Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

scholarly journals MEMBANGUN MODEL DINAMIS PENANGKARAN POPULASI MALEO (Macrochepalon Maleo) YANG MEMPERTAHANKAN EKSISTENSINYA DARI PREDATOR

2018 ◽  
Vol 15 (2) ◽  
pp. 144-156
Author(s):  
T Gusmawan ◽  
R Ratianingsih ◽  
N Nacong
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Captive Breeding ◽  
Growth Dynamics ◽  
Growth Cycle ◽  
Extinction Condition ◽  
Spawning Habitat ◽  
Conservation Areas ◽  
Free Zone ◽  
The Stability

Maleo (Macrocephalon maleo) is one of the endangered endemic species of Sulawesi due to diminishing spawning habitat, community exploitation and predators. The dynamic model of maleo population captivity to conserve its existence from predators is a mathematical model that describes the dynamics of maleo population growth cycle (M) with the threat of predators (P). In this study, the population of eggs maleo divided into two groups that are eggs in the free zone (Tb) and eggs in breeding (Tp). The eggs are in the captive breeding will be transfered to the exposure group (E). The model represents the interaction between the predators and populations reflecting maleo in each growth phase. The model has two critical points, namely the critical point 𝑇1 = ( 0,0,0,0, 𝜑 µ2 ) describing maleo extinction condition and critical point 𝑇2 = (𝑀∗ , 𝑇𝑝∗ ,𝐸 ∗ , 𝑇𝑏∗ , 𝑃 ∗ ) which describes the endemic conditions of maleo growth dynamics. The stability analysis shows that the system is unstable at both critical points. It is because the values of the first column in the Routh Hurwitz table changes in sign. Simulations of the endemic conditions showed that the maleo and egg populations in the free zone are decreasing with respect to time even though the exposed maleo still exist. The unstable endemic indicates that the existence of maleo breeding program in conservation areas still need another efforts support.

scholarly journals Dynamics of nonlinear interacting dark energy models

2019 ◽  
Vol 28 (12) ◽  
pp. 1950161 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Supriya Pan ◽  
Weiqiang Yang
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Critical Points ◽  
Cosmological Parameters ◽  
Late Time ◽  
Interacting Dark Energy ◽  
Energy Models ◽  
Flrw Universe ◽  
The Stability ◽  
Interacting Dark Energy Models

We investigate the cosmological dynamics of interacting dark energy models in which the interaction function is nonlinear in terms of the energy densities. Considering explicitly the interaction between a pressureless dark matter and a scalar field, minimally coupled to Einstein gravity, we explore the dynamics of the spatially flat FLRW universe for the exponential potential of the scalar field. We perform the stability analysis for three nonlinear interaction models of our consideration through the analysis of critical points and we investigate the cosmological parameters and discuss the physical behavior at the critical points. From the analysis of the critical points we find a number of possibilities that include the stable late-time accelerated solution, [Formula: see text]CDM-like solution, radiation-like solution and moreover the unstable inflationary solution.

scholarly journals On the existence and stability of traversable wormhole solutions in modified theories of gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Oleksii Sokoliuk ◽  
Alexander Baransky
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Modified Theories Of Gravity ◽  
Energy Tensor ◽  
Field Equations ◽  
Traversable Wormhole ◽  
Existence And Stability ◽  
Theories Of Gravity ◽  
The Stability

AbstractWe study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$ f ( R ) = R + a R 2 , power-law $$f({\mathscr {R}}) = f_0{\mathscr {R}}^n$$ f ( R ) = f 0 R n , log-corrected $$f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$$ f ( R ) = R + α R 2 + β R 2 ln β R theories, and finally on the exponential hybrid metric-Palatini gravity $$f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$$ f ( R ^ ) = ζ ( 1 + e - R ^ Φ ) . Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state $$p_t=\omega \rho $$ p t = ω ρ . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

scholarly journals Dynamical Behavior of some families of cubic functions in complex plane

2019 ◽  
Vol 24 (7) ◽  
pp. 122
Author(s):  
Mizal H. Alobaidi ◽  
Omar Idan Kadham
Keyword(s):  
Fixed Points ◽  
Critical Point ◽  
Complex Plane ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Open Disc ◽  
Origin Point

The current study deals with the dynamical behavior of three cubic functions in the complex plane. Critical and fixed points of all of them were studied . Properties of every point were studied and the nature of them was determined if it is either attracting or repelling. First function  such that have two critical points  and three fixed points  such that is attracting when  is origin point As shown in figure (2).And  are attracting when  is the region specified by open disc  shown in figure (1.(c)).Second function  such that have two critical points   and three fixed points such that  is attracting when  and that its path is to the origin point as shown in figure (4).And  are attractive when  represents the open disc shown in the figure (3.(c)).Third function  such that  have one critical point  and three fixed points  is attracting that is path is the origin point and  are repelling as shown in figure (5). And all 2-cycles of  are repelling and unstable .   http://dx.doi.org/10.25130/tjps.24.2019.139

scholarly journals Screenings in modified gravity: a perturbative approach

2019 ◽  
Vol 622 ◽  
pp. A62 ◽  
Author(s):  
Alejandro Aviles ◽  
Jorge L. Cervantes-Cota ◽  
David F. Mota
Keyword(s):  
Theoretical Models ◽  
Modified Theories Of Gravity ◽  
Jordan Frame ◽  
Third Order ◽  
Perturbative Approach ◽  
Growth Functions ◽  
Perturbative Methods ◽  
Klein Gordon ◽  
Theories Of Gravity ◽  
Jordan And Einstein Frames

We present a formalism to study screening mechanisms in modified theories of gravity through perturbative methods in different cosmological scenarios. We consider Einstein-frame posed theories that are recast as Jordan-frame theories, where a known formalism is employed, although the resulting nonlinearities of the Klein–Gordon equation acquire an explicit coupling between matter and the scalar field, which is absent in Jordan-frame theories. The obtained growth functions are then separated into screening and non-screened contributions to facilitate their analysis. This allows us to compare several theoretical models and to recognize patterns that can be used to distinguish models and their screening mechanisms. In particular, we find anti-screening features in the symmetron model. In contrast, chameleon-type theories in both the Jordan and Einstein frames always present a screening behaviour. Up to third order in perturbation, we find no anti-screening behaviour in theories with a Vainshtein mechanism, such as the Dvali Gabadadze Porrati braneworld model and the cubic Galileon.

scholarly journals MODEL MATEMATIKA KEARIFAN LOKAL MASYARAKATDESA TRUSMI DALAM MENJAGA EKSISTENSIKERAJINAN BATIK TULIS

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Arif Muchyidin
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Numerical Simulation ◽  
National Identity ◽  
Differential Equations ◽  
Critical Point ◽  
Critical Points ◽  
System Of Differential Equations ◽  
The Stability ◽  
The Village

Batik as an Indonesian national identity has contributed greatly to the Indonesian economy. However, the value of exports and other economic potentials are not supported by the number of batik, especially batik artisans in the village Trusmi. Trusmi batik artisans in the village is a craftsman who has been there all the time and remain there for generations. The phenomenon that occurs in the craft of batik Trusmi analyzed with mathematical modeling approach, in this case the dynamical system. From the resulting system of differential equations, then analyzed the stability around the critical point. From the resulting model, gained two critical points. The first critical point is a condition where there is no proficient craftmen (not expected), whereas at the second critical point is the potential of batik craftmen and proficient craftmen mutually exist, or in other words batik will still exist. From the results of numerical simulation, if , then batik Trusmi will still exist. However, if , then the number of proficient craftmen would quickly dwindle and slowly batik will be extinct.Key Words : dinamical system, critical points, stability

scholarly journals From Critical Point to Critical Point: The Two-States Model Describes Liquid Water Self-Diffusion from 623 to 126 K

Molecules ◽  
2021 ◽  
Vol 26 (19) ◽  
pp. 5899
Author(s):  
Carmelo Corsaro ◽  
Enza Fazio
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Liquid Water ◽  
Dynamical Behavior ◽  
Configurational Entropy ◽  
Industrial Applications ◽  
Detailed Knowledge ◽  
Primary Role ◽  
Self Diffusion ◽  
Liquid States

Liquid’s behaviour, when close to critical points, is of extreme importance both for fundamental research and industrial applications. A detailed knowledge of the structural–dynamical correlations in their proximity is still today a target to reach. Liquid water anomalies are ascribed to the presence of a second liquid–liquid critical point, which seems to be located in the very deep supercooled regime, even below 200 K and at pressure around 2 kbar. In this work, the thermal behaviour of the self-diffusion coefficient for liquid water is analyzed, in terms of a two-states model, for the first time in a very wide thermal region (126 K < T < 623 K), including those of the two critical points. Further, the corresponding configurational entropy and isobaric-specific heat have been evaluated within the same interval. The two liquid states correspond to high and low-density water local structures that play a primary role on water dynamical behavior over 500 K.

scholarly journals Phase space analysis of interacting dark energy in f(T) cosmology

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Mubasher Jamil ◽  
Kuralay Yesmakhanova ◽  
Davood Momeni ◽  
Ratbay Myrzakulov
Keyword(s):  
Dark Energy ◽  
Phase Space ◽  
Critical Points ◽  
Local Stability ◽  
Dark Energy Model ◽  
Dynamical Equation ◽  
Interacting Dark Energy ◽  
Attractor Solution ◽  
Interacting Dark Energy Model ◽  
The Stability

AbstractIn this paper, we examine the interacting dark energy model in f(T) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form f(T) = β√T. We show that there is one attractor solution to the dynamical equation of f(T) Friedmann equations. Further we investigate the stability in phase space for a general f(T) model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet u* = (c − 1)v* in the phase space, spanned by coordinates (u, v, Ω, T). From this critical sheet, we conclude that the coupling between the dark energy and matter c ∈ (−2, 0).

Calculation of Separatrices in Multistable Chemical Reaction Systems

1978 ◽  
Vol 33 (11) ◽  
pp. 1341-1345
Author(s):  
B. Denzel ◽  
F. F. Seelig
Keyword(s):  
Phase Space ◽  
Chemical Reaction ◽  
Critical Points ◽  
Direct Method ◽  
Initial Value ◽  
Stability Boundaries ◽  
Reaction Systems ◽  
Chemical Reaction Systems ◽  
Direct Approximation ◽  
The Stability

In multistable chemical reaction systems the space of variables is partitioned by separatrices into different cells which are the domains of attraction of the respective critical points. By numerically solving an initial value problem, which is based on the particular stability properties of separatrix manifolds, we achieve a direct approximation of the stability boundaries in the phase space. The method is principally applicable to nonlinear systems of any number of variables and, other than the direct method of Liapunov, also in regions of the phase space which are far from the critical points.

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