A computational method to find dual solutions of the one-dimensional Bratu problem

2021 ◽  
Vol 388 ◽  
pp. 113309
Author(s):  
Nasibeh Karamollahi ◽  
Ghasem Barid Loghmani ◽  
Mohammad Heydari
Keyword(s):  
Dual Solutions ◽  
Computational Method ◽  
One Dimensional ◽  
The One ◽  
Bratu Problem

A modified perturbation solution to the one-dimensional Bratu problem

2019 ◽  
Vol 354 ◽  
pp. 296-304 ◽  
Author(s):  
Mina B. Abd-el-Malek ◽  
Amr Abdelrazek ◽  
Mohammed Ghazy ◽  
Gehad Gamal
Keyword(s):  
Perturbation Solution ◽  
One Dimensional ◽  
The One ◽  
Bratu Problem

scholarly journals A computational method to solve for the heat conduction temperature field based on data-driven approach

2021 ◽  
pp. 165-165
Author(s):  
Kun Li ◽  
Shiquan Shan ◽  
Qi Zhang ◽  
Xichuan Cai ◽  
Zhou Zhijun
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Steady State ◽  
Transient State ◽  
Absolute Error ◽  
Computational Method ◽  
Data Driven ◽  
One Dimensional ◽  
Data Driven Approach ◽  
The One

In this paper, a computational method for solving for the one-dimensional heat conduction temperature field is proposed based on a data-driven approach. The traditional numerical solution requires algebraic processing of the heat conduction differential equations, and necessitates the use of a complex mathematical derivation process to solve for the temperature field. In this paper, a temperature field solution model called HTM (Hidden Temperature Method) is proposed. This model uses an artificial neural network to establish the correspondence relationship of the node temperature values during the iterative process, so as to obtain the "Data to Data" solution. In this work, one example of one-dimensional steady state and three examples of one-dimensional transient state are selected, and the calculated values are compared to those obtained by traditional numerical methods. The mean-absolute error(MAE)of the steady state is only 0.2508, and among the three transient cases, the maximum mean-square error(MSE) is only 2.6875, indicating that the model is highly accurate in both steady-state and transient conditions. This shows that the HTM simulation can be applied to the solution of the heat conduction temperature field. This study provides a basis for the further optimization of the HTM algorithm.

scholarly journals ONE-DIMENSIONAL σ-MODELS WITH N = 5, 6, 7, 8 OFF-SHELL SUPERSYMMETRIES

2009 ◽  
Vol 24 (23) ◽  
pp. 4317-4326 ◽  
Author(s):  
M. GONZALES ◽  
M. ROJAS ◽  
F. TOPPAN
Keyword(s):  
Extended Supersymmetry ◽  
Computational Method ◽  
Conformally Flat ◽  
One Dimensional ◽  
Special Geometry ◽  
The One ◽  
Inequivalent Representations

We computed the actions for the one-dimensional (1D)N = 5 σ-models with respect to the two inequivalent (2, 8, 6) multiplets. Four supersymmetry generators are manifest, while the constraint originated by imposing the fifth supersymmetry automatically induces a full N = 8 off-shell invariance. The resulting action coincides in the two cases and corresponds to a conformally flat 2D target satisfying a special geometry of rigid type. To obtain these results we developed a computational method (for Maple 11) which does not require the notion of superfields and is instead based on the nowadays available list of the inequivalent representations of the 1DN-extended supersymmetry. Its application to systematically analyze the σ-models off-shell invariant actions for the remaining N = 5, 6, 7, 8(k, 8, 8-k) multiplets, as well as for the N>8 representations, only requires more cumbersome computations.

A DISCREPANCY PRINCIPLE FOR THE SOURCE POINTS LOCATION IN USING THE MFS FOR SOLVING THE BHCP

2009 ◽  
Vol 06 (02) ◽  
pp. 181-197 ◽  
Author(s):  
Y. C. HON ◽  
M. LI
Keyword(s):  
Heat Conduction Problem ◽  
Linear Equations ◽  
Fundamental Solutions ◽  
Computational Method ◽  
Method Of Fundamental Solutions ◽  
Discrepancy Principle ◽  
Regularization Technique ◽  
One Dimensional ◽  
Curve Method ◽  
The One

Based on the discrepancy principle, we develop in this paper a new method of choosing the location of source points to solve the backward heat conduction problem (BHCP) by using the method of fundamental solutions (MFS). The standard Tikhonov regularization technique with the L curve method for an optimal regularized parameter is adopted for solving the resultant highly ill-conditioned system of linear equations. Numerical verifications of the proposed computational method are presented for both the one-dimensional and the two-dimensional BHCP.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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