scholarly journals Collapsing stellar filament and exotic matter in Palatini f(R) gravity

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Rubab Manzoor ◽  
Abdul Jawad ◽  
Muhammad Adeel ◽  
Muhammad Saeed ◽  
Shamaila Rani
Keyword(s):  
Gravitational Waves ◽  
Radial Pressure ◽  
Surface Boundary ◽  
Baryonic Matter ◽  
Junction Conditions ◽  
Stability Criteria ◽  
Theoretical Relation ◽  
Gravitational Effects ◽  
Proportional Relation ◽  
The Stability

Abstract We explore the dynamics of collapsing stellar filament in the presence of exotic material like dark matter. We use Palatini f(R) theory to include exotic substance in the collapsing process. We derive a collapse equation by applying Darmois junction conditions on collapsing surface boundary $$\Sigma $$Σ. It is found that the radial pressure related to baryonic matter remains non-zero at $$\Sigma $$Σ. We then discuss the stability criteria of the collapsing process in the framework of three parameteric model, $$f(R)=R+\lambda R_{c}[ 1-(1+\frac{R^{2}}{R^{2}_{c}})^{-n}]$$f(R)=R+λRc[1-(1+R2Rc2)-n]. It is concluded that the stability of collapsing filament depends upon a directly proportional relation of gravitational effects of exotic terms with the radial pressure of seen matter. Stability criteria of family of polytropic filamentary structures are also discussed. For all stable polytropic filaments, it is found that the density of seen material is exponentially related to the exotic forces. Finally, we explore theoretical relation between gravitational waves and dark terms. It is theoretically predicted that the presence of exotic material can affect the propagation of gravitational waves.

Dynamics of collapsing stellar filament and exotic matter

2020 ◽  
Vol 29 (05) ◽  
pp. 2050036
Author(s):  
Rubab Manzoor ◽  
M. Adeel ◽  
M. Saeed
Keyword(s):  
Radial Pressure ◽  
Matter Density ◽  
Junction Conditions ◽  
Stability Criteria ◽  
Filamentary Structure ◽  
Gravitational Effects ◽  
Starobinsky Model ◽  
Visible Matter ◽  
Polytropic Equation ◽  
The Stability

This paper studies the collapse of stellar filaments in the presence of dark matter (DM). We use [Formula: see text] gravity to involve DM in the collapse. We apply Darmois junction conditions (DJCs) on the surface of collapsing boundary [Formula: see text] and obtain the collapse equation. The radial pressure associated with the seen matter is found to be nonzero at [Formula: see text]. We then use Starobinsky model, [Formula: see text], as a candidate of DM to obtain stability criteria (SC) of the collapsing body. It is found that the stability of filamentary structure relates radial pressure of baryonic directly with the gravitational effects of DM. Stability of polytropic family of filaments are studied by applying polytropic equation of state to baryonic contribution. For all polytropic stable filaments, it turns out that the visible matter density is exponentially linked to effects of DM. Finally, we discuss connection between exotic terms and gravitational waves (GW). It is theoretically indicated that the presence of DM can affect the GW propagation.

Dissipative instability of the MHD tangential discontinuity in magnetized plasmas with anisotropic viscosity and thermal conductivity

1996 ◽  
Vol 56 (2) ◽  
pp. 285-306 ◽  
Author(s):  
M. S. Ruderman ◽  
E. Verwichte ◽  
R. Erdélyi ◽  
M. Goossens
Keyword(s):  
Thermal Conductivity ◽  
Dispersion Equation ◽  
Viscosity Coefficient ◽  
Tangential Discontinuity ◽  
Stability Criteria ◽  
Threshold Velocity ◽  
Cold Plasmas ◽  
The Difference ◽  
The Stability ◽  
Anisotropic Viscosity

The stability of the MHD tangential discontinuity is studied in compressible plasmas in the presence of anisotropic viscosity and thermal conductivity. The general dispersion equation is derived, and solutions to this dispersion equation and stability criteria are obtained for the limiting cases of incompressible and cold plasmas. In these two limiting cases the effect of thermal conductivity vanishes, and the solutions are only influenced by viscosity. The stability criteria for viscous plasmas are compared with those for ideal plasmas, where stability is determined by the Kelvin—Helmholtz velocity VKH as a threshold for the difference in the equilibrium velocities. Viscosity turns out to have a destabilizing influence when the viscosity coefficient takes different values at the two sides of the discontinuity. Viscosity lowers the threshold velocity V below the ideal Kelvin—Helmholtz velocity VKH, so that there is a range of velocities between V and VKH where the overstability is of a dissipative nature.

Intrinsic Thermal Stability of Anisotropic Thin-Film Superconductors

1990 ◽  
Vol 112 (1) ◽  
pp. 10-15 ◽  
Author(s):  
M. I. Flik ◽  
C. L. Tien
Keyword(s):  
Thin Film ◽  
Thermal Stability ◽  
Stability Criterion ◽  
High Temperature Superconductors ◽  
Stability Criteria ◽  
Anisotropic Thermal Conductivity ◽  
Operating Current ◽  
Released Energy ◽  
The Stability ◽  
Thermal Stability Of

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without resistance at all times after the occurrence of a localized release of thermal energy. This novel stability criterion is different from the cryogenic stability criteria for magnets and has particular relevance to thin-film superconductors. Crystals of ceramic high-temperature superconductors are likely to exhibit anisotropic thermal conductivity. The resultant anisotropy of highly oriented films of superconductors greatly influences their thermal stability. This work presents an analysis for the maximum operating current density that ensures intrinsic stability. The stability criterion depends on the amount of released energy, the Biot number, the aspect ratio, and the ratio of the thermal conductivities in the plane of the film and normal to it.

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

An anisotropic charged fluids with Chaplygin equation of state

2021 ◽  
Vol 36 (21) ◽  
pp. 2150153
Author(s):  
Joaquin Estevez-Delgado ◽  
Noel Enrique Rodríguez Maya ◽  
José Martínez Peña ◽  
Arthur Cleary-Balderas ◽  
Jorge Mauricio Paulin-Fuentes
Keyword(s):  
Speed Of Sound ◽  
Radial Pressure ◽  
State Equation ◽  
Stellar Model ◽  
Compact Objects ◽  
Anisotropic Fluid ◽  
The Stability ◽  
Electrically Charged ◽  
Chaplygin Equation ◽  
Graphic Description

A stellar model with an electrically charged anisotropic fluid as a source of matter is presented. The radial pressure is described by a Chaplygin state equation, [Formula: see text], while the anisotropy [Formula: see text] is annulled in the center of the star [Formula: see text] is regular and [Formula: see text], the electric field, is also annulled in the center. The density pressures and the tangential speed of sound are regular, while the radial speed of sound is monotonically increasing. The model is physically acceptable and meets the stability criteria of Harrison–Zeldovich–Novikov and in respect of the cracking concept the solution is unstable in the region of the center and potentially stable near the surface. A graphic description is presented for the case of an object with a compactness rate [Formula: see text], mass [Formula: see text] and radius [Formula: see text] km that matches the star Vela X-1. Also, the interval of the central density [Formula: see text], which is consistent with the expected magnitudes for this type of stars, which shows that the behavior is accurate for describing compact objects.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

scholarly journals Dynamical system analysis of three-form field dark energy model with baryonic matter

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Soumya Chakraborty ◽  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
Cold Dark Matter ◽  
System Analysis ◽  
Evolution Equations ◽  
Matter Field ◽  
Baryonic Matter ◽  
Form Field ◽  
The Stability ◽  
Manifold Theory

AbstractA cosmological model having matter field as (non) interacting dark energy (DE) and baryonic matter and minimally coupled to gravity is considered in the present work with flat FLRW space time. The DE is chosen in the form of a three-form field while radiation and dust (i.e; cold dark matter) are the baryonic part. The cosmic evolution is studied through dynamical system analysis of the autonomous system so formed from the evolution equations by suitable choice of the dimensionless variables. The stability of the non-hyperbolic critical points are examined by Center manifold theory and possible bifurcation scenarios have been examined.

Effect of Low-Frequency Modulation on Thermal Convection Instability

2001 ◽  
Vol 56 (6-7) ◽  
pp. 509-522 ◽  
Author(s):  
P. K. Bhatia ◽  
B. S. Bhadauria
Keyword(s):  
Asymptotic Solution ◽  
Temperature Difference ◽  
Frequency Modulation ◽  
Thermal Convection ◽  
Low Frequency ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Stability Criteria ◽  
Steady Temperature ◽  
The Stability

Abstract The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the horizontal walls of the layer a time-dependent low-frequency per­ turbation is applied to the wall temperatures. An asymptotic solution is obtained which describes the be­ haviour of infinitesimal disturbances to this configuration. Possible stability criteria are analyzed and the results are compared with the known experimental as well as numerical results.

scholarly journals Predicting Collapse of Complex Ecological Systems: Quantifying the Stability-Complexity Continuum

2019 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the Extinction Continuum. We also develop a metric that locates the position of the system within the Extinction Continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

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