Mechanical Representation and Stability of Dynamical Systems Containing Fractional Springpot Elements

2018 ◽  
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Dynamical System ◽  
Potential Energy ◽  
Lyapunov Functional ◽  
Analogue Model ◽  
Infinite Dimensional ◽  
Mechanical Analogue ◽  
Stability Of Dynamical Systems ◽  
Functional Differential ◽  
Invariance Theorem ◽  
Simple Dynamical System

In this article we consider the Lyapunov stability of mechanical systems containing fractional springpot elements. We obtain the potential energy of a springpot by an infinite dimensional mechanical analogue model. Furthermore, we consider a simple dynamical system containing a springpot as a functional differential equation and use the potential energy of the springpot in a Lyapunov functional to prove uniform stability and discuss asymptotic stability of the equilibrium with the help of an invariance theorem.

The Effect of Cutoffs on the Uplift Pressure Beneath the Hydraulic Structures Floor

2018 ◽  
Vol 6 (3) ◽  
pp. 20-28
Author(s):  
Faisal Al Tabatabaie ◽  
Dhabia Sabeeh Al Waily
Keyword(s):  
Potential Energy ◽  
Hydraulic Structure ◽  
Hydraulic Structures ◽  
Outer Face ◽  
Analogue Model ◽  
Electrical Analogue ◽  
Uplift Pressure ◽  
Different Depths ◽  
The Stability ◽  
Critical Sections

The use of cutoffs underneath the hydraulic structures is considered a safe solution to ensure the stability of hydraulic structure against uplift pressure and piping phenomenon in addition to the sliding and overturning forces of the water. These cutoffs are used at critical sections underneath the floor of hydraulic structure to substitute with their depths the horizontal lengths of the creep line of the hydraulic structure base. In this paper, the experimental method- by using electrical analogue model- was carried out to plot the flow net and study the efficiency of the front and rear faces of the cutoffs for dissipating the potential energy of the percolating water underneath the floor of hydraulic structure. An electrical analogue model which was used in this study consists of twenty five models with different depths of upstream and downstream cutoffs. After plotting the flow net for all models, it is concluded that the efficiency of the inner sides are less than that of the outer sides which were investigated before in this topic of this work that both faces reduction values in the uplift pressure are considered the same, where the efficiency of the outer face of upstream cutoff is (70.35) % and for the inner face is (29.64)%, while for the downstream cutoff the efficiency for the outer face is (76.21)% and for the inner face is (23.79)% .

scholarly journals Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems

2005 ◽  
Vol 2005 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Hilbert Space ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Dimensional Lattice ◽  
Reaction Diffusion Systems ◽  
Infinite Dimensional ◽  
Diffusion Systems ◽  
Lattice Dynamical System ◽  
Lattice Dynamical Systems

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert spacel2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.

On the equation ut = ∆uα + uβ

1993 ◽  
Vol 123 (2) ◽  
pp. 373-390 ◽  
Author(s):  
Yuan-Wei Qi
Keyword(s):  
Dynamical System ◽  
Blow Up ◽  
Uniqueness Result ◽  
Fast Diffusion ◽  
Negative Solution ◽  
Fast Diffusion Equation ◽  
Infinite Dimensional ◽  
The Cauchy Problem ◽  
Dimensional Dynamical System ◽  
Infinite Dimensional Dynamical System

SynopsisThe Cauchy problem of ut, = ∆uα + uβ, where 0 < α < l and α>1, is studied. It is proved that if 1< β<α + 2/n then every nontrivial non-negative solution is not global in time. But if β>α+ 2/n there exist both blow-up solutions and global positive solutions which decay to zero as t–1/(β–1) when t →∞. Thus the famous Fujita result on ut = ∆u + up is generalised to the present fast diffusion equation. Furthermore, regarding the equation as an infinite dimensional dynamical system on Sobolev space W1,s (W2.s) with S > 1, a non-uniqueness result is established which shows that there exists a positive solution u(x, t) with u(., t) → 0 in W1.s (W2.s) as t → 0.

scholarly journals ON BARYON NUMBER NONCONSERVATION IN TWO-DIMENSIONAL O(2N+1) QCD

2010 ◽  
Vol 25 (06) ◽  
pp. 1253-1266
Author(s):  
TAMAR FRIEDMANN
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Matrix Models ◽  
Gauge Group ◽  
Baryon Number ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Field Approach ◽  
Large N ◽  
Classical Dynamical System

We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O (2N+1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

scholarly journals The method of averaging and functional differential equations with delay

2001 ◽  
Vol 26 (8) ◽  
pp. 497-511 ◽  
Author(s):  
Mustapha Lakrib
Keyword(s):  
Differential Equations ◽  
Nonstandard Analysis ◽  
Functional Differential Equations ◽  
Natural Extension ◽  
Method Of Averaging ◽  
Infinite Dimensional ◽  
Classical Mathematics ◽  
Internal Set ◽  
Functional Differential ◽  
Equations With Delay

We present a natural extension of the method of averaging to fast oscillating functional differential equations with delay. Unlike the usual approach where the analysis is kept in an infinite-dimensional Banach space, our analysis is achieved inℝn. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is an axiomatic description of nonstandard analysis.

scholarly journals A simple dynamical system that mimics open‐flow turbulence

1990 ◽  
Vol 2 (11) ◽  
pp. 1983-2001 ◽  
Author(s):  
G. S. Bhat ◽  
R. Narasimha ◽  
S. Wiggins
Keyword(s):  
Dynamical System ◽  
Open Flow ◽  
Flow Turbulence ◽  
Simple Dynamical System
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