Measurements of the Statistical Microgeometry of Engineering Surfaces

1979 ◽  
Vol 101 (4) ◽  
pp. 409-417 ◽  
Author(s):  
R. S. Sayles ◽  
T. R. Thomas
Keyword(s):  
Nearest Neighbor ◽  
Sampling Interval ◽  
Random Surface ◽  
Geometrical Properties ◽  
Grid Sampling ◽  
Anisotropic Structures ◽  
Basic Relationship ◽  
Moment Approach ◽  
Non Gaussian ◽  
Good Agreement

Surface and profile measurements and their resulting statistics, based on samples of up to half a million heights, are compared and their interrelationship examined for several common engineering surfaces. The measurements are employed to check the applicability of the spectral moment approach to random surface specification. This technique relates many important geometrical properties of a surface to those of its constituent profiles. A relationship is found to exist between the sampling interval and the spatial size of features accommodated by this form of approach. This explains, for example, why 4 and 8 nearest neighbor summit-density analyses based on the same square grid sampling interval reveal very different results. Having established this basic relationship, good agreement is found between theory and measurement over a large range of sampling intervals. In particular, summit densities and distributions are shown to agree well with theory even for non-Gaussian height distributions. It is shown how the isotropic analysis can be extended to cover directionally anisotropic structures such as ground surfaces by defining equivalent movements based on two profiles at right angles. Here again measurements are in good agreement with theory.

The effect of a footprint on perceived surface roughness

1986 ◽  
Vol 405 (1829) ◽  
pp. 303-327 ◽  
Keyword(s):  
Surface Roughness ◽  
Weighting Function ◽  
Sampling Interval ◽  
Asymptotic Convergence ◽  
Reference Surface ◽  
Two Dimensional ◽  
Random Surface ◽  
Spectral Density Functions ◽  
Continuous Theory ◽  
Discrete Theory

A two-dimensional homogeneous random surface { y ( X )} is generated from another such surface { z ( X )} by a process of smoothing represented by y ( X ) = ∫ ∞ d u w ( u – X ) z ( u ), where w ( X ) is a deterministic weighting function satisfying certain conditions. The two-dimensional autocorrelation and spectral density functions of the smoothed surface { y ( X )} are calculated in terms of the corresponding functions of the reference surface { z ( X )} and the properties of the ‘footprint’ of the contact w ( X ). When the surfaces are Gaussian, the statistical properties of their peaks and summits are given by the continuous theory of surface roughness. If only sampled values of the surface height are available, there is a corresponding discrete theory. Provided that the discrete sampling interval is small enough, profile statistics calculated by the discrete theory should approach asymptotically those calculated by the continuous theory, but it is known that such asymptotic convergence may not occur in practice. For a smoothed surface { y ( X )} which is generated from a reference surface { z ( X )} by a ‘good’ footprint of finite area, it is shown in this paper that the expected asymptotic convergence does occur always, even if the reference surface is ideally white. For a footprint to be a good footprint, w ( X ) must be continuous and smooth enough that it can be differentiated twice everywhere, including at its edges. Sample calculations for three footprints, two of which are good footprints, illustrate the theory.

Polynomial Model Set and its Interacting Multiple Model Algorithms

2012 ◽  
Vol 562-564 ◽  
pp. 2038-2044
Author(s):  
Jin Xiao Zhao ◽  
Jian Qiu Zhang ◽  
Dong Ming Zhou
Keyword(s):  
Sampling Interval ◽  
Polynomial Model ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Geometrical Properties ◽  
Filter Performance ◽  
Maneuvering Target ◽  
Polynomial Curve ◽  
Motion Modes ◽  
Model Set

From the maneuvering target orbit on the geometrical properties, according to different motion modes track corresponding to different order number polynomial curve, using the least squares fitting structure, this paper gives out a group of various motion modes matching the mathematical model—polynomial model set (PMS), and gives distinct mathematical process. PMS covers all the motion modes theoretically, easy to choose according to the practical situation and expand, especially suitable for single model can not accurately describe the complex sports scene. The model need not consider sampling interval, without lowering the filter performance at the same time, reduced prior knowledge dependence. Finally, simulation results indicate that the correctness and validity and practicality.

Photonic Band Structure of Nanochannel Glass Materials

1996 ◽  
Vol 431 ◽  
Author(s):  
A. Rosenberg ◽  
R. J. Tonucci ◽  
H.-B. Lin
Keyword(s):  
Band Structure ◽  
Brillouin Zone ◽  
Near Infrared ◽  
Nearest Neighbor ◽  
Dielectric Structure ◽  
Zone Boundary ◽  
Photonic Band Structure ◽  
Brillouin Zone Boundary ◽  
Photonic Band ◽  
Good Agreement

AbstractWe demonstrate that nanochannel glass (NCG) materials are ideal for investigating twodimensional (2D) photonic band-structure effects. The NCG materials we have studied consist of triangular arrays of glass cylinders embedded in a glass matrix, having center-tocenter nearest-neighbor separations from 0.54 to 1.08 μm. The indices of refraction of the two glasses differ by less than 0.02 in the relevant spectral region. Narrow attenuation features occur whenever the dispersion relation for light propagating within such a periodic dielectric structure crosses a Brillouin zone boundary. The attenuations corresponding to the first Brillouin zone appear in the near-infrared (IR), at wavelengths between 1 and 3 μm, in good agreement with calculations.

Atomic Interchange Potentials Calculation of Ni-Al-Cr Alloy Based on Microscopic Phase Field Method

2013 ◽  
Vol 747-748 ◽  
pp. 739-746
Author(s):  
Wei Ping Dong ◽  
Zhang Jing ◽  
Zheng Chen
Keyword(s):  
Field Theory ◽  
Phase Field ◽  
Nearest Neighbor ◽  
Field Method ◽  
Phase Field Method ◽  
Precipitation Process ◽  
Atomic Interaction ◽  
Long Range Order ◽  
Nearest Neighbour ◽  
Good Agreement

The effects of increasing atomic interchange potentials to the precipitation process and microstructure of Ni-Al-Cr alloy have been simulated based on the microscopic phase field theory. The first nearest neighbour atomic interchange potentials of Ni-Al-Cr alloys for L12 and D022 phase was calculated out according to the formula which were referenced on the relation equation between atomic interchange potentials and long range order parameters by Khachaturyan. The results indicated that Ni-Al (WNi-Al) and Ni-Cr (WNi-Cr) s first nearest neighbor atomic interaction potentials will increase linearly while the temperatures rose. Moreover WNi-Al increased but WNi-Cr decreased roughly linearly if Al atoms concentration rose, and conversely inversed. In addition, these atomic interchange potentials changing with temperature and concentration were in good agreement with earlier study.

Mutual Passivation in Dilute GaNxAs1-x Alloys

2005 ◽  
Vol 864 ◽  
Author(s):  
K. M. Yu ◽  
W. Walukiewicz ◽  
J. Wu ◽  
D. E. Mars ◽  
M. A. Scarpulla ◽  
...  
Keyword(s):  
Nearest Neighbor ◽  
Diffusion Length ◽  
Average Distance ◽  
Alloy System ◽  
Group Iv ◽  
Semiconductor Alloys ◽  
Drastic Reduction ◽  
Free Electron Concentration ◽  
Ternary Semiconductor ◽  
Good Agreement

AbstractThe dilute GaNxAs1-x alloys (with x up to 0.05) have exhibited many unusual properties as compared to the conventional binary and ternary semiconductor alloys. We report on a new effect in the GaNxAs1-x alloy system in which electrically active substitutional group IV donors and isoelectronic N atoms passivate each other's activity. This mutual passivation occurs in dilute GaNxAs1-x doped with group IV donors through the formation of nearest neighbor IVGa- NAs pairs when the samples are annealed under conditions such that the diffusion length of the donors is greater than or equal to the average distance between donor and N atoms. The passivation of the shallow donors and the NAs atoms is manifested in a drastic reduction in the free electron concentration and, simultaneously, an increase in the fundamental bandgap. This mutual passivation effect is demonstrated in both Si and Ge doped GaNxAs1-x alloys. Analytical calculations of the passivation process based on Ga vacancy mediated diffusion show good agreement with the experimental results.

Three-State Lattice-Gas Model of H-S on Pt(111)

1987 ◽  
Vol 111 ◽  
Author(s):  
Per Arne Rikvold ◽  
Joseph B. Collins ◽  
G. D. Hansen ◽  
J. D. Gunton ◽  
E. T. Gawlinski
Keyword(s):  
Adsorption Isotherms ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Numerical Study ◽  
Finite Size ◽  
Lateral Interaction ◽  
Finite Size Scaling ◽  
Enhanced Adsorption ◽  
Good Agreement

AbstractWe consider a three-state lattice-gas with nearest-neighbor interactions on a triangular lattice as a model for multicomponent chemi- and physisorption. By varying the lateral interaction constants between the adsorbate particles, this model can be made to exhibit either enhanced adsorption or poisoning (inhibited adsorption). We discuss here the conditions on the interaction constants that lead to poisoning. We present the results of a ground-state calculation and detailed numerical study of the phase diagram for a set of interactions that exhibits poisoning. We calculate the phase diagrams and adsorption isotherms by the finite-size scaling transfer-matrix method. We consider the result as a simple model for the coadsorption of Sulphur and Hydrogen on a Platinum (111) surface, with interaction constants estimated from experimental data. The resulting adsorption isotherms are in good agreement with experimental results.

Lattice relaxation around impurity pairs in alkali halides

1976 ◽  
Vol 54 (19) ◽  
pp. 2010-2017
Author(s):  
T. L. Templeton ◽  
B. P. Clayman
Keyword(s):  
Nearest Neighbor ◽  
Molecular Model ◽  
Linear Chain ◽  
Alkali Halides ◽  
Lattice Relaxation ◽  
Resonant Absorption ◽  
Force Constants ◽  
Chain Model ◽  
Absorption Frequencies ◽  
Good Agreement

The rigid ion model is applied to the calculation of the relaxation of the lattice around single impurities and pairs of impurities in alkali halide host-defect systems. The calculated relaxation of nearest neighbors is typically a few percent of the host crystal lattice constant. Relaxation falls off with increasing distance from the defects. Nearest neighbor force constants derived from this calculation are, in some cases, in good agreement with those obtained by fitting the resonant absorption frequencies of the vibrational modes of these impurity centres to a molecular model. In other cases the extreme anisotropy of the relaxed force constants is seen to prevent the application of a simple molecular model. The calculated force constants, when used in a linear chain model, give good qualitative agreement with experiment.

THEORETICAL STUDIES OF THE LOCAL STRUCTURES AND SPIN HAMILTONIAN PARAMETERS FOR THE RHOMBICNi2+CENTERS INAgX(X=Cl,Br)

2009 ◽  
Vol 23 (11) ◽  
pp. 1415-1424 ◽  
Author(s):  
ZHI-HONG ZHANG ◽  
SHAO-YI WU ◽  
CHUAN-JI FU ◽  
LI-HUA WEI ◽  
XUE-FENG WANG
Keyword(s):  
Nearest Neighbor ◽  
Charge Compensation ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Spin Hamiltonian ◽  
Small Shift ◽  
Local Structures ◽  
Distorted Octahedra ◽  
Hamiltonian Parameters ◽  
Good Agreement

The local structures and the spin Hamiltonian parameters (zero-field splittings D and E and the anisotropic g factors gx, gyand gz) for the rhombic Ni2+centers in AgX ( X = Cl , Br ) are theoretically studied from the perturbation formulas of these parameters for a 3d8ion under rhombically distorted octahedra. In these formulas, the ligand p- and s-orbital and spin-orbit coupling contributions are included on the basis of the cluster approach. The rhombic centers are attributed to the impurity Ni2+associated with one nearest-neighbor silver vacancy VAgalong the [110] direction as charge compensation. Based on the calculations, Ni2+is found to suffer an off-center displacement 0.092 Å (or 0.335 Å) for AgCl (or AgBr ) towards the VAgalong the [110] axis, while the ligands closest to the VAgundergo a small shift 0.065 Å (or 0.006 Å) away from (or towards) the VAg. The theoretical spin Hamiltonian parameters based on the above defect structures show good agreement with the experimental data.

scholarly journals On the Turns of Digital Images

2015 ◽  
Vol 20 (2) ◽  
pp. 157-165
Author(s):  
P. G. Parfenov
Keyword(s):  
Nearest Neighbor ◽  
Hexagonal Lattice ◽  
Rectangular Lattice ◽  
Characteristic Set ◽  
Arbitrary Angle ◽  
Characteristic Sets ◽  
Predicted Values ◽  
Analytical Expressions ◽  
Eulerian Characteristic ◽  
Good Agreement

The images built on the basis of rectangular and hexagonal lattices are discussed in the article. For images on a rectangular lattice a formula is proposed, which gives approximate values of the components of a characteristic set of coefficients when turning at an arbitrary angle by the method of the nearest neighbor. The characteristic sets are presented in the form of diagrams, an experimental evaluation of errors is made. It was confirmed a good agreement with the predicted value component of characteristic sets and those which were obtained experimentally. For images built on the basis of a hexagonal lattice was offered a similar formula for the approximation of the components of the characteristic set for rotating at any angle, when this was applied to the modification of the nearest neighbor method for the preservation of coherence, as it was discovered its violation in some cases on a hexagonal lattice. On the basis of four-pixel fragments are built diagrams, which show a good agreement of predicted values and the obtained ones in the experiment. It was defined a system of three-pixel hexagonal fragments to which the theorem is proved on the Eulerian characteristic and were offered analytical expressions, which allow to avoid experimental detection of the characteristic sets of coefficients for all possible reference angles. Their use requires to produce only one such experiment.

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