Sufficient Extremum Conditions

1972 ◽  
pp. 114-120
Author(s):  
Igor Vladimirovich Girsanov ◽  
B. T. Poljak
Keyword(s):  
Extremum Conditions

scholarly journals Optimized random-phase approximations for arbitrary reference systems: Extremum conditions and thermodynamic consistence

1998 ◽  
Vol 57 (1) ◽  
pp. 460-464 ◽  
Author(s):  
G. Pastore ◽  
O. Akinlade ◽  
F. Matthews ◽  
Z. Badirkhan
Keyword(s):  
Random Phase ◽  
Reference Systems ◽  
Arbitrary Reference ◽  
Extremum Conditions

An Experimental Study of Plane Plumes in Cold Water

1983 ◽  
Vol 105 (2) ◽  
pp. 248-254 ◽  
Author(s):  
Y. Joshi ◽  
B. Gebhart
Keyword(s):  
Buoyancy Force ◽  
Cold Water ◽  
Pure Water ◽  
Density Variation ◽  
Complex Flow ◽  
Flow Temperature ◽  
Ambient Temperatures ◽  
Density Relation ◽  
Convective Motions ◽  
Extremum Conditions

The peculiar density variation of water with temperature makes the Boussinesq approximations invalid in the vicinity of density extremum conditions. The buoyancy force reversals which often arise from the density extremum have been studied in many recent investigations. The formulation of an accurate density relation has resulted in a simplified analysis for many convective motions. Two such analyses have dealt with the flow generated above a heated line source in cold water, around the extremum point. We present an experimental investigation of such flow. Temperature measurements have been carried out for ambient temperatures, t∞ ≥ tm, the temperature of density extremum, for pure water at atmospheric pressure. These measurements are in satisfactory agreement with the analyses. As the ambient temperature is successively increased above the density extremum temperature, the transformation of the flow behaviour from non-Boussinesq to Boussinesq is very clearly observed. Velocity measurements have been made at t∞=4°C, the extremum temperature. For t∞<tm, very complex flow patterns exist, due to the bidirectional buoyancy force. These patterns have been visualized. The influence of a bounding impermeable surface below the plume source has also been examined.

scholarly journals Localization of periodic orbits of autonomous systems based on high-order extremum conditions

2004 ◽  
Vol 2004 (3) ◽  
pp. 277-290 ◽  
Author(s):  
Konstantin E. Starkov
Keyword(s):  
Periodic Orbits ◽  
Algebraic Surface ◽  
Polynomial System ◽  
Autonomous Systems ◽  
High Order ◽  
Mass Action ◽  
Nonsingular Solution ◽  
Localization Analysis ◽  
The Mathematical Model ◽  
Extremum Conditions

This paper gives localization and nonexistence conditions of periodic orbits in some subsets of the state space. Mainly, our approach is based on high-order extremum conditions, on high-order tangency conditions of a nonsingular solution of a polynomial system with an algebraic surface, and on some ideas related to algebraically-dependent polynomials. Examples of the localization analysis of periodic orbits are presented including the Blasius equations, the generalized mass action (GMA) system, and the mathematical model of the chemical reaction with autocatalytic step.

scholarly journals Optimal regular reflection of shock and blast waves

2018 ◽  
Vol 245 ◽  
pp. 12005 ◽  
Author(s):  
Mihail Chernyshov ◽  
Alexandr Tyapko
Keyword(s):  
Gas Flow ◽  
Static Pressure ◽  
Blast Waves ◽  
Regular Reflection ◽  
Reflection Point ◽  
Equivalent Problem ◽  
Supersonic Gas Flow ◽  
Inclined Surface ◽  
Steady Shock ◽  
Extremum Conditions

The regular reflection of an oblique steady shock in supersonic gas flow is considered. The static pressure extremum conditions after the point of reflection of the shock with fixed strength depending on oncoming flow Mach number are determined analytically. The obtained results are applied to solution of the mechanically equivalent problem of the reflection of a propagating shock from an inclined surface. Non-monotonic variation of the mechanical loads on the obstacle with respect to its inclination angle is shown; the obstacle slope angles that correspond to pressure minima downwards of the unsteady shock reflection point are determined analytically.

LOCALIZING BOUNDS FOR COMPACT INVARIANT SETS OF NONLINEAR SYSTEMS POSSESSING FIRST INTEGRALS WITH APPLICATIONS TO HAMILTONIAN SYSTEMS

2010 ◽  
Vol 20 (05) ◽  
pp. 1477-1483 ◽  
Author(s):  
KONSTANTIN E. STARKOV
Keyword(s):  
Hamiltonian System ◽  
Nonlinear Systems ◽  
Hamiltonian Systems ◽  
Positive Definite ◽  
First Integrals ◽  
Invariant Sets ◽  
Yang Mills ◽  
First Order ◽  
Special Case ◽  
Extremum Conditions

In this paper, we study the localization problem of compact invariant sets of nonlinear systems possessing first integrals by using the first order extremum conditions and positive definite polynomials. In the case of natural polynomial Hamiltonian systems, our results include those in [Starkov, 2008] as a special case. This paper discusses the application to studies of the generalized Yang–Mills Hamiltonian system and the Hamiltonian system describing dynamics of hydrogenic atoms in external fields.

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