Modeling of Electric Field and Dielectrophoretic Force in a Parallel-Plate Cell Separation Device with an Electrode Lid and Analytical Formulation Using Fourier Series by Daiki Nishikawa, Yoshinori Seki, Shigeru Tada

“…The solution was approximated by extrapolating a novel approximate equation as a boundary condition for the potential between adjacent fingers of interdigitated electrodes and changing the underlying differential equation into a solvable form. The distributions of the potential and electric fields obtained by the analytical solution were compared with those from numerical simulations using finite element method software to verify their accuracy. …”
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Partial Volume Reduction by Interpolation with Reverse Diffusion

“…The gray level of each subvoxel is considered as “material” able to move between subvoxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a “reverse” diffusion process. …”
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Advanced technique for flexible cable analysis by A. V. Chesnokov, V. V. Mikhailov

“…The technique proposed is based on the sine-series expansion of the external load and the shape function of the flexible cable. The differential equation of cable equilibrium is thus transformed into the set of algebraic equations. …”
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THE SOLUTION TO THE PROBLEM OF USING GROUND WATER TO COOL LIVESTOCK BUILDINGS by Thay Ngok Shon, Vo Ti Tin

“…For this purpose, the authors have created a heat balance equation at steady state for any infinitesimal element of the fin, and solved the differential equation afterwards. The authors applied the results for calculating practical problem of ground water irrigation of a roof of a livestock shed made of metal areas tiles.…”
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Experimental Validation of Numerical Model for Bi-Tilt-Isolator by Ming-Hsiang Shih, Wen-Pei Sung, Chia-Yu Ho

“…Then, BTI element of nonlinear analysis program, GENDYN, is developed by the fourth-order Runge-Kutta method, the discretized ordinary differential equation for three movement stages of BTI. Then, test set-up of superstructure installed with BTI is tested and recorded the real displacement and acceleration responses under conditions of full lubrication, mild lubrication, and without lubrication between interface of bi-tilt beveled substrate and slider with three various initial displacements. …”
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Nonlinear compressive reduced basis approximation for PDE’s by Cohen, Albert, Farhat, Charbel, Maday, Yvon, Somacal, Agustin

“…Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. …”
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Impact of Cell Size Effect on Nutrient-Phytoplankton Dynamics by Tiancai Liao, Hengguo Yu, Chuanjun Dai, Min Zhao

“…In this paper, a nutrient-phytoplankton model, which is described by a system of ordinary differential equations incorporating the effect of cell size, and its corresponding stochastic differential equation version are studied analytically and numerically. …”
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Estimating the Force of Infection with Helicobacter pylori in Japan by Taishi Kayano, Ki-Deok Lee, Hiroshi Nishiura

“…Solving the McKendrick partial differential equation model, the seroprevalence was modeled as a function of survey year and age. …”
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Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties by Joaquin Alvarez-gallegos, Sishu Shankar Muni, Hector Gilardi-velázquez, Rıcardo Cuesta-garcía, J. L. Echenausía-monroy

“…The study of dynamical systems is based on the solution of differential equations that may exhibit various behaviors, such as fixed points, limit cycles, periodic, quasi-periodic attractors, chaotic behavior, and coexistence of attractors, to name a few. …”
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Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions by A. Beléndez, M. L. Alvarez, J. Francés, S. Bleda, T. Beléndez, A. Nájera, E. Arribas

“…To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. …”
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A Hybrid Renewable Sources Implementation for a DC Microgrid with Flatness-Nonlinear Control to Achieve Efficient Energy Management Strategy by Furqan A. Abbas, Adel A.Obed, Ammar Alhasiri, Salam J. Yaqoob

“…Because of the nonlinear system's behavior, differential flatness-based control has been applied mainly in nonlinear systems where the number of variables to the outputs is reduced with a robust control system established through inherited parameter reductions and equality constraints due to the system trajectories (x, u) is straightforwardly estimated from flat output trajectories y and their derivatives without any differential equation integration. The PI control is executed when the SC adjusts the DC bus voltage variation. …”
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Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising by Khursheed Alam, Alka Chauhan, Santosh Kumar

“…The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. …”
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The relative biologic effectiveness versus linear energy transfercurve as an output-input relation for linear cellular systems by Quoc T. Luu, Paul DuChateau

“…Here we introduce a differential equation formulation for a signal-and-system model that sees cells as systems, different radiation types as input, and cellular responses as output. …”
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Temperature and state-dependent electrical conductivity of soft biological tissue at hyperthermic temperatures by Junren Ran, Martin Ostoja-Starzewski

“…Methods: We model the denaturation process with an Arrhenius-type differential equation for chemical kinetics and a modified Stogryn equation for electrical conductivity under state transition. …”
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Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials by Luc Leroy Mambou Ngueyep, Joseph Ndop, Elise Rose Atangana Nkene, Jean-Marie Bienvenu Ndjaka

“…By choosing that the inhomogeneity parameter is between -0.5 and 0.5, we have established the differential equation which describes the equilibrium of the hollow cylinder in rotation under an axial load. …”
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The significance of heat transfer through natural convection in stagnation point flow of prandtl fluid by Salman Zeb, Zakir Ullah, A.B. Albidah, Ilyas Khan, Waqar A. Khan

“…The analysis integrates velocity, concentration slips, and temperature jumps within a nonlinear partial differential equation framework. These equations are converted into nonlinear partial differential equations using appropriate dimensionless variables. …”
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Stability of hybrid composite rod to high temperatures by Yu. V. Nemirovskiy, D. V. Mokhovnev

“…The stability problem is reduced to solving a linear homogeneous differential equation with linear homogeneous boundary conditions. …”
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Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak by Tianzeng Li, Yu Wang, Weiqiu Pan

“…To provide the numerical solution of the single-term (or multiterm) fractional-order nonlinear differential equation, the GMMP scheme and Newton method are introduced. …”
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A Coupled Thermo-Hydromechanical Model of Soil Slope in Seasonally Frozen Regions under Freeze-Thaw Action by Yongxiang Zhan, Zheng Lu, Hailin Yao, Shaohua Xian

“…Based on the partial differential equation defined using the COMSOL Multiphysics software, a thermo-hydromechanical coupling model considering water migration, ice-water phase change, ice impedance, and frost heave is constructed, and the variations in the temperature field, migration of liquid water, accumulation of solid ice, and deformation of frost heave in frozen soil slopes are analysed. …”
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A simplified version of the method of calculation of multilayer composite rods according to the theory of A.R. Rzhanitsyn by V. V. Filatov, Thi Linh Quyen Hoang

“…This assumption allows us to reduce the problem of determining the functions of shear forces to solving one ordinary differential equation of the second order. Thus, the number of simultaneously solved differential equations describing the problem is reduced from n + 2 to three for any number of layers.Materials and methods. …”
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