Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Review on lumped parameter method for modeling the blood flow in systemic arteries

The cardiovascular system is characterized by complex interactions between various control mechanisms and physiological processes. Different approaches are used to provide better diagnostics and physiological understanding, cardiac prosthesis and medical planning. The mathematical description and modelling of the human cardiovascular system plays nowadays an important role in the comprehension of the genesis and development of cardiovascular disorders by providing computer based simulation of dynamic processes in this system. This paper aims to give an overview on lumped parameter models that have been developed by many researchers all over the world, to simulate the blood flow in systemic arteries. Surveying various references we make a review of different approaches to arterial tree modelling and discuss on the applications of such models.

Analysis of Do D inkjet printhead performance for printable electronics fabrication using dynamic lumped element modeling and swarm intelligence based optimal prediction

The major challenge in printable electronics fabrication is to effectively and accurately control a drop-on-demand(Do D) inkjet printhead for high printing quality. In this work, an optimal prediction model, constructed with the lumped element modeling(LEM) and the artificial bee colony(ABC) algorithm, was proposed to efficiently predict the combination of waveform parameters for obtaining the desired droplet properties. For acquiring higher simulation accuracy, a modified dynamic lumped element model(DLEM) was proposed with time-varying equivalent circuits, which can characterize the nonlinear behaviors of piezoelectric printhead. The proposed method was then applied to investigate the influences of various waveform parameters on droplet volume and velocity of nano-silver ink, and to predict the printing quality using nano-silver ink. Experimental results show that, compared with two-dimension manual search, the proposed optimal prediction model perform efficiently and accurately in searching the appropriate combination of waveform parameters for printable electronics fabrication.

New lumped-mass-stick model based on modal characteristics of structures: development and application to a nuclear containment building

In this study, a new lumped-mass-stick model （LMSM） is developed based on the modal characteristics of a structure such as eigenvalues and eigenvectors. The simplified model, named the ＂frequency adaptive lumped-massstick model,＂ hasonly a small number of stick elements and nodes to provide the same natural frequencies of the structure and is applied to a nuclear containment building. To investigate the numerical performance of the LMSM, a time history analysis is carried out on both the LMSM and the finite element model （FEM） for a nuclear containment building. A comparison of the results shows that the dynamic responses of the LMSM in terms of displacement and acceleration are almost identical to those of the FEM. In addition, the results in terms of floor response spectra at certain elevations are also in good agreement.

A modified lumped parameter model of distribution transformer winding

The modelling of the distribution transformer winding is the starting point and serves as important basis for the transformer characteristics analysis and the lightning pulse response prediction.A distributed parameters model can depict the winding characteristics accurately,but it requires complex calculations.Lumped parameter model requires less calculations,but its applicable frequency range is not wide.This paper studies the amplitude-frequency characteristics of the lightning wave,compares the transformer modelling methods and finally proposes a modified lumped parameter model,based on the above comparison.The proposed model minimizes the errors provoked by the lumped parameter approximation,and the hyperbolic functions of the distributed parameter model.By this modification it becomes possible to accurately describe the winding characteristics and rapidly obtain the node voltage response.The proposed model can provide theoretical and experimental support to lightning protection of the distribution transformer.

Study on Lumped Kinetic Model for FDFCC I. Establishment of Model

According to the process features and the reaction mechanism of FDFCC technology, its two reaction subsystems, one for heavy oil riser reactor, the other for gasoline riser reactor, were respec-tively studied. Correspondingly, a 12-lump kinetic model for heavy oil FCC and a 9-lump kinetic model for gasoline catalytic upgrading were presented. Based on this work, mathematical correlation of the lumps in the feeds and products involved in the reaction subsystems and those of the overall reaction system were analyzed in detail. Then, a combined kinetic model for FDFCC, which was based on the data recovered from a commercial unit, was put forward. The reaction performance embodied by the kinetic constants for the combined model of FDFCC was in accordance with catalytic cracking reaction mechanism. The model-calculated values were close to the data obtained in commercial scale. The model was easy to be applied in practice and could also provide some theoretical groundwork for further re-search on kinetic model for FDFCC.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems

This paper is an introduction to mesh based generated reluctance network modeling.An overview of scientific works which led to the development of this approach is first presented.Basic concepts of the approach are then presented in the case of electromagnetic devices.A step-by-step procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB and Scilab environments are also included.

IMPROVEMENT OF FLUID PIPE LUMPED PARAMETER MODEL

The traditional lumped parameter model of fluid pipe is introduced and itsdrawbacks are pointed out. Furthermore, two suggestions are put forward to remove these drawbacks.Firstly, the structure of equivalent circuit is modified, and then the evaluation of equivalentfluid resistance is change to take the frequency-dependent function into account. Both simulationand experiment prove that this model is precise to characterize the dynamic behaviors of fluid inpipe.

Lumped parameter analytic modeling and behavioral simulation of a 3-DOF MEMS gyro-accelerometer

A new analytical model of a 3-degree-of-freedom （3-DOF） gyro-accelerometer system consisting of a 1-DOF drive and 2-DOF sense modes is presented. The model constructs lumped differential equations associated with each DOFof the system by vector analysis. The coupled differential equations thus established are solved analytically for their responses in both the time and frequency domains. Considering these frequency response equations, novel device design concepts are derived by forcing the sense phase to zero, which leads to a certain relationship between the structural frequencies, thereby causing minimization of the damping effect on the performance of the system. Furthermore, the feasibility of the present gyro-accelerometer structure is studied using a unique discriminatory scheme for the detection of both gyro action and linear acceleration at their events. This scheme combines the formulated settled transient solution of the gyro-accelerometer with the processes of synchronous demodulation and filtration, which leads to the in-phase and quadrature components of the system＇s output signal. These two components can be utilized in the detection of angular motion and linear acceleration. The obtained analytical results are validated by simulation in a MATLAB/Simulink environment, and it is found that the results are in excellent agreement with each other.

(2+1)维Korteweg-de Vries-Sawada-Kotera-Ramani方程中lump波和其它非线波碰撞前后的轨迹方程

本文首先基于Hirota双线性方法研究了(2+1)维Korteweg-de Vries-Sawada-Kotera-Ramani(KdVSKR)方程的多孤子解,接着利用长波极限法推导出KdVSKR方程的lump波与线波、呼吸波以及lump波的相互作用解.其次,根据lump波沿直线运动的特点,将KdVSKR方程的精确解沿着某些平行直线,在无穷远处进行逼近,进而推导出lump波与线波、呼吸波及lump波撞前后的轨迹方程,并给出了波峰高度以及波的相移.更进一步地,将上述情形推广到lump波与任意多个线波、任意阶呼吸波及任意阶lump波碰撞的情形.最后验证了lump波与其它非线性波的碰撞是弹性碰撞,并绘制了碰撞过程的相关图像.

Numerical analysis of the resonance mechanism of the lumped parameter system model for acoustic mine detection

The method of numerical analysis is employed to study the resonance mechanism of the lumped parameter system model for acoustic mine detection. Based on the basic principle of the acoustic resonance technique for mine detection and the characteristics of low-frequency acoustics, the “soil-mine” system could be equivalent to a damping “mass-spring” resonance model with a lumped parameter analysis method. The dynamic simulation software, Adams, is adopted to analyze the lumped parameter system model numerically. The simulated resonance frequency and anti-resonance frequency are 151 Hz and 512 Hz respectively, basically in agreement with the published resonance frequency of 155 Hz and anti-resonance frequency of 513 Hz, which were measured in the experiment. Therefore, the technique of numerical simulation is validated to have the potential for analyzing the acoustic mine detection model quantitatively. The influences of the soil and mine parameters on the resonance characteristics of the soil–mine system could be investigated by changing the parameter setup in a flexible manner.

Application of Discrete Lumped Kinetic Modeling on Vacuum Gas Oil Hydrocracking

The kinetic model of vacuum gas oil （VGO） hydrocracking based on discrete lumped approach was investigated, and some improvement was put forward at the same time in this article. A parallel reaction scheme to describe the conver- sion of VGO into products （gases, gasoline, and diesel） proposed by Orochko was used. The different experimental data were analyzed statistically and then the product distribution and kinetic parameters were simulated by available data. Fur- thermore, the kinetic parameters were correlated based on the feed property, reaction temperature, and catalyst activity. An optimization code in Matlab 2011b was written to fine-me these parameters. The model had a favorable ability to predict the product distribution and there was a good agreement between the model predictions and experiment data. Hence, the ki- netic parameters indeed had something to do with feed properties, reaction temperature and catalyst activity.

An improved lumped parameter model predicting attenuation of earmuff with air leakage

Since air leakage is inevitable when earmuffs are worn improperly or together with safety glasses in factory or military,it is required to be considered to accurately predict earmuff attenuation.Besides unwanted air leakage,under controlled air leakage is introduced to earmuff to achieve adjustable attenuations in different signal-to-noise ratios(SNRs)and balance between attenuation and speech intelligibility.This work is to develop an improved lumped parameter model(LPM)to predict earmuff attenuation with consideration of air leakage.Air leakage paths are introduced into conventional LPM without air leakage,and air leakage path impedance is analytically described by Maa’s microperforated tube impedance.Earmuff passive attenuation behavior can be analytically described and analyzed with the improved LPM.Finally,the validity of improved LPM is verified experimentally.The results indicate that the improved LPM can predict earmuff attenuation with air leakage,and air leakage deteriorates earmuff attenuation and turns resonance frequency higher.

LUMPED-PARAMETER MODEL OF MASS TRANSFER IN HEMODIALYZER WITH ULTRAFILTRATION

1 INTRODUCTIONHemodialysis with ultrafiltration,also called hemodiafiltration(HDF),is a main methodof treatment for patients with chronic renal failure.The HDF procedure providesadequate removals of both small and middle molecular weight toxic substamces fromuremic blood,which is not possible by dialysis or ultrafiltration alone.According toclinical experience[1],the HDF procedure is well accepied by the patients,and thetreatment time is reduced by using it.

Lumped Parameter Mass Flow Rate and Pressure Control Characteristics Model for High-Speed Pneumatic PWM on/off Valve

Aiming at solving the problem of strong coupling characteristic of the key parameters of high-speed pneumatic pulse width modulation( PWM) on / off valve, a general lumped parameter mathematical model based on the valves time periods was well developed. With this model,the mass flow rate and dynamic pressure characteristics of constant volumes controlled by high-speed pneumatic PWM on /off valves was well described. A variable flow rate coefficient model was proposed to substitute for the constant one used in most of the prior works to investigate PWM on /off valves' dynamical pressure response, and a formula for disclosing the inherent relationship among the PWM command signal,static mass flow rate,and sonic conductance of the valve was newly derived.Finally,an extensive set of analytical experimental comparisons were implemented to verify the validity of the proposed mathematica model. With the proposed model, PWM on /off valves' characteristics,such as mass flow rate,step pressure response of the valve control system,mean pressure and ripple amplitude,not only in the linear range,but also in the nonlinear range can be wel predicted; Good agreement between measured and calculated results was obtained,which proved that the model is helpful for designing a control strategy in a closed loop control system.

A Lumped Kinetic Model for Low-and Medium-Temperature Coal Tar Hydrocracking Process

A five-lump kinetic model for hydrocracking of coal tar is proposed to simulate the product distribution on the basis of the experimental data of coal tar in a laboratory fixed-bed downflow reactor with a Ni/Mo catalyst at a temperature of 360―380°C.The kinetic model includes 5 lumps,viz.:unreacted coal tar,diesel,gasoline,gas,and coke.The product distribution predicted and measured were compared and analyzed,indicating that the kinetic model in this research is suitable for the hydrocracking process of coal tar.Meanwhile,the hydrocracking mechanism of coal tar was further analyzed on the basis of the kinetic model.During the entire hydrocracking process of coal tar,the diesel fraction served as an intermediate component of the reaction.

Study on Lumped Kinetic Model for FDFCC Ⅱ.Validation and Prediction of Model

On the basis of formulating the 9-lump kinetic model for gasoline catalytic upgrading and the 12- lump kinetic model for heavy oil FCC, this paper is aimed at development of a combined kinetic model for a typical FDFCC process after analyzing the coupled relationship and combination of these two models. The model is also verified by using commercial data, the results of which showed that the model can better predict the product yields and their quality, with the relative errors between the main products of the unit and commercial data being less than five percent. Furthermore, the combined model is used to predict and optimize the operating conditions for gasoline riser and heavy oil riser in FDFCC. So this paper can offer some guidance for the processing of FDFCC and is instructive to model research and development of such multi-reactor process and combined process.

Development of basic technique to improve seismic response accuracy of tributary area-based lumped-mass stick models

Although a detailed finite element(FE) model provides more precise results, a lumped-mass stick(LMS) model is preferred because of its simplicity and rapid computational time. However, the reliability of LMS models has been questioned especially for structures dominated by higher modes and seismic inputs. Normally, the natural frequencies and dynamic responses of a LMS model based on tributary area mass consideration are different from the results of the FE model. This study proposes a basic updating technique to overcome these discrepancies; the technique employs the identical modal response, D(t), to the detailed FE model. The parameter D(t) is a time variable function in the dynamic response composition and it depends on frequency and damping ratio for each mode, independent of the structure's mode shapes. The identical response D(t) for each mode is obtained from the frequency adaptive LMS model; the adaptive LMS model which can provide identical modal frequencies as the detailed FE model. Theoretical backgrounds and formulations of the updating technique are proposed. To validate the updating technique, two types of structures(a symmetric straight column and an unsymmetric T-shaped structure) are considered. From the seismic response results including base shear and base moment, the updating technique considerably improves the seismic response accuracy of the tributary area-based LMS model.

An Experiment to Improve the Model of Lumped Element Circuit

The model of lumped element circuit ignores the finite time of signals to propagate around a circuit. However, using modern oscilloscope, the time of nanoseconds in a circuit can be measured. Then the speed of alternating electricity can be obtained in a RL circuit. A typical RL circuit is formed by a power source, wire, resistance and inductance. The basic formula is: U(t)=I(t)R+LdI(t)/dt. It can be derived from the Ohm’s law and Kirchhoff laws. Based on our experimental results, this paper has discussed the new explanation of this equation in a RL circuit. As a result, the speed of alternating electricity is greater than light in a special RL circuit. The model of lumped element circuit can be improved when considering the finite time of signals.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems using Triangular Elements

This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.