Small perturbations of unsteady one-dimensional axisymmetric motions of an ideal incompressible liquid

1979 ◽  
Vol 20 (2) ◽  
pp. 136-140 ◽  
Author(s):  
V. M. Men'shchikov
Keyword(s):  
Incompressible Liquid ◽  
Ideal Incompressible Liquid ◽  
Small Perturbations ◽  
One Dimensional

ROBUSTNESS OF COMPLETE STABILITY FOR 1-D CIRCULAR CNNs

2006 ◽  
Vol 16 (08) ◽  
pp. 2177-2190
Author(s):  
MAURO DI MARCO ◽  
CHIARA GHILARDI
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Nearest Neighbor ◽  
Perturbation Parameter ◽  
Relative Magnitude ◽  
Loss Of Stability ◽  
Unique Equilibrium ◽  
Small Perturbations ◽  
Structure Preserving ◽  
One Dimensional

This paper investigates the issue of robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominally symmetric interconnections. More specifically, a class of circular one-dimensional (1-D) CNNs with nearest-neighbor interconnections only, is considered. The class has sparse interconnections and is subject to perturbations which preserve the interconnecting structure. Conditions assuring that the perturbed CNN has a unique equilibrium point at the origin, which is unstable, are provided in terms of relative magnitude of the perturbations with respect to the nominal interconnection weights. These conditions allow one to characterize regions in the perturbation parameter space where there is loss of stability for the perturbed CNN. In turn, this shows that even for sparse interconnections and structure preserving perturbations, robustness of complete stability is not guaranteed in the general case.

scholarly journals Interaction instability of localization in quasiperiodic systems

2018 ◽  
Vol 115 (18) ◽  
pp. 4595-4600 ◽  
Author(s):  
Marko Žnidarič ◽  
Marko Ljubotina
Keyword(s):  
Transport Properties ◽  
Quantum Systems ◽  
Theoretical Physics ◽  
Solvable Models ◽  
Many Body ◽  
Small Perturbations ◽  
One Dimensional ◽  
Quasiperiodic Potential ◽  
Quasiperiodic Systems ◽  
Small Interactions

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

Note on the Smith-Stone theory of fish propulsion

1964 ◽  
Vol 280 (1382) ◽  
pp. 398-408 ◽  
Keyword(s):  
Incompressible Liquid ◽  
Velocity Potential ◽  
Present Note ◽  
Flexible Plate ◽  
Two Dimensional ◽  
Ideal Incompressible Liquid ◽  
Wake Effect ◽  
Fish Propulsion ◽  
Perturbation Velocity ◽  
Two Dimensional Flow

The present note extends the theory of fish propulsion by E. H. Smith & D. E. Stone, taking into account the wake effect which was not discussed in the original paper. The motion of a fish is simulated by a flexible plate of infinitesimal thickness, infinite span, and constant chord length, moving in the two-dimensional flow field of an ideal incompressible liquid. The perturbation velocity potential for the flexible plate is obtained by solving the Laplace equation in an elliptic cylindrical co-ordinate system, while the wake velocity potential follows from the application of a method which is due to Theodorsen. The results are shown to be identical with those derived previously by Siekmann. A simple example is given for illustration and results predicted by theory are compared with experimental data.

scholarly journals On preservation of an exponentially stable invariant torus

2015 ◽  
Vol 63 (1) ◽  
pp. 215-222 ◽  
Author(s):  
Mykola Perestyuk ◽  
Petro Feketa
Keyword(s):  
Simple Structure ◽  
Linear Extensions ◽  
Qualitative Behaviour ◽  
Small Perturbations ◽  
One Dimensional ◽  
Exponentially Stable ◽  
Invariant Toroidal Manifold ◽  
Dimensional Dynamical System ◽  
Stable Invariant ◽  
Stable Invariant Torus

Abstract New conditions of the preservation of an exponentially stable invariant toroidal manifold of linear extension of one-dimensional dynamical system on torus under small perturbations in ω-limit set are established. This approach is applied to the investigation of the qualitative behaviour of solutions of linear extensions of dynamical systems with simple structure of limit sets.

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