scholarly journals Growth rate of cosmological perturbations in standard model: Explicit analytical solution

2003 ◽  
Vol 399 (1) ◽  
pp. 19-21 ◽  
Author(s):  
A. D. Chernin ◽  
D. I. Nagirner ◽  
S. V. Starikova
Keyword(s):  
Growth Rate ◽  
Analytical Solution ◽  
Standard Model ◽  
Cosmological Perturbations ◽  
Explicit Analytical Solution

scholarly journals Boundary problem on semi-direct for pseudoparabolic equation with a small parametr

2020 ◽  
pp. 29-41
Author(s):  
Б.С. Аблабеков ◽  
А.Т. Муканбетова
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Boundary Problem ◽  
Unique Solvability ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Pseudoparabolic Equation ◽  
Explicit Analytical Solution ◽  
Initial Boundary Value

Данная статья посвящена построению классического решения краевой задачи на полупрямой для линейного псевдопараболического уравнения с малым параметром. Для построения явного решения используется метод преобразование Фурье. В работе исследуется вопрос об однозначной разрешимости начально-краевой задачи для псевдопараболического уравнения с малым параметром на полуоси. Получено явное аналитическое решение поставленной задачи. In this paper, we study the question of the unique solvability of the initial-boundary-value problem for a pseudoparabolic equation with a small parameter on the semi-axis. An explicit analytical solution to the problem is obtained.

ENTANGLEMENT DYNAMICS IN THE THREE-ATOM TAVIS-CUMMINGS MODEL

2009 ◽  
Vol 07 (05) ◽  
pp. 1001-1007 ◽  
Author(s):  
JIAN-SONG ZHANG ◽  
AI-XI CHEN
Keyword(s):  
Electromagnetic Field ◽  
Analytical Solution ◽  
Quantum System ◽  
Single Mode ◽  
Interaction Time ◽  
Entanglement Dynamics ◽  
Cavity Field ◽  
W States ◽  
Explicit Analytical Solution

We investigate the entanglement dynamics in a quantum system consisting of three two-level atoms resonantly coupled to a single mode electromagnetic field in a cavity. An explicit analytical solution of the system is obtained and the entanglement of the system is studied with the help of the concurrence and tangle. It is also shown that the W states could be generated if the interaction time of the two-level atoms and the cavity field is chosen appropriately.

scholarly journals Hints of modified gravity in cosmos and in the lab?

2019 ◽  
Vol 28 (05) ◽  
pp. 1942001 ◽  
Author(s):  
Leandros Perivolaropoulos ◽  
Lavrentios Kazantzidis
Keyword(s):  
Growth Rate ◽  
Modified Gravity ◽  
Gravitational Theory ◽  
Fine Tuning ◽  
Cosmological Perturbations ◽  
Accelerating Expansion ◽  
Wide Range ◽  
Expansion Of The Universe ◽  
Gravity Theories ◽  
Parameter Values

General Relativity (GR) is consistent with a wide range of experiments/observations from millimeter scales up to galactic scales and beyond. However, there are reasons to believe that GR may need to be modified because it includes singularities (it is an incomplete theory) and also it requires fine-tuning to explain the accelerating expansion of the universe through the cosmological constant. Therefore, it is important to check various experiments and observations beyond the above range of scales for possible hints of deviations from the predictions of GR. If such hints are found it is important to understand which classes of modified gravity theories are consistent with them. The goal of this review is to summarize recent progress on these issues. On sub-millimeter scales, we show an analysis of the data of the Washington experiment [D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle and H. E. Swanson, Phys. Rev. Lett. 98 (2007) 021101, arXiv:hep-ph/0611184 [hep-ph]] searching for modifications of Newton’s Law on sub-millimeter scales and demonstrate that a spatially oscillating signal is hidden in this dataset. We demonstrate that even though this signal cannot be explained in the context of standard modified theories (viable scalar tensor and [Formula: see text] theories), it is a rather generic prediction of nonlocal gravity theories. On cosmological scales we review recent analyses of Redshift Space Distortion (RSD) data which measure the growth rate of cosmological perturbations at various redshifts and show that these data are in some tension with the [Formula: see text]CDM parameter values indicated by Planck/2015 CMB data at about [Formula: see text] level. This tension can be reduced by allowing for an evolution of the effective Newton constant that determines the growth rate of cosmological perturbations. We conclude that even though this tension between the data and the predictions of GR could be due to systematic/statistical uncertainties of the data, it could also constitute early hints pointing towards a new gravitational theory.

An explicit analytical solution for calculating horizontal stress changes and displacements around an excavated diaphragm wall panel

2003 ◽  
Vol 40 (4) ◽  
pp. 780-792 ◽  
Author(s):  
C WW Ng ◽  
G H Lei
Keyword(s):  
Analytical Solution ◽  
Uniaxial Stress ◽  
Horizontal Stress ◽  
Ease Of Use ◽  
Elastic Solution ◽  
Diaphragm Wall ◽  
Wall Panel ◽  
Principle Of Superposition ◽  
Explicit Analytical Solution ◽  
Stress Changes

A new, simple, and explicit analytical solution has been derived for calculating horizontal stress changes and displacements caused by the excavation for a diaphragm wall panel. The theoretical solution is obtained by applying the principle of superposition appropriately to model diaphragm wall construction using a basic elastic solution to the problem of an infinite horizontal plate with a rectangular opening subjected to a uniaxial stress at infinity. The basic elastic solution can be obtained by using the method of complex variables with a simplified conformal transformation function. Key parameters governing the magnitude of horizontal stress changes and displacements are identified. Computed results are given in a normalized form in terms of aspect ratio (length to width) of a diaphragm wall panel. Two extreme cases for diaphragm wall panels with dimensions 1 m × 1 m and 10 m × 1 m have been analysed to investigate the distributions of stress changes and deformations around the panels during the bentonite stage. By performing a parametric study, calculation charts have been developed for computing horizontal stress changes and displacements for practising engineers and researchers to carry out preliminary designs and for numerical modellers to verify their sophisticated predictions. The ease of use of the charts is illustrated by two examples, and the limitations of the derived solutions are discussed.Key words: diaphragm wall, elasticity, stress change, displacement, stress analysis, earth pressure.

ENTANGLEMENT DYNAMICS OF TWO TWO-MODE TWO-PHOTON JAYNES–CUMMINGS MODELS IN THE PRESENCE OF PHASE DECOHERENCE

2008 ◽  
Vol 22 (08) ◽  
pp. 561-568 ◽  
Author(s):  
JIAN-SONG ZHANG ◽  
JING-BO XU
Keyword(s):  
Analytical Solution ◽  
Finite Time ◽  
Entanglement Dynamics ◽  
Two Photon ◽  
Explicit Analytical Solution ◽  
Phase Decoherence ◽  
Entangled Atoms

We investigate the entanglement of two two-mode two-photon Jaynes–Cummings models in the presence of phase decoherence. We find an explicit analytical solution of the system and discuss the influence of the phase decoherenc on the entanglement dynamics. Our results shows that the entanglement of the two initially entangled atoms can remain zero for a finite time and revive later. However, if the phase decoherence is taken into accounted, the entanglement cannot revive completely.

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