Search results for: Elfriede Friedmann

Authors: Hamidreza Fazlollahi

Abstract:

The Re ́nyi entropy comprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has found numerous applications in information theory. In the Re ́nyi’s argument, the area law of the black hole entropy plays a significant role. However, the total entropy can be modified by some quantum effects, motivated by the randomness of a system. In this note, by employing this modified entropy relation, we have derived corrections to Friedmann equations. Taking this entropy associated with the apparent horizon of the Friedmann-Robertson-Walker Universe and assuming the first law of thermodynamics, dE=T_A (dS)_A+WdV, satisfies the apparent horizon, we have reconsidered expanding Universe. Also, the second thermodynamics law has been examined.

Keywords: Friedmann equations, dark energy, first law of thermodynamics, Reyni entropy

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Authors: Judith Stein, Elfriede Friedmann

Abstract:

The injection of a drug into the vitreous body for the treatment of retinal diseases like wet aged-related macular degeneration (AMD) is the most common medical intervention worldwide. We develop mathematical models for drug transport in the vitreous body of a human eye to analyse the impact of different rheological models of the vitreous on drug distribution. In addition to the convection diffusion equation characterizing the drug spreading, we use porous media modeling for the healthy vitreous with a dense collagen network and include the steady permeating flow of the aqueous humor described by Darcy's law driven by a pressure drop. Additionally, the vitreous body in a healthy human eye behaves like a viscoelastic gel through the collagen fibers suspended in the network of hyaluronic acid and acts as a drug depot for the treatment of retinal diseases. In a completely liquefied vitreous, we couple the drug diffusion with the classical Navier-Stokes flow equations. We prove the global existence and uniqueness of the weak solution of the developed initial-boundary value problem describing the drug distribution in the healthy vitreous considering the permeating aqueous humor flow in the realistic three-dimensional setting. In particular, for the drug diffusion equation, results from the literature are extended from homogeneous Dirichlet boundary conditions to our mixed boundary conditions that describe the eye with the Galerkin's method using Cauchy-Schwarz inequality and trace theorem. Because there is only a small effective drug concentration range and higher concentrations may be toxic, the ability to model the drug transport could improve the therapy by considering patient individual differences and give a better understanding of the physiological and pathological processes in the vitreous.

Keywords: coupled PDE systems, drug diffusion, mixed boundary conditions, vitreous body

Procedia PDF Downloads 101

Authors: A. K. Sethi, R. N. Patra, B. Nayak

Abstract:

In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: bulk viscosity, lyra geometry, generalized chaplygin gas, cosmology

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Authors: Kwok W. Cheung

Abstract:

A scientific interpretation of creation reconciling the beliefs of six literal days of creation and a 13.7-billion-year-old universe currently perceived by most modern cosmologists is proposed. We hypothesize that the reference timeframe of God’s creation is associated with some cosmic time different from the earth's time. We show that the scale factor of earth time to cosmic time can be determined by the solution of the Friedmann equations. Based on this scale factor and some basic assumptions, we derive a Cosmic Time Dilation model that harmonizes the literal meaning of creation days and scientific discoveries with remarkable accuracy.

Keywords: cosmological expansion, time dilation, creation, genesis, relativity, Big Bang, biblical hermeneutics

Procedia PDF Downloads 31

Authors: Evariste Boj, Jan Schee

Abstract:

We present the temperature anisotropy of the cosmic microwave background radiation due to the inhomogeneity region constructed on a 3-brane in the framework of a Randall-Sundrum one brane immersed into a 5D bulk $AdS_5$ spacetime. We employ the Brane-World Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model to describe the cosmic expansion on the brane. The inhomogeneity is modeled by the static, spherically symmetric spacetime that replaces the spherically symmetric part of a dust-filled universe and is connected to the FLRW spacetime through the junction conditions. As the vacuum region expands it induces an additional frequency shift to a CMBR photon passing through this inhomogeneity in comparison to the case of a photon propagating through a pure FLRW spacetime. This frequency shift is associated with the effective temperature change of the CMBR in the corresponding direction. We give an estimate of the CMBR effective temperature changes with the change of the value of the tidal charge parameter.

Keywords: CMBR, Randall-Sundrum model, Rees-Sciama effect, Braneworld

Procedia PDF Downloads 187