Related papers: On delay-partial-differential and delay-differenti…
The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear…
Simulation of transport properties of confined, low-dimensional fluids can be performed efficiently by means of Multi-Particle Collision (MPC) dynamics with suitable thermal-wall boundary conditions. We illustrate the effectiveness of the…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…
A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the…
This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called "reduced-order model" (ROM) is obtained from reduction of the…
We present a proof of concept for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED) by adapting the finite-difference time-domain (FDTD) method. The…
Atomic heating is a fundamental phenomenon governed by the thermal spike effect during energetic deposition. This work presented another insight into thermal spike using a coupled classical oscillator model instead of a typical heat…
The last years saw a renewal of interest for hypersonic research in general and regenerative cooling specifically, with a large increase of the number of dedicated facilities and technical studies. In order to quantify the heat transfer in…
We prove global existence of a solution to an initial and boundary value problem for a highly nonlinear PDE system. The problem arises from a thermomechanical dissipative model describing hydrogen storage by use of metal hydrides. In order…
In this paper we develop and significantly extend the thermal phase change model, introduced in [12], describing the process of paraffinic wax layer formation on the interior wall of a circular pipe transporting heated oil, when subject to…
Due to ample applications from medical services to industrial activities, the study of flow and heat transfer through a curved duct has attracted considerable attention to the researchers. In this paper, a comprehensive numerical study is…
The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
The paper is concerned with modeling and simulating approaches of wall distance functions based on Partial Differential Equations (PDE). The distance to the nearest wall is required for many industrial problems in Computational Fluid…
A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
We formulate a nonlinear optimal control problem for intra-day operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are…
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of the permeability tensor under the influence of a diffusion…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
A new approach to the study of similarity of temperature profiles is presented. It is applicable for any 2-D fluid flow along an isothermal heated (cooled) wall. The approach is based on a simple concept; the area under a set of scaled…