scholarly journals Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Haifa Bin Jebreen ◽  
Yurilev Chalco-Cano
Keyword(s):  
Stability Analysis ◽  
Exponential Function ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Kink Solution ◽  
Engineering Sciences ◽  
Hirota Bilinear Form ◽  
The Stability ◽  
Wave Methods ◽  
Selection Of

In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2-dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics.

scholarly journals Stability analysis of the Kosciuszko Mound using terrestrial laser scanner and numerical modelling

2018 ◽  
Vol 66 ◽  
pp. 01018
Author(s):  
Elżbieta Pilecka ◽  
Karolina Tomaszkiewicz
Keyword(s):  
Stability Analysis ◽  
Laser Scanner ◽  
Technical Condition ◽  
Point Of View ◽  
Terrestrial Laser Scanner ◽  
The Finite Element Method ◽  
Anthropogenic Soils ◽  
Differential Model ◽  
The Stability ◽  
Selection Of

Landslides which form in anthropogenic soils are complicated from a geological engineering and geotechnical point of view. Each case requires a detailed investigation and the selection of effective reinforcements is a difficult project issue. The study presents the problem of the stability analysis of landslides occurring in the anthropogenic soils of the Kosciuszko Mound in Cracow. The previously performed protections are discussed to highlight their ineffectiveness and the current technical condition of the mound is also presented. By overlapping the results of displacement measurements made with a terrestrial laser scanner, a differential model of the terrain was created which made it possible to determine the size and direction of the deformation of the slopes of the mound and the tendencies for the development of landslide movements in this area. A cross-section, selected on the basis of the model, was numerically analysed using the finite element method (FEM) in the Midas GTS NX program. As a result of the analysis, the values of the displacements and strains occurring in the Mound were calculated. On the basis of the value of the safety factor obtained, it was also possible to assess the risk of landslide movements.

scholarly journals Stability Analysis for Yield and Its Component Characters in Blackgram [Vigna mungo (L.) Hepper]

2021 ◽  
Author(s):  
C. Shobanadevi ◽  
R. Elangaimannan ◽  
K. Vadivel
Keyword(s):  
Stability Analysis ◽  
Seed Yield ◽  
Climatic Conditions ◽  
Vigna Mungo ◽  
Indian Agriculture ◽  
Stable Performance ◽  
High Yielding Varieties ◽  
The Stability ◽  
High Seed Yield ◽  
Selection Of

Background: Blackgram [Vigna mungo (L.) Hepper] is an important pulse crop occupying a unique position in Indian agriculture. Blackgram provides a major share of the protein requirement of the vegetarian population of the country. The crop is resistant to adverse climatic conditions and improves the soil fertility by fixing atmospheric nitrogen in the soil. Phenotypically stable genotypes are of great importance because the environmental conditions vary from season to season and year to year. Stable performance of blackgram genotypes across contrasting environments is essential for the successful selection of stable and high yielding varieties. Methods: A total of seven genotypes of blackgram were evaluated one season (Rabi - 2019) in three environments to study the G x E interaction for three traits.Result: Based on the stability analysis of Eberhart and Russell model, two genotypes viz., MDU 1 and NRIB 002 were found to be stable across the environments for seed yield. These genotypes had high seed yield with a unity regression coefficient and deviation from regression equal to zero.

scholarly journals ANALISIS STABILITAS MENGGUNAKAN MODEL MATERIAL PERALIHAN TANAH-BATUAN

2019 ◽  
Vol 1 (3) ◽  
pp. 225-230
Author(s):  
Putera Agung ◽  
Ardianto A
Keyword(s):  
Stability Analysis ◽  
Friction Stress ◽  
Model Material ◽  
Dam Construction ◽  
Stress Strain ◽  
Angle Of Internal Friction ◽  
Analysis Of Stability ◽  
The Stability ◽  
Selection Of

AbstractAn analysis of stability needs to predict stress-strain values of soil, rock, and/or intermediate material (soil-rock) layers around the gate shaft during excavation works. Selection of stress-strain of intermediate material foccused on this paper will affect to the analysis result. This analysis concerned on some consideration to the selection the stress-strain parameters in determination of c’ and f’ parameters. In excavation works,the parameters were applied to the stability analysis of gate shaft construction of dam construction. The stability analysis used a 2 D software of PLAXIS. Each condition of gate shaft was reinforcement and un-reinforcement wall types. From several analyses, the parameters of c’ and f’ from stress-strain of soil was smaller than intermediate material.Keywords: Cohesion; angle of internal friction, stress, strain, gate shaft.Abstrak Suatu analisis stabilitas perlu untuk memperkirakan besarnya tegangan-regangan tanah, batuan, dan atau lapisan material peralihan tanah-batuan (intermediate material) di sekitar lubang galian vertikal. Pemilihan tegangan-regangan dari material peralihan tanah-batuan yang difokuskan pada paper ini akan berpengaruh terhadap hasil analisis. Analisis ini memusatkan perhatian pada beberapa pertimbangan pemilihan parameter tegangan-regangan dalam analisis stabilitas saluran pengalihn vertikal pada konstruksi dam. Analisis stabilitas ini menggunakan software Plaxis 2 D (dimensi). Masing-masing tipe dinding saluran vertikal ini adalah dengan dan tanpa perkuatan tulangan. Dari beberapa analisis, parameter c’ dan f’ dari tanah adalah lebih kecil dari material peralihan.  Katakunci: Kohesi, sudut geser dalam, tegangan, regangan, saluran pengalihan vertikal.

scholarly journals Convergent Properties of Riccati Equation with Application to Stability Analysis of State Estimation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
X. Cai ◽  
Y. S. Ding ◽  
S. Y. Li
Keyword(s):  
Stability Analysis ◽  
State Estimation ◽  
Kalman Filters ◽  
Sufficient Conditions ◽  
Time Instant ◽  
Novel Method ◽  
Finite Memory ◽  
The Stability ◽  
Time Invariant ◽  
Selection Of

Since the recursive nature of Kalman filtering always results in a growing size of the optimization problem, state estimation is usually realized by use of finite-memory, receding horizon, sliding window, or “frozen” techniques, which causes difficulties on stability analysis. This paper proposes a novel method on selection of an initial covariance matrix and a horizon for the Kalman filter to make sure that a sequence of the closed-loop Kalman filters are stable as time-invariant filters at subsequent time instant. Convergent properties of Riccati Difference Equation (RDE) are first exploited. Based on these properties, sufficient conditions for stability of a sequence of Kalman filters are obtained. Compared with the existent literature, the convergent properties and the stability conditions are less conservative since they provide analytic results and are applicable to more common cases where the RDEs are not monotonic.

Probabilistic stability analysis of excavations in jointed rock

1995 ◽  
Vol 32 (3) ◽  
pp. 397-407 ◽  
Author(s):  
C.F. Leung ◽  
S.T. Quek
Keyword(s):  
Stability Analysis ◽  
Site Investigation ◽  
Jointed Rock ◽  
Rock Block ◽  
Dispersion Data ◽  
Discontinuity Orientation ◽  
The Mean ◽  
The Stability ◽  
Selection Of ◽  
Block Volume

Excavations in jointed rock may liberate rock blocks that may fall by gravity or slide along the discontinuity. The orientation of discontinuities is one of the major input parameters in the conventional deterministic stability analysis of rock blocks. As the mean orientation of a discontinuity is often derived from a large number of joint-set data obtained from site investigation, Fisher's constant is commonly employed to represent the degree of dispersion of individual discontinuity orientation. However, such dispersion factors are rarely used in the conventional analysis. A probabilistic-based approach is proposed in this paper to incorporate Fisher's constant in the stability analysis of rock blocks. To account for the uncertainty reflected by the sample dispersion, data are generated systematically around each mean discontinuity normal, based on its Fisher's constant. The probability of rock block failure at a certain location and the largest possible block volume are determined in a logical manner. A microcomputer program has been developed to automate the analysis, and illustrative examples are shown to demonstrate the importance of incorporating the Fisher's constant of individual discontinuity in the stability analysis. In addition, risk mapping plots are presented to enable visual selection of an optimal route for excavation from one location to another. Key words : discontinuity, factor of safety, probability of failure, rock block, rock excavation, stability analysis.

Rayleigh–Taylor and Richtmyer–Meshkov instabilities of flat and curved interfaces

2009 ◽  
Vol 625 ◽  
pp. 387-410 ◽  
Author(s):  
R. KRECHETNIKOV
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Velocity Field ◽  
Systematic Approach ◽  
Ad Hoc ◽  
Frame Of Reference ◽  
Boundary Perturbation ◽  
The Stability ◽  
Selection Of ◽  
Wavenumber Selection

In this work we discuss a non-trivial effect of the interfacial curvature on the stability of uniformly and suddenly accelerated interfaces, such as liquid rims. The new stability analysis is based on operator and boundary perturbation theories and allows us to treat the Rayleigh–Taylor and Richtmyer–Meshkov instabilities as a single phenomenon and thus to understand the interrelation between these two fundamental instabilities. This leads, in particular, to clarification of the validity of the original Richtmyer growth rate equation and its crucial dependence on the frame of reference. The main finding of this study is the revealed and quantified influence of the interfacial curvature on the growth rates and the wavenumber selection of both types of instabilities. Finally, the systematic approach taken here also provides a generalization of the widely accepted ad hoc idea, due to Layzer (Astrophys. J., vol. 122, 1955, pp. 1–12), of approximating the potential velocity field near the interface.

scholarly journals Stability of Traveling Waves Based upon the Evans Function and Legendre Polynomials

2020 ◽  
Vol 10 (3) ◽  
pp. 846 ◽  
Author(s):  
H. M. Srivastava ◽  
H. I. Abdel-Gawad ◽  
Khaled M. Saad
Keyword(s):  
Stability Analysis ◽  
Fiber Optics ◽  
Traveling Waves ◽  
Legendre Polynomials ◽  
Reaction Diffusion ◽  
Evans Function ◽  
Reaction Diffusion Equations ◽  
Engineering Sciences ◽  
The Stability ◽  
Linearized Operator

One of the tools and techniques concerned with the stability of nonlinear waves is the Evans function which is an analytic function whose zeros give the eigenvalues of the linearized operator. Here, in this paper, we propose a direct approach, which is based essentially upon constructing the eigenfunction solution of the perturbed equation based upon the topological invariance in conjunction with usage of the Legendre polynomials, which have presumably not considered in the literature thus far. The associated Legendre eigenvalue problem arising from the stability analysis of traveling waves solutions is systematically studied here. The present work is of considerable interest in the engineering sciences as well as the mathematical and physical sciences. For example, in chemical industry, the objective is to achieve a great yield of a given product. This can be controlled by depicting the initial concentration of the reactant, which is determined by its value at the bifurcation point. This analysis leads to the point separating stable and unstable solutions. As far as chemical reactions are described by reaction-diffusion equations, this specific concentration can be found mathematically. On the other hand, the study of stability analysis of solutions may depict whether or not a soliton pulse is well-propagated in fiber optics. This can, and should, be carried out by finding the solutions of the coupled nonlinear Schrödinger equations and by analyzing the stability of these solutions.

Stability Analysis of a Moored Vessel

2004 ◽  
Vol 126 (2) ◽  
pp. 164-174
Author(s):  
A. Umar ◽  
S. Ahmad ◽  
T. K. Datta
Keyword(s):  
Stability Analysis ◽  
Harmonic Balance ◽  
Variational Approach ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Periodic Wave ◽  
Mooring System ◽  
Wave Excitation ◽  
The Stability ◽  
Slack Mooring

A procedure for the stability analysis of a slack mooring system is presented for periodic wave excitation by finding its approximate response using a two term harmonic balance method (HBM). The conditions for determining the local and global stability of the approximate solutions are established using Hill’s variational approach and Floquet’s theory. A number of instability phenomena are identified for the mooring system for certain frequencies of excitations which fall outside the range of frequencies obtained from the analytically derived stability boundaries. The instability phenomena include symmetry breaking bifurcation, subharmonics, 3T and 5T solutions. Even chaotic motion is exhibited under certain cases.

scholarly journals Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Xian Li ◽  
Yao Wang ◽  
Meidan Chen ◽  
Biao Li
Keyword(s):  
Symbolic Computation ◽  
Exponential Function ◽  
Bilinear Form ◽  
Quadratic Function ◽  
Hyperbolic Function ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Hirota Bilinear Form ◽  
Dynamical Properties ◽  
Hirota Bilinear

Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

scholarly journals Mathematical Model and Stability Analysis of Inverter-Based Distributed Generator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Alireza Khadem Abbasi ◽  
Mohd Wazir Mustafa
Keyword(s):  
Stability Analysis ◽  
Signal Model ◽  
Proper Selection ◽  
Distributed Generator ◽  
Small Signal Model ◽  
Proposed Model ◽  
The Stability ◽  
Frequency Variations ◽  
Selection Of ◽  
Prime Source

This paper presents a mathematical (small-signal) model of an electronically interfaced distributed generator (DG) by considering the effect of voltage and frequency variations of the prime source. Dynamic equations are found by linearization about an operating point. In this study, the dynamic of DC part of the interface is included in the model. The stability analysis shows with proper selection of system parameters; the system is stable during steady-state and dynamic situations, and oscillatory modes are well damped. The proposed model is useful to study stability analysis of a standalone DG or a Microgrid.

Sign in / Sign up

Export Citation Format

Share Document