scholarly journals Effect of Vegetation Roots on the Threshold of Slope Instability Induced by Rainfall and Runoff

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Gang Huang ◽  
Mingxin Zheng ◽  
Jing Peng
Keyword(s):  
Factor Of Safety ◽  
Rainfall Amount ◽  
Slope Instability ◽  
Two Dimensional ◽  
Drying Time ◽  
One Dimensional ◽  
Rainfall Duration ◽  
Safe Area ◽  
The Stability ◽  
Dimensional Instability

Although vegetation is increasingly used to mitigate landslide risks, how vegetation roots affect the landslide threshold of slope has rarely been explored, particularly in the case of lateral runoff. In this study, we established a two-dimensional saturated-unsaturated infiltration equation considering the hydraulic effects of vegetation roots. The analytical solution for the shallow unsaturated two-dimensional coupled infiltration of vegetated slope (VS) was obtained by a Fourier transform technique. The numerical method was used to evaluate the stability of VS caused by four root architectures, the rainfall amount, and the rainfall duration. Subsequently, the transformation law in runoff, vegetation evaporation, and landslide threshold was analyzed. The results indicate that the factor of safety (FOS) increases with increasing drying time and decreases with increasing depth; the minimum FOS is at the junction of the root-rootless zone. Runoff and vegetation evaporation are favorable for the shallow stability of VS. The time of the safe area is 35 h for rainfall amount 500 m in the uniformly root clay slope. Moreover, four landslide threshold curves that reflected the root architecture, rainfall amount, and rainfall duration are developed, which are more realistic than those created using one-dimensional instability modeling.

Chaos in the Rulkov Neuron Model Based on Marotto’s Theorem

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Penghe Ge ◽  
Hongjun Cao
Keyword(s):  
Neuron Model ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Fast Subsystem ◽  
One Dimensional ◽  
Sensitive Dependence ◽  
The Stability ◽  
Slow Subsystem

The existence of chaos in the Rulkov neuron model is proved based on Marotto’s theorem. Firstly, the stability conditions of the model are briefly renewed through analyzing the eigenvalues of the model, which are very important preconditions for the existence of a snap-back repeller. Secondly, the Rulkov neuron model is decomposed to a one-dimensional fast subsystem and a one-dimensional slow subsystem by the fast–slow dynamics technique, in which the fast subsystem has sensitive dependence on the initial conditions and its snap-back repeller and chaos can be verified by numerical methods, such as waveforms, Lyapunov exponents, and bifurcation diagrams. Thirdly, for the two-dimensional Rulkov neuron model, it is proved that there exists a snap-back repeller under two iterations by illustrating the existence of an intersection of three surfaces, which pave a new way to identify the existence of a snap-back repeller.

A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1997 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Stability Criteria ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms a in low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short lengthscale disturbance known as a ‘spike’, and the second with a longer lengthscale disturbance known as a ‘modal oscillation’. In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented which relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: long lengthscale disturbances are related to a two-dimensional instability of the whole compression system, while short lengthscale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed which explains the type of stall inception pattern observed in a particular compressor. Measurements from a single stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

Steady-State Bifurcation for a Biological Depletion Model

2016 ◽  
Vol 26 (04) ◽  
pp. 1650066 ◽  
Author(s):  
Yan’e Wang ◽  
Jianhua Wu ◽  
Yunfeng Jia
Keyword(s):  
Steady State ◽  
Bifurcation Theory ◽  
Steady States ◽  
Two Dimensional ◽  
Implicit Function ◽  
Flux Boundary Condition ◽  
One Dimensional ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Theoretical Results

A two-species biological depletion model in a bounded domain is investigated in which one species is a substrate and the other is an activator. Firstly, under the no-flux boundary condition, the asymptotic stability of constant steady-states is discussed. Secondly, by viewing the feed rate of the substrate as a parameter, the steady-state bifurcations from constant steady-states are analyzed both in one-dimensional kernel case and in two-dimensional kernel case. Finally, numerical simulations are presented to illustrate our theoretical results. The main tools adopted here include the stability theory, the bifurcation theory, the techniques of space decomposition and the implicit function theorem.

von Neumann Stability Analysis of a Segregated Pressure-Based Solution Scheme for One-Dimensional and Two-Dimensional Flow Equations

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Santosh Konangi ◽  
Nikhil K. Palakurthi ◽  
Urmila Ghia
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Two Dimensional ◽  
Von Neumann ◽  
One Dimensional ◽  
Flow Equations ◽  
Solution Scheme ◽  
Von Neumann Stability ◽  
The Stability ◽  
Stability Limits

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

scholarly journals Robustness of Polynomial Stability of Damped Wave Equations

2022 ◽  
Author(s):  
Dmytro Baidiuk ◽  
Lassi Paunonen
Keyword(s):  
Boundary Condition ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Acoustic Boundary Condition ◽  
The Stability ◽  
Perturbed Equation ◽  
Dimensional Wave

AbstractIn this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation with an acoustic boundary condition. In the case of Webster’s equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.

A modified two-dimensional triangular lattice model under honk environment

2020 ◽  
Vol 31 (06) ◽  
pp. 2050089
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
High Dimensional ◽  
Two Dimensional ◽  
Lattice Hydrodynamic Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The Stability ◽  
Honk Effect ◽  
Real Traffic

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

scholarly journals Stability analysis of three-dimensional breather solitons in a Bose–Einstein condensate

2005 ◽  
Vol 461 (2063) ◽  
pp. 3561-3574 ◽  
Author(s):  
M Matuszewski ◽  
E Infeld ◽  
G Rowlands ◽  
M Trippenbach
Keyword(s):  
Three Dimensional ◽  
Einstein Condensate ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stability Properties ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Dimensional Soliton

We investigated the stability properties of breather soliton trains in a three-dimensional Bose–Einstein condensate (BEC) with Feshbach-resonance management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is confined only by a one-dimensional optical lattice and we consider strong, moderate and weak confinement. By strong confinement we mean a situation in which a quasi two-dimensional soliton is created. Moderate confinement admits a fully three-dimensional soliton. Weak confinement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in effective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully confirmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully three-dimensional analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We find that in the three-dimensional case the stability region splits into two parts. However, as we tighten the confinement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for the quasi two-dimensional case. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust three-dimensional solitons in experiments in a BEC in a one-dimensional lattice.

Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations

2016 ◽  
Vol 19 (5) ◽  
pp. 1221-1241 ◽  
Author(s):  
Hua Wu ◽  
Jiajia Pan ◽  
Haichuan Zheng
Keyword(s):  
Domain Decomposition Method ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
One Dimensional ◽  
Collocation Points ◽  
The Matrix ◽  
Vorticity Equations ◽  
Legendre Spectral Method ◽  
Legendre Galerkin Method ◽  
The Stability

AbstractWe extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkin method while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and in parallel way. The numerical analysis results in the case of one-dimensional multi-domain are generalized to two-dimensional case. The stability and convergence of the method are proved. Numerical results are given.

scholarly journals Modeling of carbon monoxide oxidation on the catalytic surface in the two-dimensional case

2017 ◽  
pp. 83-89
Author(s):  
Iryna Ryzha
Keyword(s):  
Carbon Monoxide ◽  
Co Oxidation ◽  
Stability Region ◽  
Pt Catalyst ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Catalytic Surface ◽  
One Dimensional ◽  
Co Oxidation Reaction ◽  
The Stability

A two-dimensional model of carbon monoxide (CO) catalytic oxidation on a platinum (Pt) surface for the Langmuir-Hinshelwood mechanism is investigated. The adsorbate-driven (1×1)-(1×2) structural phase transition of Pt(110) and the formation of new crystal planes on the catalytic surface (faceting) as well as the effect of the substrate temperature are taken into account. It is shown that the stability region for CO oxidation reaction changes when two dimensions are taken into account. Similarly to the one-dimensional case, the reaction of CO oxidation on Pt-catalyst surface is periodic in the stability region. Mixed-mode oscillations (MMO) for CO and oxygen (O) surface coverages as well as the fraction of the surface in the non-reconstructed (1×1)-state were found. Such behavior cannot be predicted by one-dimensional models when the equation for the change of degree of faceting is not taken into account.

scholarly journals Constructing of Digital Watermark Based on Generalized Fourier Transform

Electronics ◽  
2020 ◽  
Vol 9 (7) ◽  
pp. 1108 ◽  
Author(s):  
Ivanna Dronyuk ◽  
Olga Fedevych ◽  
Natalia Kryvinska
Keyword(s):  
Fourier Transform ◽  
High Stability ◽  
Digital Watermark ◽  
Two Dimensional ◽  
Generalized Fourier Transform ◽  
Trigonometric Functions ◽  
Unauthorized Access ◽  
One Dimensional ◽  
The Stability ◽  
The One

We develop in this paper a method for constructing a digital watermark to protect one-dimensional and two-dimensional signals. The creation of a digital watermark is based on the one-dimensional and two-dimensional generalized Fourier and Hartley transformations and the Ateb-functions as a generalization of trigonometric functions. The embedding of the digital watermark is realized in the frequency domain. The simulation of attacks on protected files is carried out to confirm the stability of the proposed method. Experiments proved the high stability of the developed method conformably to the main types of attacks. An additional built-in digital watermark can be used to identify protected files. The proposed method can be used to support the security of a variety of signals—audio, images, electronic files etc.—to protect them from unauthorized access and as well for identification.

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