scholarly journals First order necessary conditions of optimality for the two dimensional tidal dynamics system

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Manil T. Mohan ◽  
Author(s):  
Jonathan Cagan ◽  
Brian C. Williams

Abstract The first-order necessary conditions of optimality are extended to include information about robust design — cost insensitivity to model inaccuracies and changes in design specification, as well as the manufacturing tolerances treated in more traditional approaches. In these extended conditions, the Lagrangian is formulated as a tradeoff between cost and cost variability, where variability is measured as the flatness and curvature of the objective relative to local variations in design variables and constraints. During optimization these conditions allow cost and robustness to be considered simultaneously at each iteration.


2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.


1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.


1972 ◽  
Vol 39 (3) ◽  
pp. 689-695 ◽  
Author(s):  
W. W. Recker

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.


1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.


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