Numerical study of multilayer adsorption on fractal surfaces

We report a numerical study of van der Waals adsoprtion and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distributin of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to crossover effects, consistent with the findings of recent experiments. The effects of pore coupling and curvature dependent surface tension were also studied.Comment: 11 pages, 3 figure

Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric

In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy--momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.Comment: added publication informatio

He Scattering from Random Adsorbates, Disordered Compact Islands and Fractal Submonolayers: Intensity Manifestations of Surface Disorder

A theoretical study is made on He scattering from three fundamental classes of disordered ad-layers: (a) Translationally random adsorbates, (b) disordered compact islands and (c) fractal submonolayers. The implications of the results to experimental studies of He scattering from disordered surfaces are discussed, and a combined experimental-theoretical study is made for Ag submonolayers on Pt(111). Some of the main theoretical findings are: (1) Structural aspects of the calculated intensities from translationally random clusters were found to be strongly correlated with those of individual clusters. (2) Low intensity Bragg interference peaks appear even for scattering from very small ad-islands, and contain information on the ad-island local electron structure. (3) For fractal islands, just as for islands with a different structure, the off-specular intensity depends on the parameters of the He/Ag interaction, and does not follow a universal power law as previously proposed in the literature. In the experimental-theoretical study of Ag on Pt(111), we use first experimental He scattering data from low-coverage (single adsorbate) systems to determine an empirical He/Ag-Pt potential of good quality. Then, we carry out He scattering calculations for high coverage and compare with experiments. The conclusions are that the actual experimental phase corresponds to small compact Ag clusters of narrow size distribution, translationally disordered on the surface.Comment: 36 double-spaced pages, 10 figures; accepted by J. Chem. Phys., scheduled to appear March 8. More info available at http://www.fh.huji.ac.il/~dani

First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short range substrate forces or in strong fluctuation regimes, wetting of a self-affine rough wall in 2D turns first-order as soon as the wall roughness exponent exceeds the anisotropy index of bulk interface fluctuations. Different thresholds apply with long range forces in mean field regimes. For bond-disordered bulk, fixed point stability suggests similar results, which ultimately rely on basic properties of quantum bound states with asymptotically power-law repulsive potentials.Comment: 11 pages, 1 figur

A Theory of Cheap Control in Embodied Systems

We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments show that the sufficient controller complexity predicted by our theory is tight, which means that the theory has direct practical implications. Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machineComment: 27 pages, 10 figure

Innovative marketing. The concept and function

This article is theoretical in nature. Any development of innovation begins with the development of creative ideas that will is the starting point for innovation Innovative marketing is aimed at the efficient introduction of these new ideas

Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field and a negligibly reflecting dielectric. The Gordon momentum is easily identified as the total momentum by the fact that it is, by virtue of being invariant in time, conserved. We construct continuity equations for the energy and the Gordon momentum and use the continuity equations to construct an array that has the properties of a traceless, diagonally symmetric energy-momentum tensor. Then the century-old Abraham-Minkowski momentum controversy can be viewed as a consequence of attempting to construct an energy-momentum tensor from continuity equations that contain densities that correspond to nonconserved quantities.Comment: added publication informatio