scholarly journals DARBOUX CLASS OF COSMOLOGICAL FLUIDS WITH TIME-DEPENDENT ADIABATIC INDICES

2000 ◽  
Vol 15 (15) ◽  
pp. 979-990 ◽  
Author(s):  
H. C. ROSU
Keyword(s):  
Mathematical Method ◽  
Cosmological Constant ◽  
Time Dependence ◽  
Adiabatic Index ◽  
Time Dependent ◽  
Accelerating Universe ◽  
Constant Parameter ◽  
Darboux Transformations ◽  
Scale Factors ◽  
Experimental Findings

A one-parameter family of time-dependent adiabatic indices is introduced for any given type of cosmological fluid of constant adiabatic index by a mathematical method belonging to the class of Darboux transformations. The procedure works for zero cosmological constant at the price of introducing a new constant parameter related to the time dependence of the adiabatic index. These fluids can be the real cosmological fluids that are encountered at cosmological scales and they could be used as a simple and efficient explanation for the recent experimental findings regarding the present day accelerating universe. In addition, new types of cosmological scale factors, corresponding to these fluids, are presented.

TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

scholarly journals Time Dependence of Various Cosmological Parameters in the Framework of Kaluza-Klein Space-Time

2019 ◽  
pp. 211-220
Author(s):  
Sudipto Roy ◽  
Anirban Sarkar ◽  
Pritha Ghosh
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Cosmological Parameters ◽  
Accelerated Expansion ◽  
Accelerating Universe ◽  
Field Equations ◽  
Eos Parameter ◽  
Klein Theory ◽  
Time Variations ◽  
Kaluza Klein

A theoretical model, regarding the time dependence of several cosmological parameters, has been constructed in the present study, in the framework of Kaluza-Klein theory, using its field equations for a spatially flat metric. Time dependent empirical expressions of the cosmological constant and the equation of state (EoS) parameter have been substituted into the field equations to determine the time dependence of various cosmological parameters. Time variations of these parameters have been shown graphically. The cosmological features obtained from this model are found to be in agreement with the observed characteristics of the accelerating universe. Interestingly, the signature flipping of the deceleration parameter, from positive to negative, is predicted by this model, indicating a transformation of the universe from a state of decelerated expansion to accelerated expansion, as obtained from astrophysical observations. Time dependence of the gravitational constant (G), energy density (?), cosmological constant (?) and the EoS parameter (?) have been determined and depicted graphically in the present study.

scholarly journals Renormalization Group Approach to Pandemics as a Time-Dependent SIR Model

2021 ◽  
Vol 8 ◽  
Author(s):  
Michele Della Morte ◽  
Francesco Sannino
Keyword(s):  
Renormalization Group ◽  
Time Dependence ◽  
Recovery Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Cumulative Number ◽  
Group Approach ◽  
Renormalization Group Approach

We generalise the epidemic Renormalization Group framework while connecting it to a SIR model with time-dependent coefficients. We then confront the model with COVID-19 in Denmark, Germany, Italy and France and show that the approach works rather well in reproducing the data. We also show that a better understanding of the time dependence of the recovery rate would require extending the model to take into account the number of deaths whenever these are over 15% of the cumulative number of infected cases.

scholarly journals The Diffraction of Transient Electro-Magnetic Waves by a Wedge

1958 ◽  
Vol 11 (2) ◽  
pp. 95-103 ◽  
Author(s):  
A. C. Butcher ◽  
J. S. Lowndes
Keyword(s):  
Wave Equation ◽  
Time Dependence ◽  
Half Plane ◽  
Line Source ◽  
Time Dependent ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Electro Magnetic ◽  
Infinite Wedge ◽  
Magnetic Waves

Much of the work on the theory of diffraction by an infinite wedge has been for cases of harmonic time-dependence. Oberhettinger (1) obtained an expression for the Green's function of the wave equation in the two dimensional case of a line source of oscillating current parallel to the edge of a wedge with perfectly conducting walls. Solutions of the time-dependent wave equation have been obtained by Keller and Blank (2), Kay (3) and more recently by Turner (4) who considered the diffraction of a cylindrical pulse by a half plane.

scholarly journals The Large Number Hypothesis and Einstein's Theory of Gravitation

1985 ◽  
Vol 38 (4) ◽  
pp. 547 ◽  
Author(s):  
Yun-Kau Lau
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Matter Density ◽  
Time Dependent ◽  
Field Equations ◽  
Large Number Hypothesis ◽  
Theory Of Gravitation ◽  
The Mean ◽  
Limiting Case ◽  
The Universe

In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch.

scholarly journals Time dependence of recruitment and derecruitment in the lung: a theoretical model

2002 ◽  
Vol 93 (2) ◽  
pp. 705-713 ◽  
Author(s):  
Jason H. T. Bates ◽  
Charles G. Irvin
Keyword(s):  
Mechanical Ventilation ◽  
Theoretical Model ◽  
Lung Injury ◽  
Time Dependence ◽  
Computer Model ◽  
Lung Volume ◽  
Critical Pressure ◽  
Time Dependent ◽  
Lung Elastance ◽  
Parallel Arrangement

Recruitment and derecruitment (R/D) of air spaces within the lung is greatly enhanced in lung injury and is thought to be responsible for exacerbating injury during mechanical ventilation. There is evidence to suggest that R/D is a time-dependent phenomenon. We have developed a computer model of the lung consisting of a parallel arrangement of airways and alveolar units. Each airway has a critical pressure (Pcrit) above which it tends to open and below which it tends to close but at a rate determined by how far pressure is from Pcrit. With an appropriate distribution of Pcrit and R/D velocity characteristics, the model able to produce realistic first and second pressure-volume curves of a lung inflated from an initially degassed state. The model also predicts that lung elastance will increase transiently after a deep inflation to a degree that increases as lung volume decreases and as the lung becomes injured. We conclude that our model captures the time-dependent mechanical behavior of the lung due to gradual R/D of lung units.

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