A Reduced Order Model Based on ANN-POD Algorithm for Steady-State Neutronics and Thermal-Hydraulics Coupling Problem by Hanxing Liu, Han Zhang

“…Due to the high-dimensional partial differential equations (PDEs) derived from the N/TH system, it is usually time consuming to solve such a large-scale nonlinear equation by the traditional numerical solution method of PDEs. …”
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Effects of Thermodiffusion and Chemical Reaction on Magnetohydrodynamic-Radiated Unsteady Flow Past an Exponentially Accelerated Inclined Permeable Plate Embedded in a Porous Mediu... by B. Prabhakar Reddy, M. H. Simba, Alfred Hugo

“…The governing nondimensional set of coupled nonlinear partial differential equations with related initial and boundary conditions are solved numerically by using the accurate and efficient DuFort–Frankel’s explicit finite difference method. …”
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Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform by Nehad Ali Shah, Essam R. El-Zahar, Ali Akgül, Adnan Khan, Jeevan Kafle

“…In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest.…”
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The Feyn-structure of Yangian symmetry by Florian Loebbert, Harshad Mathur

“…Previous applications of the Yangian suggest to employ the resulting differential equations for bootstrapping multi-loop integrals beyond the dual conformal case. …”
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On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations by Peter I. Kogut, Olha P. Kupenko, Rosanna Manzo

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Qualitative Properties of the Solution of a Conjugate Problem of Thermal Convection by A. A. Azanov, E. N. Lemeshkova

“…Thus, the problem was reduced to a system of 10 nonlinear integro-differential equations. Its conjugate and inverse nature is determined by the four functions of time. …”
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Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption by Xiaofeng Li, Yulong Bai, Weishuan Pan, Di Wang, Yong-Jie Ma

“…Fourth-order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth-order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. …”
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Study of the Radical Chain Mechanism of Hydrocarbon Oxidation for In Situ Combustion Process by Alexandra Ushakova, Vladislav Zatsepin, Mikhail Varfolomeev, Dmitry Emelyanov

“…The system of differential equations based on the equations of oxidation reactions was solved. …”
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Exploring the implications of ternary Jeffrey nanofluid on pulsating flow and heat transfer through unsymmetrical corrugated micro conduit by Mohamed S. Abdel-wahed, Khaled S. Mekheimer, Ahmed Y. Sayed, Shaaban I. Ahmed

“…Using the perturbation method and Mathematica software, we derived semi-analytical solutions for the governing partial differential equations in their complex form. nanoparticle-enhanced blood exhibits improved thermal performance compared to pure fluid, with the type and concentration of nanoparticles (Fe3O4, Au, SWCNTs) significantly impacting heat dissipation and temperature distribution within the microfluidic conduit. …”
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Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics by Karen R. Ríos-Soto, Baojun Song, Carlos Castillo-Chavez

“…A metapopulation framework based on a system of nonlinear ordinary differential equations is used to study the transmission dynamics and control of avian diseases. …”
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The analysis of the influence of the turbulence model selection on the parameters of interaction of a supersonic jet with an obstacle by R. A. Peshkov, A. S. Shmetkova, O. V. Ispravnikova, Ju. L. Suskina

“…The study analyzes the case of interaction of a single supersonic gas jet with a flat barrier oriented perpendicular to the direction of the jet. Differential equations describing the motion of a compressible viscous heatconducting gas (Navier-Stokes equations) are presented, and a method for averaging them by Reynolds is described. …”
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Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen by Gregory Zitelli, Seddik M. Djouadi, Judy D. Day

“…The inflammatory responseaims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen.In cases of acute systemic inflammation, the possibility of collateral tissuedamage arises, which leads to a necessary down-regulation of the response.A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. …”
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The Multi-Functional Modelling Shear Lag Method for Accurate Calculation of Static Response and Accordion Effect of Improved Composite Box Girders by Ya-Nan Gan, Zi-Chen Zhang, Gen-Hui Wang

“…Therefore, MFMSL is a method to calculate the static response and accordion effect of the CW-SBS composite box girders. Structural differential equations based on the energy-variation principle present that the MFMSL method effectively improves the calculating accuracy of the CW-SBS box girder static response, which can be verified by both experimental and simulative results. …”
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Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands by Yuan Feng, Jongwan Eun, Seunghee Kim, Yong-Rak Kim

“…Recently, physics-informed neural networks (PINNs), which incorporate partial differential equations (PDEs) to solve forward and inverse problems, have attracted increasing attention in machine learning research. …”
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Investigation of Micro- and Nanosized Particle Erosion in a 90° Pipe Bend Using a Two-Phase Discrete Phase Model by M. R. Safaei, O. Mahian, F. Garoosi, K. Hooman, A. Karimipour, S. N. Kazi, S. Gharehkhani

“…The 3-D governing differential equations were discretized using finite volume method. …”
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Control optimization of air traffic emissions in a two-variable dynamic model by F. A. Buendía-Hernández, M. J. OrtizBevia, F. J. Alvarez-Garcia, A. RuizdeElvira, J. M. Salazar

“…This study used a two variable differential equations model with a non-linear control term to address several aspects of the emissions stabilization issue. …”
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Robust pareto multiobjective optimum design of FG-Beam under moving mass by Moein Abdollah-Salimi, Nader Nariman-Zadeh, Reza Ansari

“…By substituting terms of energy into the Lagrange equation, differential equations of motion are obtained. Displacement fields as a function of time and x-coordinate are calculated by means of the numerical solution of the above-mentioned equations. …”
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Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents by Raimund BÜrger, Gerardo Chowell, Elvis GavilÁn, Pep Mulet, Luis M. Villada

“…An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. …”
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Optimal Control of Endemic Epidemic Diseases With Behavioral Response by Francesco Parino, Lorenzo Zino, Alessandro Rizzo

“…In particular, we propose a parsimonious model that couples an epidemic compartmental model with a population game that captures the behavioral response, obtaining a nonlinear system of ordinary differential equations. Grounded on prevalence-elastic behavior—the empirically proven assumption that the disease prevalence affects the adherence to self-protective behavior—we consider a nontrivial negative feedback between contagions and adoption of self-protective behavior. …”
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Modeling bacterial attachment to surfaces as an early stage of biofilm development by Fadoua El Moustaid, Amina Eladdadi, Lafras Uys

“…While much is known about the later stages of biofilm formation, less is known about its initiation which is an important first step in the biofilm formation.In this paper, we develop a non-linear system of partial differential equations of Keller-Segel type model in one-dimensional space, which couples the dynamics of bacterial movement to that of the sensing molecules. …”
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