scholarly journals Wormhole Solutions in Symmetric Teleparallel Gravity with Noncommutative Geometry

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1260
Author(s):  
Zinnat Hassan ◽  
Ghulam Mustafa ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Linear Model ◽  
Noncommutative Geometry ◽  
Teleparallel Gravity ◽  
Exponential Model ◽  
Model Parameter ◽  
Exponential Models ◽  
Feasible Solutions ◽  
The Stability ◽  
Tov Equation

This article describes the study of wormhole solutions in f(Q) gravity with noncommutative geometry. Here, we considered two different f(Q) models—a linear model f(Q)=αQ and an exponential model f(Q)=Q−α1−e−Q, where Q is the non-metricity and α is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

The Periodic Impact Responses of Human-Body in a Vehicle Traveling on the Rough Terrain

2002 ◽  
Author(s):  
Ke Yu ◽  
Albert C. J. Luo
Keyword(s):  
Linear Model ◽  
Human Body ◽  
Rotational Motion ◽  
Large Mass ◽  
Rough Terrain ◽  
Lumped Mass ◽  
The Stability ◽  
Vehicle Chassis ◽  
Specific Number ◽  
Impact Motion

The human-body in a vehicle traveling on the rough terrain is modeled through the lumped mass approach and its periodic impact motions and stability are investigated through a linear model of vehicle and passenger systems. The linear model assumes the motion response of vehicle is very small compared to passenger’s rotational motion since the vehicle chassis has a very large mass and moment of inertia. The period-1 impact motion for two impacts respectively on two walls for a specific number of periods is predicted analytically and numerically. The stability and bifurcation of such a period-1 impact motion are developed analytically. The phase planes of the periodic impact motions are illustrated for a better understanding of the human-body impacting motion in the vehicle.

Analysis of observational parameters and stability in extended teleparallel gravity

2020 ◽  
Vol 17 (11) ◽  
pp. 2050158
Author(s):  
A. Y. Shaikh ◽  
B. Mishra
Keyword(s):  
Thermodynamic Temperature ◽  
Teleparallel Gravity ◽  
Entropy Density ◽  
Accelerated Expansion ◽  
Late Time ◽  
General Relativistic ◽  
Basic Equations ◽  
The Stability ◽  
The Universe ◽  
Early Phases

In this paper, we have investigated the stability of General Relativistic Hydrodynamics (GRHD) model in a Friedmann–Robertson–Walker space-time with the volumetric power law in teleparallel gravity. The basic equations are derived along with its thermodynamical aspects. Thermodynamic temperature and entropy density of the model are also obtained. The state finder diagnostic pair and jerk parameter are analyzed to characterize different phases of the universe and the well-known astrophysical phenomena such as look-back time, the luminosity distance with redshift are derived. The model shows an accelerated expansion with inflationary era in the early and the very late time of the cosmic evolution. The GRHD model is stable at the early phases of the universe and is unstable at late times.

scholarly journals Lorenz gauge fixing of f(T) teleparallel cosmology

2017 ◽  
Vol 26 (14) ◽  
pp. 1750154 ◽  
Author(s):  
W. El Hanafy ◽  
G. G. L. Nashed
Keyword(s):  
Degrees Of Freedom ◽  
Teleparallel Gravity ◽  
Phase Portraits ◽  
De Sitter ◽  
Phantom Divide ◽  
Type Iv ◽  
Gauge Fixing ◽  
Phantom Divide Line ◽  
Lorenz Gauge ◽  
The Stability

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or [Formula: see text]CDM as separate scenarios. We reconstruct the [Formula: see text] gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular [Formula: see text] gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

Dynamical properties of scaling solutions in teleparallel dark energy cosmologies with nonminimal coupling

2017 ◽  
Vol 26 (09) ◽  
pp. 1750103 ◽  
Author(s):  
Mihai Marciu
Keyword(s):  
Dark Energy ◽  
Power Law ◽  
Scalar Fields ◽  
Teleparallel Gravity ◽  
Inverse Power ◽  
Coupling Coefficients ◽  
Potential Term ◽  
Inverse Power Law ◽  
The Stability ◽  
The Impact

The dynamical aspects of scaling solutions for the dark energy component in the theoretical framework of teleparallel gravity are considered, where dark energy is represented by a scalar field nonminimally coupled with the torsion and with a boundary term, where the boundary coupling term represents the divergence of the torsion vector. The behavior and stability of the scaling solutions are studied for scalar fields endowed with inverse power law potentials and with exponential potentials. It is shown that for scalar fields endowed with inverse power-law potentials, the stability conditions are not affected by the coupling coefficients. For the scalar fields endowed with exponential potentials, two cases are studied: at first, we have considered an infinitesimal deviation from the scaling solution in the corresponding Klein–Gordon equation, and the impact of distinct coupling coefficients on the stability of the solution are analyzed. Secondly, the potential-free case is considered where the dominance of the coupling terms over the potential term is analyzed, discussing the validity of the corresponding particular solution.

Compression characteristics of agglomerated food powders: Effect of agglomerate size and water activity Características de la compresión de alimentos en polvo: Efecto del tamaño del aglomerado y del contenido de humedad

1997 ◽  
Vol 3 (5) ◽  
pp. 351-359 ◽  
Author(s):  
H. Yan ◽  
G.V. Barbosa-Cánovas
Keyword(s):  
Particle Size ◽  
Water Activity ◽  
Flow Characteristics ◽  
Exponential Model ◽  
Compression Tests ◽  
Food Powders ◽  
Powder Flowability ◽  
Compression Data ◽  
The Stability ◽  
Compression Characteristics

The stability of food agglomerates is very important for keeping optimal instant properties as well as flow characteristics. Compression tests have been proven not only to be useful tools in char acterizing attrition, but also excellent descriptors for powder flowability. The purpose of this work was to study the effects of particle size and water activity ( a w) on the compression characteristics of selected agglomerated food powders, and then to identify suitable mathematical models by using a non-linear regression program for predicting the compression characteristics of food agglomerates when partial attrition takes place. Three agglomerated food powders - non-fat milk, low fat milk and instant coffee - were classified by size into five or six fractions with a set of RX-29 sieve screens. Each fraction was conditioned at three aw levels, placed in a cylindrical compression cell, and compressed with a piston attached to the crosshead of a TA-XT2 texture analyser. The crosshead speed was 1 mm/s in all tests and the maximum force applied was 245 N. Particle size was found to play a significant role in compression tests in that the greater the particle size, the greater the volume reduction. It was easier to compress the low aw samples, but in all tests changing aw did not significantly affect compression characteristics. Sone's two- parameter model accurately described the combination of compaction and attrition when compres sion pressure did not exceed a certain level, while Peleg's double-exponential model with four parameters best fitted the compression data.

Stability of charged neutron star in Palatini f(R) gravity

2019 ◽  
Vol 34 (31) ◽  
pp. 1950252 ◽  
Author(s):  
M. Z. Bhatti ◽  
Z. Yousaf ◽  
Zarnoor
Keyword(s):  
Chemical Composition ◽  
Neutron Star ◽  
Modified Gravity ◽  
Equilibrium Equation ◽  
Hydrostatic Equilibrium ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Symmetric Geometry ◽  
The Stability ◽  
Tov Equation

In this work, we discuss the stability of charged neutron star in the background of [Formula: see text] gravity and construct the generalized Tolman–Oppenheimer–Volkoff (TOV) equations. For this, we consider static spherically symmetric geometry to construct the hydrostatic equilibrium equation and deduce TOV equations from modified field equations with electromagnetic effects. We conclude that the generalized TOV equation depicts the stable stars configuration independent of the generic function of the modified gravity if the condition of uniform entropy and chemical composition is assumed.

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