Application of the method of direct separation of motions to the parametric stabilization of an elastic wire

The paper considers the application of the method of direct separation of motions to the investigation of distributed systems. An approach is proposed which allows one to apply the method directly to the initial equation of motion and to satisfy all boundary conditions, arising for both slow and fast components of motion. The methodology is demonstrated by means of a classical problem concerning the so-called Indian magic rope trick (Blekhman et al. in Selected topics in vibrational mechanics, vol. 11, pp. 139–149, [2004]; Champneys and Fraser in Proc. R. Soc. Lond. A 456:553–570, [2000]; in SIAM J. Appl. Math. 65(1):267–298, [2004]; Fraser and Champneys in Proc. R. Soc. Lond. A 458:1353–1373, [2002]; Galan et al. in J. Sound Vib. 280:359–377, [2005]), in which a wire with an unstable upper vertical position is stabilized due to vertical vibration of its bottom support point. The wire is modeled as a heavy Bernoulli–Euler beam with a vertically vibrating lower end. As a result of the treatment, an explicit formula is obtained for the vibrational correction to the critical flexural stiffness of the nonexcited system.     

Combinatorial optimization with interaction costs: Complexity and solvable cases

We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear costs and the interaction costs between elements of the two selected structures is minimized. COPIC generalizes the quadratic assignment problem and many other well studied combinatorial optimization problems, and hence covers many real world applications. We show how various topics from different areas in the literature can be formulated as special cases of COPIC. The main contributions of this paper are results on the computational complexity and approximability of COPIC for different families of combinatorial structures (e.g. spanning trees, paths, matroids), and special structures of the interaction costs. More specifically, we analyze the complexity if the interaction cost matrix is parameterized by its rank and if it is a diagonal matrix. Also, we determine the structure of the intersection cost matrix, such that COPIC is equivalent to independently solving linear optimization problems for the two given families of combinatorial structures.     

Vibration energy harvesting for low frequency using auto-tuning parametric rolling pendulum under exogenous multi-frequency excitations

An electromagnetic parametrically excited rolling pendulum energy harvester with self-tuning mechanisms subject to multi-frequency excitation is proposed and investigated in this paper. The system consists of two uncoupled rolling pendulum. The resonance frequency of each the rolling pendulum can be automatically tuned by adjusting its geometric parameters to access parametric resonance. This harvester can be used to harvest the energy at low frequency. A prototype is developed and evaluated. Its mathematical model is derived. A cam with rolling follower mechanism is employed to generate multi-frequency excitation. An experimental study is conducted to validate the proposed concept. The experimental results are confirmed by the numerical results. The harvester is successfully tuned when the angular velocity of the cam is changed from 1.149 to 1.236 Hz.     

Application of ultrasound technology in the drying of food products

This study presents a state-of-the-art overview on the application of ultrasound technology in the drying of food products, including the ultrasound pre-treatment and ultrasound assisted drying. The effect of main parameters and ultrasound technology on the drying kinetics and food quality were discussed. Inconsistencies were pointed out and analyzed in detail. Results showed that for ultrasound pre-treatment, the food products may lose or gain water and increase of ultrasonic parameters (sonication time, amplitude and ultrasound power) promoted the water loss or water gain. When ultrasound technology was applied prior to drying, an increase in drying kinetics was always observed, though some different results were also presented. For ultrasound assisted drying, the ultrasound power always gave a positive effect on the drying process, however, the magnitude of ultrasound improvement was largely dependent on the process variables, such as air velocity, air temperature, microwave power and vacuum pressure, etc. The application of ultrasound technology will somehow affect the food quality, including the physical and chemical ones. Generally, the ultrasound application can decrease the water activity, improve the product color and reduce the nutrient loss.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

New techniques of local damage detection in machinery based on stochastic modelling using adaptive Schur filter

Vibration signal analysis is one of the most effective techniques of monitoring machinery and detecting local damage in their parts, e.g. bearings and gearboxes. However, such detection is sometimes difficult, especially in heavy industrial machines, because of a small proportion of damage-induced components in relation to the remaining components of registered signals. Therefore, more effective signal processing algorithms are being looked for. Moreover, local damage (cracking, pitting, spalling, breakage, etc.) in bearings and gearboxes generates broad-spectrum impulse signals, while the other type can be effectively modelled as a sum of narrowband signals. In this article, techniques based on Schur adaptive filter are proposed for local damage detection. In such an approach, the analysed signal is modelled by means of autoregressive process and the filter is described by so-called reflection coefficients. Schur algorithm is an effective algorithm with very good numerical properties and it is capable of tracking rapid changes in second order statistics of the analysed signal. Thus, the method is well-suited to analysing non-stationary signals and it is potentially interesting for use in bearing and gearbox monitoring.Reflection coefficients describing the signal model, defined with the use of Schur algorithm, may be applied in a variety of ways, giving a chance of employing different solutions in different conditions. In the first proposed solution, detection is based on the weighted sum of derivatives of reflection coefficients, while in the other one – on new signal obtained as power in frequency bands calculated from a parametric spectrogram, whose starting point are reflection coefficients. All these operations are aimed at enhancing changes that occur in the signal at the moments when damage-induced impulses appear. The article also presents guidelines for methods of determining parameter values in the employed analyses. The proposed solutions have been applied for analysing signals coming from a two-stage gearbox of a large machine driving a mining belt conveyor and the obtained results were analysed. They prove the effectiveness of the proposed techniques. It is worth emphasizing that these techniques can be easily adapted for monitoring machinery in varying operating conditions.     

基于光纤光参量放大的光脉冲压窄技术的研究

在高重复频率的光窄脉冲源中,为了获得更窄的脉冲,需要增加泵浦功率|但泵浦功率的提高会使光放大器的增益趋于饱和,放大的自发辐射噪音增强,脉冲光信噪比下降.为此,提出了利用啁啾管理和光纤光参量放大相结合的脉冲压窄方案.将强度调制后的泵浦光通过相位调制引入线性负啁啾,由于经参量过程后在新的闲频光上啁啾会加倍,从而进一步增大了信号的谱宽,并通过色散补偿介质实现了光脉冲压缩.实验给出了10 GHz速率下的结果,通过泵浦光的相位调制在0.5 W平均泵浦光功率条件下得到了脉宽19 ps的光脉冲,结果与理论分析基本吻合.     

Convex Parametric Programming in Abstract Spaces

This article studies stability and optimality for convex parametric programming models in abstract spaces. Necessary conditions for continuity of the feasible set mapping are given in complete metric spaces. This continuity is characterized for models in which the space of decision variables is reflexive Banach space. The main result on optimality characterizes locally optimal parameters relative to stable perturbations of the parameter. The result is stated in terms of the existence of a saddle-point for a Lagrangian that uses a finite Borel measure. It does not hold for unstable perturbations even if the model is finite dimensional. The results are applicable to various formulations of control and optimal control problems.     

Large amplitude electron plasma oscillations

We consider a cold plasma in order to find new large-amplitude wave solutions in the long-wavelength limit. Accordingly we derive two generic coupled equations which describe the energy exchange between the electrostatic and electromagnetic waves. A new kind of quasi-periodic behavior is found. Our derivations may be considered as a prerequisite to extended studies of stimulated Raman scattering for cases where the wave amplitudes are so large that standard perturbation techniques are not applicable.