scholarly journals Variational principle and its boundary and additional boundary conditions for inverse shape design problem of heat conduction

2010 ◽  
Vol 59 (9) ◽  
pp. 6326
Author(s):  
Wu Zhao-Chun
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Boundary Conditions ◽  
Design Problem ◽  
Shape Design ◽  
Additional Boundary Conditions

Heat Conduction in Heterogeneous Materials

1985 ◽  
Vol 107 (1) ◽  
pp. 39-43 ◽  
Author(s):  
J. Baker-Jarvis ◽  
R. Inguva
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Green Function ◽  
General Solution ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Heterogeneous Materials ◽  
Composite Media ◽  
Polar Moment ◽  
Homogeneous Media

A new solution to the heat equation in composite media is derived using a variational principle developed by Ben-Amoz. The model microstructure is fed into the equations via a term for the polar moment of the inclusions in a representative volume. The general solution is presented as an integral in terms of sources and a Green function. The problem of uniqueness is studied to determine appropriate boundary conditions. The solution reduces to the solution of the normal heat equation in the limit of homogeneous media.

Additional boundary conditions in unsteady-state heat conduction problems

2017 ◽  
Vol 55 (4) ◽  
pp. 541-548 ◽  
Author(s):  
I. V. Kudinov ◽  
V. A. Kudinov ◽  
E. V. Kotova
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Unsteady State ◽  
Additional Boundary Conditions ◽  
State Heat

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

Creation and Manipulation of Complex Displacement Features During the Conceptual Phase of Design

1996 ◽  
Author(s):  
P. A. van Elsas ◽  
J. S. M. Vergeest
Keyword(s):  
Boundary Conditions ◽  
Surface Feature ◽  
Free Form ◽  
Shape Design ◽  
Surface Model ◽  
Test Results ◽  
Base Surface ◽  
Feature Design ◽  
Data Explosion ◽  
Free Form Surface

Abstract Surface feature design is not well supported by contemporary free form surface modelers. For one type of surface feature, the displacement feature, it is shown that intuitive controls can be defined for its design. A method is described that, given a surface model, allows a designer to create and manipulate displacement features. The method uses numerically stable calculations, and feedback can be obtained within tenths of a second, allowing the designer to employ the different controls with unprecedented flexibility. The algorithm does not use refinement techniques, that generally lead to data explosion. The transition geometry, connecting a base surface to a displaced region, is found explicitly. Cross-boundary smoothness is dealt with automatically, leaving the designer to concentrate on the design, instead of having to deal with mathematical boundary conditions. Early test results indicate that interactive support is possible, thus making this a useful tool for conceptual shape design.

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