Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations

In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.     

A Bilinear Backlund Transformation and Lax Pair for a （1＋1）-Dimensional Differential-Difference sine-Gordon Equation

In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.     

Optimization of the CIGS based thin film solar cells: Numerical simulation and analysis

Chalcopyrite Cu(In,Ga)Se (CIGS) is a very promising material for thin film photovoltaics and offers a number of interesting advantages compared to the bulk silicon devices. CIGS absorbers today have a typical thickness of about 1–2 μm. However, on the way toward mass production, it will be necessary to reduce the thickness even further. This paper indicates a numerical study to optimization of CIGS based thin film solar cells. An optimum value of the thickness of this structure has been calculated and it is shown that by optimizing the thickness of the cell efficiency has been increases and cost of production can be reduces. Numerical optimizations have been done by adjusting parameters such as the combination of band gap and mismatch as well as the specific structure of the cell. It is shown that by optimization of the considered structure, open circuit voltage increases and an improvement of conversion efficiency has been observed in comparison to the conventional CIGS system. Capacitance–voltage characteristics and depletion region width versus applied voltage for optimized cell and typical cell has been calculated which simulation results predict that by reducing cell layers in the optimized cell structure, there is no drastically changes in depletion layer profile versus applied voltage. From the simulation results it was found that by optimization of the considered structure, optimized value of CIGS and transparent conductive oxide thickness are 0.3 μm and 20 nm and also an improvement of conversion efficiency has been observed in comparison to the conventional CIGS which cell efficiency increases from 17.65 % to 20.34%, respectively.     

The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law

An Otto cycle engine with internal and external irreversibilities of friction and heat leakage, in which the heat transfer between the working fluid and the environment obeys linear phenomenological heat transfer law [q ∝△(T -1)], is studied in this paper. The optimal piston motion trajectory for maximizing the work output per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases of with and w...     

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.      

Investigation on optimization design of equivalent water depth truncated mooring system

The oil industry is now increasingly concentrating their efforts and activities in connection with developing fields in deeper waters, ranging typically from 500 m to 3000 m worldwide. However, the modeling of a full-depth system has become difficult presently; no tank facility is sufficiently large to perform the testing of a complete FPS with compliant mooring in 1000 m to 3000 m depth, within reasonable limits of model scale. Until recently, the most feasible procedure to meet this challenge seems to be the so-called “hybrid model testing technique”. To implement this technique, the first and important step is to design the equivalent water depth truncated mooring system. In this work, the optimization design of the equivalent water depth truncated mooring system in hybrid model testing for deep sea platforms is investigated. During the research, the similarity of static characteristics between the truncated and full depth system is mainly considered. The optimization mathematical model for the equivalent water depth truncated system design is set up by using the similarity in numerical value of the static characteristics between the truncated system and the full depth one as the objective function. The dynamic characteristic difference between the truncated and full depth mooring system can be minished by selecting proper design rule. To calculate the static characteristics of the mooring system, the fourth order Runge-Kutta method is used to solve the static equilibrium equation of the single mooring line. After the static characteristic of the single mooring line is calculated, the static characteristic of the whole mooring system is calculated with Lagrange numerical interpolation method. The mooring line material database is established and the standard material name and the diameter of the mooring line are selected as the primary key. The improved simulated annealing algorithm for continual & discrete variables and the improved complex algorithm for discrete variables are employed to perform the optimization calculation. The C++ programming language is used to develop the computer program according to the object-oriented programming idea. To perform the optimization calculation with the two algorithms mentioned above respectively and the better result is selected as the final one. To examine the developed program, an example of equivalent water depth truncated mooring system optimum design calculation on a 100,000-t, turret mooring FPSO in water depth of 320 m are performed to obtain the conformation parameters of the truncated mooring system, in which the truncated water depth is 160 m. The model test under some typical environment conditions are performed for both the truncated and the full depth system with model scale factor λ=80. After comparing the corresponding results from the test of the truncated system with those from the full depth system test, it’s found that the truncated mooring system design in this work is successful. Supported by the National Natural Science Foundation of China (Grant Nos. 10602055 and 40776007) and the Natural Science Foundation of China Jiliang University (Grant No. XZ0501)     

Recent Results on Recurrent Solutions and Limit Distributions of SDEs

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.     

小功率高转速蒸汽透平试验研究和优化

小功率高转速蒸汽透平试验研究和优化邵振麒（同济大学汽车工程系上海２０００９２）关键词：小蒸汽透平，效率，优化１前言回收能量和工业装置的余热及利用太阳能等新能源是节能和环保的重要措施，由此产生的机械能可供发电，气体增压等多种用途。在一些废热量不大且不宜...