Search results for " function"
showing 10 items of 9395 documents
Isolated roundings and flattenings of submanifolds in Euclidean spaces
2005
We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.
New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation
2011
An independent derivation of solutions to the Camassa-Holm equation in terms of multi-dimensional theta functions is presented using an approach based on Fay's identities. Reality and smoothness conditions are studied for these solutions from the point of view of the topology of the underlying real hyperelliptic surface. The solutions are studied numerically for concrete examples, also in the limit where the surface degenerates to the Riemann sphere, and where solitons and cuspons appear.
INITIAL PARAMETRIC REPRESENTATION OF BLOBS
2009
Blobs, developed by J.F. Blinn in 1982, are the implicit surfaces obtained by composition of a real numerical function and a distance function. Since, many authors (C. Murakami, H. Nishimura, G. Wyvill…) defined their own function of density, from these implicit surfaces are interesting from several points of view. In particular, their fusion makes it possible to easily obtain an implicit equation of resulting surface. However, these surfaces do not admit a parametric equation yet. In this article, we will establish the parametric equation of two blobs in fusion, defined by the function of density of C. Murakami, by using an algebraic method. Then, we will develop another method, based on …
Polarity Effects on ZnO Films Grown along the Nonpolar[112¯0]Direction
2005
The surface electrical properties of ZnO thin films grown along the nonpolar $[11\overline{2}0]$ direction have been investigated by Kelvin probe microscopy on a nanometer scale. Two different charge domains, with a 75 meV work function difference, coexist within the ZnO surface, which is covered by rhombohedral pyramids whose sidewalls are shown to be ${10\overline{1}1}$-type planes. The presence and relative orientation of the two kinds of charge domains are explained in terms of the atomic arrangement at the ${10\overline{1}1}$ polar surfaces.
Roughening of the Cu(110) surface
1993
The structure of the Cu(110) surface is studied at high temperatures using a combination of lattice-gas Monte Carlo and molecular dynamics methods with identical many-atom interactions derived from the effective medium theory. The anisotropic six-vertex model is used in the interpretation of the lattice-gas results. We find a clear roughening transition around T_R=1000K and T_R/T_M=0.81. Molecular dynamics reveals the clustering of surface defects as the atomistic mechanism of the transition and allows us to estimate characteristic time scales. For the system of size 50x50, the time scale of the local roughening at 1150 K of an initially smooth surface is of the order of 100 ps.
Bundlet Model for Single-Wall Carbon Nanotubes, Nanocones and Nanohorns
2012
This paper discusses the existence of single-wall carbon nanocones (SWNCs), especially nanohorns (SWNHs), in organic solvents in the form of clusters. A theory is developed based on a bundlet model describing their distribution function by size. Phenomena have a unified explanation in bundlet model in which free energy of an SWNC, involved in a cluster, is combined from two components: a volume one, proportional to number of molecules n in a cluster, and a surface one proportional to n1/2. Bundlet model enables describing distribution function of SWNC clusters by size. From purely geometrical differences, bundlet (SWNCs) and droplet (fullerene) models predict different behaviours. The SWNCs…
Calculations of atomic and electronic structure for (100) surfaces of SrTiO3 perovskite
2002
AbstractWe present and discuss main results of the calculations for the surface relaxation and rumpling of SrTiO3 surfaces with TiO2 and SrO terminations using a wide variety of methods of modern computational physics and chemistry, including the shell model (SM) and ab initio methods based on Hartree-Fock (HF) and Density Functional Theory (DFT). The HF and DFT formalisms with different exchange-correlation functionals are implemented into Crystal-98 computer code using a Gaussian-type basis set. We demonstrate that a hybrid B3PW formalism gives the best results for the bulk SrTiO3 properties. Results are compared with previous ab initio plane-wave LDA calculations and LEED experiments. Ou…
Single-shot ultrafast laser processing of high-aspect-ratio nanochannels using elliptical Bessel beams
2017
Ultrafast lasers have revolutionized material processing, opening a wealth of new applications in many areas of science. A recent technology that allows the cleaving of transparent materials via non-ablative processes is based on focusing and translating a high-intensity laser beam within a material to induce a well-defined internal stress plane. This then enables material separation without debris generation. Here, we use a non-diffracting beam engineered to have a transverse elliptical spatial profile to generate high aspect ratio elliptical channels in glass of dimension 350 nm x 710 nm, and subsequent cleaved surface uniformity at the sub-micron level.
Monotony Based Imaging in EIT
2010
We consider the problem of determining conductivity anomalies inside a body from voltage‐current measurements on its surface. By combining the monotonicity method of Tamburrino and Rubinacci with the concept of localized potentials, we derive a new imaging method that is capable of reconstructing the exact (outer) shape of the anomalies. We furthermore show that the method can be implemented without solving any non‐homogeneous forward problems and show a first numerical result.
Does Young's equation hold on the nanoscale? A Monte Carlo test for the binary Lennard-Jones fluid
2010
When a phase-separated binary ($A+B$) mixture is exposed to a wall, that preferentially attracts one of the components, interfaces between A-rich and B-rich domains in general meet the wall making a contact angle $\theta$. Young's equation describes this angle in terms of a balance between the $A-B$ interfacial tension $\gamma_{AB}$ and the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall, $\gamma _{AB} \cos \theta =\gamma_{wA}-\gamma_{wB}$. By Monte Carlo simulations of bridges, formed by one of the components in a binary Lennard-Jones liquid, connecting the two walls of a nanoscopic slit pore, $\theta$ is estimated from the inc…