Boundary Conditions Research Articles

Critical Temperature and Order Parameter in Superconductor/Inhomogeneous Ferromagnet Heterostructures

A method for solving a self-consistent boundary value problem for the linearized Usadel equation is proposed. The method makes it possible to find the sample-normalized distribution of the superconducting order parameter and the critical temperature as functions of the problem parameters and to solve relatively complex spatially inhomogeneous problems, e.g., superconducting heterostructures containing inhomogeneous magnetic layers. Within this approach, layered structures containing superconducting and domain-split ferromagnetic layers are considered. The theory is compared with experiment for the Fe 20 Å/V 340 Å/Fe 8 Å/Cr/Fe 8 Å system.

Characteristics of solution to singular fractional differential equation with two Riemann-Stieltjesdintegral boundary value conditions

The purpose of this paper is to study unique solution and iterative sequence of approximate solution for uniformly approaching unique solution to a new class of singular fractional differential equations with two kinds of Riemann-Stieltjes integral boundary value conditions by using some fixed point theorems. Because of different properties of the nonlinear terms and complexity of the boundary conditions in equations, we first probe several fixed point theorems of sum-type operators which expand many existing works in this research area. It is essential to point out that some conditions in our works greatly simplify the proof process of fixed point theorems. By applying the operator conclusions obtained in this paper, some sufficient conditions that guarantee the existence and uniqueness of solutions to singular differential equations are obtained, two iterative schemes that uniformly converges to the unique solution are given which provide computational methods of approximating solutions. As applications, some examples are provided to illustrate our main results.

On the stability of electrovacuum space-times in scalar–tensor gravity

AbstractWe study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter $$\xi $$ ξ . The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Modal and harmonic analysis of femur bone using different boundary conditions by Finite Element Analysis.

The longest and largest bone in the human body is the femur. Pelvic bone sustains the weight of the body to which the femur bone is connected. Many researches have been carried out to identify the behaviour of the femur bone. The study aimed to explore the natural frequencies and mode shapes of vibrating devices to gain insights into the dynamic behavior of the femur bone during various physical activities. Examining the impact of patient-specific bone shape and density on bone natural frequencies is crucial. The primary goals of femur bone analysis involve employing computer simulations for fracture detection and employing Finite Element (FE) models to determine natural frequencies and vibration modes. To obtain the natural frequency of the femur bone, different boundary conditions such as free-fixed and fixed-fixed are applied. Avoiding the coincidence of the natural frequency with external excitation frequencies is crucial to prevent femur bone fractures. Also, for different magnitude of loads, femur bone is involved in harmonic analysis is to identify the amplitude and stress against acceleration.

An innovative subdivision collocation algorithm for heat conduction equation with non-uniform thermal diffusivity.

This paper presents a subdivision collocation algorithm for numerically solving the heat conduction equation with non-uniform thermal diffusivity, considering both initial and boundary conditions. The algorithm involves transforming the differential form of the heat conduction equation into a system of equations and discretizing the time variable using the finite difference formula. The numerical solution of the system of heat conduction equations is then obtained. The feasibility of the algorithm is verified through theoretical and numerical analyses. Additionally, numerical and graphical representations of the obtained numerical solutions are provided, along with a comparison to existing methods. The results demonstrate that our proposed method outperforms the existing methods in terms of accuracy.

Influence of flexoelectricity on coupled electromechanical response of 2D MXene/graphene-based hybrid piezocomposites.

This study investigates the influence of flexoelectricity on the coupled electromechanical behavior of MXene/graphene-based hybrid piezocomposite (MGHPC) plates. We developed an analytical model based on Navier's solution and Kirchhoff's plate theory, as well as an approximate model based on the Ritz method for validation purposes. A three-phase micromechanical modeling is developed for determining the effective properties of MGHPC composed of 2D MXene and graphene nano-reinforcements embedded in an epoxy matrix. These micromechanical models were implemented to predict the static and dynamic electromechanical response of MGHPC plates subject to various edge support and loading conditions. Both the analytical and approximate solutions provided unequivocal evidence of the profound impact of the flexoelectric effect on the bending and modal analysis of MGHPC nanoplates. The flexoelectric effect enhanced the stiffness of the nanoplate, irrespective of the support condition. This implies that MGHPC plates can be tailored for precise resonance frequencies and static deflection within nanoelectromechanical systems. This can be achieved by manipulating parameters such as boundary conditions and geometric attributes, including plate thickness/aspect ratio and graphene/MXene nano-reinforcements volume fractions.

A Semi‐Analytical Method for Simulating Near‐Field Antiplane Wave Propagation in Layered Fluid‐Saturated Porous Media

ABSTRACTA semi‐analytical method for the near‐field antiplane wave propagation analysis in the layered fluid‐saturated porous media (FSPM) is proposed based on the Biot u–U dynamic formulation. The wave propagation equations of the FSPM are decoupled by the variable‐separating method. The thin‐layer element method (TLEM) is applied to discretize the infinite domain and construct the consistent artificial boundary condition. The finite element method (FEM) is adopted for the space discretization of the finite domain and the numerical solution of the dynamic response. The proposed method is validated by the comparison of the numerical results of this method with those in the published references and acquired from the remote artificial boundary. Subsequently, this method is applied to investigate typical near‐field antiplane wave propagation problems in the FSPM. Parametric sensitivity investigations are also executed to explore the impact of mechanical parameters, including permeability coefficients, porosity, and shear modulus of the solid phase, on the dynamic response of the FSPM. The study results confirm the efficacy and efficiency of the proposed method in the near‐field antiplane wave propagation analysis in the FSPM.

Existence, Uniqueness, and Stability of Solutions for Nabla Fractional Difference Equations

In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some sufficient conditions in order to ensure existence and uniqueness results. Also, we establish some conditions under which the solution to the considered problem is generalized Ulam–Hyers–Rassias stable. In the end, some examples are included in order to illustrate our main results.

Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part II

Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part II

Steady-State Shape Factor for a Slug Test in an Unconfined Aquifer

A new solution is presented for the steady-state shape factor of a partially penetrating well in an unconfined aquifer. The problem is solved by taking into account mixed boundary conditions at the well, i.e., zero flux at the well casing and constant head at the well screen equal to the head in the well so that the flow through the well screen is non-uniform. The new method is compared with established methods, such as those of Bouwer and Rice and Zlotnik et al., demonstrating that the new approach provides more accurate results under certain conditions. The comparison highlights that the new method is particularly effective in scenarios where the assumptions of uniform flow through the well screen do not hold. This study assumes idealized conditions, such as homogeneity, isotropy, and negligible storativity in the aquifer, which may limit the method’s applicability in more complex environments. The computational demands of the iterative solution process may pose challenges for practical use, especially in resource-constrained settings.

Thermal analysis of bioconvective flow of Williamson nanofluid with Stefan blowing and multiple slip boundary conditions on a porous stretching surface

Thermal analysis of bioconvective flow of Williamson nanofluid with Stefan blowing and multiple slip boundary conditions on a porous stretching surface

Heat Flux Correlations for Condensation From Steam and Air Mixtures on Vertical Flat Plates

Abstract In this study, heat fluxes qc for condensation from steam and air mixtures on vertical flat plates were evaluated by using existing experimental data and qc correlations, in order to provide one of boundary conditions for computational fluid dynamics (CFD) analysis in a primary containment vessel (PCV) of nuclear power plants during accident conditions. Existing qc,fc correlations for forced convection condensation overestimated or underestimated experimental data qc,exp measured with the CONAN facility, and a combination of the selected existing qc,fc correlation and the suction correction factor θC was proposed to obtain good agreement between the qc,cal values computed with the combination and the qc,exp values. For natural convection condensation, it was found that the qc,nc values were largely different between those measured in closed vessels with evaporation and condensation and in flow channels with decreasing the mixture velocity, and hence, the present evaluation focused on qc,nc obtained in the flow channels. It was also found that uncertainty became large when the qc,nc values were computed by changing the Sherwood number Shfc in the qc,fc correlation to Shnc for natural convection. The qc,exp values measured with the COPAIN facility were well expressed by the qc,nc correlation proposed by Corradini (1984, “Turbulent Condensation on a Cold Wall in the Presence of a Noncondensable Gas,” Nucl. Technol., 64(2), pp. 186–195), but the published data were few. Therefore, collection of experimental or numerical qc,nc values is necessary in the future.

Influence of temperature and pressure on the wetting progress in 21700 lithium‐ion battery cells: Experiment, model, and lattice Boltzman simulation

The electrolyte filling and subsequent wetting of the active material is a time‐critical process in the manufacturing of lithium‐ion batteries. Due to the metallic cell housing, the process phenomena are insufficiently accessible, preventing the replication of the wetting processes by mathematical or simulative methods and hindering efforts to accelerate the wetting process. Therefore, this publication employs a glass cell housing for electrolyte filling of a 21700 cylindrical cell to investigate the wetting at different temperatures and process pressures. In parallel, a mathematical replication of the wetting, as well as a lattice Boltzmann pore‐scale simulation, is used to evaluate the influence of these varying process boundary conditions. The results show a strong temperature dependence on electrolyte wetting and the positive effect of pressure changes in the wetting process. These findings are particularly relevant to the process design of large‐scale cylindrical cell manufacturing.

Heuristic assumptions

AbstractInterpreting any decision requires making auxiliary assumptions regarding how the decision makers viewed their options and related them to their lives. Theories constrain those assumptions. The more general the theory, the fewer constraints it imposes and the more assumptions must be made in any application. Like the rational actor models that they challenged, Daniel Kahneman and Amos Tversky’s heuristics-and-biases and prospect theory research programs were general theories, with broad application. One of the many marvels of their landmark studies is that they rarely test their auxiliary assumptions. Rather, readers were trusted to agree about how people interpret the tasks (e.g., select anchors in studies of that heuristic). Subsequent studies have often accepted those interpretations in order to examine boundary conditions (e.g., extreme anchors). Applying the theories to naturally occurring tasks requires making additional auxiliary assumptions. This article illustrates three ways to evaluate those assumptions: direct assessment, systematic manipulation, and archival analysis. It concludes with proposals for loosely coordinated evaluation of shared and contested assumptions.

Stokes flow with Tresca boundary condition: a posteriori error analysis

Stokes flow with Tresca boundary condition: a posteriori error analysis

Fractional Sobolev space: Study of Kirchhoff-Schrödinger systems with singular nonlinearity

This study extensively investigates a specific category of Kirchhoff-Schrödinger systems in fractional Sobolev space with Dirichlet boundary conditions. The main focus is on exploring the existence and multiplicity of non-negative solutions. The non-linearity of the problem generally exhibits singularity. By employing minimization arguments involving the Nehari manifold and a variational approach, we establish the existence and multiplicity of positive solutions for our problem with respect to the parameters \(\eta\) and \(\zeta\) in suitable fractional Sobolev spaces. Our key findings are novel and contribute significantly to the literature on coupled systems of Kirchhoff-Schrödinger system with Dirichlet boundary conditions.

Intensity correlations in measurement-device-independent quantum key distribution

The intensity correlations due to imperfect modulation during the quantum-state preparation in a measurement-device-independent quantum key distribution (MDI QKD) system compromise its security performance. Therefore, it is crucial to assess the impact of intensity correlations on the practical security of MDI QKD systems. In this work, we propose a theoretical model that quantitatively analyzes the secure key rate of MDI QKD systems under intensity correlations. Furthermore, we apply the theoretical model to a practical MDI QKD system with measured intensity correlations, which shows that the system struggles to generate keys efficiently under this model. We also explore the boundary conditions of intensity correlations to generate secret keys. This study extends the security analysis of intensity correlations to MDI QKD protocols, providing a methodology to evaluate the practical security of MDI QKD systems.

First mixed Laplace eigenfunctions with no hot spots

The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in R n \mathbb {R}^n attains its extrema only on the boundary of the domain. We present an analogous problem for domains with mixed Dirichlet-Neumann boundary conditions. We then solve this problem for Euclidean triangles and a class of planar domains bounded by the graphs of certain piecewise smooth functions.

Finite Morse index solutions of a nonlinear Schrödinger equation in half-space with nonlinear boundary value conditions

Finite Morse index solutions of a nonlinear Schrödinger equation in half-space with nonlinear boundary value conditions

Far-Zone Effects for Spherical Integral Transformations II: Formulas for Horizontal Boundary Value Problems and Their Derivatives

AbstractIntegral formulas represent a methodological basis for the determination of gravitational fields generated by planetary bodies. In particular, spherical integral transformations are preferred for their symmetrical properties with the integration domain being the entire surface of the sphere. However, global coverage of boundary values is rarely guaranteed. In practical calculations, we therefore split the spherical surface into a near zone and a far zone, for convenience, by a spherical cap. While the gravitational effect in the near zone can be evaluated by numerical integration over available boundary values, the contribution of the far zone has to be precisely quantified by other means. Far-zone effects for the isotropic integral transformations and those depending on the direct azimuth have adequately been discussed. On the other hand, this subject has only marginally been addressed for the spherical integral formulas that are, except for other variables, also functions of the backward azimuth. In this article, we significantly advance the existing geodetic methodology by deriving the far-zone effects for the two classes of spherical integral transformations: (1) the analytical solutions of the horizontal, horizontal–horizontal, and horizontal–horizontal–horizontal BVPs including their generalisations with arbitrary-order vertical derivative of respective boundary conditions and (2) spatial (vertical, horizontal, or mixed) derivatives of these generalised analytical solutions up to the third order. The integral and spectral forms of the far-zone effects are implemented in MATLAB software package, and their consistency is tested in closed-loop simulations. The presented methodology can be employed in upward/downward continuation of potential field observables or for a quantification of error propagation through spherical integral transformations.