scholarly journals An Analytical Approximation of the Luminosity Distance in Flat Cosmologies with a Cosmological Constant

2012 ◽  
Vol 127 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Masaru Adachi ◽  
Masumi Kasai
Keyword(s):  
Cosmological Constant ◽  
Analytical Approximation ◽  
Luminosity Distance

scholarly journals The effect of the cosmological constant on a quadrupole signal in the linearized approximation

2018 ◽  
Vol 27 (02) ◽  
pp. 1850004 ◽  
Author(s):  
László Ábel Somlai ◽  
Mátyás Vasúth
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Equations Of Motion ◽  
Luminosity Distance ◽  
Background Term ◽  
Self Consistent ◽  
Linearized Theory

In this study the effects of a nonzero cosmological constant [Formula: see text] on a quadrupole gravitational wave (GW) signal are analyzed. The linearized approximation of general relativity was used, so the perturbed metric can be written as the sum of [Formula: see text] GWs and [Formula: see text] background term, originated from [Formula: see text]. The [Formula: see text] term was also included in this study. To derive physically relevant consequences of [Formula: see text] comoving coordinates are used. In these coordinates, the equations of motion (EoMs) are not self-consistent so the result of the linearized theory has to be transformed to the FRW frame. The luminosity distance and the same order of the magnitude of frequency in accordance with the detected GWs were used to demonstrate the effects of the cosmological constant.

scholarly journals A new analytical approximation of luminosity distance by optimal HPM-Padé technique

2021 ◽  
Vol 31 ◽  
pp. 100772
Author(s):  
Bo Yu ◽  
Jian-Chen Zhang ◽  
Tong-Jie Zhang ◽  
Tingting Zhang
Keyword(s):  
Analytical Approximation ◽  
Luminosity Distance

An Analytical Thermodynamic Approach to Friction of Rubber on Ice

2012 ◽  
Vol 40 (2) ◽  
pp. 124-150
Author(s):  
Klaus Wiese ◽  
Thiemo M. Kessel ◽  
Reinhard Mundl ◽  
Burkhard Wies
Keyword(s):  
Coefficient Of Friction ◽  
Liquid Layer ◽  
Contact Area ◽  
Leading Edge ◽  
Viscous Friction ◽  
Analytical Approximation ◽  
Real Contact Area ◽  
Length Scales ◽  
Real Contact ◽  
Ice Surface

ABSTRACT The presented investigation is motivated by the need for performance improvement in winter tires, based on the idea of innovative “functional” surfaces. Current tread design features focus on macroscopic length scales. The potential of microscopic surface effects for friction on wintery roads has not been considered extensively yet. We limit our considerations to length scales for which rubber is rough, in contrast to a perfectly smooth ice surface. Therefore we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible. The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water, and heat flow into the cold underlying ice. In addition, the microscopic “squeeze-out” phenomena of melted water resulting from rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area. The derived one-dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi-liquid layer,” which already exists on the “free” ice surface. It turns out that this approach meets the measured coefficient of friction in the laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed, and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in the laboratory.

An analytical approximation for the GARCH option pricing model

1999 ◽  
Vol 2 (4) ◽  
pp. 75-116 ◽  
Author(s):  
Jin-Chuan Duan ◽  
Geneviève Gauthier ◽  
Jean-Guy Simonato
Keyword(s):  
Option Pricing ◽  
Analytical Approximation ◽  
Pricing Model ◽  
Option Pricing Model
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