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Journal articles on the topic 'Steady-state differential characteristics'
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1
Washio, Seiichi, Satoshi Takahashi, Yonguang Yu, and Satoshi Yamaguchi. "Study of Unsteady Orifice Flow Characteristics in Hydraulic Oil Lines." Journal of Fluids Engineering 118, no. 4 (December 1, 1996): 743–48. http://dx.doi.org/10.1115/1.2835504.
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A technique to measure fluctuating differential pressures with high fidelity has been developed first. When applied to detecting differential pressures generated by an accelerated or decelerated liquid column, the technique turned out to be effective in finding unsteady flow rates. An experimental study has been carried out on periodically changing hydraulic oil flows through an orifice. The results support the validity of the traditional standpoint that characteristics of an unsteady orifice flow can be approximately represented by those of a steady-state one. When inspected in detail, however, a net pressure loss across an orifice in a periodical flow is delayed against a change of the flow rate. The resulting relation between the pressure loss and the flow rate describes a loop with a counter-clockwise hysteresis and a nonlinear twist along the steady-state one. Pressure recovery in a pulsating orifice flow varies with the flow rate almost along the steady-state relation, which is confirmed when the change is not fast.
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DUBKOV, ALEXANDER. "STEADY-STATE DISTRIBUTIONS FOR HARMONIC OSCILLATOR WITH VERY FAST FREQUENCY FLUCTUATIONS." Fluctuation and Noise Letters 11, no. 03 (September 2012): 1242009. http://dx.doi.org/10.1142/s0219477512420096.
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The moment and probability steady-state characteristics of harmonic oscillator with frequency fluctuations in the form of white noise are investigated. Based on well-known functional approach, we derive integro-differential Kolmogorov equation for the joint probability density function of oscillator coordinate and velocity. For white Gaussian noise, using a set of equations for joint moments, we reconstruct the approximate form of coordinate and velocity distributions in the limit of small friction. As shown, these probability density functions do not exist for zero friction because they cannot be normalized.
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Korotyeyev, Igor. "Frequency response analysis of periodically time varying circuits." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 3 (May 8, 2018): 1204–13. http://dx.doi.org/10.1108/compel-07-2017-0275.
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Purpose The purpose of this paper is to introduce a method for the analysis of steady-state processes in periodically time varying circuits. The method is based on a new definition of frequency responses for periodic time-varying circuits. Design/methodology/approach Processes in inverter circuits are often described by differential equations with periodically variable coefficients and forcing functions. To obtain a steady-state periodic solution, the expansion of differential equations into a domain of two independent variables of time is made. To obtain differential equations with constant coefficients the Lyapunov transformation is applied. The two-dimensional Laplace transform is used to find a steady-state solution. The steady-state solution is obtained in the form of the double Fourier series. The transfer function and frequency responses for the inverter circuit are introduced. Findings A set of frequency characteristics are defined. An example of a boost inverter is considered, and a set of frequency responses for voltage and current are presented. These responses show a resonance that is missed if the averaged state-space method is used. Originality/value A new definition of frequency responses is presented. On the basis of frequency responses, a modulation strategy and filters can be chosen to improve currents and voltages.
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WHITTLE, M., R. FIROOZIAN, D. J. PEEL, and W. A. BULLOUGH. "A MODEL FOR THE ELECTRICAL CHARACTERISTICS OF AN ER VALVE." International Journal of Modern Physics B 06, no. 15n16 (August 1992): 2683–704. http://dx.doi.org/10.1142/s0217979292001377.
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We present a simple model which can account for the electrical response characteristics of an Electrorheological (ER) parallel plate valve restrictor. We find that a self-consistent electrical model which can describe the current response to transient and biased sine wave voltage exitations must incorporate the non-linear dependence of current on voltage found at steady state. In addition, the steady state current characteristics are a function of the fluid flow rate. This can be described analytically and included in the model. Analytical solutions show that non-linearity affects the detailed shape of the current response to large voltage inputs. The initial current response is well described by a numerical solution to the model differential equation using the experimental voltage as input. In the case of the relatively small fluctuations involved in the sine wave experiments, a linearised form of this model is found to be an adequate approximation. Parameters are obtained for the model which are, within a generous margin of error, independent of valve dimension.
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Rizvi, S. M. H., and B. Mazhari. "Investigation of Traps in Thin-Film Organic Semiconductors Using Differential Analysis of Steady-State Current–Voltage Characteristics." IEEE Transactions on Electron Devices 65, no. 8 (August 2018): 3430–37. http://dx.doi.org/10.1109/ted.2018.2849346.
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Bert, C. W., and M. Malik. "Transient Analysis of Gas-Lubricated Journal Bearing Systems by Differential Quadrature." Journal of Tribology 119, no. 1 (January 1, 1997): 91–99. http://dx.doi.org/10.1115/1.2832489.
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This paper is an extension of an earlier work in which the present authors demonstrated the application of the differential quadrature method (DQM) to the steady-state analysis of incompressible and compressible lubrication problems. In the present work, the DQM is applied to the transient-state analysis of compressible lubrication problems. For this purpose, the analysis of gas-lubricated plain journal bearings under the conditions of nonuniform journal rotation is considered. The computed results from the solutions of the reference problem included in the paper provide a comparison of the convergence characteristics and computational efficiency of the differential quadrature and finite element methods.
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Huang, Dongmei, Shengxi Zhou, and Zhichun Yang. "Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations." Complexity 2019 (December 14, 2019): 1–20. http://dx.doi.org/10.1155/2019/1050143.
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To improve energy harvesting performance, this paper investigates the resonance mechanism of nonlinear vibrational multistable energy harvesters under narrow-band stochastic parametric excitations. Based on the method of multiple scales, the largest Lyapunov exponent which determines the stability of the trivial steady-state solutions is derived. The first kind modified Bessel function is utilized to derive the solutions of the responses of multistable energy harvesters. Then, the first-order and second-order nontrivial steady-state moments of multistable energy harvesters are considered. To explore the stochastic bifurcation phenomenon between the nontrivial and trivial steady-state solutions, the Fokker–Planck–Kolmogorov equation corresponding to the two-dimensional Itô stochastic differential equations is solved by using the finite difference method. In addition, the mechanism of the stochastic bifurcation of multistable energy harvesters is analyzed for revealing their unique dynamic response characteristics.
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Abou El-Ela, F. M., and A. Z. Mohamed. "Electron Transport Characteristics of Wurtzite GaN." ISRN Condensed Matter Physics 2013 (September 9, 2013): 1–6. http://dx.doi.org/10.1155/2013/654752.
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A three-valley Monte Carlo simulation approach was used to investigate electron transport in wurtzite GaN such as the drift velocity, the drift mobility, the average electron energy, energy relaxation time, and momentum relaxation time at high electric fields. The simulation accounted for polar optical phonon, acoustic phonon, piezoelectric, intervalley scattering, and Ridley charged impurity scattering model. For the steady-state transport, the drift velocity against electric field showed a negative differential resistance of a peak value of 2.9×105 m/s at a critical electric field strength 180×105 V/m. The electron drift velocity relaxes to the saturation value of 1.5×105 m/s at very high electric fields. The electron velocities against time over wide range of electric fields are reported.
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Chen, Yu Mei, Fei Tan, and Tao Fan. "Design of Multi-Mode PID Controller and Application in Time-Delay Process." Applied Mechanics and Materials 511-512 (February 2014): 637–42. http://dx.doi.org/10.4028/www.scientific.net/amm.511-512.637.
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Through brief analysis of characteristics of conventional control, a new type of multi-mode intelligent control algorithm based on error information is put forward. The algorithm consists of proportional acceleration control for rapidity of transient response, differential deceleration control for stationarity of transient response and steady state excitation control for accuracy of steady response. The control algorithm is applied to time-delay process, compared with other algorithms. Simulation results show its good performance with MATLAB language. The algorithm has simple structure, good generality and easy adjustment.
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Zhu, Xue Gui, Zhi Hong Fu, and Xing Zhe Hou. "Modification of Neuron PID Control in Case of Improper Learning Factors." Advanced Materials Research 433-440 (January 2012): 6795–801. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.6795.
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Some modifications of conventional neuron proportional-integral-differential controller (NPID) are presented in this paper to prevent its slow dynamic response and loss of control in case of improper learning factors. The quasi-step signal replaces the step signal as the reference signal to improve the dynamic characteristics. The control output of NPID is modified every step by multiplying a penalty factor called senior teacher signal to suppress further the overshoot and compress the settling time. The steady-state error from the modified NPID (MNPID) is reduced or removed by adjusting dynamically reference input signal while excluding the pseudo steady state. Lots of simulation experiments are done to prove the stability and convergence of the MNPID control algorithm.
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Zhao, Pengcheng, Jingang Wang, Qian Wang, Qianbo Xiao, Ruiqiang Zhang, Shucheng Ou, and Yaqin Tao. "Simulation, Design, and Test of a Dual-Differential D-Dot Overvoltage Sensor Based on the Field-Circuit Coupling Method." Sensors 19, no. 15 (August 3, 2019): 3413. http://dx.doi.org/10.3390/s19153413.
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Accurate measurement of overvoltage in power grids is of great significance to study the characteristics of overvoltage and design of insulation coordination. Based on the research of D-dot voltage sensor, we designed a Dual-Differential D-dot overvoltage sensor. In order to quantify the structural parameters of the sensor, improve the performance and measurement accuracy of the sensor. The Field-Circuit Coupling method was proposed to be used in the parameter design of D-dot overvoltage sensor. The joint simulation of space electromagnetic field model and equivalent circuit model of the Dual-Differential D-dot overvoltage sensor was established with the finite element simulation software Ansoft Maxwell and circuit simulation software Simplorer. Finally, the actual sensor was manufactured. A test platform was built to verify the steady-state and transient performance of the sensor. The results show that the Dual-Differential D-dot sensor has excellent steady-state and transient performance, the error of phase and amplitude are small, and the sensor can achieve the non-contact measurement of power transmission line. Simultaneously, the rationality of the Field-Circuit Coupling method was further verified.
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Shvets, Aleksandr, and Alexander Makaseyev. "Deterministic chaos in pendulum systems with delay." Applied Mathematics and Nonlinear Sciences 4, no. 1 (February 12, 2019): 1–8. http://dx.doi.org/10.2478/amns.2019.1.00001.
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AbstractDynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".
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Shiau, Ting-Nung, and An-Nan Jean. "Prediction of Periodic Response of Flexible Mechanical Systems With Nonlinear Characteristics." Journal of Vibration and Acoustics 112, no. 4 (October 1, 1990): 501–7. http://dx.doi.org/10.1115/1.2930135.
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A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotordynamic systems is addressed. Using this method, the set of nonlinear differential equations governing the motion of the rotor systems is transformed to a set of nonlinear algebraic equations. A condensation technique is proposed to reduce the nonlinear algebraic equations to those only related to the physical coordinates associated with nonlinear components. The method allows for the inclusion of searching for sub, super, ultra-sub and ultra-super harmonic components of the system response. Furthermore it can be used to locate limit cycles of an autonomous system. Three examples are employed to demonstrate the accuracy and the efficiency of the present method.
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Ibrahim, Yusuf, Bashir Yusuf, Mansur Babagana, Baffa Sani, and Muhammad Auwal Lawan. "Some reliability characteristics of a linear consecutive 2-out-of-4 system connected to 2-out-of-4 supporting device for operation." International Journal of Engineering & Technology 7, no. 1 (February 4, 2018): 135. http://dx.doi.org/10.14419/ijet.v7i1.8037.
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This paper presents the Markov model for the reliability analysis of a linear consecutive 2-out-of-4 repairable system operating with the help of a linear consecutive 2-out-of-4 external supporting device. The system is analyzed using first order linear differential equation to develop the explicit expression for steady-state availability, busy period and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. In addition, the effect of failure and repair on availability and profit are researched.
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Jensen, Rune, Jesper Larsen, Kasper Lassen, Matthias Mandø, and Anders Andreasen. "Implementation and Validation of a Free Open Source 1D Water Hammer Code." Fluids 3, no. 3 (September 3, 2018): 64. http://dx.doi.org/10.3390/fluids3030064.
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This paper presents a free code for calculating 1D hydraulic transients in liquid-filled piping. The transient of focus is the Water Hammer phenomenon which may arise due to e.g., sudden valve closure, pump start/stop etc. The method of solution of the system of partial differential equations given by the continuity and momentum balance is the Method of Characteristics (MOC). Various friction models ranging from steady-state and quasi steady-state to unsteady friction models including Convolution Based models (CB) as well as an Instantaneous Acceleration Based (IAB) model are implemented. Furthermore, two different models for modelling cavitation/column separation are implemented. Column separation may occur during low pressure pulses if the pressure decreases below the vapour pressure of the fluid. The code implementing the various models are compared to experiments from the literature. All experiments consist of an upstream reservoir, a straight pipe and a downstream valve.
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San Andres, Luis, Zhou Yang, and Dara W. Childs. "Thermal Effects in Cryogenic Liquid Annular Seals—Part II: Numerical Solution and Results." Journal of Tribology 115, no. 2 (April 1, 1993): 277–84. http://dx.doi.org/10.1115/1.2921002.
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A numerical thermohydrodynamic model for solution of the nonlinear differential equations describing the turbulent flow of a single-phase, cryogenic liquid annular seal is presented. A perturbation method is used for calculation of the zeroth and first-order flow solutions to determine the seal steady-state response and dynamic force coefficients. Numerical predictions for a high speed liquid oxygen seal with a roughened stator surface show that, relative to an isothermal-barotropic fluidmodel, the adiabatic THD solution presents a significant temperature-rise with a profound effect on the liquid material properties and seal performance characteristics. The calculations show the onset of two-phase flow conditions at moderate eccentricities despite the large pressure differential across the seal. Comparisons of the static performance characteristics for the reference seal show excellent agreement between the approximate analytical solution developed in Part I and the full numerical results.
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Bhandari, Anupam. "Numerical solution through mathematical modelling of unsteady MHD flow past a semi-infinite vertical moving plate with chemical reaction and radiation." Studia Geotechnica et Mechanica 40, no. 4 (December 31, 2018): 270–81. http://dx.doi.org/10.2478/sgem-2018-0041.
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Abstract In the present manuscript, unsteady magnetohydrodynamic (MHD) flow over a moving porous semi-infinite vertical plate with time-dependent suction has been studied in the presence of chemical reaction and radiation parameters. Time-dependent partial differential equations in the dimensionless form are solved numerically through mathematical modelling in COMSOL Multiphysics. The results are obtained for velocity, temperature and concentration profiles at different times. Steady state results are also presented for different values of physical parameters. The parameters involved in the problem are useful to change the characteristics of velocity, heat transfer and concentration profiles. The numerical solution of partial differential equations involved in the problem is obtained without sacrificing the relevant physical phenomena.
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Rabby, Md Insiat Islam, Siti Ujila Masuri, Ahmad Syakir Fariz Samsul Kamal, Zulkiflle Leman, Abdul Aziz Hairuddin, and Nuraini Abdul Aziz. "Flow Characteristics of Disk Bypass Pipeline Inspection Gauge (PIG) in Natural Gas Pipelines using Computational Fluid Dynamics." CFD Letters 13, no. 4 (April 17, 2021): 11–37. http://dx.doi.org/10.37934/cfdl.13.4.1137.
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Disk bypass pipeline inspection gauge (PIG) is considered as an efficient device for pigging operations including cleaning, maintaining and inspecting pipelines. The PIG performance is influenced by the fluid flow characteristics as PIG moves forward due to differential pressure of fluid around the PIG. This study focuses on flow characterization of fluid around disk bypass PIG for natural gases pipelines including methane, ethane, and butane using computational fluid dynamics approach. The control volume method with steady state Turbulent k-? model was applied for simulation purposes using ANSYS Fluent 19 software. Fluid velocities at different sections around PIG and differential pressure were investigated for various bypass opening percentages. The results showed that by increasing bypass opening percentages from 5% to 15%, fluid velocity at bypass opening section has reduced 28.28%, 40.43%, and 21.21% for ethane, butane, and methane, respectively, while differential pressure reduced 88%, 86% and 89%. This indicated that 15% bypass opening percentage provided the best flow characteristics among all cases considered. At 15% bypass opening percentage, methane resulted in the lowest fluid velocity at bypass opening section and lowest differential pressure compared to others. Additionally, a correlation of differential pressure of these gases as a function of bypass opening percentage and other parameters was also developed for first time. All results are important for design selection of PIG parameters for efficient pigging operation.
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Bożek, Bogusław, H. Leszczyński, Katarzyna Tkacz-Śmiech, and Marek Danielewski. "Electrochemistry of Symmetrical Ion Channel: Three-Dimensional Nernst-Planck-Poisson Model." Defect and Diffusion Forum 363 (May 2015): 68–78. http://dx.doi.org/10.4028/www.scientific.net/ddf.363.68.
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The paper provides a physical description of ionic transport through the rigid symmetrical channel. A three-dimensional mathematical model, in which the ionic transport is treated as the electrodiffusion of ions, is presented. The model bases on the solution of the 3D Nernst-Planck-Poisson system for cylindrical geometry. The total flux includes drift (convection) and diffusion terms. It allows simulating the transport characteristics at the steady-state and time evolution of the system. The numerical solutions of the coupled differential diffusion equation system are obtained by finite element method. Examples are presented in which the flow characteristics at the stationary state and during time evolution are compared. It is shown that the stationary state is achieved after about 2×10 -8 s since the process beginning. Various initial conditions (channel charging and dimensions) are considered as the key parameters controlling the selectivity of the channel. The model allows determining the flow characteristic, calculating the local concentration and potential across the channel. The model can be extended to simulate transport in polymer membranes and nanopores which might be useful in designing biosensors and nanodevices.
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MOXNES, JOHN F., and KJELL HAUSKEN. "A MATHEMATICAL MODEL FOR TRAINING IMPULSE AND LACTATE INFLUX AND OUTFLUX DURING EXERCISE." International Journal of Modern Physics C 20, no. 01 (January 2009): 147–77. http://dx.doi.org/10.1142/s0129183109013522.
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This paper provides a mathematical description based on the theory of differential equations, for the dynamics of lactate production and removal. Analytical and numerical results for training/exercise of endurance of athletes are presented based on the common concept of training impulse (Trimp). The relationships between activity, production rate, and removal strategies of lactate are studied. Parameters are estimated from published data. A model for optimum removal of lactate after exercise is developed. The model provides realistic predictions when compared with experimental results. We show some specific examples for the usefulness of the mathematical model by studying some recent problems discussed in the literature. (a) Is interval exercise more beneficial than steady-state exercise? (b) What is the optimum aerobic power during recovery? We discuss whether steady-state exercise gives higher Trimp than interval exercise, when imposing an upper boundary for the lactate concentration as a constraint. The model allows for testing all imaginable kinds of steady-state and interval exercises in search of the optimal exercise regime for individuals with various kinds of characteristics. In general, the dynamic model constitute a powerful tool describing the processes by which the concentration of lactate can be studied and controlled to decrease fatigue and increase endurance.
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Lin, Tianliang, Qiang Chen, Haoling Ren, Ruoxi Lv, Chen Miao, and Qihuai Chen. "Computational fluid dynamics and experimental analysis of the influence of the energy recovery unit on the proportional relief valve." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 4 (January 10, 2017): 697–705. http://dx.doi.org/10.1177/0954406216687790.
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The overflow energy loss in relief valve, which is one of the main reasons leading to the low efficiency of the hydraulic system, had been considered to be impossible to solve. The principle of the overflow energy loss of the relief valve is analyzed and a novel method to reduce the overflow loss using an energy recovery unit, which can improve the return line pressure of the pilot proportional relief valve, is proposed. The influence of the energy recovery unit on the pressure control characteristics and steady-state flow force of the pilot proportional relief valve are discussed. The effects of the return line pressure on the distribution of the flow field and the pressure control characteristics are analyzed through computational fluid dynamics simulation and experiment. The results show that with the increase of the return line pressure, the displacement of the main valve spool increases and the reset spring force increases accordingly. While the steady-state flow force decreases dramatically with the increase of the return line pressure, which results in a smaller pressure differential the pressure differential can be reduced from 15% to 2.5%. It is also observed that the flow rate of the pilot proportional relief valve can be maintained at a certain value with a small oscillation and that the pilot proportional relief valve can release the redundant flow of hydraulic system. This verifies that the pilot proportional relief valve with the outlet connecting to the energy recovery unit to recovery the overflow energy loss cannot reduce the pressure control characteristics, but can achieve a better pressure control accuracy of the pilot proportional relief valve.
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Ishak, A., R. Nazar, and I. Pop. "Heat transfer over an unsteady stretching surface with prescribed heat flux." Canadian Journal of Physics 86, no. 6 (June 1, 2008): 853–55. http://dx.doi.org/10.1139/p08-005.
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The unsteady laminar boundary-layer flow over a continuously stretching surface in a viscous and incompressible quiescent fluid is studied. The unsteadiness in the flow and temperature fields is caused by the time dependence of the stretching velocity and the surface heat flux. The nonlinear partial differential equations of continuity, momentum, and energy, with three independent variables, are reduced to nonlinear ordinary differential equations, before they are solved numerically by the Keller-box method. Comparison with available data from the open literature as well as the exact solution for the steady-state case of the present problem is made, and found to be in good agreement. Effects of the unsteadiness parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.PACS No.: 47.15.Cb
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Freundlich, Jan. "Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation." Shock and Vibration 20, no. 6 (2013): 1103–12. http://dx.doi.org/10.1155/2013/126735.
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The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.
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CASCANTE, MARTA, RAUL CURTO, and ALBERT SORRIBAS. "TESTING THE ROBUSTNESS OF THE STEADY-STATE CHARACTERISTICS OF A METABOLIC PATHWAY: PARAMETER SENSITIVITIES AS A BASIC FEATURE FOR MODEL VALIDATION." Journal of Biological Systems 03, no. 01 (March 1995): 105–13. http://dx.doi.org/10.1142/s0218339095000101.
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Mathematical models are useful for analyzing metabolic problems. To build up these models, we need: (1) A scheme of the target system, (2) Measurements of concentrations and fluxes in steady-state, (3) The rate law of each reaction and (4) The set of differential equations that reflects the model behaviour. Usually, the rate-laws are identified from in vitro data, which could result in unrealistic models when compared with the behavior of the intact system. Hence, mathematical models must be carefully validated before one can trust their behavior. We can use different features of a biological system as a reference for validating a model. The steady-state robustness to parameter changes can be used as an index for such an evaluation. In this sense, a realistic model should reflect a fundamental property of a living system: small perturbations are compatible with system performance. We present an example of such analysis in the case of the ethanolic fermentation pathway of Saccharomyces cerevisiae. The parameter sensitivities of the model are computed in two experimental conditions and a diagnostic is made on the validity of the corresponding model. Translation of the mechanistic model into an S-system model facilitates the analysis of parameter sensitivity. After the analysis, a high parameter sensitivity suggest the need for a careful estimation of the involved parameters.
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Li, Xiao-Huan, Fang Liu, Jia Xu, and Zhi-Wen Zhu. "Nonlinear dynamic characteristics and control of Galfenol-Shape Memory Alloy composite plate subjected to stochastic excitation." International Journal of Applied Electromagnetics and Mechanics 64, no. 1-4 (December 10, 2020): 1547–54. http://dx.doi.org/10.3233/jae-209476.
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In this paper, the nonlinear dynamic characteristics and control of a Galfenol-shape memory alloy (SMA) composite plate under stochastic excitation are studied. New nonlinear differential terms are applied in the constitutive modeling of Galfenol alloy and SMA, and the nonlinear dynamic model of the composite system is developed. The drift coefficient and the diffusion coefficient are calculated to obtain the steady-state probability density function of the system, and finally the optimal control strategy is proposed to improve the effects of vibration reduction. Numerical simulation and experiments results show that the system has abundant nonlinear dynamic characteristics, including stochastic Hopf bifurcation and limit cycle bifurcation. The stochastic optimal control strategy can improve the effects of vibration reduction efficiently. These results are helpful for the application of Galfenol-SMA composite structures.
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Alqahtani, Rubayyi T., Abdullahi Yusuf, and Ravi P. Agarwal. "Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative." Mathematics 9, no. 6 (March 22, 2021): 675. http://dx.doi.org/10.3390/math9060675.
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In this paper, the wastewater treatment model is investigated by means of one of the most robust fractional derivatives, namely, the Caputo fractional derivative. The growth rate is assumed to obey the Contois model, which is often used to model the growth of biomass in wastewaters. The characteristics of the model under consideration are derived and evaluated, such as equilibrium, stability analysis, and steady-state solutions. Further, important characteristics of the fractional wastewater model allow us to understand the dynamics of the model in detail. To this end, we discuss several important analyses of the fractional variant of the model under consideration. To observe the efficiency of the non-local fractional differential operator of Caputo over its counter-classical version, we perform numerical simulations.
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Pyatetska, O. V. "Bending vibrations of viscoelastic plates within the Kirchhoff-Love model." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2019): 64–67. http://dx.doi.org/10.17721/1812-5409.2019/4.8.
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Within the framework of the hypotheses of the classical Kirchhoff-Love theory, complete systems of resolving equations are constructed to determine the stress-strain state and the temperature of dissipative heating under steady transverse vibrations of plates made of a linear viscoelastic material, the properties of which depend on the frequency of external excitation and temperature. The equations were obtained without any preliminary suggestions about the law of temperature variation over the plate thickness. This law is determined in the process of solving the problem. The unrelated problem of vibrational bending of viscoelastic plates for complicated way of fixing a contour and different types of thermal boundary conditions is considered. Mathematical models of problems on the steady-state transverse vibrations of plates made of a linear viscoelastic material, the properties of which depend on temperature for an arbitrary law of its change over the thickness of the object. If the material characteristics depend on temperature, investigation of the influence of temperature of dissipative heating is reduced to solution of complicated non-linear systems of differential equations.
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Sundukov, A. E. "Investigation of the characteristics of the component of vibration of gas turbine engine gearbox that causes fatigue failures of its structural elements in case of tooth flank wear." VESTNIK of Samara University. Aerospace and Mechanical Engineering 19, no. 4 (December 31, 2020): 70–79. http://dx.doi.org/10.18287/2541-7533-2020-19-4-70-79.
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The paper presents an analysis of the component of vibration of the NK-12MP turboprop engine differential gearbox that is generated by the wear of the flanks of the teeth of the sun gear planet gear assembly pair and at certain values of its intensity may cause fatigue breakdown of the engines structural elements. A complex of diagnostic indicators is determined on the basis of this component. Its intensity is shown to be maximal in steady-state operation of the engine with the greatest run time. The data obtained by the spectrum of maxima are shown to have higher information content as compared to the autospectrum data. The complex of diagnostic indicators proposed on the basis of the component under consideration makes it possible to successfully control the technical condition of the differential gearbox by the defects of gear tooth flank wear.
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Rashidi Meybodi, R., M. Zare Mehrjardi, and A. D. Rahmatabadi. "Tilt angle effects on the performance of micropolar lubricated noncircular journal bearings." Industrial Lubrication and Tribology 69, no. 4 (July 10, 2017): 536–49. http://dx.doi.org/10.1108/ilt-03-2016-0041.
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Purpose The purpose of this paper is to study tilt angle effects as design parameters of noncircular bearings, on the linear dynamic analyses of micropolar lubricated circular, two, three and four lobe journal bearings. Design/methodology/approach Reynolds equation in dynamic state is modified considering the micropolarity characteristics of lubricant, and it is solved using generalized differential quadrature method. The perturbed components of the dynamic pressure are extracted based on the linear dynamic model. To explain the transient state of the governing equation, through the linear dynamic approach, the whirling motion of rotor around the steady state position is assumed to be harmonic. Findings It is observed from the results that tilt angle has significant effects on the steady state and stability performance of lobed journal bearings. It may be selected suitably to improve the performance of rotor-bearing system, while all other lubricant properties and noncircular bearing design parameters are kept fixed. Results show that among the three types of bearings considered, the dynamic performance of two lobe bearings are more affected by the variation of tilt angle. Originality/value The present study is mainly concerned with the effects of tilt angle as a design parameter on the stability performance of a hydrodynamic noncircular journal bearing lubricated with micropolar fluid.
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Liu, Yunshan, Xueliang Zhang, Dawei Gu, Lei Jia, and Bangchun Wen. "Synchronization of a Dual-Mass Vibrating System with Two Exciters." Shock and Vibration 2020 (January 21, 2020): 1–12. http://dx.doi.org/10.1155/2020/9345652.
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From the perspective of theoretical derivation, numerical simulation, and engineering application, the vibratory synchronization characteristics of a dual-mass vibrating system driven by two exciters, were studied. The differential motion equations of the total system were calculated using Lagrange’s equations, and the responses of the vibrating system in the steady state were derived by Laplace transform. The synchronization criterion between two exciters was deduced by using the averaging method. Based on the Hamilton principle, the stability criterion of the vibrating system in synchronous states is given. According to the theoretical results, the coupling characteristics between two exciters such as synchronization and stability were analyzed numerically. Some analyses of the numerical simulation of the system were carried out, which fully support the theoretical results. The rotational speed of two exciters, their phase difference, responses, and difference of responses of two rigid bodies were studied quantitatively in the subresonant state and super-resonant state of the system. This paper presents a practical example of vibratory synchronization of a dual-mass system driven by two exciters in engineering.
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Wu, Liang, Yong-Tao Zhang, Shuhai Zhang, and Chi-Wang Shu. "High Order Fixed-Point Sweeping WENO Methods for Steady State of Hyperbolic Conservation Laws and Its Convergence Study." Communications in Computational Physics 20, no. 4 (October 2016): 835–69. http://dx.doi.org/10.4208/cicp.130715.010216a.
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AbstractFixed-point iterative sweeping methods were developed in the literature to efficiently solve static Hamilton-Jacobi equations. This class of methods utilizes the Gauss-Seidel iterations and alternating sweeping strategy to achieve fast convergence rate. They take advantage of the properties of hyperbolic partial differential equations (PDEs) and try to cover a family of characteristics of the corresponding Hamilton-Jacobi equation in a certain direction simultaneously in each sweeping order. Different from other fast sweeping methods, fixed-point iterative sweeping methods have the advantages such as that they have explicit forms and do not involve inverse operation of nonlinear local systems. In principle, it can be applied in solving very general equations using any monotone numerical fluxes and high order approximations easily. In this paper, based on the recently developed fifth order WENO schemes which improve the convergence of the classical WENO schemes by removing slight post-shock oscillations, we design fifth order fixed-point sweeping WENO methods for efficient computation of steady state solution of hyperbolic conservation laws. Especially, we show that although the methods do not have linear computational complexity, they converge to steady state solutions much faster than regular time-marching approach by stability improvement for high order schemes with a forward Euler time-marching.
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Christopherson, J., M. Mahinfalah, and Reza N. Jazar. "Suspended Decoupler: A New Design of Hydraulic Engine Mount." Advances in Acoustics and Vibration 2012 (December 22, 2012): 1–11. http://dx.doi.org/10.1155/2012/826497.
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Because of the density mismatch between the decoupler and surrounding fluid, the decoupler of all hydraulic engine mounts (HEM) might float, sink, or stick to the cage bounds, assuming static conditions. The problem appears in the transient response of a bottomed-up floating decoupler hydraulic engine mount. To overcome the bottomed-up problem, a suspended decoupler design for improved decoupler control is introduced. The new design does not noticeably affect the mechanism's steady-state behavior, but improves start-up and transient response. Additionally, the decoupler mechanism is incorporated into a smaller, lighter, yet more tunable and hence more effective hydraulic mount design. The steady-state response of a dimensionless model of the mount is examined utilizing the averaging perturbation method applied to a set of second-order nonlinear ordinary differential equations. It is shown that the frequency responses of the floating and suspended decoupled designs are similar and functional. To have a more realistic modeling, utilizing nonlinear finite elements in conjunction with a lumped parameter modeling approach, we evaluate the nonlinear resorting characteristics of the components and implement them in the equations of motion.
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Piao, Daqing. "Phenomenological Interpretations of Some Somatic Temporal and Spatial Patterns of Biophoton Emission in Humans." Journal of Scientific Exploration 35, no. 2 (June 15, 2021): 345–82. http://dx.doi.org/10.31275/20211685.
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Biophoton emission remains controversial. The photo-genic origin of biophoton has been attributed to the oxidative stress or free radical production. However, there are considerable gaps in quantitative understanding of biophoton emission. I propose an analytical hypothesis for interpreting a few patterns of steady-state biophoton emission of human, including the dependency on age, the diurnal variation, and the geometric asymmetry associated with serious asymmetrical pathological conditions. The hypothesis is based on an alternative form of energy state, termed vivo-nergy, which is associated with only metabolically active organisms that are also under neuronal control. The hypothesis projects a decrease of the vivo-nergy in human during growth beyond puberty. The hypothesis also proposes a modification of the vivo-nergy by the phases of systematic or homeostatic physiology. The hypothesis further postulates that the deviation of the physiology-modified vivo-nergy from the pre-puberty level is deteriorated by acquired organ-specific pathological conditions. A temporal differential change of vivo-nergy is hypothesized to proportionally modulate oxidative stress that functions as the physical source of biophoton emission. The resulted steady-state diffusion of the photon emitted from a photo-genic source in a human geometry simplified as a homogeneous spherical domain is modeled by photon diffusion principles incorporating an extrapolated zero-boundary condition. The age and systematic physiology combined determines the intensity of the centered physiological steady-state photo-genic source. An acquired pathology sets both the intensity and the off-center position of the pathological steady-state photo-genic source. When the age-commemorated, physiology-commanded, and pathology-controlled modifications of the steady-state photo-genetic sources are implemented in the photon diffusion model, the photon fluence rate at the surface of the human-representing spherical domain reveals the patterns on age, the temporal variation corresponding to systematic physiology, and the geometric asymmetry associated with significant asymmetric pathological condition as reported for spontaneous biophoton emission. The hypothesis, as it provides conveniences for quantitative estimation of biophoton emission patterns, will be extended in future works towards interpreting the temporal characteristics of biophoton emission under stimulation.
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Luongo, A., G. Rega, and F. Vestroni. "On Nonlinear Dynamics of Planar Shear Indeformable Beams." Journal of Applied Mechanics 53, no. 3 (September 1, 1986): 619–24. http://dx.doi.org/10.1115/1.3171821.
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The planar forced oscillations of shear indeformabie beams with either movable or immovable supports are studied through a unified approach. An exact nonlinear beam model is referred to and a consistent procedure up to order three nonlinearities is followed. By eliminating the longitudinal displacement component through a constraint condition and assuming one mode, the problem is reduced to one nonlinear differential equation. A perturbational solution in the neighborhood of the resonant frequency is determined and the stability of the steady-state solutions is studied. The dependence of the phenomenon on the geometrical and mechanical characteristics of the system is put into light and the frequency-response curves for different boundary conditions are furnished.
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Xiao, Shenping, Zhouquan Ou, Junming Peng, Yang Zhang, and Xiaohu Zhang. "Single-Phase Photovoltaic Grid-Connected Inverter Based on Fuzzy Neural Network." Journal of Advanced Computational Intelligence and Intelligent Informatics 25, no. 3 (May 20, 2021): 310–16. http://dx.doi.org/10.20965/jaciii.2021.p0310.
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Based on a single-phase photovoltaic grid-connected inverter, a control strategy combining traditional proportional–integral–derivative (PID) control and a dynamic optimal control algorithm with a fuzzy neural network was proposed to improve the dynamic characteristics of grid-connected inverter systems effectively. A fuzzy inference rule was established after analyzing the proportional, integral, and differential coefficients of the PID controller. A fuzzy neural network was applied to adjust the parameters of the PID controller automatically. Accordingly, the proposed dynamic optimization algorithm was deduced in theory. The simulation and experimental results showed that the method was effective in making the system more robust to external disruption owing to its excellent steady-state adaptivity and self-learning ability.
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Ryzhkov, Alexander V., Matthew R. Kumjian, Scott M. Ganson, and Alexander P. Khain. "Polarimetric Radar Characteristics of Melting Hail. Part I: Theoretical Simulations Using Spectral Microphysical Modeling." Journal of Applied Meteorology and Climatology 52, no. 12 (December 2013): 2849–70. http://dx.doi.org/10.1175/jamc-d-13-073.1.
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AbstractSpectral (bin) microphysics models are used to simulate polarimetric radar variables in melting hail. Most computations are performed in a framework of a steady-state, one-dimensional column model. Vertical profiles of radar reflectivity factor Z, differential reflectivity ZDR, specific differential phase KDP, specific attenuation Ah, and specific differential attenuation ADP are modeled at S, C, and X bands for a variety of size distributions of ice particles aloft. The impact of temperature lapse rate, humidity, vertical air velocities, and ice particle density on the vertical profiles of the radar variables is also investigated. Polarimetric radar signatures of melting hail depend on the degree of melting or the height of the radar resolution volume with respect to the freezing level, which determines the relative fractions of partially and completely melted hail (i.e., rain). Simulated vertical profiles of radar variables are very sensitive to radar wavelength and the slope of the size distribution of hail aloft, which is correlated well with maximal hail size. Analysis of relative contributions of different parts of the hail/rain size spectrum to the radar variables allows explanations of a number of experimentally observed features such as large differences in Z of hail at the three radar wavelengths, unusually high values of ZDR at C band, and relative insensitivity of the measurements at C and X bands to the presence of large hail exceeding 2.5 cm in diameter. Modeling results are consistent with S- and C-band polarimetric radar observations and are utilized in Part II for devising practical algorithms for hail detection and determination of hail size as well as attenuation correction and rainfall estimation in the presence of hail.
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Barone, M. R., and D. A. Caulk. "A New Method for Thermal Analysis of Die Casting." Journal of Heat Transfer 115, no. 2 (May 1, 1993): 284–93. http://dx.doi.org/10.1115/1.2910678.
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A new approach is developed for solving the initial value, steady periodic heat conduction problem in steady-state die casting. Three characteristics found in nearly all die casting processes are exploited directly: The casting is thin compared with its overall size, its thermal conductivity is high compared with that of the mold, and the cycle time is short compared with the start-up transient of the process. Under these conditions, it is reasonable to neglect the transverse temperature gradients in the casting and assume that all die temperatures below a certain depth from the cavity surface are independent of time. The transient die temperatures near the cavity surface are represented by a polynomial expansion in the depth coordinate, with time-varying coefficients determined by a Galerkin method. This leads to a set of ordinary differential equations on the cavity surface, which govern the transient interaction between the casting and the die. From the time-averaged solution of these equations, special conditions are derived that relate the transient solution near the cavity surface to the three-dimensional steady solution in the die interior. With these conditions, the steady temperatures in the bulk of the die can be determined independently of the explicit surface transients. This reduces the effort of solving a complex transient heat conduction problem to little more than finding a steady solution alone. The overall approach provides a general analytical tool, which is capable of predicting complex thermal interactions in large multicomponent dies.
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Kikuuwe, Ryo. "A Brush-Type Tire Model with Nonsmooth Representation." Mathematical Problems in Engineering 2019 (December 17, 2019): 1–13. http://dx.doi.org/10.1155/2019/9747605.
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This paper proposes a brush-type tire model with a new mathematical representation. The presented model can be seen as a generic model that describes the distributed viscoelastic force and Coulomb-like friction force, which are balancing each other at each point, in the contact patch. The model is described as a partial differential algebraic inclusion (PDAI), which involves the set-valuedness to represent the static friction. A numerical integration algorithm for this PDAI is derived through the implicit Euler discretization along both space and time. Some numerical comparisons with Magic Formula and a LuGre-based tire model are presented. The results show that, with appropriate choice of parameters, the proposed model is capable of producing steady-state characteristics similar to those of Magic Formula. It is also shown that the proposed model realizes a proper static friction state, which is not realized with a LuGre-based tire model.
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Ji, Xin, Aichen Wang, and Xinhua Wei. "Precision Control of Spraying Quantity Based on Linear Active Disturbance Rejection Control Method." Agriculture 11, no. 8 (August 10, 2021): 761. http://dx.doi.org/10.3390/agriculture11080761.
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Current methods to control the spraying quantity present several disadvantages, such as poor precision, a long adjustment time, and serious environmental pollution. In this paper, the flow control valve and the linear active disturbance controller (LADRC) were used to control the spraying quantity. Due to the disturbance characteristics in the spraying pipeline during the actual operation, the total disturbance was observed by a linear extended state observer (LESO). A 12 m commercial boom sprayer was used to carry out practical field operation tests after relevant intelligent transformation. The experimental results showed that the LADRC controller adopted in this paper can significantly suppress the disturbance in practical operation under three different operating speeds. Compared with the traditional proportional–integral–differential controller (PID) and an improved PID controller, the response speed of the proposed controller improved by approximately 3~5 s, and the steady-state error accuracy improved by approximately 2~9%.
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Yang, Z. J., Z. Q. Wang, L. Q. Tang, and X. Y. Sun. "Ceramics Toughening Mechanism Study of Mixed-Mode I-III Cracks with a New Yield Criterion." Journal of Mechanics 27, no. 3 (August 31, 2011): 409–14. http://dx.doi.org/10.1017/jmech.2011.43.
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ABSTRACTConsidering the SD (strength differential) effect on compressive strength and tensile strength in zirconia ceramic material, a yield criterion with a special parameter is introduced. In addition, by analogy with associated flow rule, the constitutive model of phase transformation ceramic material has been established. Under generalized plane strain condition, the theoretical toughening expressions of mixed-mode I-III stationary cracks and steady-state growing cracks have been developed with the constitutive model. The crack toughening effect has been discussed in detail with the Poisson ratio, parameters k / α (the ratio of nominal yield strength and SD effect factor) and ω (the scale factor of mode I crack and mode III). The integral calculation shows that phase transformation toughening of stationary cracks is negative shielding effect and the toughening effect of the steady-state growing cracks change obviously with the increase of parameter k / α. Comparison between experimental data and theoretical data indicates that the yield criterion is in accord with the actual characteristics of the zirconia ceramic, when the expression of mixed-mode I-III crack is reduced to mode I crack. The results obtained in present paper can provide the useful theoretical reference for the research of phase transformation toughening in ceramic materials.
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Li, Yu, and Jun-Sheng Duan. "The periodic response of a fractional oscillator with a spring-pot and an inerter-pot." Journal of Mechanics 37 (December 18, 2020): 108–17. http://dx.doi.org/10.1093/jom/ufaa009.
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Abstract The fractional oscillation system with two Weyl-type fractional derivative terms $_{ - \infty }D_t^\beta x$ (0 < β < 1) and $_{ - \infty }D_t^\alpha x$ (1 < α < 2), which portray a “spring-pot” and an “inerter-pot” and contribute to viscoelasticity and viscous inertia, respectively, was considered. At first, it was proved that the fractional system with constant coefficients under harmonic excitation is equivalent to a second-order differential system with frequency-dependent coefficients by applying the Fourier transform. The effect of the fractional orders β (0 < β < 1) and α (1 < α < 2) on inertia, stiffness and damping was investigated. Then, the harmonic response of the fractional oscillation system and the corresponding amplitude–frequency and phase–frequency characteristics were deduced. Finally, the steady-state response to a general periodic incentive was obtained by utilizing the Fourier series and the principle of superposition, and the numerical examples were exhibited to verify the method. The results show that the Weyl fractional operator is extremely applicable for researching the steady-state problem, and the fractional derivative is capable of describing viscoelasticity and portraying a “spring-pot”, and also describing viscous inertia and serving as an “inerter-pot”.
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Wan, Zhiguo, Yu Wang, Binqiang Chen, Yihua Dou, and Xinjuan Wei. "The Vibration of a Transversely Cracked Rotor Supported by Anisotropic Journal Bearings with Speed-Dependent Characteristic." Applied Sciences 10, no. 16 (August 13, 2020): 5617. http://dx.doi.org/10.3390/app10165617.
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This paper presents the vibration of a transversely cracked rotor supported by anisotropic journal bearings, where the speed-dependent characteristic of bearing is considered. A 3D finite element model and the contact-based approach are employed for the shaft and crack. The governing differential equations of the whole cracked rotor-bearing system were obtained by synthesizing the equations of the cracked shaft, the breathing crack and the journal bearings. In order to solve the computational difficulties caused by the high dimensions of model, the free-interface complex component mode synthesis method (CMS) is employed to reduce the order of the model. On this basis, the eigenvalue and the steady-state forced response of the cracked rotor-bearing system are obtained by the Hill’s method. Finally, the effects of the anisotropic and speed-dependent characteristics of bearings on the vibration of the system are studied. Numerical results show that both the two characteristics can significantly affect the response of the system. The anisotropy in the bearing leads to the split of resonant peaks and influence the amplitudes of the peaks. The speed-dependent characteristic mainly affects the responses at the speeds close to the resonant regions, because the parametric excitation effect of the resonance region is greater than other speeds.
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Grolman, Eric, and Jan M. H. Fortuin. "Transient Gas-Liquid Flow in Upward Sloping Pipes, Approaching the Wavy-to-Slug Flow Transition." Journal of Fluids Engineering 118, no. 4 (December 1, 1996): 729–35. http://dx.doi.org/10.1115/1.2835502.
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A model is presented for transient, cocurrent gas-liquid pipe flow in the stratified-smooth and stratified-wavy flow regimes. It is based on the equations of continuity and motion in the direction of flow and results in two hyperbolic partial differential equations, which are solved numerically using the combined methods of lines (Schiesser, 1991) and characteristics (Stoker, 1957). In wavy gas-liquid pipe flow, three different interfacial areas and corresponding shear stresses are identified. Three friction-factor correlations were derived on the basis of an extensive set of 2500 steady-state measurements. The transient behavior of inclined gas-liquid pipe flow is successfully simulated and compares well with the results obtained from on-line measurements, right up to the onset of slug flow.
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R., Durga Devi, and Nageswari S. "Mathematical modelling and analysis of voltage super-lift power dc-dc converter for enhanced dynamic characteristics in CCM." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 2 (March 4, 2019): 759–76. http://dx.doi.org/10.1108/compel-12-2017-0505.
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Purpose The purpose of this paper is to propose a mathematical model for voltage super-lift dc-dc power converter in continuous conduction mode (CCM). Using the presented mathematical model, the analysis of dynamics of power stage for voltage super-lift dc-dc power converter can be performed. Design/methodology/approach The proposed method is based on the average state space model using the state equations of the dc-dc power converter. In the proposed method, the converter is represented as a set of differential equations derived for each switching state of the power switch in terms of inductor current and capacitor voltage. The proposed method describes the dynamic behaviour of the system. The controller is designed to meet performance requirement of the system such as to maintain the dynamics such as stability, steady-state accuracy and the speed of response of the system. Using the obtained model, the analysis of dynamic response of the voltage super-lift dc-dc power converter can be performed. Findings The converter is modelled and verified using conventional circuit analysis method employing state-space averaging technique, and their corresponding transfer function is also derived. The dynamics of the converter is investigated using frequency response characteristics obtained using MATLAB programming environment. In addition, to improve the stability of the converter, proportional-integral controller is designed using Ziegler–Nichols tuning rules, and the effect of the compensator in the plant is also investigated. Originality/value The proposed method can be used for analysing the dynamics of power stage for voltage super-lift DC-DC power converter.
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Ali, Kashif, Muhammad Ashraf, and Nimra Jameel. "Numerical simulation of magnetohydrodynamic micropolar fluid flow and heat transfer in a channel with shrinking walls." Canadian Journal of Physics 92, no. 9 (September 2014): 987–96. http://dx.doi.org/10.1139/cjp-2013-0324.
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We numerically study the steady hydromagnetic (magnetohydrodynamic) flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with shrinking walls. Unlike the classical shooting methodology, two distinct numerical techniques are employed to solve the transformed self-similar nonlinear ordinary differential equations (ODEs). One is the combination of a direct and an iterative method (successive over-relaxation with optimal relaxation parameter) for solving the sparse system of linear algebraic equations arising from the finite difference discretization of the linearised ODEs. For the second one, a pseudotransient method is used where time plays the role of an iteration parameter until the steady state is reached. The two approaches may be easily extended to other geometries (for example, sheets, disks, and cylinders) with possible wall conditions like slip, stretching, rotation, suction, and injection. Effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. Detailed description of the computational procedure and the results of the study may be beneficial for the researchers in the flow and thermal control of polymeric processing.
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Kim, Hyun-Sil, and Jerry H. Ginsberg. "Transient Wave Propagation in a Harmonically Heterogeneous Elastic Solid." Journal of Applied Mechanics 59, no. 2S (June 1, 1992): S145—S151. http://dx.doi.org/10.1115/1.2899479.
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Transient propagation of a one-dimensional dilatational wave in a harmonically heterogeneous elastic solid is studied by several techniques. A regular perturbation analysis in terms of the characteristics of the differential equation shows that initiation of a temporally harmonic excitation that generates a signal whose wavelength is twice the periodicity of the heterogeneity leads to secularity in the first approximation. The frequency at which this situation occurs matches the frequency at which Floquet theory predicts that steady-state waves may be unstable. A finite difference algorithm based on integrating along the characteristics is developed and implemented to obtain a numerical solution. In the critical case, backscattering of the wave from the heterogeneity results in a mixture of propagating and standing wave features. However, rather than being unstable, the heterogeneity in this condition is shown to result in maximum interference with forward propagation. A comparable analysis for a step excitation on the boundary provides additional insight into the underlying propagation phenomena.
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Chaurasiya, Kanhaiya Lal, Bishakh Bhattacharya, AK Varma, and Sarthak Rastogi. "Dynamic modeling of a cabin pressure control system." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 2 (August 9, 2019): 401–15. http://dx.doi.org/10.1177/0954410019867578.
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Cabin pressure control system of an aircraft maintains cabin pressure in all flight modes as per the aircraft cabin pressurization characteristics by controlling the air flow from the cabin through the outflow valve of the cabin pressure control valve. The movement of outflow valve in turn depends on the air flow from the control chamber of cabin pressure control valve, which is controlled by the clapper and the poppet valves. These valves are actuated by absolute pressure and the differential pressure capsules, respectively depending upon the operating flight conditions. Mathematical models have been developed to simulate the air outflow rates from the cabin and the control chamber of cabin pressure control valve during steady-state and transient flight conditions. These mathematical models have then been translated into a MATLAB program to obtain plots of cabin pressures as a function of aircraft altitudes. The mathematical models are validated for standard cabin pressurization characteristics of a multirole light fighter/trainer aircraft. The model developed, thus can be used to produce a number of variants of cabin pressure control valve to suit different cabin pressurization characteristics.
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Huang, C. L. "Kinetic isoforms of intramembrane charge in intact amphibian striated muscle." Journal of General Physiology 107, no. 4 (April 1, 1996): 515–34. http://dx.doi.org/10.1085/jgp.107.4.515.
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The effects of the ryanodine receptor (RyR) antagonists ryanodine and daunorubicin on the kinetic and steady-state properties of intramembrane charge were investigated in intact voltage-clamped frog skeletal muscle fibers under conditions that minimized time-dependent ionic currents. A hypothesis that RyR gating is allosterically coupled to configurational changes in dihydropyridine receptors (DHPRs) would predict that such interactions are reciprocal and that RyR modification should influence intramembrane charge. Both agents indeed modified the time course of charging transients at 100-200-microM concentrations. They independently abolished the delayed charging phases shown by q gamma currents, even in fibers held at fully polarized, -90-mV holding potentials; such waveforms are especially prominent in extracellular solutions containing gluconate. Charge movements consistently became exponential decays to stable baselines in the absence of intervening inward or other time-dependent currents. The steady-state charge transfers nevertheless remained equal through the ON and the OFF parts of test voltage steps. The charge-voltage function, Q(VT), shifted by approximately +10 mV, particularly through those test potentials at which delayed q gamma currents normally took place but retained steepness factors (k approximately 8.0 to 10.6 mV) that indicated persistent, steeply voltage-dependent q gamma contributions. Furthermore, both RyR antagonists preserved the total charge, and its variation with holding potential, Qmax (VH), which also retained similarly high voltage sensitivities (k approximately 7.0 to 9.0 mV). RyR antagonists also preserved the separate identities of q gamma and q beta species, whether defined by their steady-state voltage dependence or inactivation or pharmacological properties. Thus, tetracaine (2 mM) reduced the available steady-state charge movement and gave shallow Q(VT) (k approximately 14 to 16 mV) and Qmax (VH) (k approximately 14 to 17 mV) curves characteristic of q beta charge. These features persisted with exposure to test agent. Finally, q gamma charge movements showed steep voltage dependences with both activation (k approximately 4.0 to 6.5 mV) and inactivation characteristics (k approximately 4.3 to 6.6 mV) distinct from those shown by the remaining q beta charge, whether isolated through differential tetracaine sensitivities, or the full approximation of charge-voltage data to the sum of two Boltzmann distributions. RyR modification thus specifically alters q gamma kinetics while preserving the separate identities of steady-state q beta and q gamma charge. These findings permit a mechanism by which transverse tubular voltage provides the primary driving force for configurational changes in DHPRs, which might produce q gamma charge movement. However, they attribute its kinetic complexities to the reciprocal allosteric coupling by which DHPR voltage sensors and RyR-Ca2+ release channels might interact even though these receptors reside in electrically distinct membranes. RyR modification then would still permit tubular voltage change to drive net q gamma charge transfer but would transform its complex waveforms into simple exponential decays.
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Sukhanovskii, A., A. Evgrafova, and E. Popova. "Helicity of Convective Flows from Localized Heat Source in a Rotating Layer." Archive of Mechanical Engineering 64, no. 2 (June 1, 2017): 177–88. http://dx.doi.org/10.1515/meceng-2017-0011.
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AbstractExperimental and numerical study of the steady-state cyclonic vortex from isolated heat source in a rotating fluid layer is described. The structure of laboratory cyclonic vortex is similar to the typical structure of tropical cyclones from observational data and numerical modelling including secondary flows in the boundary layer. Differential characteristics of the flow were studied by numerical simulation using CFD software FlowVision. Helicity distribution in rotating fluid layer with localized heat source was analysed. Two mechanisms which play role in helicity generation are found. The first one is the strong correlation of cyclonic vortex and intensive upward motion in the central part of the vessel. The second one is due to large gradients of velocity on the periphery. The integral helicity in the considered case is substantial and its relative level is high.
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Batool, Iqra, and Naim Bajcinca. "Evolution of cancer stem cell lineage involving feedback regulation." PLOS ONE 16, no. 5 (May 20, 2021): e0251481. http://dx.doi.org/10.1371/journal.pone.0251481.
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Tumor emergence and progression is a complex phenomenon that assumes special molecular and cellular interactions. The hierarchical structuring and communication via feedback signaling of different cell types, which are categorized as the stem, progenitor, and differentiated cells in dependence of their maturity level, plays an important role. Under healthy conditions, these cells build a dynamical system that is responsible for facilitating the homeostatic regulation of the tissue. Generally, in this hierarchical setting, stem and progenitor cells are yet likely to undergo a mutation, when a cell divides into two daughter cells. This may lead to the development of abnormal characteristics, i.e. mutation in the cell, yielding an unrestrained number of cells. Therefore, the regulation of a stem cell’s proliferation and differentiation rate is crucial for maintaining the balance in the overall cell population. In this paper, a maturity based mathematical model with feedback regulation is formulated for healthy and mutated cell lineages. It is given in the form of coupled ordinary and partial differential equations. The focus is laid on the dynamical effects resulting from acquiring a mutation in the hierarchical structure of stem, progenitor and fully differentiated cells. Additionally, the effects of nonlinear feedback regulation from mature cells into both stem and progenitor cell populations have been inspected. The steady-state solutions of the model are derived analytically. Numerical simulations and results based on a finite volume scheme underpin various expected behavioral patterns of the homeostatic regulation and cancer evolution. For instance, it has been found that the mutated cells can experience significant growth even with a single somatic mutation, but under homeostatic regulation acquire a steady-state and thus, ensuing healthy cell population to either a steady-state or a lower cell concentration. Furthermore, the model behavior has been validated with different experimentally measured tumor values from the literature.