Revisiting the models of vibration screening process

This talk presents two approaches for modeling of the vibration screening process. The first approach is analytical. It models the screening process as a diffusion of undersize fraction taking into account the special term for vibration separation (the Brazil nut effect). The talk provides a solution of the corresponding partial differential equation. The solution in turn allows estimation of the screening performance dependence on both deterministic and stochastic factors as well as evaluation of the factors dominance conditions. The talk presents simple evaluation formulae for the screening process performance. The second approach is based on a simulation model. The model deals with monolayer dynamics. Embodying traditional concepts of vibration transportation, the approach introduces some novel techniques of evaluation of the effect of the granular particles shape. Taking into account the particle shape factor may significantly improve the modeling precision for nonspherical particles

Rare events – rare attractors; formalization and examples

Analogy between attractors in nonlinear dynamics, called “rare attractors” by M.V. Zakrzhevsky and his colleagues [1] and emergencies, such as natural and technogenic catastrophes as well as downfalls caused by risky economic policies and strategies has been discussed. Examples of rare but technically significant attractors in nonlinear dynamics have been give

Extension of the Method of Direct Separation of Motions for Problems of Oscillating Action on Dynamical Systems

AbstractA general approach to study oscillating action on nonlinear dynamical systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics equations). The approach is named as the Oscillatory Strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that represent the averaged effect of the oscillating action. The method of direct separation of motions (MDSM) appears to be an efficient and simple tool to derive these equations. A modification of the method applicable to study problems that do not imply restrictions on the spectrum of excitation frequencies is proposed. It allows also to abandon other restrictions usually introduced when employing the classical asymptotic methods, e.g. the requirement for the involved nonlinearities to be weak.Several relevant examples from Mechanics, Physics, Chemistry, and Biophysics are considered by means of the conventional MDSM and, in more details, by the modified MDSM, illustrating the efficiency the methods

Predict-prevent control method for perturbed excitable systems

We present a control method based on two steps: prediction and prevention. For prediction we use the anticipated synchronization scheme, considering unidirectional coupling between excitable systems in a master-slave configuration. The master is the perturbed system to be controlled, meanwhile the slave is an auxiliary system which is used to predict the master's behavior. We demonstrate theoretically and experimentally that an efficient control may be achieved.Comment: 4 pages, 5 figure

Zum Einfluss eines inneren Freiheitsgrades auf das Verhalten eines Pendels mit vibrierender Aufhängung

Die Vibration der Lagerachse eines einfachen Pendels im Schwerefeld kann bekanntlich das Gleichgewicht des stehenden Pendels (Überkopfpendel) stabilisieren; sie kann aber auch dasjenige des hängenden Pendels destabi-lisieren. In der vorliegenden Arbeit wird das Pendelmodell durch einen mit dem Pendelkörper elastisch und viskos gedämpft verbundenen Massenpunkt mit einem zusätzlichen radialen Freiheitsgrad verallgemeinert. Für den Fall der vertikalen Vibration der Lagerachse wird gezeigt, dass das Vorhandensein dieser Zusatzmasse das Verhalten des Pendels unter bestimmten Bedingungen wesentlich verändert: Instabile Gleichgewichtslagen wer-den stabil und umgekehrt. Das Vorhandensein des zusätzlichen Freiheitsgrades gestattet die Stabilisierung des stehenden Pendels bei wesentlich kleineren Werten der Geschwindigkeitsamplitude der Achsschwingungen. Zur Lösung der Aufgabe wird die Methode der direkten Bewegungsteilung angewendet

Thermodynamic limit of the first-order phase transition in the Kuramoto model

In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic dependence of the order parameter above criticality: $r-r_c \propto (K-K_c)^{2/3}$. For a finite population, we demonstrate that the population size $N$ may be included into a self-consistency equation relating $r$ and $K$ in the synchronized state. We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies. Other frequency distributions different from the uniform one are also considered.Comment: 6 page

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.Comment: 10 pages, 9 figure

Rare events – rare attractors; formalization and examples

Analogy between attractors in nonlinear dynamics, called “rare attractors” by M.V. Zakrzhevsky and his colleagues [1] and emergencies, such as natural and technogenic catastrophes as well as downfalls caused by risky economic policies and strategies has been discussed. Examples of rare but technically significant attractors in nonlinear dynamics have been give

Multiobjective synchronization of coupled systems

Copyright @ 2011 American Institute of PhysicsSynchronization of coupled chaotic systems has been a subject of great interest and importance, in theory but also various fields of application, such as secure communication and neuroscience. Recently, based on stability theory, synchronization of coupled chaotic systems by designing appropriate coupling has been widely investigated. However, almost all the available results have been focusing on ensuring the synchronization of coupled chaotic systems with as small coupling strengths as possible. In this contribution, we study multiobjective synchronization of coupled chaotic systems by considering two objectives in parallel, i. e., minimizing optimization of coupling strength and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach. The constraints on the coupling form are also investigated by formulating the problem into a multiobjective constraint problem. We find that the proposed evolutionary method can outperform conventional adaptive strategy in several respects. The results presented in this paper can be extended into nonlinear time-series analysis, synchronization of complex networks and have various applications