Search results for "Dimension"
showing 10 items of 2766 documents
Correlating Solution‐ and Solid‐State Structures of Conformationally Flexible Resorcinarenes: Significance of a Sulfonyl Group in Intramolecular Self…
2020
Abstract The synthesis of tetramethoxyresorcinarene podands bearing p‐toluene arms connected by ‐SO3‐ (1) and ‐CH2O‐ (2) linkers is presented herein. In the solid state, the resorcinarene podand 1 forms an intramolecular self‐inclusion complex with the pendant p‐toluene group of a podand arm, whereas the resorcinarene podand 2 does not show self‐inclusion. The conformations of the flexible resorcinarene podands in solution were investigated by variable‐temperature experiments using 1D and 2D NMR spectroscopic techniques as well as by computational methods, including a conformational search and subsequent DFT optimisation of representative structures. The 1H NMR spectra of 1 and 2 at room te…
Multiscale analyses and characterizations of surface topographies
2018
International audience; This work studies multiscale analyses and characterizations of surface topographies from the engineering and scientific literature with an emphasis on production engineering research and design. It highlights methods that provide strong correlations between topographies and performance or topographies and processes, and methods that can confidently discriminate topographies that were processed or that perform differently. These methods have commonalities in geometric characterizations at certain scales, which are observable with statistics and measurements. It also develops a semantic and theoretical framework and proposes a new system for organizing and designating …
Hybrid approach to surface roughness evaluation in multistage machining processes
2003
Abstract An assessment of surface quality in turned, ground and honed specimens is made by means of a computer-based processing of digitised surface profiles. Three different methods of surface finish characterisation, i.e. statistical, fractal and neural network-based approaches are examined and compared. Correlations between some representative roughness parameters and the fractal dimension (D) values estimated were found. Consequently, they can be converted to their corresponding roughness parameters, i.e. Ra, Rz and RΔa. Finally, a set of parameters including the minimum surface finish data for machining of external cylindrical surfaces when using complex technological process, is propo…
Principal configurations and umbilicity of submanifolds in $\mathbb R^N$
2004
We consider the principal configurations associated to smooth vector fields $\nu$ normal to a manifold $M$ immersed into a euclidean space and give conditions on the number of principal directions shared by a set of $k$ normal vector fields in order to guaranty the umbilicity of $M$ with respect to some normal field $\nu$. Provided that the umbilic curvature is constant, this will imply that $M$ is hyperspherical. We deduce some results concerning binormal fields and asymptotic directions for manifolds of codimension 2. Moreover, in the case of a surface $M$ in $\mathbb R^N$, we conclude that if $N>4$, it is always possible to find some normal field with respect to which $M$ is umbilic and …
Vassiliev invariants for braids on surfaces
2000
We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface.
Deducing a Drain Spacing Formula by Applying Dimensional Analysis and Self-Similarity Theory
2016
For designing a steady state drainage system a drain flow formula coupled with the Dupuit-Forcheimer form of the differential equation of groundwater flow is used. At first, in this paper the most applied drain flow formulas in steady-state conditions are reviewed and compared using as dependent variable the ratio between the maximum water table height and the distance between two lines of parallel drains. These equation are also tested using experimental field data measured in three plot drained by surface pipe drains having different value of drain spacing. Then, applying the dimensional analysis and the self-similarity theory, a new drain spacing formula is theoretically deduced and comp…
Study on Interfacial Surface in Modified Spray Tower
2019
This paper presents an analysis of the changes in interfacial surface and the size of droplets formed in a spray tower. The interfacial surface and the size of droplets formed are of fundamental importance to the performance of the equipment, both in terms of pressure drop and process efficiency. Liquid film and droplet sizes were measured using a microphotography technique. The confusors studied were classical, with profiled inside surface, and with double profiled inside surface. The liquids studied were water and aqueous solutions of high-molecular polyacrylamide (PAA) of power-law characteristics. The ranges of process Reynolds number studied were as follows: ReG &isin
MESH COMPARISON USING ATTRIBUTE DEVIATION METRIC
2004
We propose a mesh comparison method using a new attribute deviation metric. The considered meshes contain geometrical and appearance attributes (material color, texture, temperature, etc.). The proposed deviation metric computes local differences between the attributes of two meshes. A mesh comparison assessment can be done easily and quickly using this metric. The techniques proposed are applicable in a number of ways, e.g. 3D matching and registration, and the example described in the paper is the simplification of a surface by iteratively reducing its complexity according to an error metric. The results are presented showing the success of the algorithm through comparisons with other me…
Vectorized ‘‘TOPO’’ Program for the Theoretical Simulation of Molecular Shape
1991
The TOPO program for theoretical simulation of molecular shape is presented here. Molecular shape is characterized by a set of electrostatic and geometrical descriptors and topological indices including the fractal dimension of the accessible surface. An atom-atom analysis of all descriptors has been implemented. The program has been adapted for the realization of high-performance computing. Results are reported for porphine and phthalocyanine molecules.
Critical behavior of the surface-layer magnetization at the extraordinary transition in the three-dimensional Ising model.
1990
We have used a vectorized multispin-coding Monte Carlo method to determine the behavior of the surface-layer magnetization ${\mathit{m}}_{1}$ at the bulk transition in a simple-cubic Ising film with strongly enhanced surface coupling, i.e., at the extraordinary transition. In contrast to recent renormalization-group calculations we find no evidence for a discontinuous slope in the temperature dependence of ${\mathit{m}}_{1}$; the data are consistent with a free-energy-like (T-${\mathit{T}}_{\mathit{c}}$${)}^{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ behavior plus background terms.