Constructing the grid orthogonal and having the given nodal clustering near the boundary of a two-dimensional domain

2011 ◽  
Vol 3 (5) ◽  
pp. 637-645 ◽  
Author(s):  
B. N. Azarenok
Keyword(s):  
Two Dimensional ◽  
The Given ◽  
Dimensional Domain

Evaluation of a Two-Dimensional Conductivity Function Based on Boundary Measurements

1999 ◽  
Vol 122 (2) ◽  
pp. 367-371 ◽  
Author(s):  
M. Tadi
Keyword(s):  
Optimal Estimation ◽  
Two Dimensional ◽  
Zeroth Order ◽  
First Order ◽  
Conductivity Profile ◽  
Boundary Measurements ◽  
Conductivity Function ◽  
The Given ◽  
Close Estimate ◽  
Dimensional Domain

This paper is concerned with an inverse problem for the conduction of heat in a two-dimensional domain. It seeks to recover the subsurface conductivity profile based on the measurements obtained at the boundary. The method considers a temporal interval for which time-dependent measurements are provided. It formulates an optimal estimation problem which seeks to minimize the error difference between the given data and the response from the system. It uses a combination of the zeroth-order and the first-order Tikhonov regularization to stabilize the inversion. The method leads to an iterative algorithm which, at every iteration, requires the solution to a two-point boundary value problem. A number of numerical results are presented which indicate that a close estimate of the thermal conductivity function can be obtained based on the boundary measurements only. [S0022-1481(00)00902-6]

Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain

1997 ◽  
Vol 49 (2) ◽  
pp. 269-280
Author(s):  
Yu. A. Mitropol’skii ◽  
A. A. Berezovskii ◽  
M. Kh. Shkhanukov-Lafishev
Keyword(s):  
Parabolic Equation ◽  
Two Dimensional ◽  
Nonlocal Problems ◽  
Dimensional Domain

Two dimensional fractional projectile motion in a resisting medium

Open Physics ◽  
2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Juan Rosales ◽  
Manuel Guía ◽  
Francisco Gómez ◽  
Flor Aguilar ◽  
Juan Martínez
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Two Dimensional ◽  
Auxiliary Parameter ◽  
Derivative Operator ◽  
Projectile Motion ◽  
Resisting Medium ◽  
Fractional Differential ◽  
The Given ◽  
Physical Quantities

AbstractIn this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)−1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.

Design of a Two-Piece Brassiere Cup From its Data Points Toward its Automation

2020 ◽  
Author(s):  
Kotaro Yoshida ◽  
Hidefumi Wakamatsu ◽  
Eiji Morinaga ◽  
Takahiro Kubo
Keyword(s):  
Three Dimensional ◽  
Developable Surface ◽  
Two Dimensional ◽  
Trial And Error ◽  
Design Efficiency ◽  
Developable Surfaces ◽  
Data Points ◽  
Dimensional Shape ◽  
The Given ◽  
Three Dimensional Shape

Abstract A method to design the two-dimensional shapes of patterns of two piece brassiere cup is proposed when its target three-dimensional shape is given as a cloud of its data points. A brassiere cup consists of several patterns and their shapes are designed by repeatedly making a paper cup model and checking its three-dimensional shape. For improvement of design efficiency of brassieres, such trial and error must be reduced. As a cup model for check is made of paper not cloth, it is assumed that the surface of the model is composed of several developable surfaces. When two lines that consist in the developable surface are given, the surface can be determined. Then, the two-piece brassiere cup can be designed by minimizing the error between the surface and given data points. It was mathematically verified that the developable surface calculated by our propose method can reproduce the given data points which is developable surface.

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