MATHEMATICAL MODEL OF THE FORMATION OF THE SPIRAL STRUCTURE OF GALAXIES UNDER THE ACTION OF CORIOLIS FORCES ON A FOUR-DIMENSIONAL HYPERSPHERE

The topic of the top motions is not new but the known publications represent wrong mathematical models for its gyroscopic effects. Recent investigations have demonstrated the physics of gyroscopic effects is more complex. On any spinning objects are acting the system of interrelated internal torques generated by their rotating mass elements and center mass. The inertial torque is produced by the centrifugal, common inertial and Coriolis forces, as well as the change in the angular momentum. These inertial torqueses represent the fundamental principle of gyroscope theory. The new inertial torques enables deriving mathematical models for the motions of any rotating objects that were impossible for a long time. The aim of this work is to represent mathematical models for the motions of the well-balanced top on the flat horizontal surface. This work describes the physics of the top motions and closes the problem of many years of discussion. The new analytical approach for the top’s motions definitely responds to the practical results and represents a good example of the educational process.

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Modeling of the upwelling hydrodynamics in the Aegean Sea

Mediterranean Marine Science ◽

10.12681/mms.205 ◽

2004 ◽

Vol 5 (1) ◽

pp. 5 ◽

Cited By ~ 6

Author(s):

Y.G. SAVVIDIS ◽

M.G. DODOU ◽

Y.N. KRESTENITIS ◽

C.G. KOUTITAS

Keyword(s):

Mathematical Model ◽

Significant Contribution ◽

Numerical Models ◽

Aegean Sea ◽

Coastal Zones ◽

Initial Water ◽

Coriolis Forces ◽

Heated Zone ◽

Finite Differences Method ◽

Water Layers

The special features of the hydrodynamic circulation in the Aegean Sea referring to the development of regional upwelling coastal zones are studied by means of a mathematical model. The modeling effort is focused on the tracing of coastal areas, where upwelling events are frequently observed during the summer meteorological conditions. These areas are characterized by the enrichment of surface waters with nutrients and, consequently, increased fish production. The phenomenon is studied by the use of a two-layer mathematical model comprising the surface heated zone and the rest of the water column. The numerical solution of the model is based on the finite differences method. The wind shear applied over the stratified basin, with predefined density stratification and initial water-layers thickness, and the gravity and Coriolis forces taken into account, constitute the basic external factors for the generation of the hydrodynamic circulation in the area of the Aegean Sea. The calibration and the validation of the model are performed by the comparison of the model output to the data and observations reported in valid scientific sources. The aim of the paper is to demonstrate the significant contribution of numerical models to the better understanding of the hydrodynamics governing the Aegean water circulation as well as the tracing of upwelling zones.

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Density waves in disk galaxies

Symposium - International Astronomical Union ◽

10.1017/s0074180900101135 ◽

1967 ◽

Vol 31 ◽

pp. 313-317 ◽

Cited By ~ 8

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.

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