Three-Dimensional Surface Characterization by Two-Dimensional Autoregressive Models

1995 ◽  
Vol 117 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Min S. Hong ◽  
Kornel F. Ehmann
Keyword(s):  
Surface Characterization ◽  
Three Dimensional ◽  
Surface Characteristics ◽  
Analytical Tool ◽  
Autoregressive Models ◽  
Density Functions ◽  
Two Dimensional ◽  
Engineered Surfaces ◽  
Spectrum Density ◽  
Dimensional Surface

An attempt is made to characterize and synthesize engineered surfaces. The proposed method, based on two-dimensional difference equations and two-dimensional linear autoregressive models, is not only an analytical tool to characterize but also to generate/synthesize three-dimensional surfaces with desired properties. The developed method expresses important three-dimensional surface characteristics such as the autocorrelation or power spectrum density functions in terms of the two-dimensional autoregressive coefficients.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

Algorithm of Hardy Function Interpolation and its Visualization in the Formation of the Virtual Battlefield Terrain

2013 ◽  
Vol 709 ◽  
pp. 495-498
Author(s):  
Shi Bin Liu ◽  
Cheng Wang ◽  
Yan Ping Yang ◽  
Xing Yan Liu
Keyword(s):  
Three Dimensional ◽  
Reference Value ◽  
Two Dimensional ◽  
C Language ◽  
Hardy Function ◽  
Data Points ◽  
Comparison And Analysis ◽  
Searching Method ◽  
Dimensional Surface

this thesis puts forward the idea of using the searching method to retrieve two kinds of data points of the circle and the square to generate DEM data of the collected discrete points by means of using C# language and OpenGL DLL, thus realizing the visualization of the three-dimensional virtual terrain from contours on the two-dimensional surface. This thesis makes a comparison and analysis of the visualization effect which indicates that this algorithm is quick and effective. This research has a certain reference value for the formation of the virtual battlefield terrain.

Electrochemical treatment of residual ammonia nitrogen in biologically pretreated coking wastewater with three-dimensional electrodes

2011 ◽  
Vol 63 (11) ◽  
pp. 2732-2736 ◽  
Author(s):  
Xu-wen He ◽  
Li-yuan Liu ◽  
Hao Wang ◽  
Gong Zhang ◽  
Jing-wen Gong ◽  
...  
Keyword(s):  
Current Density ◽  
Three Dimensional ◽  
Surface Characteristics ◽  
Electrochemical Treatment ◽  
Ammonia Nitrogen ◽  
Electrode System ◽  
Coking Wastewater ◽  
Two Dimensional ◽  
Electrode Distance ◽  
Good Surface

The electrochemical oxidation of the residual ammonia nitrogen contained in biologically pretreated coking wastewater using three-dimensional electrode system was studied. The results show the Ti/RuO2/IrO2 anode plates and the coke have good surface characteristics for the purpose of this study. In addition, studies also show that the three-dimensional electrode system should be able to give a satisfied solution to the residual bio-refractory ammonia nitrogen in biologically pretreated coking wastewater in comparison to conventional two-dimensional electrodes. At coke size of 10–20 mesh, electrode distance of 1.0 cm and current density of 4.5 mA/cm2, the residual ammonia nitrogen in the three-dimensional electrode system was almost completely removed in 60 min.

Controlling three-dimensional ice template via two-dimensional surface wetting

AIChE Journal ◽  
2016 ◽  
Vol 62 (12) ◽  
pp. 4186-4192 ◽  
Author(s):  
Miao Yang ◽  
Jingjun Wu ◽  
Hao Bai ◽  
Tao Xie ◽  
Qian Zhao ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Wetting ◽  
Dimensional Surface
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