Related Experiment Video
Updated: Jun 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Chaotic Hamiltonian systems: survival probability
1NN Semenov Institute of Chemical Physics, Russian Academy of Sciences, 1199911 Moscow, Russia.
Abstract:
We consider the dynamical system described by the area-preserving standard mapping. It is known for this system that P(t), the normalized number of recurrences staying in some given domain of the phase space at time t (so-called "survival probability") has the power-law asymptotics, P(t) approximately t{-nu}. We present new semiphenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective "ultrametric diffusion" on the boundary of a treelike space with hierarchically organized transition rates. In the framework of our approach we have estimated the exponent nu as nu=ln 2/ln(1+r{g}) approximately 1.44, where rg=([square root] 5-1)/2 is the critical rotation number.
Related Concept Videos
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Second Order systems II
If ζ...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Second Order systems I
By reinterpreting the system, one can derive the closed-loop transfer function, which...