Dynamic Boundary Conditions Research Articles

Hierarchical control problem for the heat equation with dynamic boundary conditions

Abstract This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg–Pareto strategy.

The Coupled Temperature Field Model of Difficult-to-Deform Mg Alloy Foil High-Efficiency Electro-Rolling and Experimental Study

In response to the challenging difficult-to-deform of magnesium foils, a high-efficiency and high-precision electro-rolling temperature field coupled model is established. This model is designed to simulate the non-annealing electric rolling (NAER) process of Mg foils under conditions of high current density, rapid temperature rise rates, and large temperature gradients. Firstly, a coupled temperature field difference model for the guide roller, roll, and Mg foil is established, based on the equipment for NAER and the electrification conditions. The Joule heat, distortion heat, and friction heat in the electric rolling process were precisely considered. Secondly, considering the peculiarity of the heat source and the heat transfer mechanism during NAER, the influence of the dynamic boundary conditions on the instantaneous temperature of the Mg foil was analyzed, which was closer to the actual situation. The experimental results show that the original model can accurately simulate the transient temperature change in Mg foils during NAER, and the error between the predicted value and the measured value is within 7.1%. According to the calculation of the model, the microstructure of completely recrystallized magnesium foil with a grain size of 4.61 μm and a texture strength of 11.3 can be obtained at an inlet temperature of 250 °C.

Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions

We consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.

VERIFICATION OF LAMINATE COMPOSITEPLATE SIMULATION UNDER COMBINED LOADINGS THERMALSTRESSES

This study deals with thermal cyclic loading phenomena of plates which were fabricated from composite materials (woven roving fiber glass + polyester) were exposed to (75 C°) temperature gradient thermal shock for ten times in different stage of conditioning times due to the effect of thermal fatigue using the method of Levy solution and compared these results with both results from experimental published work and (ANSYS Ver. 9) program. A composite laminate plate with fiber volume fraction (υf =25.076%) is selected in this study and applying the combined loadings like bending moment (Mo), and in-plane force (Nxx) beside the effect of thermal fatigue. It involves multi theoretical and finite element fields; but the theoretical one contains the derived equation of stresses distribution and evaluating the normal deflection of a middle point for dynamic analysis applying different boundary conditions for heating and cooling. The main present numerical results for a composite plate with (80%) fiber volume fraction claim that the relative reduction in normal deflection and dynamic load factor are (78.593%) and (9.421%) during cooling to (-15 respectively.

Investigation of near-wall particle statistics in CFD-DEM simulations of dense fluidised beds and derivation of an Eulerian particle dynamic wall boundary condition

In two-fluid simulations of gas–solid fluidised beds, the gaseous phase and the particulate phase are modelled as continuous media. The stress exerted by the particulate medium on the container walls should be modelled to predict accurately the bed dynamics. This paper addresses the modelling of sliding particle–wall contacts in two-fluid simulations, based on reference simulations coupling computational fluid dynamics with the discrete element method (CFD-DEM), in which the individual movement of the particles is tracked. The analysis of the CFD-DEM highlights the complex near-wall behaviour of the particles, which is not reproduced by two-fluid models. Nevertheless, the particle–wall shear stress can be expressed based on the total granular pressure within the first cell off the wall. The model is validated for the two-fluid simulation of a bubbling gas–solid fluidised bed of olefin particles in the dense-fluidisation regime.

Study on the dynamic thermal response of phase change material integrated wall under indoor-outdoor dual thermal disturbances

The study mainly explored the dynamic thermal response of phase change material integrated wall (PCMW) under indoor-outdoor dual thermal disturbances (IODTD). A dual wave thermal disturbance dynamic boundary condition was proposed for PCMW based on the outdoor meteorological data and typical solar energy building analytical models of Lhasa, Yinchuan and Xi'an in China. The influence of different construction modes on the thermal performance of PCMW was numerically investigated by the sensible heat capacity method under IODTD. Then determined the crucial thermophysical parameters of PCM and analyzed the variation characteristics of temperature and heat flux fields of PCMW. The heat transfer frequency responses of different walls to outdoor thermal disturbances were calculated by the harmonic response method. The results indicated that the optimal location of PCM was on the interior side of the wall, and the critical values of phase change temperature and latent heat were 16 °C and 120 kJ/kg, respectively. It presented the maximum temperature and heat flux were 10 % and 36.2 % greater than ordinary walls (OW). Compared with OW, the attenuation and delay time of PCMW on outdoor sol-air temperature wave performed significantly, which plotted a higher decrement factor and longer time lag under external disturbances of different orders.

Численное моделирование водородопроницаемости с концентрационной зависимостью коэффициента диффузии

The paper presents a nonlinear mathematical model of alloys hydrogen permeability for membrane technologies of high-purity hydrogen production. Diffusion processes in the material bulk are taken into account as well as physical and chemical phenomena at the surface: adsorption, desorption and relatively fast dissolution. The iterative computational algorithm and software in Scilab have been developed to model the hydrogen permeability with dynamic boundary conditions and concentration-dependent diffusion coefficient.

Numerical Reconstruction of the Source in Dynamical Boundary Condition of Laplace’s Equation

In this work, we consider Cauchy-type problems for Laplace’s equation with a dynamical boundary condition on a part of the domain boundary. We construct a discrete-in-time, meshless method for solving two inverse problems for recovering the space–time-dependent source and boundary functions in dynamical and Dirichlet boundary conditions. The approach is based on Green’s second identity and the forward-in-time discretization of the non-stationary problem. We derive a global connection that relates the source of the dynamical boundary condition and Dirichlet and Neumann boundary conditions in an integral equation. First, we perform time semi-discretization for the dynamical boundary condition into the integral equation. Then, on each time layer, we use Trefftz-type test functions to find the unknown source and Dirichlet boundary functions. The accuracy of the developed method for determining dynamical and Dirichlet boundary conditions for given over-determined data is first-order in time. We illustrate its efficiency for a high level of noise, namely, when the deviation of the input data is above 10% on some part of the over-specified boundary data. The proposed method achieves optimal accuracy for the identified boundary functions for a moderate number of iterations.

Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size

We study the homogenization of a nonlinear problem given by the Poisson equation, in a domain with arbitrarily shaped perforations (or particles) and with a dynamic unilateral boundary condition (of Signorini type), with a large coefficient, on the boundary of these perforations (or particles). This problem arises in the study of chemical reactions of zero order. The consideration of a possible asymmetry in the perforations (or particles) is fundamental for considering some applications in nanotechnology, where symmetry conditions are too restrictive. It is important also to consider perforations (or particles) constituted by small different parts and then with several connected components. We are specially concerned with the so-called critical case in which the relation between the coefficient in the boundary condition, the period of the basic structure, and the size of the holes (or particles) leads to the appearance of an unexpected new term in the effective homogenized equation. Because of the dynamic nature of the boundary condition this ``strange term'' becomes now a non-local in time and non-linear operator. We prove a convergence theorem and find several properties of the ``strange operator'' showing that there is a kind of regularization through the homogenization process.
 For more information see https://ejde.math.txstate.edu/Volumes/2024/03/abstr.html

A ternary mixture model with dynamic boundary conditions.

The influence of short-range interactions between a multi-phase, multi-component mixture and a solid wall in confined geometries is crucial in life sciences and engineering. In this work, we extend the Cahn-Hilliard model with dynamic boundary conditions from a binary to a ternary mixture, employing the Onsager principle, which accounts for the cross-coupling between forces and fluxes in both the bulk and surface. Moreover, we have developed a linear, second-order and unconditionally energy-stable numerical scheme for solving the governing equations by utilizing the invariant energy quadratization method. This efficient solver allows us to explore the impacts of wall-mixture interactions and dynamic boundary conditions on phenomena like spontaneous phase separation, coarsening processes and the wettability of droplets on surfaces. We observe that wall-mixture interactions influence not only surface phenomena, such as droplet contact angles, but also patterns deep within the bulk. Additionally, the relaxation rates control the droplet spreading on surfaces. Furthermore, the cross-coupling relaxation rates in the bulk significantly affect coarsening patterns. Our work establishes a comprehensive framework for studying multi-component mixtures in confined geometries.

Adaptive prescribed performance control for wave equations with dynamic boundary and multiple parametric uncertainties

<abstract><p>In modern engineering, the dynamics of many practical problems can be described by hyperbolic distributed parameter systems. This paper is devoted to the adaptive prescribed performance control for a class of typical uncertain hyperbolic distributed parameter systems, since uncertainties are inevitable in practice. The systems in question simultaneously have unknown in-domain spatially varying damping coefficient and unknown boundary constant damping coefficient. Moreover, dynamic boundary condition is considered in the present paper. These characteristics make the control problem in the paper essentially different from those in the related works. To solve the problem, using adaptive technique based projection operator, backstepping method developed for ODEs and Lyapunov stability theories, a powerful adaptive prescribed performance control scheme is proposed to successfully guarantee that all states of the resulting closed-loop system are bounded, furthermore, the original system state converges to an arbitrary prescribed small neighborhood of the origin. Compared with the existing results, the developed control schemes can not only effectively handle the serious uncertainties, but also overcome the technical difficulties in the infinite-dimensional backstepping control design method caused by the dynamic boundary condition and guarantee prescribed performance.</p></abstract>

Existence, uniqueness, and blow-up analysis of a quasi-linear bi-hyperbolic equation with dynamic boundary conditions

<abstract><p>For this study, we investigate the existence and uniqueness of local solutions and derive a blow-up solution for a quasi-linear bi-hyperbolic equation under dynamic boundary conditions. We utilize the contraction mapping concept to demonstrate the solution's local well-posedness and employ a concavity approach to establish the blow-up result.</p></abstract>

Null controllability for parabolic systems with dynamic boundary conditions

Null controllability for parabolic systems with dynamic boundary conditions

Structure-preserving schemes for Cahn–Hilliard equations with dynamic boundary conditions

Structure-preserving schemes for Cahn–Hilliard equations with dynamic boundary conditions

Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Exponential Decay of Solutions of Damped Wave Equations in One Dimensional Space in the Lp Framework for Various Boundary Conditions

We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based on the study of the corresponding hyperbolic systems associated with the Riemann invariants. The key ingredient in the study of these systems is the use of the internal dissipation energy to estimate the difference of solutions with their mean values in an average sense.

Critical slowing down for relaxation in the Cahn–Hilliard equation with dynamic boundary conditions

Critical slowing down for relaxation in the Cahn–Hilliard equation with dynamic boundary conditions

A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions

A Direct Discontinuous Galerkin Method for Time Fractional Diffusion Equations with Fractional Dynamic Boundary Conditions

Stability for variable-coefficient wave equation with local frictional damping and memory type dynamic boundary conditions

Stability for variable-coefficient wave equation with local frictional damping and memory type dynamic boundary conditions

Aeolian Liquid Vibrations in Conical Tanks with Baffles under Wind Loading with Fuzzy Parameters

The Aeolian liquid vibrations in conical reservoirs caused by low-velocity, steady winds have been under consideration. Both amplitudes and dominant frequencies of wind loadings have been constantly changed, so to adequately describe the vibration process, fuzzy logic methods have been applied. At the first stage, the crisp initial value problem for conical shells with and without baffles has been considered. The liquid inside the reservoirs has been supposed to be an incompressible and ideal one, and its flow induced by the forced harmonic excitation, has been considered as potential. So, there exists a potential to satisfy the Laplace equation. The impermeable condition has been used at wetted surface boundaries of the shell, whereas the dynamic and kinematic boundary conditions have been set on the free liquid surface. A system of singular integral equations has been obtained for values of the velocity potential and the function describing the free surface rise. Its solution has been gained by boundary element methods. The crisp boundary value problem has been reduced to the second-order system of differential equations. After receiving the crisp solution of this system, the initial data have been fuzzified, involving triangular fuzzy numbers, and the fuzzy initial value problem has been formulated. The numerical solution to this problem with uncertain intervals involved has been obtained and analyzed.