Graphical representation of the effect of source and load immittance on the stability of orthogonal networks

1976 ◽  
Vol 12 (7) ◽  
pp. 153
Author(s):  
Jacqueline Glover
Keyword(s):  
Graphical Representation ◽  
The Stability ◽  
Orthogonal Networks

scholarly journals Kantowski–Sachs Tsallis holographic dark energy model with sign-changeable interaction

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Y. Sobhanbabu ◽  
M. Vijaya Santhi
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Deceleration Parameter ◽  
Graphical Representation ◽  
Holographic Dark Energy ◽  
State Parameter ◽  
Field Equations ◽  
Dynamical Parameters ◽  
Frame Work ◽  
The Stability

AbstractIn this work devoted to the investigation of the Tsallis holographic dark energy (IR cut-off is Hubble radius) in homogeneous and anisotropic Kantowski–Sachs Universe within the frame-work of Saez–Ballester scalar tensor theory of gravitation. We have constructed non-interacting and interacting Tsallis holographic dark energy models by solving the field equations using the relationship between the metric potentials. This relation leads to a viable deceleration parameter model which exhibits a transition of the Universe from deceleration to acceleration. In interacting case, we focus on sign-changeable interaction between Tsallis holographic dark energy and dark matter. The dynamical parameters like equation of state parameter, energy densities of Tsallis holographic dark energy and dark matter, deceleration parameter, and statefinder parameters of the models are explained through graphical representation. And also, we discussed the stability analysis of the our models.

scholarly journals Charged anisotropic compact star core-envelope model with polytropic core and linear envelope

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
S. A. Mardan ◽  
I. Noureen ◽  
A. Khalid
Keyword(s):  
Graphical Representation ◽  
Compact Star ◽  
Compact Object ◽  
Compact Objects ◽  
Compact Stars ◽  
Physical Parameters ◽  
Polytropic Equation ◽  
Envelope Model ◽  
Linear Envelope ◽  
The Stability

AbstractThis manuscript is related to the construction of relativistic core-envelope model for spherically symmetric charged anisotropic compact objects. The polytropic equation of state is considered for core, while it is linear in the case of envelope. We present that core, envelope and the Reissner Nordstr$$\ddot{o}$$ o ¨ m exterior regions of stars match smoothly. It has been verified that all physical parameters are well behaved in the core and envelope region for the compact stars SAX J1808.4-3658 and 4U1608-52. Various physical parameters inside star are discussed herein, non-singularity and continuity at the junction has been catered as well. Impact of charged compact object together with core-envelope model on the mass, radius and compactification factor is described by graphical representation in both core and envelop regions. The stability of the model is worked out with the help of Tolman–Oppenheimer–Volkoff equations and radial sound speed.

scholarly journals Methodology for Assessing the Stability of Drilling Rigs Based on Analytical Tests

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8588
Author(s):  
Łukasz Bołoz ◽  
Artur Kozłowski
Keyword(s):  
Computational Model ◽  
Design Process ◽  
Computational Models ◽  
Dynamic Models ◽  
Graphical Representation ◽  
Underground Mining ◽  
Drilling Rig ◽  
Centre Of Gravity ◽  
The Stability ◽  
Drilling Rigs

Underground mining machines, such as wheel-tyre drilling rigs, are articulated and equipped with booms that project far beyond the undercarriage. Such a structure makes these machines prone to losing stability. Hence, it is necessary to analyse the distribution of masses and geometry as well as their broadly understood stability during the entire design process, taking into account many factors resulting from the manner and conditions of their operation. However, there are no appropriate computational models that would enable analytical tests to be carried out for machines with this kind of construction. This article is concerned with the author’s computational model, which allows the stability of single- and twin-boom drilling rigs to be quickly assessed. The model makes it possible to perform analyses without having to solve differential equations that are present in dynamic models or using specialist software based on CAD and CAE tools. The developed model allows determination of the pressure of wheels and jacks as a function of many important parameters and variables. Additionally, the distances of the centre of gravity from the tipping edge are calculated. The developed computational model was verified by comparing the obtained results with the results of the full dynamic model, the results of model tests carried out in the CAD/CAE program, and the results of empirical tests of wheel and jack pressures on the ground for the selected drilling rig. The model was subjected to verification and validation, which proved that it was fully correct and useful. The model was used to prepare a practical and user-friendly calculation sheet. Apart from the numerical values, the calculation sheet contains a graphical representation of the machine, the location of the centre of gravity, the tipping edges, as well as graphs of the wheel and jack pressures. Next, analytical tests of the stability of the selected drilling rig were carried out. The obtained calculation results are consistent with the results of empirical research. The computational model and the spreadsheet provide handy tools used during the design process by one of the Polish company’s producing drilling rigs.

scholarly journals Assessment of the stability of the gas-diesel automatic control system

2021 ◽  
Vol 2094 (5) ◽  
pp. 052067
Author(s):  
G M Mikheev ◽  
P L Lekomtsev ◽  
O P Lopatin ◽  
V A Likhanov
Keyword(s):  
Internal Combustion Engines ◽  
Graphical Representation ◽  
Transition Process ◽  
Dynamic Mode ◽  
Combustion Engines ◽  
Functional Dependencies ◽  
Engine Torque ◽  
Steady State Operation ◽  
Transition Modes ◽  
The Stability

Abstract Any steady-state operation of the engine is evaluated by qualitative and quantitative parameters. For internal combustion engines, the qualitative parameter is the speed of the crankshaft, and the quantitative parameter is the engine torque. There are functional dependencies between these parameters, the graphical representation of which is called speed characteristics. However, the transition modes of engines are much more complex than the established ones, especially in gas-diesel engines, where the relationship between the parameters of the engine and the characteristics of the gas supply units is quite complex, and the transition process is accompanied by a change in the parameters of its working process over time and is a dynamic mode.

Structure Topology and Graphical Representation of Decorated and Undecorated Chains of Edge-Sharing Octahedra

2021 ◽  
Author(s):  
Aaron J. Lussier ◽  
Frank C. Hawthorne
Keyword(s):  
Graphical Representation ◽  
Building Blocks ◽  
Finite Graph ◽  
Topological Information ◽  
Structure Topology ◽  
Edge Sharing Octahedra ◽  
Form Part ◽  
The Stability ◽  
Multiple Chain ◽  
Symmetry Operations

ABSTRACT Infinite chains of edge-sharing octahedra occur as fundamental building blocks (FBBs) in the structures of several hundred mineral species. Such chains consist of a backbone of octahedra to which decorating polyhedra may be attached. The general, stoichiometric formula of such chains may be written as c[MATxФz] where M is any octahedrally coordinated cation, T is any cation coordinated by a decoration polyhedron (regardless of coordination geometry), Ф is any possible ligand [O2–, (OH)–, (H2O), Cl–, or F–], and c indicates the configuration of backbone octahedra. In the minerals in which they occur, these types of chains will commonly (though not exclusively) form part of the structural unit (i.e., the strongly bonded part) of a mineral. Hence, investigating the topology, configuration, and arrangement of such chains may yield fundamental insights into the stability of minerals in which they occur. A discussion of the topological variability of chains is presented here, along with the formulae necessary for their characterization. It is shown that many aspects of chain topology can be efficiently communicated by a pair of values with the form ([x], [Bopqrst]), where [x] summarizes the symmetry operations necessary to characterize the configuration of backbone octahedra, B indicates the length of the topological repeat, and o through t indicate the number of individual decorations (related to B). A methodology for developing finite graphical representations for infinite chains is presented in detail, showing that for any given chain, a single, irreducible finite graph exists that contains all topological information. Such a graph, however, can correspond to multiple chain topologies, highlighting the importance of geometrical isomerism. The utility of the graphical approach in facilitating the development of a hierarchy of chains and chain-bearing structures is also discussed.

scholarly journals Observational constraint on interacting Tsallis holographic dark energy in logarithmic Brans–Dicke theory

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Y. Aditya ◽  
Sanjay Mandal ◽  
P. K. Sahoo ◽  
D. R. K. Reddy
Keyword(s):  
Dark Energy ◽  
Graphical Representation ◽  
Holographic Dark Energy ◽  
Accelerated Expansion ◽  
Observational Constraint ◽  
Tensor Theory ◽  
Dynamical Parameters ◽  
Expansion Of The Universe ◽  
The Stability ◽  
The Universe

AbstractIn this paper, we investigate the dark energy phenomenon by studying the Tsallis holographic dark energy within the framework of Brans–Dicke (BD) scalar–tensor theory of gravity (Brans and Dicke in Phys. Rev. 124:925, 1961). In this context, we choose the BD scalar field $$\phi $$ϕ as a logarithmic function of the average scale factor a(t) and Hubble horizon as the IR cutoff ($$L=H^{-1}$$L=H-1). We reconstruct two cases of non-interacting and interacting fluid (dark sectors of cosmos) scenario. The physical behavior of the models are discussed with the help of graphical representation to explore the accelerated expansion of the universe. Moreover, the stability of the models are checked through squared sound speed $$v_s^2$$vs2. The well-known cosmological plane i.e., $$\omega _{de}-\omega ^{\prime }_{de}$$ωde-ωde′ is constructed for our models. We also include comparison of our findings of these dynamical parameters with observational constraints. It is also quite interesting to mention here that the results of deceleration, equation of state parameters and $$\omega _{de}-\omega ^{\prime }_{de}$$ωde-ωde′ plane coincide with the modern observational data.

Dynamics of Bipedal Gait: Part II—Stability Analysis of a Planar Five-Link Biped

1993 ◽  
Vol 60 (2) ◽  
pp. 337-343 ◽  
Author(s):  
Y. Hurmuzlu
Keyword(s):  
Stability Analysis ◽  
Parameter Space ◽  
Graphical Representation ◽  
Rigid Bodies ◽  
Bipedal Locomotion ◽  
Dimensional Parameter ◽  
Bipedal Gait ◽  
Stable Gait ◽  
Mapping Techniques ◽  
The Stability

A general approach based on discrete mapping techniques is presented to study stability of bipedal locomotion. The approach overcomes difficulties encountered by others on the treatment of discontinuities and nonlinearities associated with bipedal gait. A five-element bipedal locomotion model with proper parametric formulation is considered to demonstrate the utility of the proposed approach. Changes in the stability of the biped as a result of bifurcations in the four-dimensional parameter space are investigated. The structural stability analysis uncovered stable gait patterns that conform to the prescribed motion. Stable nonsymmetric locomotion with multiple periodicity was also observed, a phenomenon that has never been considered before. Graphical representation of the bifurcations are presented for direct correlation of the parameter space with the resulting walking patterns. The bipedal model includes some idealizations such as neglecting the dynamics of the feet and assuming rigid bodies. Some additional simplifications were performed in the development of the controller that regulates the motion of the biped.

scholarly journals Generalizing of Finite Difference Method for Certain Fractional Order Parabolic PDE’s

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Madeha Shaltagh Yousif ◽  
Ahmed Mohamed Shukur ◽  
Eman Hassan Ouda ◽  
Raghad Kadhim Salih
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Graphical Representation ◽  
Classical Equation ◽  
Stability And Convergence ◽  
Implicit Methods ◽  
Integral Term ◽  
The Stability ◽  
Implicit And Explicit

Space-time fractional differential equation with integral term (S-TFDE) has been considered. The finite difference method (implicit and explicit) combined with the trapezoidal integration formula has been used to find special formula to solve this equation. The stability and convergence have been discussed. The effect of adding an integral term to the common classical equation has been considered.  Graphical representation of the calculate solutions (obtained by the explicit and the implicit methods) for three numerical examples with their exact solution, are considered. All the calculations and graphs are designed with the help of MATLAB.

scholarly journals On the criteria for the stability of small motions

1929 ◽  
Vol 124 (795) ◽  
pp. 642-654 ◽  
Keyword(s):  
Graphical Representation ◽  
Steady Motion ◽  
Test Functions ◽  
Small Motion ◽  
Determinantal Equation ◽  
Test Function ◽  
Conventional Procedure ◽  
Linear Differential ◽  
State Of Rest ◽  
The Stability

When a dynamical system receives a small disturbance from a state of rest or steady motion, the ensuing small motion is governed by a system of linear differential equations. In order to determine the stability, the conventional procedure is to examine the signs of certain "test functions," which can be constructed in succession from the coefficients of the determinantal equation by Routh's well-known rules (see Routh's "Rigid Dynamics," vol. 2, 6th ed., p. 228). However, the series of test functions for a determinantal equation of general degree are not stated by Routh in an explicit form; and the expressions would, in fact, be exceedingly cumbersome. An alternative is to use for the stability criteria the signs of certain "test determinants." This method, which is very convenient in practice, is not described in works on dynamics known to the writers, and may be novel. The present paper contains a brief account of these determinants and of certain other simple forms of test function. The stability of a system is usually dependent upon so many factors that the exact influence of individual factors may be extremely difficult to trace in a purely algebraic discussion of the test functions; but such obscurities can often be avoided by a graphical representation of the criteria. A suitable graphical treatment for problems of a certain wide class will be described. For a detailed illustration of the application of the method to the stability of aeroplane wings, the reader is referred to R. and M. 1155.

scholarly journals The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Salih Djilali ◽  
Behzad Ghanbari
Keyword(s):  
Infectious Disease ◽  
Fractional Order ◽  
Graphical Representation ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Hunting Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Interaction ◽  
The Stability

AbstractIn this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency.

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