A modified and compact form of Krylov-Bogoliubov-Mitropolskii unified method for solving an nth order non-linear differential equation

A modified and compact form of Krylov-Bogoliubov-Mitropolskii (KBM) (Introduction to Nonlinear Mechanics, Princeton University Press, Princeton, NJ, 1947; Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961) unified method (J. Franklin Inst. 339 (2002) 239) is determined for obtaining the transient response of an nth order (n?2) differential equation with small non-linearities. The formula presented in (J. Franklin Inst. 339 (2002) 239) is a changed form of KBM method. For n=2,3,4, some previous formulas were found separately by several authors in terms of amplitude and phase variables; but the formula of Shamsul Alam, J. Franklin Inst. 339 (2002) 239) is derived in terms of some unusual variables instead of amplitudes and phases. The formula of Shamsul Alam, J. Franklin Inst. 339 (2002) 239) is a general form and used arbitrarily to obtain asymptotic solution for n=2,3,4,…. However, a solution obtained by formula Shamsul Alam, J. Franklin Inst. 339 (2002) 239) is transformed to a formal form replacing the unusual variables by amplitude and phase variables. In the present paper, the formula of Shamsul Alam, J. Franklin Inst. 339 (2002) 239) is itself transformed to a usual form (i.e. in terms of amplitude and phase variables). The later form of the formula is similar to most of the previous formulas found by several authors when n=2,3,4. This form of the formula is also generalized and it is easier than those obtained in all previous papers (extension) and identical to that initiated by original contributors (Introduction to Nonlinear Mechanics, Princeton University Press, Princeton, NJ, 1947; Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961).     

An approximate method for solving Hopf's equation of Burger's model of turbulence

The Hopf functional equation of Burger's model of turbulence is considered and the Lewis-Kraichnan version of the functional formulation is discussed. An approximate method based on series expansion of natural logarithm of the characteristic functional is presented. The equations governing the hierarchy of cumulants are derived. Several possible methods of closing the system of equations are discussed.Presently academic visitor at the Department of Civil and Geological Engineering, Princeton University, Princeton, NJ, USA.     

High speed digital imaging of cavitating vortices

 Researchers at the Cavitation and Multiphase Flow Laboratory of the University of Michigan worked in conjunction with Princeton Scientific Instruments (PSI) engineers to employ a new digital imaging system in the study of partial attached cavitation. The new high speed solid state system, the Princeton Scientific Ultra Fast Framing Camera (UFFC), was designed for cavitation studies where framing rates of 10⁵–10⁶ frames/s are required to image the detailed mechanisms of cavitating flows. The UFFC, which uses a PSI patented Charge Coupled Device (CCD) array image sensor, was designed to capture 30 frames at a maximum framing rate of 1 million frames/second. In these experiments, a maximum framing rate of 125000 frames per second (8 μs/frame) was used to examine cavitating vortices in the closure region of a partial attached cavity. The vortical structures in the closure region of the attached cavity were imaged, and the evolution and collapse of these flow structures were examined. Relationships between the cavitating vortices size, strength, and collapse time were observed. Received: 15 November 1996/Accepted: 1 December 1997     

Impact of Atmospheric Front Parameters on Free and Forced Oscillations of Level and Current in the Sea of Azov

Level and current oscillations in the basin of the Sea of Azov have been studied by hydrodynamic modeling using the Princeton ocean model (POM). The hypothesis on the role of the resonance mechanism in the occurrence of extremely large amplitudes of storm surge and seiche oscillations depending on the velocity and time of motion of atmospheric fronts of the Sea of Azov has been tested. It is found that at the same wind, pressure perturbations moving over the Sea of Azov induce forced oscillations, and after the perturbations cease, free oscillations with amplitudes that are 14% higher than those obtained at constant atmospheric pressure. It is shown that the motion of the atmospheric front (whose velocity and time are selected under the assumption that waves with maximum amplitudes are generated) plays an important but not decisive role in the formation of the structure of currents and level oscillations in the Sea of Azov.     

海上溢油迁移转化的双层数学模型

海上溢油的双层数学模型将泄漏在海域中的溢油考虑为表层油膜和分布在整个水体中的悬浮 油滴两层组成. 采用Lagrangian追踪法模拟油膜的输移扩散. 在此方法中，油膜可用大量的小油滴表示，对每个油滴都规定随时间而变化的坐标系，油滴 的运动受到风、潮流和周围油的浓度影响. 油的迁移过程包括对流、扩展、湍动扩 散、附着在岸边以及沉降到海底等过程. 转化过程包括挥发、溶解、乳化等. 此外，光化学反应、生物降解能够改变油的特征以及减小油的污染. 该模型可以用于瞬时和连续溢油的情况，不仅可以用于模拟油，也可以模拟其它与油的密度 相近的有害物质的泄漏. 水动力学模型采用美国普林斯顿海洋模式(POM). 该溢油模型已应用于渤海海峡突发性溢油事故的模拟与预报.     

Remedies for artificial diapycnal mixing in a σ co‐ordinated model of Tokyo Bay1

False diapycnal mixing often occurs due to horizontal diffusion in the simulation of heat, salinity, or water quality in estuaries by using a σ co‐ordinated ocean model. The Princeton ocean model (POM) is used as a basic σ co‐ordinated model and is applied to Tokyo Bay. Only river discharges are introduced into the model as external forces. Two remedies recommended in the POM, Stelling's horizontal diffusion approximation, Huang's new diffusion formula, Song and Haidvogel's s co‐ordinates, and Smolarkiewicz advection scheme have all been examined for suppressing the false diapycnal mixing. The conclusions are that the simultaneous use of POM's remedy and Stelling's approximation and the simultaneous use of POM's remedy and s co‐ordinates are the most effective. Copyright © 2001 John Wiley & Sons, Ltd.     

Gelatin models for photoelastic analysis of gravity structures

The potential of gelatin as a highly sensitive photoelastic material has long been known but seldom utilized. This paper describes a series of tests to show that body-force stress distributions can be conveniently found with gelatin models. Problems arising from the extreme variability of gelatin, including edge dehydration and bacterial attack which have plagued investigators in the past, may be overcome or even turned to advantage by careful control of the mixture and simultaneous calibration. Previous work with gelatin in this country and abroad has been reviewed in order to indicate the available information on the instantaneous physical and optical properties. Data from the calibration test performed at Princeton were used to obtain both the instantaneous and the linearly viscoelastic creep behavior of the gelatin mixture chosen in terms of constant moduli which can be compared with other time-dependent, prototype materials. Apparatus and procedure for both calibration and model tests are outlined, and test results for one of the wedge-shaped gravity structures investigated are compared with analytic predictions.     

Parallel spectral-element—Fourier simulation of turbulent flow over riblet-mounted surfaces

The flow in a channel with its lower wall mounted with streamwise V-shaped riblets is simulated using a highly efficient spectral-element—Fourier method. The range of Reynolds numbers investigated is 500 to 4000, which corresponds to laminar, transitional, and turbulent flow states. Our results suggest that in the laminar regime there is no drag reduction, while in the transitional and turbulent regimes drag reduction up to 10% exists for the riblet-mounted wall in comparison with the smooth wall of the channel. For the first time, we present detailed turbulent statistics in a complex geometry. These results are in good agreement with available experimental data and provide a quantitative picture of the drag-reduction mechanism of the riblets.This work was supported by National Science Foundation Grants CTS-8906432, CTS-8906911, and CTS-8914422, AFOSR Grant No. AFOSR-90-0124, and DARPA Grant No. N00014-86-K-0759. The computations were performed on the Cray Y/MP's of NAS at NASA Ames and the Pittsburgh Supercomputing Center, and on the Intel 32-node iPSC/860 hypercube at Princeton University.     

A feasible neuron for estimating the magnetic field effect

Biological neurons are capable of encoding a variety of stimuli, and the synaptic plasticity can be enhanced for activating appropriate firing modes in the neural activities. Artificial neural circuits are effective to reproduce the main biophysical properties of neurons when the nonlinear circuits composed of reliable electronic components with distinct physical properties are tamed to generate similar firing patterns as biological neurons. In this paper, a simple neural circuit is proposed to estimate the effect of magnetic field on the neural activities by incorporating two physical electronic components. A magnetic flux-controlled memristor and an ideal Josephson junction in parallel connection are used to percept the induction currents induced by the magnetic field. The circuit equations are obtained according to the Kirchhoff’s theorem and an equivalent neuron model is acquired by applying scale transformation on the physical variables and parameters in the neural circuit. Standard bifurcation analysis is calculated to predict possible mode transition and evolution of firing patterns. The Hamilton energy is also obtained to find its dependence on the mode selection in electronic activities. Furthermore, External magnetic field is applied to estimate the mode transition of neural activities because the phase error and the junction current across the Josephson junction can be adjusted to change the dynamics of the neural circuit. It is found that the biophysical functional neuron can present rapid and sensitive response to external magnetic field. Nonlinear resonance is obtained when stochastic phase error is induced by external time-varying magnetic field. The neural circuit can be suitable for further calculating the collective behaviors of neurons exposed to magnetic field.

     

PHCA实验中犬心脏的非线性动力学研究

按照非线性理论,实施了犬的深低温停循环（Profound Hypothermia and Circulatory Arrest,简称PHCA）实验,并应用混沌理论对实验中采集的心电信号进行了研究,得出以下结论：（1）混沌特征参数可反映心脏的总体动态特征,并可作为心血管疾病早期诊断的依据。（2）在正常的生理状态下心脏的运动是混沌的,而在病理状态下则趋于有序。     

纳米晶铜单向拉伸变形的分子动力学模拟

纳米材料是由尺度在1－100nm的微小颗粒组成的体系，由于它具有独特的性能而备受关注。本文简要地回顾了分子动力学在纳米材料研究中的应用，并运用它模拟了平均晶粒尺寸从1．79－5．38nm的纳米晶体的力学性质。模拟结果显示：随着晶粒尺寸的减小，系统与晶粒内部的原子平均能量升高，而晶界上则有所下降；纳米晶体的弹性模量要小于普通多晶体，并随着晶粒尺寸的减小而减小；纳米晶铜的强度随着晶粒的减小而减小，显示了反常的Hall-Petch效应；纳米晶体的塑性变形主要是通过晶界滑移与运动，以及晶粒的转动来实现的；位错运动起着次要的、有限的作用；在较大的应变下（约大于5％），位错运动开始起作用；这种作用随着晶粒尺寸的增加而愈加明显。     

Further development of the losipescu shear test method

Recent activities by the present investigators to further develop the losipescu-shear-test method for use with composite materials are summarized. Finite-element analyses used to predict the stress states in the specimen are described, with particular emphasis on how they are influenced by the specific test-fixture configuration used. These same analytical tools were also used to predict the influence of specimen notch depth, notch angle, and notch-root radius. The result was a redesign of the original Wyoming version of the losipescu-shear-test fixture, and the establishment of guidelines for preparing specimens. These are discussed in some detail. Many references to available literature are included. An attempt has been made to put the work performed to date into perspective, to aid the potential user of the losipescu-shear-test method in establishing proper test procedures.     

Effects of the electromagnetic radiation on cognitive performance: a model study

We constructed a two-layer network model to study the effect of electromagnetic radiation on the cognitive functions. The network model was used to simulate two cognitive tasks under the electromagnetic radiation: the visual-guided saccade task and the memory-guided saccade task. The performance of these tasks showed that the electromagnetic radiation could induce faster ramping up activities, higher level of persistent activities and shorter reaction time, but the basic functions of the network such as working memory and motor output did not impair. We found that the electromagnetic radiation have both excitatory effect and inhibitory effect on the neuronal activities of the network model, but the excitatory effect played a major role. Finally, we concluded an excitatory mechanism to explain the effects of the electromagnetic radiation on the cognitive performance.

     

Terrain classification using ToF sensors for the enhancement of agricultural machinery traversability

Ground properties influence various aspects of mobile machinery navigation including localization, mobility status or task execution. Excessive slipping, skidding or trapping situations can compromise the vehicle itself or other elements in the workspace. Thus, detecting the soil surface characteristics is an important issue for performing different activities in an efficient, safe and satisfactory manner. In agricultural applications, this point is specially important since activities such as seeding, fertilizing, or ploughing are carried on within off-road landscapes which contain a diversity of terrains that modify the navigation behaviour of the vehicle. Thus, the machinery requires a cognitive capability to understand the surrounding terrain type or its characteristics in order to take the proper guidance or control actions. This work is focused on the soil surface classification by implementing a visual system capable to distinguish between five usual types of off-road terrains. Computer vision and machine learning techniques are applied to characterize the texture and color of images acquired with a Microsoft Kinect V2 sensor. In a first stage, development tests showed that only infra-red and RGB streams are useful to obtain satisfactory accuracy rates (above 90%). The second stage included field trials with the sensor mounted on a mobile robot driving through various agricultural landscapes. These scenarios did not present illumination restrictions nor ideal driving roads; hence, conditions can resemble real agricultural operations. In such circumstances, the proposed approach showed robustness and reliability, obtaining an average of 85.20% of successful classifications when tested along 17 trials within agricultural landscapes.     

天水地区断裂活动性与地质灾害的相关性研究

在对天水地区断裂活动性的实地调查和断裂带氡气含量测试的基础上,对研究区内断裂的活动性进行了分析评价分级,分析了地质灾害的发育与分布特征,研究了断裂活动性与地质灾害发育程度之间的关系。研究表明,研究区断裂活动性与地质灾害的发育程度之间有着密切的联系,断裂活动是本区地质灾害的主要影响因素之一。     

黄淮地区巨厚松散层岩性结构特征以及采矿对其水动态的影响

本文选择地处黄淮地区的淮南、淮北、大屯、兖州和邢台等矿区中典型矿井的巨厚松散层，分析了该地区巨厚松散层的岩性结构特征，从水体、地层和采矿波及类型等方面论述了采矿对松散层地下水动态的影响特征，解释和解决了某些实际工程问题。     

西安地区断裂构造活动性的地质力学模拟研究

在对地质原型研究的基础上，采用相似材料三维地质力学模拟方法，对西安地区的断裂构造活动性进行了两个方案的模拟试验。建立了断裂构造近期活动的动力学模型，并阐明了西安地裂缝的形成与断裂构造活动的关系。本文详细论述了这项研究的模型设计、模拟方法和技术以及全部研究成果。     

Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

The cubic-polynomial nonlinearity with N-shaped curve plays a crucial role in generating abundant electrical activities for the original FitzHugh-Nagumo (FHN) neuron model. The pioneer FHN neuron model is efficient in theoretical analysis and numerical simulation for these abundant electrical activities, but analog multipliers are indispensable in hardware implementation since the involvement of cubic-polynomial nonlinearity. Analog multiplier goes against the circuit integration of FHN neuron model due to its huge implementation costs. To avoid the involvement of analog multiplier in hardware implementation, a nonlinear function possessing N-shaped curve and multiplier-free implementation is presented in this paper. To confirm the availability of this nonlinear function in generating electrical activities, numerical simulations and hardware experiments are successfully executed on an improved two-dimensional (2D) FHN neuron model with externally applied stimulus. The results demonstrate that the improved FHN neuron model can generate rich electrical activities of periodic spiking behavior, chaotic behavior, and quasi-periodic behavior. Analog circuit implementation without any multiplier and its hardware experiment show the availability of the proposed nonlinear function, which is appropriate for analog circuit implementation of FHN neuron-based neuromorphic intelligence.

     

The S. P. Timoshenko Institute of Mechanics at the beginning of the third millennium

A brief historical review of the main scientific activities at the S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, is outlined. Current trends are examined, in the Institute as a whole and in particular departments. As a resource, reviews of the Institute's activity published between 1955 and 1999 in this journal and elsewhere are listed in a bibliography. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 6–24, January, 2000.     

Simulating electric activities of neurons by using PSPICE

Electric activities in the Morris–Lecar neuron and Josephson junction coupled resonator are investigated in a numerical way, and electric circuits are also designed by using the Personal Simulation Program with Integrated Circuit Emphasis (PSPICE). Within the improved Morris–Lecar circuit, a new integrator for the ion channel of potassium is designed, and the transition of electric activities, quiescent state to spiking to bursting to quiescent state could be observed. In the circuit of the Josephson-junction coupled resonator, an equivalent circuit is designed to reproduce several types of electric activity. The detailed parameter regions are detected to generate spiking and bursting states in the electric circuits for neurons, and these results are consistent with the numerical results. Bifurcation diagrams for interspike interval (ISI) vs. the forcing current are calculated to detect the excitability of the neuron model.