An invariant manifold approach to nonlinear normal modes of oscillation

Summary A method for determining the amplitude-dependent mode shapes and the corresponding modal dynamics of weakly nonlinear vibratory systems is described. The method is a combination of a Galerkin projection and invariant manifold techniques and is applied to a class of distributed parameter vibratory systems. In this paper the general theory for a class of conservative systems is outlined and applied to determine the nonlinear mode shapes and modal dynamics of a linear Euler-Bernoulli team attached to a nonlinear elastic foundation.     

CSTR中H2O2-KSCN-CuSO4非线性反应体系的研究

非统性化学反应现象（包括化学振荡、化学波和化学混饨等）的研究近二十年来进展较快，BZ反应＊、NADH氧化的生化反应＊及卤类化合物主导的其它反应体系［’－’］的混饨、双节律等复杂非线性现象不断被发现并得到不同程度的确证．无卤无机反应体系的复杂非线性现象未见报导，我们选择H202－KSCN－CllS04－N。OH无卤体系K7］进行探索，此反应在连续搅拌反应器（CSTR）和封闭反应器（batch）皆有振荡现象，在体系中加入鲁米诺（11J．－－－－n由产生发光振荡现象问，我们对这个反应体系的进一步研究发现复杂振荡（包括非周期过程）…     

Stochastic bi-resonance induced by external noise for Ca<Superscript>2+</Superscript> signaling in hepatocytes

The influence of external noise on intracellular Ca²⁺ oscillations dynamics in a single cell of rat hepatocytes is studied. The coherence of noise-induced intracellular Ca²⁺ oscillations reached two maxima for multiple external noise intensity, indicating the occurrence of external noise stochastic bi-resonance (SBR). This phenomenon is compared with our previous result that was induced by internal noise. Additionally, the deterministic bifurcation character of the system was also discussed.     

Nonstationary theory and simulation of the backward wave peniotron oscillator

The oscillations build-up process from raising until reaching steady-state in the backward wave peniotron oscillator (BWPO) are analased in the frame of the nonstationary nonlinear theory. By analytical and numerical calculations it is indicated that single-frequency and multi-frequency oscillations including chaotic ones can be generated by BWOP with high efficiency.     

Period-doubling and chaotic oscillations the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction, the oxidation of malonic acid by acidic bromate, is the most commonly investigated chemical system for understanding spatial pattern formation. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at Iow flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy(o)rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition, it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

In this paper we consider the onset of shimmy oscillations of an aircraft nose landing gear. To this end we develop and study a mathematical model with torsional and lateral bending modes that are coupled through a wheel-mounted elastic tyre. The geometric effects of a positive rake angle are fully incorporated into the resulting five-dimensional ordinary differential equation model. A bifurcation analysis in terms of the forward velocity and the vertical force on the gear reveals routes to different types of shimmy oscillations. In particular, we find regions of stable torsional and stable lateral shimmy oscillations, as well as transient quasiperiodic shimmy where both modes are excited.     

Dynamics of rope transportation systems that carry moving distributed and concentrated inertial loads

The paper focuses on the dynamics of three types of flexible elements in transportation systems that carry (i) moving distributed inertial load with discretely arranged concentrated loads, (ii) moving concentrated loads on a fixed flexible element, and (iii) moving distributed inertial load with concentrated loads that do not move in the longitudinal direction. The modes, frequencies, and critical speeds of flexible elements are determined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 117–133, January 2007.     

4d core hole formation in silver and its role in Ag secondary ion formation/survival

The low energy mono-atomic secondary ion intensities of Ag⁻ over the transient regions from Ag under 1-5 keV Cs⁺ primary ion impact are compared. These energies are used since they appear to be above and below the collisional excitation threshold for 4d core hole formation. The lack of any work function dependence in both suggests that (a) Ag⁻ forms via resonance charge transfer of electrons from the broad 5s-5p band to Ag atoms bearing 4d core holes (Auger is disregarded for energetic reasons), and that (b) the route via which 4d core holes are formed, whether it be via collective oscillations or collisional excitation, is of minimal importance. The similarity in X-ray induced plasmon loss features from clean and Cs implanted Ag confers with these results.     

Stock mechanics: Predicting recession in S&P500, DJIA and NASDAQ

Proposed in this paper is an original method assuming potential and kinetic energies for prices and for the conservation of their sum that has been developed for forecasting exchanges. Connections with a power law are shown. Semiempirical applications on the S&P500, DJIA, and NASDAQ predict a forthcoming recession in them. An emerging market, the Istanbul Stock Exchange index ISE-100 is found harboring a potential to continue to rise.