Search Results (72)

The thermal insulation performance of liquid hydrogen (LH₂) storage tanks is critical for long-distance transportation. The active cooled shield (ACS) technologies, such as the liquid nitrogen cooled shield (LNCS) and the vapor hydrogen cooled shield (VHVCS) are important thermal insulation methods. Many researchers installed the VHVCS inside the multilayer insulation (MLI) and obtained the optimal position. However, the MLI layer is often thinner than the vacuum interlayer between the inner and outer tanks, and there is a large vacuum interlayer between the outermost side of MLI and the inner wall of the outer tank. It is unknown whether the insulation performance can be improved if we install ACS in the mentioned vacuum interlayer and separate a portion of the MLI to be installed on the outer surface of ACS. In this configuration, the number of inner MLI (IMLI) layers and the ACS position are interdependent, a coupling that has not been thoroughly investigated. Therefore, thermodynamic models for MLI, MLI-LNCS, and MLI-VHVCS schemes were developed based on the Layer-by-Layer method. By applying Robin boundary conditions, the temperature distribution and heat leakage of the MLI scheme were predicted. Considering the coupled effects of IMLI layer count and ACS position, a co-optimization strategy was adopted, based on an alternating iterative search algorithm. The results indicate that for the MLI-LNCS scheme, the optimal number of IMLI layers and LNCS position are 36 layers and 49%, respectively. For the MLI-VHVCS scheme, the optimal values are 21 layers and 39%, respectively. Compared to conventional MLI, the MLI-LNCS scheme achieves an 88.09% reduction in heat leakage. However, this improvement involves increased system complexity and higher operational costs from LN₂ circulation. In contrast, the MLI-VHVCS scheme achieves a 62.74% reduction in heat leakage, demonstrating that using sensible heat from cryogenic vapor can significantly improve the thermal insulation performance of LH₂ storage tanks. The work of this paper provides a reference for the design and optimization of the insulation scheme of LH₂ storage tanks. Full article

We numerically study wall-bounded convectively driven magneto-hydrodynamic (MHD) flows subject to rotation in a Cartesian periodic channel. For the accurate treatment of the rotating MHD equations, we develop a pseudo-spectral simulation code with accurate treatment of boundary conditions for both velocity and magnetic fields. The solenoidal condition on the magnetic field is enforced by the addition of a fictitious magnetic pressure. This allows us to employ an influence matrix method with tau correction for the treatment of velocity and magnetic fields subject to Robin boundary conditions at the confining walls. We validate the developed method for the specific case of no slip velocity and perfectly conducting magnetic boundary conditions. The validation includes the accurate reproduction of linear stability thresholds and of turbulent statistics. The code shows favorable parallel scaling properties. Full article

This study focuses on the phenomenon of boiling heat transfer during fluid flow (Fluorinert FC-72) in minichannels. The research stand was built around a specially designed test section incorporating sets of aligned minichannels, each 1 mm deep. These channel arrays varied in number, comprising configurations with 7, 15, 17, 19, 21, and 25 parallel channels. The test section was vertically orientated with upward fluid flow. To address the heat transfer problem associated with transient flow boiling, two numerical approaches grounded in the finite element method (FEM) were employed. One used the Trefftz function formulation, while the other relied on simulations performed using the commercial software ADINA (version 9.2). In both approaches, the heat transfer coefficient at the interface between the heated foil and the working fluid was determined by applying a Robin-type boundary condition, which required knowledge of the temperatures in both the foil and the fluid, along with the temperature gradient within the foil. The outcomes of both FEM-based models, as well as those of a simplified 1D method based on Newton’s cooling law, yielded satisfactory results. Full article

This study is devoted to solving the global Mittag-Leffler synchronization problem of fractional-order fuzzy reaction–diffusion inertial neural networks by using boundary control. Firstly, the considered network model incorporates the inertia term, reaction–diffusion term and fuzzy logic, thereby enhancing the existing model framework. Secondly, to prevent an increase in the number of state variables due to the reduced-order approach, a non-reduced-order method is fully utilized. Additionally, a boundary controller is designed to lower resource usage. Subsequently, under the Neumann boundary condition, the mixed boundary condition and the Robin boundary condition, three synchronization conditions are established with the help of the non-reduced-order approach and LMI technique, respectively. Lastly, two numerical examples are offered to verify the reliability of the theoretical results and the availability of the boundary controller through MATLAB simulations. Full article

In this paper, we propose a numerical method for the fractional Bagley–Torvik equation of variable coefficients with Robin boundary conditions. The problem is approximated using a finite difference scheme on a uniform mesh that combines the L1 scheme with central differences. We prove that this numerical method is almost first-order convergent. The error bounds for the numerical approximation are derived. The numerical calculations carried out for the given examples validate the theoretical results. Full article

In this paper, we investigate the existence results of solutions for Caputo-type fractional $(p,q)$-difference equations. Using Banach’s fixed-point theorem, we obtain the existence and uniqueness results. Meanwhile, by applying Krasnoselskii’s fixed-point theorem and Leray-Schauder’s nonlinear alternative, we also obtain the existence results of non-trivial solutions. Finally, we provide examples to verify the correctness of the given results. Moreover, relevant applications are presented through specific examples. Full article

In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a $(D+1)$-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions are imposed on the scalar charged quantum field on the boundaries. The particular cases of Dirichlet and Neumann boundary conditions are studied separately. Due to the coupling of the quantum scalar field with the classical gauge field, corresponding to a magnetic flux running along the string’s core, a nonzero vacuum expectation value for the current density operator along the azimuthal direction is induced. The two boundaries divide the space in three regions with different properties of the vacuum states. In this way, our main objective is to calculate the induced currents in these three regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Because the vacuum bosonic current in dS space has been investigated before, in this paper we consider only the contributions induced by the boundaries. We show that for each region the azimuthal current densities are odd functions of the magnetic flux along the string. To probe the correctness of our results, we take the particular cases and analyze some asymptotic limits of the parameters of the model. Also some graphs are presented exhibiting the behavior of the current with relevant physical parameter of the system. Full article

The present study is concerned with the numerical solution of external boundary conditions in inverse problems for one-dimensional multilayer diffusion, using the difference method. First, we formulate multispecies parabolic problems with three types of Dirichlet–Neumann–Robin internal boundary conditions that apply at the interfaces between adjacent layers. Then, using the symmetry of the diffusion operator, we prove the well-posedness of the direct (forward) problem in which the coefficients, the right-hand side, and the initial and boundary conditions are given. In inverse problems, instead of external boundary conditions of the first and the last layers, point observations of the solution within the entire domain are posed. Rothe’s semi-discretization of differential problems combined with a symmetric exponential finite difference solution for elliptic problems on each time layer is proposed to develop an efficient semi-analytical approach. Next, using special solution decomposition techniques, we numerically solve the inverse problems for the identification of external boundary conditions. Numerical test examples are discussed. Full article

This article investigates the local well-posedness of a coupled system of wave equations on a half-line, with a particular emphasis on Robin boundary conditions within Sobolev spaces. We provide estimates for the solutions to linear initial-boundary-value problems related to the coupled system of wave equations, utilizing the Unified Transform Method in conjunction with the Hadamard norm while considering the influence of external forces. Furthermore, we demonstrate that replacing the external force with a nonlinear term alters the iteration map defined by the unified transform solutions, making it a contraction map in a suitable solution space. By employing the contraction mapping theorem, we establish the existence of a unique solution. Finally, we show that the data-to-solution map is locally Lipschitz continuous, thus confirming the local well-posedness of the coupled system of wave equations under consideration. Full article

The issue of energy supply for wireless sensors is becoming increasingly severe with the advancement of the Fourth Industrial Revolution. Thus, this paper proposed a thermoelectric self−powered wireless sensor that can harvest industrial waste heat for self−powered operations. The results show that this self−powered wireless sensor can operate stably under the data transmission cycle of 39.38 s when the heat source temperature is 70 °C. Only 19.57% of electricity generated by a thermoelectric power generation system (TPGS) is available for use. Before this, the power consumption of this wireless sensor had been accurately measured, which is 326 mW in 0.08 s active mode and 5.45 μW in dormant mode. Then, the verified simulation model was established and used to investigate the generation performance of the TPGS under the Dirichlet, Neumann, and Robin boundary conditions. The minimum demand for a heat source is cleared for various data transmission cycles of wireless sensors. Low−temperature industrial waste heat is enough to drive the wireless sensor with a data transmission cycle of 30 s. Subsequently, the economic benefit of the thermoelectric self−powered system was also analyzed. The cost of one thermoelectric self−powered system is EUR 9.1, only 42% of the high−performance battery cost. Finally, the SEPIC converter model was established to conduct MPPT optimization for the TEG module and the output power can increase by up to approximately 47%. This thermoelectric self−powered wireless sensor can accelerate the process of achieving energy independence for wireless sensors and promote the Fourth Industrial Revolution. Full article

The mean first-passage time represents the average time for a migrating cell within its environment, starting from a certain position, to reach a specific location or target for the first time. In this feature article, we provide an overview of the characterization of the mean first-passage time of cells moving inside two- or three-dimensional domains, subject to various boundary conditions (Dirichlet, Neumann, Robin, or mixed), through the so-called adjoint diffusion equation. We concentrate on reducing the latter to inhomogeneous linear integral equations for certain density functions on the boundaries. The integral equations yield the mean first-passage time exactly for a very reduced set of boundaries. For various boundary surfaces, which include small deformations of the exactly solvable boundaries, the integral equations provide approximate solutions. Moreover, the method also allows to deal approximately with mixed boundary conditions, which constitute a genuine long-standing and open problem. New plots, figures, and discussions are presented, aimed at clarifying the analysis. Full article

The Schrödinger–Korteweg–de Vries (SKdV) system can describe the nonlinear dynamics of phenomena such as Langmuir and ion acoustic waves, which are highly valuable for studying wave behavior and interactions. The SKdV system has wide-ranging applications in physics and applied mathematics. In this article, we investigate the local well-posedness of the SKdV system with Robin boundary conditions and polynomial terms in the Sobolev space. We want to enhance the applicability of this type of SKdV system. Our verification process is as follows: We estimate Fokas solutions for the Robin problem with external forces. Next, we define an iteration map in suitable solution space and prove the iteration map is a contraction mapping and onto some closed ball $B(0,r)$. Finally, by the contraction mapping theorem, we obtain the uniqueness solution. Moreover, we show that the data-to-solution map is locally Lipschitz continuous and conclude with the well-posedness of the SKdV system. Full article

A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the existence of solutions to the nonlocal problem is given at the beginning in a function space suitably chosen. Next, under certain assumptions on the known data, we prove the well posedness (the existence, a priori estimates, regularity, uniqueness) of the classical solution to the local problem. At the end, we present a particularization of the local and nonlocal problems, with applications for image processing (reconstruction, segmentation, etc.). Some conclusions are given, as well as new directions to extend the results and methods presented in this paper. Full article

This paper deals with the long-wavelength behaviour of a Euler beam periodically supported by co-located rotation and compression springs. An asymptotic homogenization method is applied to derive the several macroscopic models according to the stiffness contrasts between the elastic supports and the beam. Effective models of differential order two or four are obtained, which can be merged into a single unified model whose dispersion relations at long and medium wavelengths fit those derived by Floquet-Bloch. Moreover, the essential role of rotation supports is clearly evidenced. A mixed “discrete/continuous” approach to the boundary conditions is proposed, which allows the boundary conditions actually applied at the local scale to be expressed in terms of Robin-type boundary conditions on macroscopic variables. This approach can be applied to both dominant-order and higher-order models. The modal analysis performed with these boundary conditions and the homogenised models gives results in good agreement with a full finite element calculation, with great economy of numerical resources. Full article

In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin’s-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the Dirichlet conditions are unknown functions, and the aim is to be reconstructed upon integral observations. Well-posedness both for direct and inverse problems is established. Using the given 2D integrals of the unknown solution on each of the domains and the specific interface boundary conditions, we reduce the 2D inverse problem to a forward heat 1D one. The resulting 1D problem is solved using the explicit Saul’yev finite difference method. Numerical test examples are discussed to illustrate the efficiency of the approach. Full article