scholarly journals Circular and transverse wave solutions of non-linear hyperbolic systems of equations

1968 ◽  
Vol 16 (2) ◽  
pp. 117-126
Author(s):  
Robin J. Waterston
Keyword(s):  
Hyperbolic Systems ◽  
Finite Elasticity ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Transverse Waves ◽  
Hyperbolic Systems Of Equations ◽  
Wide Range ◽  
Non Linear ◽  
Physical Phenomena ◽  
Non Linear Equations

Circularly and transversely polarised (henceforth called circular and transverse) waves have been shown to occur as solutions of non-linear equations governing a wide range of physical phenomena, including finite elasticity (1), magnetohydrodynamics (2), and gyromagnetism (3), but only when the material properties of the medium are isotropic with respect to the direction of wave propagation. This paper is an attempt to unify and generalise these results.

Equilibrium Thermodynamics of Combustion by Means of Genetic Algorithms

2005 ◽  
Author(s):  
S. Brusca ◽  
R. Lanzafame ◽  
M. Messina
Keyword(s):  
Equivalence Ratio ◽  
Linear Equations ◽  
Combustion Process ◽  
Genetic Approach ◽  
Equilibrium Equations ◽  
Linear Set ◽  
Wide Range ◽  
Non Linear ◽  
Release Analysis ◽  
Non Linear Equations

In order to carry out an accurate heat release analysis, it is necessary to solve a non linear set of chemical equilibrium equations to calculate concentrations of the species present in cylinder gases during the combustion process. So, the thermodynamics properties of the mixture can be evaluated. The present paper deals with the study of the thermodynamics of combustion using a genetic approach. A genetic algorithm was used to solve the set of non linear equations. The goal of this method is the possibility of solving the equations set in a wide range of pressure, temperature and equivalence ratio combinations, where more traditional methods are often found to fail.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

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