Boundary Conditions In Order Research Articles

Comment on: “Effects of rotation on the Landau levels in an elastic medium with a spiral dislocation”

In this Comment we analyse a model proposed recently with the purpose of studying the effects of rotation on the interaction of a point charge with a uniform magnetic field in an elastic medium with a spiral dislocation. In particular we focus on the approximation proposed by the authors that consists of changing the left boundary condition in order to obtain analytical results. We show that this approximation leads to quantitative and qualitative errors, the most relevant one being a wrong prediction of the level spacing.

3D numerical simulations and microstructural modeling of anisotropic and tension–compression asymmetric ductile materials

In the present work, we have analyzed the effect of anisotropy on void growth and stress–strain behavior for materials that exhibit remarkable tension–compression asymmetry (i.e., zirconium alloys). For that purpose, we have performed finite element simulations using a cubic 3D cell with a spherical void inside and subjected to periodic boundary conditions. Nonlinear kinematic constraints are also imposed as boundary conditions in order to maintain the values of macroscopic ratios constant during the whole loading history of the cell and account for a general (3D) stress state. The behavior of the matrix material is described by the CPB06 anisotropic criterion developed by Cazacu et al. (2006). The numerical results are compared to those considering 3D homogeneous (without void) cell with the same initial porosity as the voided one and governed by the anisotropic porous yield criterion developed by Stewart and Cazacu (2011). To investigate the influence of prescribed stress, strength differential parameter and strain hardening exponent on stress–strain behavior and void growth in the non-homogeneous (with void) and the homogeneous (without void) cells, we have used several stress ratios, three strength differential parameters and three strain hardening exponents. Finite element results obtained from different stress ratios show the strength differential parameter significantly affect void growth in both homogeneous and non-homogeneous cells. Moreover, comparison of two cells proves that both stress–strain behavior and porosity evolution are in good qualitative agreement for all three values of strength differential parameter. In contrast, as the value of strain hardening exponent increases, the agreement between results obtained from homogeneous and non-homogeneous cells is worse. An heuristic extension of the Stewart and Cazacu (2011)’s model is proposed in this work in an attempt to improve the accuracy of the model.

Blow‐up of solutions of wave equation with a nonlinear boundary condition and interior focusing source of variable order of growth

In this paper, being investigated an initial‐boundary value problem for a one‐dimensional wave equation with a nonlinear source of variable order and nonlinear dissipation at the boundary. The existence of a local solution of the problem under consideration is proved. Then the question of the absence of global solutions is investigated. Depending on the relationship between the order of growth of the nonlinear source and the nonlinear boundary dissipation, different results are obtained on the blow‐up of weak solutions in a finite time interval.

High-degree splines from discrete Fourier transforms: Robust methods to obtain the boundary conditions

Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are often not easy to approximate accurately, high-degree splines are difficult to obtain using standard approaches.In Beaudoin (1998), Beaudoin and Beauchemin (2003), and Pepin et al. (2019), a new method to compute spline approximations of low or high degree from equidistant interpolation nodes based on the discrete Fourier transform is analyzed. The accuracy of this method greatly depends on the accuracy of the boundary conditions. An algorithm for the computation of the boundary conditions can be found in Beaudoin (1998), and Beaudoin and Beauchemin (2003). However, this algorithm lacks robustness since the approximation of the boundary conditions is strongly dependant on the choice of θ arbitrary parameters, θ being the degree of the spline.The goal of this paper is therefore to propose two new robust algorithms, independent of arbitrary parameters, for the computation of the boundary conditions in order to obtain accurate splines of any degree. Numerical results will be presented to show the efficiency of these new approaches.

On the Bövik-Benveniste methodology and related approaches for modelling thin layers.

This paper reviews several leading approaches for asymptotic modelling of thin layers in elastostatics and wave propagation phenomena. The issues related to applications of the so-called 'equivalent' or 'effective' boundary conditions and their interpretations are highlighted. Comparative analysis of asymptotic models is performed for a two-dimensional elastostatic case using a novel complex variables-based modelling tool. Its implementation allows for straightforward derivations of higher order boundary conditions for problems with layers of arbitrary sufficiently smooth curvatures. Explicit expressions for the conditions up to the third order are provided. All models are tested using available benchmark solutions and the solutions for the limiting cases of the layer parameters. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

FEA_LiNbO3: Finite element analysis of novel LiNbO3 material based fiber for optical communication properties of nonlinear applications

This study introduces a distinctive LiNbO3-based five-ring heptagonal-shaped photonic crystal fiber (PCF) geometry that demonstrates exceptionally high birefringence (Br) and nonlinear coefficient (NLC). Fundamental simulation studies are conducted through the COMSOL software utilizing the finite element method (FEM) with a perfectly matched layer (PML) boundary condition in order to comprehensively explore a variety of relevant optical characteristics, including birefringence, effective area, nonlinearity, core power fraction, dispersion, numerical aperture, confinement loss and so on. The simulation outcomes reveal an ultra-high Br and NLC of 0.081 and 5843.32 W-1Km-1 sequentially, at the operative wavelength of 1.55μm. The designed PCF with ultra-high Br and NLC features can be fabricated suitably, which is an advantageous aspect for potential prospective utilization in polarization-maintaining, nonlinear optics, supercontinuum generation, etc.

A Study of MHD Fluid with Second Order Slip and Thermal Flow Over a Nonlinear Stretching Sheet

An electrically conducted viscous incompressible nanofluid flow caused by the nonlinear stretching surface with stagnation flow has been investigated numerically. The effect of Brownian motion and thermophoresis on the nanofluid is also incorporated. The governing partial differential equations with nonlinear second order boundary conditions are solved by the fourth order Runge-Kutta technique using MATLAB programming. The effect of the radiation parameter (<i>Rd</i>), stretching parameter (n), Brownian motion parameter (<i>Nb</i>), thermophoresis parameter (<i>Nt</i>) on temperature, velocity and mass transfer are shown graphically. The influence of some of these parameters on the local Nusselt number (− <i>θ</i>′(0)) and local Sherwood number (−<i>ϕ</i>′(0)) are shown by the graphs.

Influence of transport coefficients’ dependence on temperature for gas flow in microbearing

The paper presents an analytical solution for the non-isothermal compressible gas flow in a slide microbearing with different temperatures of walls. The gas flow is defined by the Navier-Stokes-Fourier system of the continuum equations and first order boundary conditions. Knudsen number corresponds to the slip and continuum flow (Kn ≤ 10−1) and Reynolds number is moderately high, so inertia needs to be included. The solution is obtained by perturbations with the first approximation that relates to the continuum flow and the second one that involves second-order effects: the rarefaction, inertia, convection, dissipation, and rate at which work is done in compressing the element of fluid. The presented model analyzes the influence of the dependence of transport coefficients on temperature. The obtained analytical solution for the pressure, velocity, and temperature is approved by a comparison with the results of other authors. The microbearings can often be a part of MEMS, so the presented method and the obtained analytical solution can serve for solving similar non-isothermal shear-driven or pressure-driven problems. The paper gives an estimation about the error in values for microbearing mass flow and load capacity if the dependence of transport coefficients on temperature are neglected.

The Effect of Gap Distance between a Pin and Water Surface on the Inactivation of Escherichia coli Using a Pin-to-Water Plasma.

Atmospheric plasmas have been applied for the inactivation of microorganisms. Industrials demand to investigate the relation of the key reactive species induced by plasmas and the operating parameters including boundary conditions in order to control plasma treatment processes. In this study, we investigated the effect of gap distance between a pin-electrode and water surface on inactivation efficacy. When the gap distance decreased from 5 mm to 1 mm, the reduction of Escherichia coli (E. coli) was increased to more than 4 log CFU/mL. The reactive oxygen species measured optically and spectrophotometrically were influenced by gap distance. The results from electron spin resonance (ESR) analysis showed that the pin-to-water plasma generated hydroxyl radical (OH•) and singlet oxygen (1O2) in the water and superoxide radical (O2−•) served as a precursor of OH•. The inactivation of E. coli was significantly alleviated by sodium azide (1O2 scavenger), indicating that 1O2 contributes the most to bacterial inactivation. These findings provide a potentially effective strategy for bacterial inactivation using a pin-to-water plasma.

Person-environment fit: a luxury good for those who can afford it?

PurposeThe study integrates organizational demography theory into person-environment fit theories to question the assumption that all employees can afford to strive for person-environment fit. The ethnic/racial diversity in organizations is investigated as a boundary condition in order to develop implications to mitigate the challenges of employees with precarious jobs, especially persons of color (POCs), in the society.Design/methodology/approachPublicly accessible and objective data from organizations in the S&P 1500 index were collected through Compustat, ExecuComp, the Bloomberg Terminal and the websites of Fortune, the United States Census Bureau and the U.S. Department of Labor. A path analysis of time-lagged data was performed to support causal relationships between the examined constructs while controlling for alternative explanations.FindingsUnsafe working conditions moderate the U-shaped relationship between ethnic/racial diversity and turnover and turn it into an inverted U-shaped relationship because employees in precarious jobs, especially POCs, cannot afford to leave unsafe working conditions. Organizations with unsafe working conditions are more likely to invest in sustainability initiatives. However, organizations' financial performance does not benefit from this investment.Originality/valueThe circumstance that not all employees can afford person-environment fit and its organizational outcomes are identified and empirically tested. Scholars can integrate this boundary condition in future research. Implications for practice and policy are also derived.

Experimentally validated numerical modeling of heat transfer in crossflow air-to-water fin-and-tube heat exchanger

The aim of this work is to analyze different tube-side inlet boundary conditions in order to properly model heat transfer mechanism in a crossflow air-to-water fin-and-tube heat exchanger (FTHEX). For accurately describing conjugated heat transfer, the entire flow length on both fluid sides should be considered. For problem simplifying, domain that include a segment inside the heat exchanger in the water flow direction, is used. This paper studies the effect of fully conjugated heat transfer, including air-side and water-side thermal resistances. Three different numerical models are analyzed by varying the tube-side inlet boundary conditions. In one of these models the water-side thermal resistance is neglected and other two models consider the water-side thermal resistance, but with different velocity and temperature boundary conditions at the water inlets: uniform and fully developed. To validate the proposed numerical models, measurements have been performed on a crossflow air-to-water plain FTHEX. The results show that the numerical model with the fully developed water inlet boundary condition coincides best with the experimental data. It can be concluded that the water-side thermal resistance cannot be neglected, especially when evaluating the air outlet temperature and the overall heat transfer coefficient of heat exchanger.

Effect of multiple forces on convective micropolar fluid flow in a permeable channel with stretching walls considering second order slip conditions

This paper is intended to study the impact of velocity and thermal slip boundary conditions of order two on MHD buoyancy driven radiative micro-polar fluid in a channel with permeable stretching walls. The governing equations are transformed and solved numerically. Convergence of the numerical results are tested with grid independence test and obtained results are validated by comparing with existing results. The influence of velocity and thermal slip of order two, suction or injection, vortex viscosity, micro-rotation, magnetic and thermal radiation parameters on fluid velocity, microrotation profiles and temperature distributions are discussed over the graphs and tables. It is worth mentioning that second- order velocity and thermal slips dominate the stretchable walls and influence the flow characteristics (axial velocity, micro-rotation and temperature) more prominently. The micro-rotation profile decreases at and increases at of the channel for the first slip. This study is useful in blood rheology and fibre spinning etc. and these findings are highly useful to enhance the effectiveness of catalytic reactors.

Finite element simulation of a viscoelastic cell entering a cylindrical channel: Effects of frictional contact

Finite element method has been extensively used to simulate the process of single cells entering a narrow channel under a prescribed pressure. Yet an in-depth understanding on the effects of the frictional boundary condition in such simulations is lacking. The main challenge lies in the continuously evolving contact region between the deformed cell and the channel wall during the entry process, which makes it difficult to apply proper boundary conditions for the friction and pressure. In this work, we present an approach to continuously update the boundary condition according to the contact status during entry. Using this approach and modeling the cell as a visco-hyperelastic sphere, we study how the pressure boundary conditions and the friction coefficient affect the simulated cell entry process. Specifically, we compare two special cases of pressure boundary conditions: positive pressure at the trailing edge of the cell or negative pressure at the leading edge. It is found that the two cases produce the same result in terms of the cell entry length under frictionless contact, but give considerably different results under frictional contact. Effects of whether the pressure boundary is updated are then studied by considering more special cases. All these results are well explained by the pressure superposition principle, and further insights into the effects of pressure boundary condition and boundary update are also acquired. Finally, focusing on the case of positive pressure with boundary updates, we obtain simulation results revealing how the entry length depends on the pressure, time and friction coefficient. In particular, a larger friction coefficient can significantly reduce the entry length under a prescribed pressure or a certain entry time. Our results suggest that it is necessary to implement accurate pressure boundary conditions (e.g., pressure magnitudes at the two edges of cell and continuously updated pressure boundary regions) in order to faithfully capture the frictional contact between the cell and the channel wall. In addition, the simulation approach can be useful in modeling the general process of a viscoelastic sphere entering a cylindrical channel involving frictional contact.

Diagnostics of psychological readiness of high school students for research activities in mathematics in the design context of a hybrid intellectual learning environment

Introduction. The problem of improving the process of organizing and supporting the project and research activities of schoolchildren through intelligent management for the purpose of self-organization of the individual, understanding and comprehending complex mathematical knowledge as a principle of personal development is relevant and far from solved. Intelligent systems provide the process of individualization of learning, the establishment of personalized and computerized feedback of cognitive and creative processes. The purpose of the article is to assess the student's readiness for research activities in the context of designing a hybrid intelligent learning environment. Materials and methods. The assessment of the student's psychological readiness for research activities in the conditions of using a hybrid intellectual environment was carried out on an experimental representative sample of students of 1-2 courses of secondary vocational education (n1=42) and students of the senior classes of secondary schools (n2=30). The diagnosis was carried out using the intelligence structure test of R. Amthauer, the creativity questionnaire of D. Johnson, the test "Individual styles of thinking" by A. Alekseev, L. Gromova, the methods of value orientations by M. Rokich, etc. The significance of the differences was established by means of Student's t-test, Fisher's angular transformation, χ2-test. The results of the study. The assessment of psychological readiness for research activities in mathematics was carried out on the basis of the developed nine parameters of scientific potential. The presented results allow us to pre-set the framework of boundary conditions in order to minimize the imprinting time of a hybrid intelligent system (including the selection of the neural network topology). For all three groups of criteria, differences by gender were established, for example, by the parameter "value orientations" (temp = 2.26 > tcr = 2.02); by the parameter "creativity" (χemp2 = 6,02 ≥ χcr2 (0,05;2) = 5,99). And also by the type of educational institution, for example, by the parameter “motivation to achieve the result” (φemp = 0,186 > φcr = 1,64). Conclusion. The results of the research are of practical value, as they serve as a technological basis for establishing the boundaries and boundary conditions of the most significant parameters for the effective realization of scientific potential, expressed in the work of a specialized web interface created with the student's personal account.

PHOTOGRAMMETRY MEASUREMENTS OF INITIAL IMPERFECTIONS FOR THE ULTIMATE STRENGTH ASSESSMENT OF PLATES

The objective of the present study is to develop a new approach to model the initial geometrical imperfections of ship plates by using Photogrammetry. Based on images, Photogrammetry is able to take measurements of the distortions of plates and to catch the dominant surface shape, including the deformations of the edges. Having this data, it is possible to generate faithful models of plate surface based on third order polynomial functions. Finally, the maximum load- carrying capacity of the plates is analysed by performing a nonlinear finite element analysis using a commercial finite element code. Three un-stiffened and four stiffened plates have been modelled and analysed. For each plate, two initial imperfection models have been generated one, based on photogrammetric measurements and the other, based on the trigonometric Fourier functions. Both models are subjected to the same uniaxial compressive load and boundary conditions in order to study the ultimate strength.

A Numerical Method for Pulse Propagation in Nonlinear Dispersive Optical Media

In this work, the pulse propagation in a nonlinear dispersive optical medium is numerically investigated. The finite difference time-domain scheme of third order and periodic boundary conditions are used to solve generalized nonlinear Schr¨odinger equation governing the propagation of the pulse. As a result a discrete system of ordinary differerential equations is obtained and solved numerically by fourth order Runge-Kutta algorithm. Varied input ultrashort laser pulses are used. Accurate results of the solutions are obtained and the comparison with other results is excellent.

An energy–momentum couple stress formula for variational-based macroscopic modelings of roving-matrix composites in dynamics

In dynamical systems, fiber-reinforced materials with fiber rovings in a cured matrix material, woven or manufactured by the technology of tailored fiber placement (TFP), for instance, have gained great significance for engineers. Therefore, many finite element simulations are currently in progress during the design of composite parts. But, standard finite element formulations do not take into account dimensions and the direction-dependent flexure and twist stiffness of the rovings. In order to avoid computationally costly mesoscopic finite element models with a discretization of roving-matrix interior boundary interfaces, a macroscopic material model can be derived by introducing micropolar rotation degrees of freedom. Micropolar rotation degrees of freedom allow for a separate constitutive description of the direction-dependent stiffness and inertia of the rovings in the cured matrix material. This continuum model represents an extended continuum formulation with an extended set of balance laws. In its computational setting, the discrete preservation of the complete set of balance laws can be realized by a mixed principle of virtual power in connection with energy–momentum tension stress and couple stress formulas. The guaranteed algorithmic energy–momentum consistency then allows an one-off virtual parameter identification of the macroscopic material constants with the mesoscopic model based on the error of the balance functions. Therefore, a mixed finite element formulation with independent micropolar rotation degrees of freedom is recently published, which are able to simulate dynamical problems by taking into account flexure and twist of the rovings. In this previously published paper, the constitutive laws are at most quadratic such that energy–momentum time integrations are possible without a special couple stress approximation. If a nonlinear strain energy function for flexure and twist of the rovings is considered, a new special couple stress approximation is necessary. Therefore, the present paper completes this mixed finite element formulation with a new couple stress approximation and shows its application by means of that numerical experiments with unidirectional rovings, which are designed for the virtual parameter identification. These fully dynamical examples with large translations, rotations and deformations demonstrate the flexure and twist stiffness of the rovings with roving curvature–twist strain energy functions of Kauderer-type by parameter studies. The complete set of discrete balance laws are satisfied independent of boundary conditions in order to allow the upcoming virtual parameter identification.

Non-isothermal vortex flow in the T-junction channel

In this work we present the numerical simulation of coolant mixing modes in the T-junction. We shows that the RANS approach is beneficial for a qualitative flow analysis to obtain relatively agreed averaged velocity and temperature. Moreover, traditionally, the RANS approach calculates only the averaged temperature distribution. It should also be emphasized that unlike the LES approach, the steady RANS approach cannot express a local flow structure in intense mixing zones. Nevertheless, apparently the used RANS approach should be used for assessing the quality of computational grids, boundary conditions in order to use the LES approach for further numerical simulation.

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.

Thermal Analysis and Experimentation of an IoT-based Video Surveillance Module

Comprehensive experimental verification and theoretical analysis of a forced convection active cooling mechanism for an internet of things (IoT) based 360° video surveillance module have been presented in this paper. The heating and cooling cycles of the proposed thermal system has been modeled considering a single insulated enclosure with variable external temperature relative to the ambient temperature. First order differential equations are framed corresponding to the heating and cooling cycles from the analogy with the charging and discharging cycles of a series resistance-capacitance (RC) circuit. Those differential equations are solved subject to appropriate boundary conditions in order to obtain temperature variation of the system as a function of time for a given processing workload. The variation of temperature with time obtained from the proposed model is found to be in good agreement with the experimentally measured data. Empirical relationship has also been developed from the experimentally measured data which relate the processing workload of the module at any instant and corresponding temperature rise.