Two-dimensional properties of random surfaces

1982 ◽  
Vol 305 (1490) ◽  
pp. 441-468 ◽  
Keyword(s):  
Autocorrelation Function ◽  
Surface Profile ◽  
General Rule ◽  
Two Dimensional ◽  
Present Contribution ◽  
One Dimensional ◽  
Dimensional Parameters ◽  
Discrete Methods ◽  
Continuous Theory ◽  
Theoretical Results

Recent work has shown that it is possible to predict surface parameters measured digitally from a surface profile by means of three points on the autocorrelation function. The weakness of this work has been that only one-dimensional parameters have been evaluated. The present contribution extends the theory to include two-dimensional parameters of the surface which are expressed in terms of between four and seven points on the autocorrelation function depending on the type of surface. It is shown that this technique provides an alternative to traditional mapping methods. It is shown also that as a general rule results obtained from the discrete analysis do not converge to those obtained from the continuous theory. The nature and magnitude of the differences between the two approaches are discussed in detail. Finally, the theoretical results are confirmed experimentally and the general significance of discrete methods reviewed.

Steady-State Bifurcation for a Biological Depletion Model

2016 ◽  
Vol 26 (04) ◽  
pp. 1650066 ◽  
Author(s):  
Yan’e Wang ◽  
Jianhua Wu ◽  
Yunfeng Jia
Keyword(s):  
Steady State ◽  
Bifurcation Theory ◽  
Steady States ◽  
Two Dimensional ◽  
Implicit Function ◽  
Flux Boundary Condition ◽  
One Dimensional ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Theoretical Results

A two-species biological depletion model in a bounded domain is investigated in which one species is a substrate and the other is an activator. Firstly, under the no-flux boundary condition, the asymptotic stability of constant steady-states is discussed. Secondly, by viewing the feed rate of the substrate as a parameter, the steady-state bifurcations from constant steady-states are analyzed both in one-dimensional kernel case and in two-dimensional kernel case. Finally, numerical simulations are presented to illustrate our theoretical results. The main tools adopted here include the stability theory, the bifurcation theory, the techniques of space decomposition and the implicit function theorem.

scholarly journals Influence of confinement on a two-dimensional wake

2011 ◽  
Vol 688 ◽  
pp. 297-320 ◽  
Author(s):  
Luca Biancofiore ◽  
François Gallaire ◽  
Richard Pasquetti
Keyword(s):  
Stability Analysis ◽  
Velocity Ratio ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Wake Flow ◽  
Two Dimensional ◽  
Dimensional Parameters ◽  
Spatio Temporal ◽  
Spatial Locations ◽  
Theoretical Results

AbstractThe spatio-temporal development of an incompressible two-dimensional viscous wake flow confined by two flat slipping plates is investigated by means of direct numerical simulation (DNS), using a spectral Chebyshev multi-domain method. The limit between unstable and stable configurations is determined with respect to several non-dimensional parameters: the confinement, the velocity ratio and two different Reynolds numbers, $100$ and $500$. The comparison of such limit curves with theoretical results obtained by Juniper (J. Fluid Mech., vol. 565, 2006, pp. 171–195) confirms the existence of a region at moderate confinement where the instability is maximal. Moreover, instabilities are also observed under sustained co-flow, in the form of a vacillating front. Using a direct computation of the two-dimensional base flow, we perform a local linear stability analysis for several velocity profiles prevailing at different spatial locations, so as to determine the local spatio-temporal nature of the flow: convectively unstable or absolutely unstable. Comparisons of the DNS and local stability analysis results are provided and discussed.

Conceptual Design and Dimensional Synthesis of a Reconfigurable Hybrid Robot

2004 ◽  
Vol 127 (3) ◽  
pp. 647-653 ◽  
Author(s):  
Meng Li ◽  
Tian Huang ◽  
Dawei Zhang ◽  
Xueman Zhao ◽  
S. Jack Hu ◽  
...  
Keyword(s):  
Conceptual Design ◽  
Parallel Mechanism ◽  
Two Dimensional ◽  
Dimensional Synthesis ◽  
One Dimensional ◽  
Reconfigurable Robots ◽  
Fixed Base ◽  
Dimensional Version ◽  
Dimensional Parameters ◽  
Moving Platform

This paper deals with the conceptual design of a novel four-degree-of-freedom (dof) modularized robot which is composed of a 2-dof parallel mechanism plus a 2-dof rotating head attached to the moving platform. Patented with the name Bicept, the robot is the two-dimensional version of the Tricept robot and is designed as a reconfigurable module that can readily be integrated with 1-dof feed mechanism or a fixed base in order to form a set of reconfigurable robots with parallel-serial architecture. The dimensional synthesis of the 2-dof parallel mechanism as a component of the Bicept robot is also carried out by solving a one-dimensional nonlinear equation associated with the strut-length constraint. The dimensional parameters corresponding to various width-height ratios of the work space are obtained via examples.

Experiments on Foucault Imaging of Superconducting Fluxons

1997 ◽  
Vol 3 (S2) ◽  
pp. 507-508
Author(s):  
T. Yoshida ◽  
J. Endo ◽  
K. Harada ◽  
H. Kasai ◽  
T. Matsuda ◽  
...  
Keyword(s):  
Phase Contrast ◽  
Theory And Practice ◽  
Structural Defects ◽  
Two Dimensional ◽  
Transmitted Beam ◽  
Standard Methods ◽  
Easy Task ◽  
One Dimensional ◽  
Lorentz Microscopy ◽  
Theoretical Results

The out-of-focus method has been successfully employed in the dynamical observation of superconducting fluxons. However, owing to the large defocus distance needed to image fluxons with enough contrast it turns out that their correlation with structural defects, better imaged at focus, is troublesome. Among the standard methods of Lorentz microscopy the Foucault technique is a good candidate for removing this drawback, since it generates phase contrast in the focused image by masking part of the transmitted beam by means of an aperture.Therefore, simulations have been carried out both for one-dimensional fluxon models and more realistic two dimensional ones, with the result that enough contrast can be generated in the focused image in order to detect them. However, although these theoretical results suggest the feasibility of Foucault experiments, filling the gap between theory and practice is not an easy task, especially when considering the small angular deflections involved, of the order of 10−5 rad.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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