Search results for "dynamical system"
showing 10 items of 523 documents
Active controlled structural systems under delta-correlated random excitation: linear and nonlinear case
2006
Abstract Reduction of structural vibration in active controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-Gaussian random process accounting for the time delay involved in the application of active control actions. Control forces acting with time-delay effects will be expanded in Taylor series evaluating response statistics by means of the extended Ito differential rule to consider the effects of the non-normality of the input processes. Numerical application provided shows the feasibility of the proposed method to analyze stochastic …
A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by P…
2020
Abstract The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For this purpose, in the present paper, a novel method based on the augmented Markov vector process for the PDF of the time-variant extreme value process for a Poisson white noise driven dynamical system is proposed. Specifically, the augmented Markov vector (AMV) process is constructed by combining the extreme value process and its underlying…
On boundaries of attractors in dynamical systems
2021
Abstract Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are a…
On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the…
2008
We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schrodinger equation \(i\epsilon \varPsi _{t}+\frac{\epsilon^{2}}{2}\varPsi _{xx}+|\varPsi |^{2}\varPsi =0\) , e ≪1, with analytic initial data of the form \(\varPsi (x,0;\epsilon)=A(x)e^{\frac{i}{\epsilon}S(x)}\) is approximately described by a particular solution to the Painleve-I equation.
Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag
2014
We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.
Measurements of the tau polarisation in Z0 decays
1995
A sample of Z0→τ+τ- events observed in the DELPHI detector at LEP in 1991 and 1992 is analysed to measure the τ polarisation in the exclusive decay channels {Mathematical expression}, {Mathematical expression}, πν, ρν and a1ν. The τ polarisation is also measured with an inclusive hadronic analysis which benefits from a higher efficiency and a better systematic precision than the use of the exclusive decay modes. The results have been combined with those published on the 1990 data. A measurement of the τ polarisation as a function of production angle yields the values for the mean τ polarisation 〈P〉τ=-0.148±0.022 and for the Z0 polarisation PZ=-0.136±0.027. These results are used to determin…
Pattern formation driven by cross–diffusion in a 2D domain
2012
Abstract In this work we investigate the process of pattern formation in a two dimensional domain for a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka–Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, and hexagonal patterns.
A Seven Mode Truncation of the Kolmogorov Flow with Drag: Analysis and Control
2009
The transition from laminar to chaotic motions in a viscous °uid °ow is in- vestigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov °ow with drag friction. An- alytical expressions of the Hopf bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynolds num- ber is increased for ¯xed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is ob- tained through a model reference approach which makes the control global. Finally, the e®ectiveness of this control strategy is numerically illustra…
From capillary condensation to interface localization transitions in colloid-polymer mixtures confined in thin-film geometry.
2008
Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer to colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core rep…
Kinetics of the Formation of Ordered Domains on Surfaces: Theoretical Considerations and Monte-Carlo Simulation
1986
When an adsorbed monolayer which initially is in a disordered state is suddenly brought to a temperature in the regime of the ordered phase, domains of the ordered phase are predicted to form and grow with time t after the quench according to a power law, i.e. linear dimension L(t) ∞ tx. At the same time, the structure function S(k,t) is predicted to satisfy a scaling law, S(k,t) = S(k,tx), k being the difference between the wave vector observed in the scattering and the Bragg wave vector describing the long range order. The theoretical ideas which lead to this behaviour are briefly reviewed, and evidence from simulations of simple lattice gas models and Potts models is presented. Particula…