On a sampling criterion -induced oscillatory behaviour

2012 ◽  
Author(s):  
M. De la Sen ◽  
J.C. Soto
Keyword(s):  
Oscillatory Behaviour

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

Analysis of the oscillatory behaviour of an industrial reactor for oxonation of propene; Combined models

1987 ◽  
Vol 52 (12) ◽  
pp. 2865-2875
Author(s):  
Josef Horák ◽  
Zdeněk Bělohlav ◽  
Petr Rosol ◽  
František Madron
Keyword(s):  
Liquid Phase ◽  
Dynamic Behaviour ◽  
Plug Flow ◽  
Equal Size ◽  
Mixed System ◽  
Oscillatory Behaviour ◽  
Industrial Reactor ◽  
Combined Models ◽  
Analysis Of Stability ◽  
Flow Element

Models have been used of the flow of the liquid phase in the reactor (cascade of two ideally mixed cells of different size, two equal-size cells with recycle, two equal-size cells with inlets to both cells and a model of two equal-size cells preceded with a back flow element with plug flow) to analyze the oscillatory states of an industrial reactor. Stable and instable steady states have been classified using analysis of pseudosteady states of conversion and temperature supplemented with a simulation of the dynamic behaviour. It has been that the deviations of the flow from an ideally mixed system may expand the region of the oscillatory behaviour. The detailed information about the character of the flow in the reactor and the way of feeding the reactor has been also found important for the analysis of stability.

Rotating elliptic cylinders in a viscous fluid at rest or in a parallel stream

1977 ◽  
Vol 79 (1) ◽  
pp. 127-156 ◽  
Author(s):  
Hans J. Lugt ◽  
Samuel Ohring
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Elliptic Cylinder ◽  
The Body ◽  
Oscillatory Behaviour ◽  
Incompressible Fluid Flow ◽  
Transient Period ◽  
Parallel Stream ◽  
Rotating Bodies

Numerical solutions are presented for laminar incompressible fluid flow past a rotating thin elliptic cylinder either in a medium at rest at infinity or in a parallel stream. The transient period from the abrupt start of the body to some later time (at which the flow may be steady or periodic) is studied by means of streamlines and equi-vorticity lines and by means of drag, lift and moment coefficients. For purely rotating cylinders oscillatory behaviour from a certain Reynolds number on is observed and explained. Rotating bodies in a parallel stream are studied for two cases: (i) when the vortex developing at the retreating edge of the thin ellipse is in front of the edge and (ii) when it is behind the edge.

scholarly journals Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner

2018 ◽  
Vol 52 (4) ◽  
pp. 1285-1313 ◽  
Author(s):  
Lucas Chesnel ◽  
Xavier Claeys ◽  
Sergei A. Nazarov
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Recent Work ◽  
Present Article ◽  
Error Estimates ◽  
Numerical Experiments ◽  
Source Term ◽  
Oscillatory Behaviour ◽  
Time Harmonic ◽  
Rounded Corner

We investigate the eigenvalue problem −div(σ∇u) = λu (P) in a 2D domain Ω divided into two regions Ω±. We are interested in situations where σ takes positive values on Ω+ and negative ones on Ω−. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [L. Chesnel, X. Claeys and S.A. Nazarov, Asymp. Anal. 88 (2014) 43–74], we highlighted an unusual instability phenomenon for the source term problem associated with (P): for certain configurations, when the interface between the subdomains Ω± presents a rounded corner, the solution may depend critically on the value of the rounding parameter. In the present article, we explain this property studying the eigenvalue problem (P). We provide an asymptotic expansion of the eigenvalues and prove error estimates. We establish an oscillatory behaviour of the eigenvalues as the rounding parameter of the corner tends to zero. We end the paper illustrating this phenomenon with numerical experiments.

Sign in / Sign up

Export Citation Format

Share Document