Analysis on Cage Dynamic Characteristic of Ultra-low Temperature Angular Contact Ball Bearing by Jing Liu, Yanguang Ni, Wenhu Zhang, Sier Deng

“…Based on the dynamics theory of the rolling bearings， the dynamics differential equations of angular contact ball bearing are established in which the pocket shape of the cage is elliptical. …”
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Modeling Multicellular Systems Using Subcellular Elements by T. J. Newman

“…We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. …”
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Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method by Haitao Zhu, Yongping Wan

“…The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. …”
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Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation by Jan Freundlich

“…This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. …”
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Research of the Transmission Error of Planetary Transmission System for Hub Motor by Chen Haoran, Qin Xunpeng, Zhang Jiang

“…Taking the planetary transmission system of hub motor as the research object,the kinematic differential equations of the system are established by considering the influence factors of time-varying mesh stiffness,meshing phase and equivalent mesh error,and the Runge-Kutta method is used to get the system transmission error. …”
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Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics by Haileyesus Tessema Alemneh

“…In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. …”
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A Bright Entanglement and Squeezing Generated by an External Pumping Radiation in a Correlated Emission Laser by Chimdessa Gashu

“…The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. …”
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Probability Density Evolution Algorithm for Stochastic Dynamical Systems Based on Fractional Calculus by Yang Yan, Xiaohong Yu

“…Dynamical models of the dynamic system and coupled system “three-car vehicle-rail-bridge” are established, the time-varying differential equations of motion are derived in detail, and the dynamic response of the system is calculated using the explicit Newmark algorithm. …”
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Analysis of the Torsional Vibration Modeling and Rigidity Excitation of K-H-V Cycloid Steel Ball Transmission by Kong Xia, Zhang Jielu, Cai Yunlong

“…By analyzing the position relationships of each engagement force and the displacement relationships of each component,the governing differential equations of the system and the dimensionless equivalent engagement rigidities of each transmission disc are derived. …”
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Review on Mathematical and Mechanical Models of the Vocal Cord by L. Cveticanin

“…The corresponding mathematical models are the systems of coupled second-order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. …”
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Identification of the boundary regime in the process of water-oil displacement from the reservoir by Gamzaev Khanlar

“…The water-oil displacement process (from a rectangular reservoir) has been considered, that is described by a nonlinear system of partial differential equations with respect to the reservoir pressure (RP) and displacing phase saturation (DPS). …”
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Application of Local Fractional Homotopy Perturbation Method in Physical Problems by Nabard Habibi, Zohre Nouri

“…Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. …”
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A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control by Yun Huang

“…Based on the three-dimensional Lorenz system, two first-order differential equations are added along with one linear coupling controller, respectively. …”
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Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation by Mehmet Emir Koksal

“…Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. …”
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Positive Position Feedback Control for High-Amplitude Vibration of a Flexible Beam to a Principal Resonance Excitation by Li Jun

“…The perturbation method of multiple scales is employed to find the general nonlinear response of the system and four first-order differential equations governing the amplitudes and phases of the responses are derived. …”
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The Dynamical Behavior of a Rigid Body Relative Equilibrium Position by T. S. Amer

“…The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. …”
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Binary mixture convection in a horizontal channel under the Soret effect action by Stepanova Irina

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Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. …”
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Control Application of Piezoelectric Materials to Aeroelastic Self-Excited Vibrations by Mohammad Amin Rashidifar, Darvish Ahmadi

“…The governing differential equations of an overhung beam are established. …”
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Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics by W. K. Chow, C. L. Chow, S. S. Li

“…Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. …”
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