Search results for " surface"
showing 10 items of 2838 documents
Symmetry of minimizers with a level surface parallel to the boundary
2015
We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…
Surface homeomorphisms with zero dimensional singular set
1998
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.
Polymer Brushes on Flat and Curved Substrates: Scaling Concepts and Computer Simulations
2007
The scaling concepts for isolated flexible macromolecules in good solvent grafted with one chain end to a flat surface (polymer mushrooms) as well as for layers of many overlapping end-grafted chain molecules (polymer brushes) are introduced. Monte Carlo attempts to test these concepts are briefly reviewed. Then the extension of these concepts to polymer brushes grafted to the interior of a cylinder surface is discussed. Molecular Dynamics results on chain average linear dimensions in the direction normal to the grafting surface and in axial direction are described, as well as distribution functions for the density of end monomers and of all monomers of the chains. It is argued that under t…
Method of Discrimination of Surface Fractality
1993
Abstract A simple method for the discrimination of surface fractality is proposed. This method is based on the comparison of the nitrogen adsorption isotherm on a given sample with the "standard" isotherm on a smooth surface. The proposed comparative method makes it possible to determine the lower limit of the scale range of surface fractality. A thermodynamic method is recommended as a complement to fractal analysis in the scale range of about 10-1000 A. The results of the investigation of surface roughness are presented with examples of typical samples of silica gels, porous glasses, apatite, and coal.
Multi-channel and multi-angle algorithms for estimating sea and land surface temperature with ATSR data
1996
Abstract A study has been carried out using LOWTRAN-7 simulations of the Along-Track Scanning Radiometer (ATSR) data at 11 and 12 μm wavelengths to compare the merits of the multi-angle technique with those of the currently used multi-channel technique (split-window method) to retrieve both sea surface temperature (SST) and land surface temperature (LST). To this end a simple single-channel double-angle viewing model is presented, which relates actual surface temperature to the two brightness temperatures measured from space in the two views of interest (ATSR nadir and forward). Subsequently, statistical retrieval coefficients for the double angle and split-window techniques are derived via…
Dispersive interactions between atoms and nonplanar surfaces
2009
We calculate the dispersive force between a ground state atom and a non planar surface. We present explicit results for a corrugated surface, derived from the scattering approach at first order in the corrugation amplitude. A variety of analytical results are derived in different limiting cases, including the van der Waals and Casimir-Polder regimes. We compute numerically the exact first-order dispersive potential for arbitrary separation distances and corrugation wavelengths, for a Rubidium atom on top of a silicon or gold corrugated surface. We discuss in detail the inadequacy of the proximity force approximation, and present a simple but adequate approximation for computing the potentia…
Boolean operations with implicit and parametric representation of primitives using R-functions
2005
We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a constructive solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition …
Tree Singularities: Limits, Series and Stability
2013
A tree singularity is a surface singularity that consists of smooth components, glued along smooth curves in the pattern of a tree. Such singularities naturally occur as degenerations of certain rational surface singularities. To be more precise, they can be considered as limits of certain series of rational surface singularities with reduced fundamental cycle. We introduce a general class of limits, construct series deformations for them and prove a stability theorem stating that under the condition of finite dimensionality of T 2 the base space of a semi-universal deformation for members high in the series coincides up to smooth factor with the “base space of the limit”. The simplest tree…
Land surface emissivity retrieval from satellite data
2012
As an intrinsic property of natural materials, land surface emissivity LSE is an important surface parameter and can be derived from the emitted radiance measured from space. Besides radiometric calibration and cloud detection, two main problems need to be resolved to obtain LSE values from space measurements. These problems are often referred to as land surface temperature LST and emissivity separation from radiance at ground level and as atmospheric corrections in the literature. To date, many LSE retrieval methods have been proposed with the same goal but different application conditions, advantages, and limitations. The aim of this article is to review these LSE retrieval methods and to…
On the significance of molecular surfaces and thermodynamic interactions for the excess viscosities of liquid mixtures
1994
The viscosities η of homogeneous binary mixtures of liquids are usually approximated as In η = ϕ1 In η1 + ϕ2 In η2 where ϕi and ηi are the volume fractions and the viscosities, resp., of the i-th pure substance; the behavior of real systems is then discussed in terms of Δ In η, the deviations from the above reference behavior. Here a semi-empirical approach is presented according to which volume fractions are replaced by the surface fractions Ωi to create a more realistic reference state, and the thermodynamic interaction parameter g is taken into account. The new equation reads (expressing it for practical purposes still in the terms of ϕi) γ is a geometric factor, measuring the difference…