scholarly journals The big contradiction between the perturbation theory and the chaotic state. A detailed mathematical analysis indicates when the plasma is stable or unstable

AIP Advances ◽  
2016 ◽  
Vol 6 (5) ◽  
pp. 055210
Author(s):  
C. L. Xaplanteris ◽  
S. C. Xaplanteris
Keyword(s):  
Perturbation Theory ◽  
Mathematical Analysis ◽  
Chaotic State ◽  
Detailed Mathematical Analysis

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

scholarly journals Structural Health Monitoring of 2D Plane Structures

2021 ◽  
Vol 11 (5) ◽  
pp. 2000
Author(s):  
Behnam Mobaraki ◽  
Haiying Ma ◽  
Jose Antonio Lozano Galant ◽  
Jose Turmo
Keyword(s):  
Mechanical Properties ◽  
Health Monitoring ◽  
Mathematical Analysis ◽  
Stiffness Matrix ◽  
State Of The Art ◽  
System Of Equations ◽  
Matrix System ◽  
Structural System ◽  
Detailed Mathematical Analysis ◽  
Structural System Identification

This paper presents the application of the observability technique for the structural system identification of 2D models. Unlike previous applications of this method, unknown variables appear both in the numerator and the denominator of the stiffness matrix system, making the problem non-linear and impossible to solve. To fill this gap, new changes in variables are proposed to linearize the system of equations. In addition, to illustrate the application of the proposed procedure into the observability method, a detailed mathematical analysis is presented. Finally, to validate the applicability of the method, the mechanical properties of a state-of-the-art plate are numerically determined.

On the Reduction of Wall Temperature Non-Uniformity of a Three-Dimensional Experimental Apparatus

2009 ◽  
Author(s):  
P. Y. C. Lee ◽  
W. H. Leong
Keyword(s):  
Heat Source ◽  
Temperature Difference ◽  
Mathematical Analysis ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Measured Temperature ◽  
Uniform Temperature ◽  
Original Design ◽  
Experimental Apparatus ◽  
Detailed Mathematical Analysis

This paper presents a detailed analysis that was performed for the design of a “uniform” temperature boundary condition imposed on a boundary of a three-dimensional cubical experimental apparatus for benchmark natural convection heat transfer study. The three-dimensional experimental apparatus was constructed with plates which were assembled to act as boundary conditions to the enclosure walls. Test measurements revealed that temperature non-uniformity along one of the plates (boundary) was significant enough that the benchmark study could not be carried out to the desired accuracy of about 1% error. A subsequent detailed mathematical analysis revealed that the temperature non-uniformity on the plate was a result of the effect of thermal spreading/constriction resistance. Modifications to the original design of the apparatus were made to reduce the temperature non-uniformity on the plate by adding a heat source around the plate where the uniform temperature setting was desired. Before the addition of this heat source, a careful mathematical analysis shows a significant reduction in temperature non-uniformity from about 4% (based on the initial design) to less than 1% (for the modified design). By examining the temperature difference between two locations on the plate, the predicted temperature difference obtained through mathematical analyses show excellent agreement with the measured temperature difference.

scholarly journals SYSTEMATIC SEARCH OF EXACTLY SOLVABLE NON-CENTRAL POTENTIALS

2005 ◽  
Vol 20 (05) ◽  
pp. 355-361 ◽  
Author(s):  
B. GÖNÜL ◽  
M. KOÇAK
Keyword(s):  
Perturbation Theory ◽  
Mathematical Analysis ◽  
Systematic Search ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
Present Formalism

Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis of the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the effectiveness of the present formalism.

QUALITATIVE RESONANCE OF SHIL'NIKOV-LIKE STRANGE ATTRACTORS, PART II: MATHEMATICAL ANALYSIS

2004 ◽  
Vol 14 (03) ◽  
pp. 893-912 ◽  
Author(s):  
OSCAR DE FEO
Keyword(s):  
Mathematical Analysis ◽  
Chaotic Behavior ◽  
Geometrical Model ◽  
Homoclinic Bifurcation ◽  
Resonance Phenomenon ◽  
External Signal ◽  
Strongly Correlated ◽  
Detailed Mathematical Analysis ◽  
And Control ◽  
Peculiar Behavior

This is the second of two papers introducing a new dynamical phenomenon, strongly related to the problems of synchronization and control of chaotic dynamical systems, and presenting the corresponding mathematical analysis, conducted both experimentally and theoretically. In particular, it is shown that different dynamical models (ordinary differential equations) admitting chaotic behavior organized by a homoclinic bifurcation to a saddle-focus (Shil'nikov-like chaos) tend to have a particular selective property when externally perturbed. Namely, these systems settle on a very narrow chaotic behavior, which is strongly correlated to the forcing signal, when they are slightly perturbed with an external signal which is similar to their corresponding generating cycle. Here, the "generating cycle" is understood to be the saddle cycle colliding with the equilibrium at the homoclinic bifurcation. On the other hand, when they are slightly perturbed with a generic signal, which has no particular correlation with their generating cycle, their chaotic behavior is reinforced. This peculiar behavior has been called qualitative resonance underlining the fact that such chaotic systems tend to resonate with signals that are qualitatively similar to an observable of their corresponding generating cycle. Here, a detailed mathematical analysis of the qualitative resonance phenomenon is presented, confirming the intuitions given by the geometrical model discussed in Part I.

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