Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks by Maya Mincheva, Gheorghe Craciun

“…If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values.On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. …”
Get full text

The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses by Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra

“…This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. …”
Get full text

Studies on the Effects of Interphase Heat Exchange during Thermal Explosion in a Combustible Dusty Gas with General Arrhenius Reaction-Rate Laws by K. S. Adegbie, F. I. Alao

“…The equations governing the physical model with realistic assumptions are stated and nondimensionalised leading to an intractable system of first-order coupled nonlinear differential equations, which is not amenable to exact methods of solution. …”
Get full text

Some Properties of Motion Equations Describing the Nonlinear Dynamical Response of a Multibody System with Flexible Elements by Maria Luminiţa Scutaru, Sorin Vlase

“…Finally, second-order differential equations with variable coefficients are obtained; these equations are strong nonlinear ones due to the time-dependent values of angular speed and acceleration, and they can be linearized considering a very short period of time, in which the motion is considered to be “frozen.” …”
Get full text

Numerical Study on Resistance Change Characteristics of Phase Change Materials by Yifang Su, Yihang Zhang, Kaifeng Lin, Guanjun Zhao, Qinzheng Yu, Zuoqi Hu, Xiongfei Tao

“…To study the characteristics of the phase change materials, a numerical simulation model of the resistive change unit based on the finite element method and the classic nucleation/growth theory is established, while the partial differential equations of electricity and heat conduction and the discrete formula of the finite element are also derived. …”
Get full text

Role of stability analysis and waste discharge concentration of ternary hybrid nanofluid in a non-Newtonian model with slip boundary conditions by Nurhana Mohamad, Shuguang Li, Umair Khan, Anuar Ishak, Ali Elrashidi, Mohammed Zakarya

“…The suitable similarity transformations are utilized to transform the partial differential equations (PDEs) into ordinary differential equations (ODEs). …”
Get full text

Non Linear Thermal Radiation Analysis of Electromagnetic Chemically Reacting Ternary Nanofluid Flow over a Bilinear Stretching Surface by Shobha V, Hasan Mulki, Baskar P, S. Suresh Kumar Raju, Saleh Mahmoud, Mostafa Abdrabboh, S.V.K. Varma

“…Methodology: The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations. …”
Get full text

Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System by Alejandro Marquez, Jairo José Espinosa Oviedo, Darci Odloak

“…Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. …”
Get full text

Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators by Dongyuan Liu, Zigen Ouyang, Huilan Wang

“…Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.…”
Get full text

Settlement Prediction Based on the Relationship between the Empirical and Analytical Solutions of a Cylindrical Cavity under Undrained Conditions by Pieride Mabe Fogang, Yang Liu, Pengqiang Yu

“…The expansion of the cylindrical cavity is solved as a linear elasticity problem using a system of first-order ordinary differential equations containing two components in the Cartesian coordinates. …”
Get full text

Heat Transfer in Boundary Layer Magneto-Micropolar Fluids with Temperature-Dependent Material Properties over a Stretching Sheet by Ephesus O. Fatunmbi, Samuel S. Okoya

“…With the aid of similarity conversion analysis, the formulated equations of the flow and heat transfer have been translated into a system of nonlinear ordinary differential equations. Subsequently, Runge–Kutta–Fehlberg integration scheme in company of shooting techniques employed to obtain numerical solutions to the reduced equations. …”
Get full text

Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics by M. de la Sen

“…As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. …”
Get full text

Static Characteristics of Improved Composite Box Girder with Corrugated Steel Webs by Shijin Wang, Genhui Wang, Zichen Zhang

“…In order to accurately calculate the cross-sectional stresses and deflections of the improved composite box girder with corrugated steel webs, the control differential equations and boundary conditions are established based on the energy variational principle, taking into account the effects of corrugated steel web properties, shear lag, and shear deformation. …”
Get full text

Aeroelastic Vibrations and Stability in Cyclic Symmetric Domains by Bernard Lalanne, Maurice Touratier

“…Firstly, general and usual cyclic symmetric properties are recovered from the Floquet theorem for differential equations, having space periodic coefficients in conjunction with a discrete space Fourier series development. …”
Get full text

Analysis of an HIV infection model incorporating latency age and infection age by Jinliang Wang, Xiu Dong

“…There is a growing interest to understand impacts of latent infection age and infection age on viral infection dynamics by using ordinary and partial differential equations. On one hand, activation of latently infected cells needs specificity antigen, and latently infected CD4+ T cells are often heterogeneous, which depends on how frequently they encountered antigens, how much time they need to be preferentially activated and quickly removed from the reservoir. …”
Get full text

Generalized Thermopiezoelectricity with Memory-Dependent Derivative and Transient Thermoelectromechanical Responses Analysis by Jianzhong Sun, Yaping Wu

“…In this paper, a novel generalized thermoelastopiezoelectric model is established by introducing memory-dependent derivative, which might be superior to fractional ones: the form is unique, while the fractional-order theories have various expressions with different authors; it is more intuitionistic for reflecting the memory effect; the physical meanings of the related memory-dependent differential equations are more clear, which are determined by the essence of their definitions; the time-delay and kernel function can be chosen freely based on the necessity of practical applications. …”
Get full text

Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation by Silvana Ilie, Monjur Morshed

“…This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. …”
Get full text

Global Dynamics of Secondary DENV Infection with Diffusion by A. M. Elaiw, A. S. Alofi

“…In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. …”
Get full text

Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and stability analysis by Benjamin Wacker

“…For that purpose, we proved some analytical results regarding the system of differential equations as our first main contribution. Specifically, we showed non-negativity and boundedness of solutions, global existence in time and global uniqueness in time and examined stability properties of two possible equilibria. …”
Get full text

Nonlinear Dynamics Modeling and Subharmonic Resonances Analysis of a Laminated Composite Plate by Ting Ma, Xiao Juan Song, Shu Feng Lu

“…The two-degree-of-freedom ordinary differential equations that describe the vibration of the rectangular plate are obtained by the Galerkin method. …”
Get full text