Boundary Conditions Research Articles

An improved radial basis reproducing kernel particle method for geometrically nonlinear problem analysis of SMAs

In this paper, the radial basis function (RBF) without shaped parameter is utilized in the radial basis reproducing kernel particle method (RRKPM), and an improved radial basis reproducing kernel particle method (IRRKPM) is proposed. Compared with traditional RKPM, the IRRKPM effectively reduces the impact of different kernel functions on calculation precision, and is further employed to examine geometrically nonlinear problems associated with shape memory alloys (SMAs). The displacement boundary condition is enforced via the penalty function method, while the Galerkin integration method in its weak form, along with the total Lagrangian (TL) approach, is utilized to derive the geometrically nonlinear equations for SMAs within the IRRKPM framework. The equilibrium equations are then solved using the Newton Raphson (N-R) iterative method. The impact of the different penalty factor and the radius control parameter of influence domain on errors is analyzed, the computational precision of the IRRKPM is compared with the RRKPM, and the computational stability is evaluated. Finally, the suitability of the IRRKPM for the analysis of geometrically nonlinearity problems in SMAs are confirmed through specific numerical examples.

Vibration and Stability Analyses of Submarine Fluid-Conveying Pipelines with Local Stiffness Variation Under External Flow Fields

This study analyzes the vibration and stability characteristics of a submarine fluid-conveying pipeline with local variation in stiffness under the influence of external flow fields. Utilizing the absolute nodal coordinate formulation (ANCF), the dynamic equation for the submarine pipeline with local stiffness variation under arbitrary boundary conditions is derived. Through numerical solutions, curves depicting complex frequency variations as a function of the internal flow velocity of the pipeline system are obtained. Additionally, the effects of external flow velocity, geometrical parameters, and local stiffness variation on the vibration and stability characteristics of the submarine pipeline under three different boundary conditions are investigated. Results indicate that the stability of the pipeline system decreases across the three boundary conditions under the influence of the external flow field. Increased external flow velocities lead to further reductions in system stability. Furthermore, as the length-to-diameter ratio increases and the thickness-to-diameter ratio decreases, the first three orders of frequencies of the pipeline gradually diminish. Enhancing local stiffness contributes to improving the stability of the system, whereas reducing local stiffness has the opposite effect.

A Review of Research on The Impact of Differential Order Atmosphere

At present, research on the differential order atmosphere mainly focuses on its impact. The outcome variables mainly focus on behavior, and cognition and emotion are often used as mediating variables between perceived differential order atmosphere and employee work behavior. Scholars have not reached a consensus on whether the impact of a differential order atmosphere on employee behavior, cognition, and emotions is negative or positive. The research on the outcome variables of differential order atmosphere mainly focuses on three aspects: team and individual performance, employee silence and indifference behavior, and knowledge sharing and destruction. Some research on the differential order atmosphere currently only focuses on the consequences of its effects, without delving into the underlying mechanisms; Moreover, the impact of differential order atmosphere on employee behavior, cognition, and emotions is uncertain, and the effect of differential order atmosphere may have boundary conditions. Previous studies have explained this through organizational factors, leadership factors, and personal factors such as team trust, narcissistic leadership, regulatory orientation, and psychological resilience.

Numerical solutions of boundary value problems via fixed point iteration

Numerical solutions of boundary value problems via fixed point iteration

Solvability of initial boundary value problems for a quasihydrodynamic system of equations in the case of a weakly compressible fluid

Subject of research: solvability of the first initial-boundary value problem for a quasi-hydrodynamic system of equations in the case of a weakly compressible fluid. Method of research: the proof is based on the Galerkin method using a priori estimates. Main results of research: the existence theorem for generalized solutions is proven.

Horizontal well hydraulics in leaky confined aquifer near a stream: analytical solutions for induced drawdown and water budget components.

Horizontal wells have gained popularity as a technology for exploring water resources and remediating aquifers over the last decades, due to costs and numerous technical benefits compared to traditional vertical wells. This study presents a set of analytical solutions for drawdown distribution and various components of water budget contributing to flow toward a horizontal well in an aquifer-aquitard system interacting with a fully penetrating stream. It is assumed that the water level in the upper unconfined aquifer remains fixed at a specific elevation during the course of the pumping in the lower leaky aquifer. The water budget components account for inflows from aquifer storage, stream depletion, and leakage across the aquifer-aquitard interface. Analytical solutions to this three-dimensional, transient, non-axisymmetric Darcian flow model are given for both transient and steady-state flow conditions, relying on a four-fold integral transform technique that includes a Robin-type boundary condition at the aquifer-aquitard interface. It is shown how various components of water budget collectively counterbalance the effect of pumping discharge, confirming that the mass is conserved under both continuous and non-continuous pumping scenarios. Response maps are prepared to assess how different components of water budget react to changes in the well position. Furthermore, it is found that the components of water budget are most sensitive to the well-to-stream distance and anisotropy ratio of the leaky aquifer.

Boundary Element Method for Viscous Flow through Out-phase Slip-patterned Microchannel under the Influence of Inclined Magnetic Field

Abstract In this paper, we investigate the impact of an inclined magnetic field of uniform intensity on viscous, incompressible pressure-driven Stokes flow through a slip-patterned, rectangular microchannel using the boundary element method based on the stream function-vorticity variables approach. The present investigation focuses only on the out-phase slip patterning of the microchannel walls. We address two scenarios of slip patterning, specifically large and fine slip patterning, which are determined by the periodicity of the patterning. We utilized the no-slip and Navier’s slip boundary conditions in an alternative manner on the walls. The Stokes equations govern the viscous flow through a microchannel. We assume a very small magnetic Reynold’s number to eliminate the equation of induced magnetic field in the present study. We analyzed the impact of considered dimensionless hydrodynamic parameters, including the Hartman number (Ha), inclination angle (θ) of the magnetic field, and the slip length (ls ) on fluid dynamics. In the case of fine slip, we observed significant variations in both velocity and pressure gradient, in contrast to large slip patterning. Fine slip patterning significantly increases the shear stress at slip regimes, while large slip periodicity significantly reduces it at no-slip regimes. The present investigation has several notable implications, such as regulation and advancement of mixing and heat transmission within microfluidic systems.

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N, due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.

Modeling photomolecular effect using generalized boundary conditions for Maxwell equations

We recently demonstrated via experiments in hydrogels and at a single air-water interface the photomolecular effect: photons directly cleaving off water molecular clusters in the visible spectrum where bulk water has negligible absorption. To model single interface experiments, here we re-derive generalized boundary conditions for Maxwell equations by assuming a transition region of the electromagnetic fields across the interface, leading naturally to the Feibelman parameters used before to describe surface photoelectric and surface plasmon effects on metals. This generalization leads to modifications of the Fresnel coefficients and an expression for the surface absorptance that can reasonably explain trends in our single-interface experimental data on the angle and polarization dependence of the beam deflection. Our work provides further support for the existence of the photomolecular effect, suggests that surface absorption should exist in many materials, and lays a foundation for assessing the impacts of such surface absorption based on the Maxwell equations.

Warped CFT duals of the Plebański-Demiański family of solutions

In this paper, we analyze the symmetry properties of the complete family of type D spacetimes generalized form the Plebański-Demiański solution in four dimensions holographically in terms of a warped CFT. The generalized Plebański-Demiański solutions are black hole-like spacetimes characterized by seven physical parameters. Most of the black holes in four dimensions are included within this family. Generically consider a solution with horizon in this family, we figure out the possible warped conformal symmetry attached to the horizon. The horizon can be either extremal or non-extremal. In the extremal case, the near horizon region can be mapped to an infinite spacetime with geometry given by a warped and twist product of AdS2 and S2. The new boundary conditions for AdS2 as well as their higher dimensional uplifts are applied here to manifest the asymptotic symmetry as the warped conformal symmetry. In the non-extremal case, the global warped conformal symmetry is singled out by analyzing the scalar wave equation with constant frequency. The local warped conformal symmetries are represented by the charge algebra associated to the vector fields which preserve the scalar wave equation as well as its frequency. In defining the variation of the covariant charges, a proper counterterm is introduced for consistency conditions which is supposed to be suitable for all the solutions within the family. As a consistency check, the horizon entropy is reproduced by the entropy formula of the warped CFT by using its modular covariance and the central terms derived in the bulk spacetimes.

Quantum lozenge tiling and entanglement phase transition

While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system L as Llog⁡L. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.

CFD Simulations of the Molten Salt Fast Reactor

The molten salt fast reactor (MSFR) is a fast-spectrum molten salt reactor concept, where the fuel salt flows freely through a toroidal core (2 m high × 2 m in diameter). The flow through this core is turbulent (Reynolds number ≈ 5 × 10 5 ) and presents several recirculation areas. Several thermal-hydraulic studies of the steady-state MSFR flow have been performed, where the thermal power distribution was fixed and the Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) approaches were used. Different geometries were considered, from 1/16th of the core to the full core. The RANS simulations were performed first. The use of symmetry boundary conditions in these simulations had a very limited impact on the results while greatly speeding up the calculations. In the LES formulation, however, the symmetry boundary conditions had a large impact on the velocity and temperature fields, and so could not be used. While the RANS fields and the LES mean fields differed quite heavily, no particular hot spots appeared in the LES fields. Analysis of the LES temperature evolution in the center of the core revealed fluctuations of ± 20°C at a speed of 100°C·s−1.

Experimental and Numerical Analysis of the Impact of Corrosion on the Failure Pressure of API 5L X65 Pipeline

This paper employs the Finite Element Method (FEM) to simulate and analyze the effects of corrosion defect parameters on the stress and failure pressure of pipelines. It investigates how the boundary conditions of the pipeline model influence stress and examines the sensitivity of failure pressure to corrosion defect parameters. A nonlinear regression equation has been developed from a dataset obtained through simulation experiments to predict the failure pressure of corroded pipelines. To validate the effects of corrosion defect parameters on failure pressure, a hydrostatic test platform for an API 5L X65 pipeline with corrosion defects was established to measure stress levels and failure pressures across varying corrosion defects. This study reveals that failure pressure is negatively correlated with corrosion length and depth, while positively correlated with corrosion width. Among these parameters, corrosion depth exerts a more significant influence on the pipeline’s failure pressure than corrosion length and width. Within the range of corrosion defect parameters examined, the maximum deviation of the prediction equation’s results from the simulation results is 8.71%, with an average deviation of 5.81%. The standard deviation of the fitted residuals is 0.01837. Additionally, the maximum deviation between the predicted results and experimental measurements is 8.39%, with an average deviation of 7.77%. The strong agreement between the predicted results from the equation and the actual measured data underscores the effectiveness of the nonlinear regression equation.

Dual-hollow-core anti-resonant fiber with silicon layers and nested resonant tubes for constructing a single-polarization 3 dB coupler

A novel dual-hollow-core anti-resonant fiber (DHC-ARF) with silicon layers and nested resonant tubes is proposed for constructing a 3 dB single-polarization coupler. High-index silicon layers are deposited inside four cladding tubes along the x-direction and then nested resonant tubes are introduced into these cladding tubes, which is beneficial to promote the mode coupling between the x-polarized fundamental mode and the dielectric mode in the silica/silicon tubes so as to achieve single-polarization characteristics of the DHC-ARF. The properties of the DHC-ARF are optimized using finite element method combined with perfectly matched layer as a boundary condition. By using a 1.51 cm long DHC-ARF, a single-polarization 3 dB coupler is constructed with a relatively wide bandwidth of 29 nm covering the wavelength range from 1530 nm to 1559 nm, in which the polarization extinction ratio (PER) is lower than -20 dB and the coupling ratio can be guaranteed within 50 ± 2%. This bandwidth is more than 2.6 times higher than the bandwidth of currently reported single-polarization coupler. At the wavelength of 1550 nm, the lowest PER reaches -74.8 dB and the loss of the coupler is as low as 0.33 dB.

A size‐dependent model of strain gradient elastic laminated micro‐beams with a weak adhesive layer

AbstractA size‐dependent model for a laminated micro‐beam with a soft adhesive is developed in the framework of strain gradient elasticity theory. The layered beam is constituted by two Euler–Bernoulli strain gradient elastic isotropic beams, joined through a strain gradient spring‐type contact law at the adhesive level. The governing bending and extensional equations and boundary conditions are obtained by using the variational principle. The differential system shows a coupling between the flexural and axial behaviors of the upper and lower beams, due to the presence of interface terms related to shear and peeling stresses. Two benchmark problems have been presented through their closed‐form solutions, namely a simply‐supported laminated beam subjected to a uniform distributed load and a mode 2‐type loading configuration of a layered axially deformable beam. Size effects and non‐local phenomena, due to high strain concentrations, are highlighted. Though simple in their features, the examples prove the efficiency of the proposed approach in designing micro‐scale layered beams.

Paradigm on Levenberg–Marquardt neural algorithm analysis of heat conduction optimization for ternary hybrid nanofluid with entropy generation

AbstractThe significance of the present article is to enhance the thermal management and energy efficiency of complex engineering infrastructures such as energy storage systems, modern electric vehicles, thermal insulations, heavy‐duty machinery, and production units. This research aims to understand the intricate relationship between the thermal conductivity performance of ternary () hybrid nanomaterial and entropy generation to optimize material design and efficacy. A synergetic combination of three distinct nanomaterials silicon dioxide, ferric oxide, and titanium oxide with ethylene glycol and water in the ratio 3:2 as a base solvent is comprised of contributing unique thermophysical properties. To elucidate the impact of this hybrid composition on thermal conductivity, various factors are analyzed. The advanced computational technique of Artificial intelligent feed‐forward neural network (AIFFNN) is utilized. The problem governed the system of PDEs, which is transformed into ODEs by dimensionless similarity. Adams method provided the dataset which is filtered and embedded into Marquardt–Levenberg Algorithm (LMA). The study examines the role of nanomaterial constituents, morphology, and boundary conditions on thermal performance and entropy generation. Graphical analysis of velocity, temperature, and entropy is provided with respect to varying parameters, including surface absorption (λ), magnetic strength (Tesla M), radiation parameter (Rd), Brownian motion (Br), and Eckert number (Ec). The findings have practical significance for optimizing material design in engineering and industrial applications.

Analysis of shear horizontal waves in heterogeneous/microstructural coupled plates: exploring the influence of interfacial bonding and the boundary conditions

Analysis of shear horizontal waves in heterogeneous/microstructural coupled plates: exploring the influence of interfacial bonding and the boundary conditions

A nonlinear least-squares convexity enforcing 𝐶⁰ interior penalty method for the Monge–Ampère equation on strictly convex smooth planar domains

We construct a nonlinear least-squares finite element method for computing the smooth convex solutions of the Dirichlet boundary value problem of the Monge-Ampère equation on strictly convex smooth domains in R 2 {\mathbb {R}}^2 . It is based on an isoparametric C 0 C^0 finite element space with exotic degrees of freedom that can enforce the convexity of the approximate solutions. A priori and a posteriori error estimates together with corroborating numerical results are presented.

Spatially mixed implicit–explicit schemes in hydro-mechanically coupled soil dynamics

Mixed implicit–explicit (IMEX) schemes combine elements of both implicit and explicit time integration methods. This allows to efficiently handle boundary value problems with severe differences in stiffness, such as often encountered in soil dynamics. A spatially mixed IMEX scheme, in which different parts of the computational domain may be treated implicitly or explicitly depending on their behaviour, is discussed in this work. Domain decomposition by means of a mortar contact discretisation is used for this purpose and multiple systems of equations are solved. The merits of the scheme in solving problems of soil dynamics are demonstrated, for which the governing equations are extended to hydro-mechanical coupling.

Spectral Tau Method with Legendre Polynomials to Approximate Second Order Boundary Value Problem

Spectral Tau Method with Legendre Polynomials to Approximate Second Order Boundary Value Problem