Related papers: On delay-partial-differential and delay-differenti…
Given the critical role played by natural gas in providing electricity, heat, and other essential services, better models are needed to understand the dynamics of natural gas networks during extreme events. This paper aims at establishing…
We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of…
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…
When analyzing thermodynamic and kinetic properties of crystals whose anisotropy is not large and the considered effects do not relate to the existence of singled-out directions in crystals, one may use a more simple model of an isotropic…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…
In this paper, we study a hydrodynamic phase-field system modeling the deformation of functionalized membranes in incompressible viscous fluids. The governing PDE system consists of the Navier-Stokes equations coupled with a convective…
The present study reports a novel physical model for simulating Pulsating Heat Pipes (PHP). Their high heat performance is due to the phase change over thin liquid films. The simulation of physically correct film behavior is thus crucial.…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems described by the equations for the conservation of mass, momentum and energy. Our goal is…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel…
A thermal diode transports heat mainly in one preferential direction rather than in the opposite direction. This behavior is generally due to the non-linear dependence of certain physical properties with respect to the temperature. Here we…
We consider transport of dilute two-dimensional electrons, with temperature between Fermi and Debye temperatures. In this regime, electrons form a nondegenerate plasma with mobility limited by potential disorder. Different kinds of…
The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort…
A transient analysis for vesicle deformation under DC electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the…
We consider the Dicke model in the ultra-strong coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers $N$ for bosonic and fermionic systems. We derive partition functions with degeneracy…