Geometrical aspects of the complex eikonal equations associated to the generalized Weierstrass representation

Certain geometrical aspects of a Laplace-Beltrami equation subjected to a complex eikonal equation are studied. It is shown that all principal curvatures of a solution surface are constant for this system. To illustrate the theoretical considerations, we look for a class of solutions of an overdetermined system composed of the sigma model and a system of complex eikonal equations. The connection between the sigma model and the generalized Weierstrass system for inducing constant mean curvature surfaces allows us to construct special classes of solutions for classical configurations of strings. Presented by A.M. Grundland at the DI-CRM Workshop held in Prague, 18–21 June 2000. This work was supported by a research grant from NSERC of Canada and the hospitality of the Doppler Institute of the Czech Republic.     

Computer modeling of a direct contact condensing heat exchanger for gas furnaces

Experiments have been performed with a direct contact condensing heat exchanger for gas furnaces, in which a direct contact bubble distributor was used to heat and criculate water through a finned-tube heat exchanger which heats the return room air blown through. This paper presents the development of a computer model simulating the system, and the results of parametric studies. The heat transfer analysis of the system indicated possible further improvement of the system. A modified system was proposed and a model was also developed for the system. Comparisons of the heat transfer performance between the two models are given. The research activity concerning this work was supported by the Gas Research Institute (U.S.A.).     

A model of a neuron with oscillatory activity below the excitation threshold

We propose a dynamic model of a neuron with spontaneous periodic oscillations below the excitation threshold. Such neurons, in particular, play an important role in the problem of coordination of motions by the brain specifying the universal rhythm of muscular contractions. The model is constructed on the basis of the known model dynamic systems and is described by a system of fourth-order differential equations. A good qualitative agreement between the model dynamics and experimental data for the actual neurons is obtained. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Lobachevsky State University of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1623–1635, December, 1998.     

Energy based simulation of a Timoshenko beam in non-forced rotation. Influence of the piano hammer shank flexibility on the sound

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a piano hammer shank coupled to a hammer head. An energy-based numerical scheme is then provided, obtained by non-classical approaches. A major difficulty for time discretization comes from the nonlinear behavior of the kinetic energy of the system. This new numerical scheme is then coupled to a global energy-preserving numerical solution for the whole piano. The obtained numerical simulations show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, or from a changing impact point, or a “longitudinal rubbing motion” on the string, since neither of these features is modeled in our study.     

Plasma-chemical model, describing the surface treatment of polymers in RF-discharge

The surface modification of the polymers has been studied in RF-discharge. A plasma-chemical model is presented, describing the alteration of the adhesion work and the wetting contact angle of the treated materials. It is presumed that the adhesion work can be expressed by its volume and surface components. In the first approximation, only the surface adhesion work is changed in the course of the plasma treatment and it is due to creating of two common functional groups. We suggest a basic system of kinetic equations for quantitatively determining these groups. The system is solved analytically. This gives possibilities to obtain the analytical solutions of the adhesion work and the contact angle as a function of the time of treatment.     

Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model

The system of equations introduced by Lorenz to model turbulent convective flow is studied here for Rayleigh numbersr somewhat smaller than the critical value required for sustained chaotic behavior. In this regime the system is found to exhibit transient chaotic behavior. Some statistical properties of this transient chaos are examined numerically. A mean decay time from chaos to steady flow is found and its dependence uponr is studied both numerically and (very close to the criticalr) analytically.This work was supported in part by NASA grant NSG 5209; partial support of computer costs was provided by the University of Maryland-Baltimore County Computer Center.     

Photonic device as a second-order system

The present work presents the analysis of a photonic device. Starting from a laser model, it is shown that, if a two-level simplification is used and both low pumping and no losses are assumed, a second-order control system model is obtained. This model no longer describes a laser, but only a photonic device. The system response to a step input is analyzed and the results are compared with experimental data obtained when pumping a neodymium crystal with a diode laser. Both theoretical and experimental results are then compared with the analyzed photonic device. A good qualitative agreement is shown between the analytical, experimental, and computational results.     

Bifurcations of oscillations of the membrane potential and the use of mappings for modeling electrically coupled neurons

In this paper, we present the results of a qualitative analysis of a generalized system of three differential equations that represent the neuron model. The main nontrivial bifurcation sets leading to the appearance of complex motions, i.e., bursts, are given. A two-dimensional mapping that models the flows generated by this system, which is considered to be the simplest model of a neuron, is proposed. The chaotic dynamics of diffusely coupled neurons is studied using the coupled mappings. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Lobachevsky State Univesity of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1572–1580, December, 1998.     

On the theory of the work function

Starting from a definition of the work function in terms of total energies of the electron system it is shown that this work function can be obtained from the single-particle Schrödinger equations in the density-functional formalism in the way suggested by the Sommerfeld model. It is also shown that the change of the equilibrium ion positions accompanying the ionization of the crystal has no influence on the work function. A comparison is made with Koopmans' theorem. The use of several potentials for computations of the work function is critically investigated.     

Resolution of front-back confusion in virtual acoustic imaging systems

A geometric model of the scattering of sound by the human head is used to generate a model of localization cues based on interaural time delay (ITD). The ITD is calculated in terms of the interaural cross-correlation function (IACC) for sources placed at a series of azimuthal angles in the horizontal plane. This model is used to simulate the pressures generated at the ears of a listener due to real sources and due to a two-channel and a four-channel virtual source imaging system. Results are presented in each case for the variation of ITD with head rotation. The simulations predict that the rate of change of the ITD with head rotation produced by a real source and replicated by the four-channel virtual source imaging system, cannot be replicated by the two-channel system. These changes to the ITD provide cues which allow resolution of front-back confusion. The results of subjective experiments are also presented for the three cases modeled. These results strongly support the findings from the modeling work indicating that, for the systems described here, front-back confusion is resolved through changes to the ITD arising from head motion.     

Modélisation dynamique en thermique du bâtiment

This work describes the advantages provided by applying the method of spectral analysis to solve problems in the thermal analysis of buildings. A reduced spectrum of the model is obtained with the analysis of the dynamic responses of the system. The model obtained is simple and efficient, since it describes with accuracy the main dynamic behaviour of the structure. The aim is to use the model for the control of ambiant temperatures in buildings. These temperatures do not require accurate precision but a good restitution of involved dynamics.     

Estimation of interfacial forces in a multi-degree of freedom isolation system using a dynamic load sensing mount and quasi-linear models

A new indirect measurement concept is developed to estimate interfacial dynamic forces by employing the hydraulic mount as a dynamic force sensor. The proposed method utilizes a combination of mathematical models and operating motion and/or pressure measurements. A laboratory experiment consisting of a powertrain, three powertrain mounts (including a dynamic load sensing hydraulic mount), a sub-frame, and four bushings is then constructed to verify the proof-of-concept. Quasi-linear fluid and mechanical system models of the experiment are proposed and evaluated in terms of transfer functions and forced sinusoidal responses. The lower chamber pressure in the hydraulic mount is estimated since it is not available from measurements. This leads to an improved estimation of the effective rubber and hydraulic path parameters with spectrally varying and amplitude-sensitive properties up to 50 Hz. Finally, the reverse path spectral method is employed to predict interfacial forces at both ends of the mount by using measured motions and upper chamber pressure signals. Overall, the proposed quasi-linear fluid system model yields better indirect estimates of forces from the measured responses when compared with direct force measurements, through a simpler mechanical system model provides some insights. This work also advances prior component and transfer path type studies by providing an improved multi-degree of freedom system perspective.     

共焦显微镜扫描工作台的系统建模与动态分析

共焦显微镜扫描工作台动态模型是研究控制系统的重要依据,它直接影响工作台的重复定位精度.提出了将机械部分和电气部分分开建模的方法,建立了系统数学模型,该方法具有较好的可移植性,建模过程简单,有利于分析系统各环节对系统控制性能的影响.在MATLAB/Simulink下进行仿真,2 s内系统达到了稳定状态,证明了系统具有很好的动态特性,满足控制的要求.     

Rainfall prediction with a limited-area model during an intense storm over northern italy

Summary Numerical experiments have been performed to simulate a severe storm in the Valtellina Valley, in the central part of Northern Italy, with a version of the limited-area model UB/NMC (University of Belgrade, U.S. National Meteorological Center model). This situation is characterized by strong and persistent rainfall over confined spatial areas in the Alpine region, where observations from synoptic and ENEL (National Electricity Board of Italy) stations revealed the intensity of the phenomenon. A first set of experiments was performed with ECMWF (European Centre for Medium Range Weather Forecasts) initialized analyses as initial and boundary conditions. These experiments were run with eta and sigma vertical-coordinate system, with different horizontal resolution and over two area domains. A second set of integrations with ECMWF operational forecasts as boundary conditions shows good agreement with observations, as is revealed by threat scores of the precipitation field. It is shown how the use of high horizontal resolution (0.25×0.25 degrees) enables the model to better resolve the spatial configuration of this situation. This work points out the capability of the ENEL version of the limited-area model UB/NMC to predict severe convective storms in mountain areas.     

Plasmonic nanostructures for local field enhancement in the UV region

In this work we describe an ultraviolet subwavelength focusing in plasmonic nanostructures. A system which provides a 20–25 times local field enhancement at a wavelength of 350 nm is proposed. This system represents a metalized V-shaped groove in a surface of a dielectric medium. Subwavelength focusing is achieved by a plasmon wave propagation along the surface of metal film and by the transfer of electromagnetic field through the dielectric medium. The influence of system parameters on a local field enhancement is investigated. A simplified model that allows for determining the geometric parameters of an optimized resonator is proposed.     

Simulation of a Helicon plasma source using a multivariable fuzzymodel

This paper reports work on the development of an automatic control system for a Helicon plasma processing source. The lack of a definitive physical model for the plasma physics of the source and the power coupling mechanism to the plasma precludes the use of traditional control algorithms. This paper develops a fuzzy model that simulates the behavior of the plasma source using the process of genetic algorithms to identify and optimize the parameters of the fuzzy model. This type of model will eventually be used to test a fuzzy control system for the plasma source. In this work, an extensive set of experimental data was acquired where the magnetic field and input power to the plasma source were varied over a wide range while the electron number density was measured. From this learning dataset, the genetic algorithm derived the values of the parameters for the difference equation that describes the system. The fuzzy model so constructed was used to predict the behavior of the source from known input parameters. Comparing the predictions with experimental observations showed that the fuzzy model was generally able to predict the behavior of the plasma as its input parameters were varied with a precision of better than 10%     

On retrial queueing model with fuzzy parameters

This work constructs the membership functions of the system characteristics of a retrial queueing model with fuzzy customer arrival, retrial and service rates. The α-cut approach is used to transform a fuzzy retrial-queue into a family of conventional crisp retrial queues in this context. By means of the membership functions of the system characteristics, a set of parametric non-linear programs is developed to describe the family of crisp retrial queues. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, more information is provided for use by management. By extending this model to the fuzzy environment, fuzzy retrial-queue is represented more accurately and analytic results are more useful for system designers and practitioners.     

Statistical model of current-coupled ion channels in nerve membranes

A statistical model of a driven system is developed. Its microscopic elements are the ion channels through a nerve membrane. Their conductances are stochastically switching under the competing influences of thermal noise and local membrane voltage. A current flow through the membrane induces a coupling between the channels via the electrolytes surrounding the membrane. The long range of the coupling permits a generalized mean field theory for the stationary membrane current as a function of the applied electrode voltage. We derive analytically the macroscopic conductance-voltage-temperature relation for the spatially uniform current state. It shows analogues of first and second order phase transitions. The critical temperature diverges at a finite coupling strength. The theory fits sodium conductance characteristics measured on nerve axon membranes from various species by a variation of only the coupling strength. This supports the hypothesis that this simplest possible model for sodium channels is universal for all species.The work of this author was partially supported by the Deutsche Forschungsgemeinschaft     

三次位相板编码系统的频率信噪比分析

建立了一个基于新型光学/数字成像系统（三次位相板编码系统—CPP系统）的信噪比模型.该模型主要考虑了读出噪音及散粒噪音两种探测器噪音,同时加入光学系统调制传递函数（Modulation Transfer Function,MTF）的影响,考虑不同空间频率下噪音对信号的影响,推导出频率信噪比模型.利用该模型对一个光学/数字成像系统进行信噪比分析,结果表明,利用该模型进行分析后此光学系统可达到的理论焦深扩展范围为5个波长.     

High power, long pulse duration, single-frequency Nd:YVO4 master-oscillator power-amplifier

An efficient single-frequency Nd:YVO₄ master-oscillator power-amplifier is described. Gated pulses from a CW diode-pumped ring laser were amplified by three Nd:YVO₄ amplifiers. Pulses of 1mJ energy; 2 kW peak power and 1 μs duration were obtained at a repetition frequency of 10 kHz. Analogue shaping of the input pulses was used to control the output pulse shape and thus extend the useful range of pulse widths from the 100 ns to the μs regime. A simple mathematical expression was used to model the results which provided reasonable agreement with the experimental work. This system offers a promising pump source for a quasi-CW singly-resonant optical parametric oscillators.