction speed indicates that surface diffusion is responsible for the neck build-up. When the surface is partially oxidized the maximum neck size is reduced. We derive a scaling relation between the maximum neck size, the retraction speed and the surface diffusion coefficient. With this relation and the temperature dependence of the maximum neck size we obtain activation energies for the neck build-up of 1.3 and 0.9 eV respectively for necks on Pb(110) and Pb(111). When a neck breaks, either a crater or a hillock is left on the surface.