Boundary Conditions Research Articles

The Behaviour of Elbow Elements at Pure Bending Applications Compared to Beam and Shell Element models

Abstract This paper studies the response of ELBOW31 and ELBOW31B element types under pure bending conditions, using shell and beam element models for benchmarking. Various model lengths are evaluated, showing that a model length of six pipe diameters exhibits a hardening effect when total strain exceeds 3.5%, though a strain up to 1% is deemed sufficient for pipeline design. The study examines the effects of ovality modes and boundary conditions such as NOWARP and NOOVAL on the bending response. ELBOW31 with one or two ovality modes yields accurate results, while additional ovality modes or zero ovality mode can lead to overprediction of the elastic bending moment capacity. The introduction of the NOWARP condition enhances the accuracy of the ELBOW31 model, while the NOOVAL condition alone produces unrealistic results. The simplified ELBOW31B model shows good agreement with the ELBOW31-NOWARP model but similarly overpredicts when zero ovality mode is used. The study also finds that Poisson?s ratio and model length have no significant impact on the bending response when no restrictions are applied. Additional analyses, as presented in Appendices A and B, highlight the importance of D/t ratios in pipeline performance. A D/t ratio of 20 offers a stiffer response with reduced ovalization, while a D/t ratio of 50 results in greater flexibility and increased ovalization. These findings provide valuable insights for the selection of element types, boundary conditions, and D/t ratios in robust pipeline design.

USLC: Universal self‐learning control via physical performance policy‐optimization neural network

AbstractThis article proposes an online universal self‐learning control (USLC) algorithm based on a physical performance policy‐optimization neural network, which aims to solve the problem of universal self‐learning optimal control laws for nonlinear systems with various uncertain dynamics. As a key system characterization, this algorithm predicts the discrepancy between the optimal and current control laws by evaluating overall performance in each iterative learning cycle, leveraging an offline‐trained universal policy network. This approach is universal, as it does not rely on an exact system model and can adaptively control performance preferences across various tasks by customizing the physical performance cost weights. Using the established control law‐performance surface and contraction Lyapunov function, the necessary assumptions and proofs for the stable convergence of the system within a three‐dimensional manifold space are provided. To demonstrate the universality of USLC, simulation experiments are conducted on two different systems: a low‐order circuit system and a high‐order variable‐span aircraft attitude control system. The stable control achieved under varying initial values and boundary conditions in each system illustrates the effectiveness of the proposed method. Finally, the limitations of this study are discussed.

Effects of rotation and chemical reactions on an electroconvection in Maxwell dielectric nanofluids within anisotropic porous media

ABSTRACT This study explores the complex interactions between rotation, chemical reactions, and electroconvection in Maxwell dielectric nanofluids within anisotropic porous media. The research aims to elucidate how these factors influence the heat transfer efficiency and fluid dynamics under the influence of external alternating current (AC) electric fields. The normal mode method is employed to analyse the stability of the system, allowing for the examination of oscillatory modes and their growth rates. By introducing perturbations in the physical parameters, the study derives a set of ordinary linear differential equations that characterize the system's response to external influences. The coupled differential equations were solved using the Galerkin approach for first approximation while meeting the necessary boundary conditions. Analytical solution of the representative equation for stress-free boundary states yields Rayleigh number formulas for nonoscillatory and oscillatory mode occur. Oscillatory modes are seen for both bottom and top-heavy nanoparticle distributions. The electric Rayleigh number, thermal Prandtl number, and stress relaxation parameter increases, whereas the Brinkman-Darcy number delays the onset of stationary and oscillatory convection. The study finds that positive concentration Rayleigh numbers stabilize the system, while negative ones lead to instability. Additionally, it demonstrates that external alternating current electric fields influence convection behavior and provides formulas for critical Rayleigh numbers, enhancing our understanding of fluid interactions in various engineering and technological applications.

Influence of cognitive control on the moral foreign language effect

Purpose: The Moral Foreign Language Effect (MFLE) is characterized by an increase in utilitarian responding when moral dilemmas are presented in a foreign language. Renewed interest in this psycholinguistic phenomenon has led to investigation of its boundary conditions and the modulatory influence of separable dimensions of foreign language experience. However, even when accounting for these additional differences, considerable variability in the MFLE is observed across participants. Recently, cognitive control, a set of mental processes that regulate thinking and behavior, has been identified as a potential modulator of the MFLE. To date, no studies have investigated whether differences in cognitive control influence the emergence of the MFLE. The present study aimed to directly explore this topic in a sample of Mandarin-English bilingual university students in Mainland China. Methodology: Participants responded to a set of moral dilemmas presented in either their native or foreign language and completed a Simon task to assess cognitive control. Findings: We report a dilemma and language context-specific modulatory role for cognitive control on the MFLE. Specifically, when presented in a foreign language, higher levels of cognitive control were associated with higher rates of utilitarian decisions on the classic Trolley dilemma. Originality: This study marks the first empirical investigation of the influence of cognitive control on the MFLE. Significance: Findings from this work highlight the role of cognitive control in moral decision-making and chart a course for future investigations on this topic.

Transition Path Dynamics of Non-Markovian Systems across a Rough Potential Barrier.

Transition paths refer to rare events in physics, chemistry, and biology where the molecules cross barriers separating stable molecular conformations. The conventional analysis of the transition path times employs a diffusive and memoryless transition over a smooth potential barrier. However, it is widely acknowledged that the free energy profile between two minima in biomolecular processes is inherently not smooth. In this article, we discuss a theoretical model with a parabolic rough potential barrier and obtain analytical results of the transition path distribution and mean transition path times by incorporating absorbing boundary conditions across the boundaries under the driving of Gaussian white noise. Further, the influence of anomalous dynamics in rough potential driven by a power-law memory kernel is analyzed by deriving a time-dependent scaled diffusion coefficient that coarse-grains the effects of roughness, and the system's dynamics is reduced to a scaled diffusion on a smooth potential. Our theoretical results are tested and validated against numerical simulations. The findings of our study show the influence of the boundary conditions, barrier height, barrier roughness, and memory effect on the transition path time distributions in a rough potential, and the validity of the scaling diffusion coefficient has been discussed.

Programmable orientation of blue phase soft photonic crystal

Understanding the structure formation and its underlying physical mechanism is a fundamental topic in condensed matter systems, with both academic and practical implications. Soft matter is playing a remarkable role in current era of information explosion, demonstrating enormous potential in integrated functional photonics. As unique soft photonic crystals with cubic symmetries, not only liquid crystalline blue phases (BPs) have circularly polarized selective reflection and ultra-fast electro-optical response, but also their three-dimensional photonic structures increase degrees-of-freedom for multiplexed optical modulation. In the thriving field of soft-matter-based photonics, precise and programmable engineering of BP crystal orientation is of vital importance for planar optical elements, which remains a challenging task due to the complexity of the nucleation process as well as the interaction between the BP building blocks and the boundary conditions. Aiming to gain a comprehensive understanding of how to tailor the orientation of BP crystals for the photonic applications of next generation, here we discuss the solutions for uniformity improvement and orientation control of BP crystals, about which a few of examples in combination with the underlying mechanisms are explained. In addition, the remaining challenges and the efforts that are expected are also reviewed. We expect this work provides a deeper understanding of phase transitions and resulting structures in soft crystals, which may open encouraging perspectives for their applications in photonics, biosensing, interfacial, and chemical engineering.

New method for predicting the free vibration characteristics of composite laminates based on generalized cell and spectral‐Tchebychev methods

AbstractThis paper presents a new method for analyzing the free vibration characteristics of composite laminates under arbitrary boundary conditions by integrating the generalized method of cells (GMC) and the Two‐Dimensional Spectral‐Tchebychev (2D‐ST) method. First, a meso‐macro correlation matrix is constructed based on the GMC, and the macroscopic performance parameters of the composite laminates are predicted. Then, virtual boundary springs are introduced to simulate the arbitrary boundary conditions, and the energy equation of the laminate is derived based on the first‐order shear deformation theory (FSDT) and Hamilton's principle. Furthermore, an approximate displacement function of the laminate is derived by using the 2D‐ST Tchebychev polynomials, and the Gauss‐Lobatto points are selected for meshless discretization of the structure to obtain the discretized characteristic equation, which is solved to obtain the free vibration frequency of the laminate. Based on Matlab programming, the free vibration frequencies of the laminate under different conditions are calculated, and the convergence, accuracy and computational efficiency of the calculation method are discussed, and the effects of boundary conditions, stacking angle, geometrical parameters, and material parameters on the free vibration frequencies of the laminate are analyzed. The numerical results show that the method has the advantages of fast convergence, high accuracy and high efficiency, and the method can be convenient and fast for parametric studies.Highlights The free vibration characteristics of composite laminates are studied. Combining generalized cell method with spectral‐Tchebychev method. The method has the characteristics of fast convergence, high accuracy and high efficiency. A parametric study is conducted on the free vibration of laminated panels.

Fast and Efficient Lunar Finite Element Gravity Model

In this paper, the finite element method (FEM) is integrated with orthogonal polynomial approximation in high-dimensional spaces to innovatively model the Moon’s surface gravity anomaly. The aim is to approximate solutions to Laplace’s classical differential equations of gravity, employing classical Chebyshev polynomials as basis functions. Using classical Chebyshev polynomials as basis functions, the least-squares approximation was used to approximate discrete samples of the approximation function. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. The first application of this project is to substitute the globally valid classical spherical harmonic series of approximations with locally valid series of orthogonal polynomial approximations (i.e., using the FEM approach). With an error tolerance set at 10−9ms−2, this method is used to adapt the gravity model radially upwards from the lunar surface. The results showcase a need for a higher degree of approximation on and near the lunar surface, with the necessity decreasing as the radius increases. Notably, this method achieves a computational speedup of five orders of magnitude when applying the method to radial adaptation. More intrinsically, the second application involves using the methodology as an effective tool in solving boundary value problems. Specifically, this approach is implemented to solve classical differential equations involved with high-precision, long-term orbit propagation. This application provides a four-order-of-magnitude speedup in computational time while maintaining an error within the 10−10ms−2 error range for various orbit propagation tests. Alongside the advancements in orthogonal approximation theory, the FEM enables revolutionary speedups in orbit propagation without compromising accuracy.

Stability of complement value problems for p-Lévy operators

We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear nonlocal integro-differential p-Lévy operators. A prototypical example of integro-differential p-Lévy operators is the well-known fractional p-Laplace operator. Our main focus is on nonlinear integro-differential equations in the presence of Dirichlet, Neumann and Robin conditions and we show well-posedness results. Several results are new even for the fractional p-Laplace operator but we develop the approach for general translation-invariant nonlocal operators. We also bridge the gap from nonlocal to local, by showing that solutions to the local Dirichlet and Neumann boundary value problems associated with p-Laplacian are strong limits of the nonlocal ones.

Exploring Novel Fixed Point Solutions in Boundary Value Problems

Within this manuscript, we present an innovative concept of contraction, building upon the foundation laid by Jleli and Samet. Subsequently, we introduce the concept of θ-contractions. Leveraging these novel ideas, we formulate a series of fresh fixed-point theorems applicable to spaces utilizing the Controlled Branciari metric. Notably, our approach integrates and consolidates diverse fixed-point outcomes, eliminating the necessity for the Hausdorff assumption. To illustrate the practicality of our findings, we provide examples and applications to boundary value problems associated with fourth-order differential equations.

Multiplicity results for Schrodinger type fractional p-Laplacian boundary value problems

In this work, we study the existence and multiplicity of solutions to the problem $$\displaylines{ -(\Delta)_p^s u + V(x)|u|^{p-2}u = \lambda f(u),\quad x\in\Omega;\cr u=0,\quad x\in \mathbb{R}^N\backslash\Omega, }$$ where \(\Omega\subset\mathbb{R}^N\) is an open bounded set with Lipschitz boundary \(\partial\Omega\), \(N\geqslant 2\), \(V\in L^{\infty}(\mathbb{R}^N)\), and \((-\Delta)_p^s\) denotes the fractional p-Laplacian with \(s\in(0,1)\), \(1<p\), \(sp<N\), \(\lambda>0\), and \(f:\mathbb{R}\to\mathbb{R}\) is a continuous function. We extend the results of Lopera et al [22] by proving the existence of a second weak solution to this problem. We apply a variant of the mountain-pass theorem due to Hofer [15] and infinite-dimensional Morse theory to obtain the existence of at least two solutions. For more information see https://ejde.math.txstate.edu/Volumes/2024/72/abstr.html

Influence of rope fastening on the spectrum of its natural transverse vibrations

According to the previously developed method, which takes into account the bending stiffness of steel ropes during their transverse oscillation, the ropes of the pedestrian bridge ‘Lovers’ in the city of Tyumen were investigated. The obtained values of tension forces and bending stiffness were within the expected range. The high variation of bending stiffness values forced to pay attention to the accuracy of the initial values of rope lengths, which were obtained from the photograph. To measure the rope lengths, a method of nodal harmonic registration was proposed, but the results obtained by this method were higher than the values obtained from the photograph. The evaluation of measurement errors did not explain this overestimation, which led to the necessity to revise the solution of the differential equation of transverse oscillations. It turned out that previously only its partial solution was considered, assuming a hinged rope attachment, whereas it is cantilevered and has a bending reaction. Taking this feature into account by introducing an additional boundary condition allowed to improve the calculation model and explain the overestimation of the rope length in the method of nodal harmonics.Taking into account the nature of the rope attachment allowed us to introduce a generalised parameter s, which takes zero value for rigid cantilever attachment, and is equal to one for articulated attachment. Then the stiffness weakening inside the anchorage will be manifested by the growth of the parameter s and can be detected by the results of the oscillation spectrum registration.

Bolstering the initiative of construction project members: a self-determination lens combining project social media use

PurposeIn today’s turbulent and complex era, initiative behavior is becoming more drawn to construction projects but challenging to arouse as it is free of the established regulations in project practice. Given the prevalence of social media (SM) in modern workplaces, this study is thereby motivated to investigate whether and how SM use can act to drive initiative behavior of construction project members (PMs) in this context.Design/methodology/approachThis study sharply examines two distinct types of SM use – work-related and social-related – to explore their roles in driving the initiative behavior of construction PMs. Additionally, self-determination theory is employed to explore their underlying translation mechanisms and associated boundary conditions. A survey dataset collected from 229 construction PMs is used to empirically test the proposed theoretical model.FindingsEmpirical results show that role-breadth self-efficacy, psychological safety and project identification, by satisfying basic psychological needs respectively, act as crucial bridging roles in translating SM use into initiative behavior of PMs. Such mediation effects are applied to both work-related and social-related SM use with varied mechanisms. Besides, prevention focus is found to be a contingent moderator on these relationships, with a strengthening role toward role-breadth self-efficacy and a weakening role toward project identification.Originality/valueThis study digs into the nuanced mechanisms of how SM use benefits construction projects, especially in terms of PMs’ initiative. The findings of this research afford new insights into effectively invigorating the initiative behavior of construction PMs under the current digital momentum.

New a Priori estimate for stochastic 2D Navier–Stokes equations with applications to invariant measure

AbstractThe paper deals with the stochastic two-dimensional Navier–Stokes equations for homogeneous and incompressible fluids, set in a bounded domain with Dirichlet boundary conditions. We consider additive noise in the form $$G\,\textrm{d}W$$ G d W , where W is a cylindrical Wiener process and G a bounded linear operator with range dense in the domain of $$A^\gamma $$ A γ , A being the Stokes operator. While it is known that existence of invariant measure holds for $$\gamma >1/4$$ γ > 1 / 4 , previous results show its uniqueness only for $$\gamma > 3/8$$ γ > 3 / 8 . We fill this gap and prove uniqueness and strong mixing property in the range $$\gamma \in (1/4, 3/8]$$ γ ∈ ( 1 / 4 , 3 / 8 ] by adapting the so-called Sobolevskiĭ-Kato-Fujita approach to the stochastic N–S equations. This method provides new a priori estimates, which entail both better regularity in space for the solution and strong Feller and irreducibility properties for the associated Markov semigroup.

Numerical Computation and Statistical Interpretations of Heat Transfer of Tween-20/ethyl Acetate Nanofluid Flow with Melting Rheological Quality and Activation Energy

Tween-20 plays a significant role in the biological, food, and pharmaceutical industries. Additionally, it plays a vital role in improving the quality of reverse mechanisms of multi-drug resistance. This paper uses artificial neural computing to examine Tween-20 nanoparticles’ behaviors in a base fluid called ethyl acetate to enhance the applications in nanomedicine, drug delivery and biotechnology. The study focuses on the nonlinear model of a viscous fluid at the stagnation point, where mixed convection processes and activation energy are present. The study incorporates slip velocity and melting boundary conditions to examine heat and mass transfer, taking into account thermal and solutal stratification. Various fields of research and technology, specially in industrial engineering that include hydrodynamics, panto-graph systems, and biomedical mathematics, extensively utilize artificial computing. The datasets are based on velocity, temperature, and concentration outlines. The fourth-order Runge-Kutta method is used to generate the datasets. To validate the LMM-ABNNs, we have compared them with a numerical solution, showing a high level of agreement. We utilize the error histogram and mean square error results to validate the performance, scrutinize the training and testing methods, and explore the validity of the approximate answer. Furthermore, the quality characteristics such as skin friction, rate of heat, and mass movement (Nusselt and Sherwood numbers) are statistically analyzed to forecast the model’s durability. This article is the best example of investigating different fluid parameters with the latest artificial neural computing.

Dynamics of Viscous Jeffrey Fluid Flow Through Darcian Medium With Hall Current and Quadratic Buoyancy.

This contribution builds on existing studies by investigating the dynamics of Hall current in Jeffery fluid under radiative heat, convective boundary conditions, Joule heating, and Darcy dissipation. Hall current, an important phenomenon in engineering applications involving strong magnetic fields, highlights the impact of electromagnetic force in examining blood flow rate, determining charge drift velocity, density, and movement, and is used in power generators and high-voltage transformers. This analysis incorporates dissipative and thermal radiative heat and employs the effects of Hall current and Joule heating, resulting from porous medium resistance, to derive the partial differential equationsgoverning the dynamic systems. These equationsare then reduced to ordinary differential equations (ODEs) through similarity variables. The Galerkin weighted residual method (GWRM) is employed to examine the dynamics of Hall current and quadratic thermal buoyancy, shedding light on the thermal properties and hydrodynamics of Jeffrey fluid convection within a porous medium. The analysis reveals that in the presence of an applied magnetic field, the contribution of Hall current to flow and heat dynamics induces a magnetic force that enhances fluid motion and negatively impacts heat energy patterns. The imposition of dissipative heat physically increases the fluid temperature, owing to an increase in buoyancy current. The occurrence of thermal radiation, Hall current, viscous dissipation, and Joule heating can efficiently optimize the rate of heat transfer and shear stress. Moreover, the tabular results indicate that Jeffrey fluid, exhibiting higher relaxation time, will experience a lower friction coefficient and heat transferrate.

Identifying the Most Probable Transition Path with Constant Advance Replicas.

Locating plausible transition paths and enhanced sampling of rare events are fundamental to understanding the functional dynamics of biomolecules. Here, a constraint-based constant advance replicas (CAR) formalism of reaction paths is reported for identifying the most probable transition path (MPTP) between two given states. We derive the temporal-integrated effective dynamics governing the projected subsystem under the holonomic CAR path constraints and show that a dynamical action functional can be defined and used for optimizing the MPTP. We further demonstrate how the CAR MPTP can be located by asymptotically minimizing an upper bound of the CAR action functional using a variational expectation-maximization framework. Essential thermodynamics and kinetic observables are retrieved by integrating the boxed molecular dynamics on the CAR MPTP using a newly proposed adaptive reflecting boundary condition. The efficiency of the proposed method is demonstrated for the Müller potential, the alanine dipeptide isomerization, and the DNA base pairing transition (Watson-Crick to Hoogsteen) in explicit solvent. The CAR representation of transition paths constitutes a robust and extensible platform that can be combined with diverse enhanced sampling methods to aid future flexible and reliable biomolecular simulations.

Identification of Boundary Conditions in a Spherical Heat Conduction Transmission Problem

Although numerous analytical and numerical methods have been developed for inverse heat conduction problems in single-layer materials, few methods address such problems in composite materials. The following paper studies inverse interface problems with unknown boundary conditions by using interior point observations for heat equations with spherical symmetry. The zero degeneracy at the left interval 0<r<R1 leads to solution difficulties in the one-dimensional interface problem. So, we first investigate the well-posedness of the direct (forward) problem in special weighted Sobolev spaces. Then, we formulate three groups of unknown boundary conditions and inverse problems upon internal point measurements for the heat equation with spherical symmetry. Second-order finite difference scheme approaches for direct and inverse problems are developed. Computational test examples illustrate the theoretical statements proposed.

Unveiling the nature of peer development groups: A systematic review, conceptual framework, and research pathways

SummaryThis research provides a systematic review of the literature on peer development groups (PDGs), a promising yet underexplored tool for individual and leadership development. Despite the growing interest in PDGs from both scholars and practitioners, the field remains fragmented, with inconsistent terminologies and limited theoretical grounding. This review seeks to clarify the core components, boundary conditions, inputs, processes, and outcomes of effective PDGs in professional settings, addressing the confusion and gaps in existing research. By adopting an adjudication approach, we provide a comprehensive synthesis of the evidence regarding the defining characteristics of PDGs and their impacts on individual development. We propose a new, scholarly definition of PDGs as organized small groups consisting of members of perceived similar status and roles who regularly meet to foster mutual growth by providing a supportive environment and a flexible agenda. We develop a conceptual framework that links key variables influencing PDG effectiveness and offers actionable insights for both researchers and practitioners. Our findings highlight opportunities for future research and suggest practical implications for implementing PDGs in organizational settings, ultimately contributing to a more cohesive and theoretically informed understanding of this valuable developmental practice.

Investigation of activation energy of Maxwell fluid with Newtonian heat effect at the boundary layer flow on a cylinder embedded in porous medium

AbstractThis study aims to investigate the flow of Maxwell fluid over a cylinder, considering the combined effect of Magnetohydrodynamics (MHD) and a permeable medium on the equation of momentum, heat generation and radiation on the equation of energy, and activation energy on the mass equation. The objective is to analyze the impression of these physical phenomena on the fluid's behavior under specified boundary conditions, with a focus on the Newtonian heating effect. The significance of this research lies in its application to industrial processes, polymer extrusion and cooling of metallic sheets, where controlling fluid flow and energy transfer is crucial. The dimensional governing equations for momentum, energy, and concentration were changed into non‐dimensional forms via appropriate dimensionless quantities and similarity variables. The subsequent nonlinear ordinary differential equations were answered using the BPV4C inbuilt MATLAB solver. The key findings reveal that the concentration outline rises with a rise in activation energy and declines with a rise in the chemical reaction. Additionally, the Nusselt number profile displays an increasing trend with the Newtonian heating parameter, indicating enhanced heat transfer. Quantitative results demonstrate that the occurrence of a porous medium and MHD significantly impacts the velocity and temperature contours. The real‐time application of this study can be seen in the optimization and design of chemical reactors, heat exchangers, and cooling systems in engineering processes. The developed model delivers insights into controlling energy and mass transfer in processes involving stretching surfaces, which is essential for improving efficiency and product excellence in various industrial applications.