Asymptotics of self-similar solutions to coagulation equations with product kernel

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel $K(\xi,\eta)= (\xi \eta)^{\lambda}$ with $\lambda \in (0,1/2)$. It is known that such self-similar solutions $g(x)$ satisfy that $x^{-1+2\lambda} g(x)$ is bounded above and below as $x \to 0$. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function $h(x)=h_{\lambda} x^{-1+2\lambda} g(x)$ in the limit $\lambda \to 0$. It turns out that $h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)$ as $x \to 0$. As $x$ becomes larger $h$ develops peaks of height $1/\lambda$ that are separated by large regions where $h$ is small. Finally, $h$ converges to zero exponentially fast as $x \to \infty$. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE

Bi-defects of Nematic Surfactant Bilayers

We consider the effects of the coupling between the orientational order of the two monolayers in flat nematic bilayers. We show that the presence of a topological defect on one bilayer generates a nontrivial orientational texture on both monolayers. Therefore, one cannot consider isolated defects on one monolayer, but rather associated pairs of defects on either monolayer, which we call bi-defects. Bi-defects generally produce walls, such that the textures of the two monolayers are identical outside the walls, and different in their interior. We suggest some experimental conditions in which these structures could be observed.Comment: RevTeX, 4 pages, 3 figure

A method addressing signal occlusion by scene objects to quantify the 3D distribution of forest components from terrestrial lidar

SilviLaser 2015, La Grande Motte, FRA, 28-/09/2015 - 30/09/2015International audienceEstimating exact 3D distribution of canopy components using terrestrial lidar in forest is limited by signal occlusion. We propose a method to address this limitation: it uses voxels, beam returns and beam propagation through the scene. The proposed method was validated using simulated forest scenes and a lidar simulator

Energy use for urban water management by utilities and Households in Los Angeles

Reducing energy consumption for urban water management may yield economic and environmental benefits. Few studies provide comprehensive assessments of energy needs for urban water sectors that include both utility operations and household use. Here, we evaluate the energy needs for urban water management in metropolitan Los Angeles (LA) County. Using planning scenarios that include both water conservation and alternative supply options, we estimate energy requirements of water imports, groundwater pumping, distribution in pipes, water and wastewater treatment, and residential water heating across more than one hundred regional water agencies covering over 9 million people. Results show that combining water conservation with alternative local supplies such as stormwater capture and water reuse (nonpotable or indirect potable) can reduce the energy consumption and intensity of water management in LA. Further advanced water treatment for direct potable reuse could increase energy needs. In aggregate, water heating represents a major source of regional energy consumption. The heating factor associated with grid-supplied electricity drives the relative contribution of energy-for-water by utilities and households. For most scenarios of grid operations, energy for household water heating significantly outweighs utility energy consumption. The study demonstrates how publicly available and detailed data for energy and water use supports sustainability planning. The method is applicable to cities everywhere

Transmission electron microscopy investigation of segregation and critical floating-layer content of indium for island formation in InGaAs

We have investigated InGaAs layers grown by molecular-beam epitaxy on GaAs(001) by transmission electron microscopy (TEM) and photoluminescence spectroscopy. InGaAs layers with In-concentrations of 16, 25 and 28 % and respective thicknesses of 20, 22 and 23 monolayers were deposited at 535 C. The parameters were chosen to grow layers slightly above and below the transition between the two- and three-dimensional growth mode. In-concentration profiles were obtained from high-resolution TEM images by composition evaluation by lattice fringe analysis. The measured profiles can be well described applying the segregation model of Muraki et al. [Appl. Phys. Lett. 61 (1992) 557]. Calculated photoluminescence peak positions on the basis of the measured concentration profiles are in good agreement with the experimental ones. Evaluating experimental In-concentration profiles it is found that the transition from the two-dimensional to the three-dimensional growth mode occurs if the indium content in the In-floating layer exceeds 1.1+/-0.2 monolayers. The measured exponential decrease of the In-concentration within the cap layer on top of the islands reveals that the In-floating layer is not consumed during island formation. The segregation efficiency above the islands is increased compared to the quantum wells which is explained tentatively by strain-dependent lattice-site selection of In. In addition, In0.25Ga0.75As quantum wells were grown at different temperatures between 500 oC and 550 oC. The evaluation of concentration profiles shows that the segregation efficiency increases from R=0.65 to R=0.83.Comment: 16 pages, 6 figures, 1 table, sbmitted in Phys. Rev.