Boundary Conditions Research Articles

Development of an innovative diffraction scattering theory of X-rays and electrons in imperfect crystals.

Fundamental equations describing the X-ray and electron diffraction scattering in imperfect crystals have been derived in the form of the matrix Fredholm-Volterra integral equation of the second kind. A theoretical approach has been developed using the perfect-crystal Green function formalism. In contrast, another approach utilizes the wavefield eigenfunctions related to the diagonalized matrix propagators of the conventional Takagi-Taupin and Howie-Whelan equations. Using the Liouville-Neumann-type series formalism for building up the matrix Fredholm-Volterra integral equation solutions, the general resolvent function solutions of the X-ray and electron diffraction boundary-valued Cauchy problems have been obtained. Based on the resolvent-type solutions, the aim is to reveal the features of the diffraction scattering onto the crystal lattice defects, including the mechanisms of intra- and interbranch wave scattering in the strongly deformed regions in the vicinity of crystal lattice defect cores. Using the two-stage resolvent solution of the second order, this approach has been supported by straightforward calculation of the electron bright- and dark-field contrasts of an edge dislocation in a thick foil. The results obtained for the bright- and dark-field profiles of the edge dislocation are discussed and compared with analogous ones numerically calculated by Howie & Whelan [Proc. R. Soc. A (1962), 267, 206].

Simulating a High-Resolution Tectonic Stress Field and Predicting the Fracture Distributions in Shale Reservoirs Based on a Heterogeneous Rock Mechanics Model with Adaptive Boundary Condition Constraints

Simulating a High-Resolution Tectonic Stress Field and Predicting the Fracture Distributions in Shale Reservoirs Based on a Heterogeneous Rock Mechanics Model with Adaptive Boundary Condition Constraints

Non linear hyperbolic--parabolic systems with Dirichlet boundary conditions

Non linear hyperbolic--parabolic systems with Dirichlet boundary conditions

A novel method to determine the critical buckling load for plates from load versus in-plane displacement diagram

Based on the literature, the load vs. in-plane displacement diagram (P-u curve) is not sufficiently indicative to provide a reliable determination of the critical buckling load, Pcr. This attitude is rooted in three issues. First, the P-u curve often exhibits very gradual slope changes, second, it concerns unavoidable graph fluctuations caused by imperfections in specimens or boundary conditions, and third, the P-u curve behavior during the buckling phenomenon is not fully understood. In the present work, a narrative review is conducted to gain a better understanding of the location of Pcr on the P-u curve. Accordingly, a novel method is introduced to correctly extract Pcr from the load vs. in-plane displacement diagram as the most accessible buckling test output, compared to out-of-plane displacement and strain monitoring data, which require additional equipment. The proposed method is highly sensitive to changes in the slope of the graph while significantly reducing the adverse effects of undesired fluctuations. This method is applied to several experimental buckling data for composite laminates as well as sandwich panels, and its reliability and accuracy are confirmed by comparison with other well-known methods.

Research on In-Plane Thermal Conductivity Detection of Fuel Cell Bipolar Plates Based on Laser Thermography

Research on In-Plane Thermal Conductivity Detection of Fuel Cell Bipolar Plates Based on Laser Thermography

Development of an initial normal-loading direct shear tester of discontinuities, with subsequent passive changes in local normal load/stiffness allowable, and an investigation of the shear behaviours of discontinuities

A widespread case of discontinuity shearing is found among local shallow rock blocks sliding along non-planer, rough, non-anchored discontinuities, which is characterized by an initial normal load in addition to free subsequent changes in local normal load/stiffness, provoked by shear dilatancy (INL). The existing direct shear apparatuses of rock discontinuities fitted for those cases are rare, and there is a lack of understanding of the shear behaviours of discontinuities under such INL boundary conditions. Here, we develop an INL direct shear tester of discontinuities for shear strength. This tester takes advantage of the direct shear test apparatus modified after the YZ-5 model without a servo-controlled system to permit the accomplishment of those boundary conditions. Shear behaviours of unfilled and infilled discontinuities under INL boundary conditions are investigated. Moreover, the possible influence of clay content on those shear behaviours of infilled discontinuities is clarified. The developed tester made it possible to test the shear performance of the local shallow rock blocks sliding along non-planer, rough, non-anchored discontinuities. This work contributes to a limited body of research on the shear behaviours of discontinuities under those INL boundary conditions. Limitations of this work are also revealed.

Piezoelectric layer guided in-plane surface waves with flexoelectricity and gradient effects

With the rapid advancement of 5 G technology, the demand for surface acoustic wave (SAW) devices is experiencing exponential growth. Precisely forecasting the speed at which Rayleigh waves propagate, taking into account size effects and flexoelectric properties, is vital for enhancing SAW device design. To address this need, the study explores Rayleigh wave propagation in a stratified system consisting of a nanoscale piezoelectric guiding layer atop an isotropic elastic substrate. The governing equations, boundary conditions, and interface continuity conditions between the guiding layer and substrate are established through the Hamiltonian principle. Following this, the dispersion equations for Rayleigh waves under electric open-circuit and electric short-circuit conditions are derived and solved numerically. Additionally, the effects of flexoelectricity, inertial gradients, strain gradients, electric field gradients, and the piezoelectric guiding layer thickness on the phase velocity of Rayleigh waves are extensively explored. Our findings indicate that flexoelectricity and strain gradients elevate the phase velocity, while inertial gradients and electric field gradients result in a decrease in the phase velocity. As the frequency of Rayleigh waves increases, the impact of these factors becomes more prominent. In addition, it is observed that electric field gradients play a less significant role compared to inertial gradients and strain gradients. The findings of this study could offer valuable insights for the advancement of miniaturized SAW devices designed for high-frequency service.

Numerical Analysis of Heat Transfer Deterioration of Hydrogen Flowing in a Circular Pipe under Transcritical Boundary Conditions

Numerical Analysis of Heat Transfer Deterioration of Hydrogen Flowing in a Circular Pipe under Transcritical Boundary Conditions

Impact of prostate MRI image quality on diagnostic performance for clinically significant prostate cancer (csPCa).

With the widespread clinical application of prostate magnetic resonance imaging (MRI), there has been an increasing demand for lesion detection and accurate diagnosis in prostate MR, which relies heavily on satisfactory image quality. Focusing on the primary sequences involved in Prostate Imaging Reporting and Data System (PI-RADS), this study have evaluated common quality issues in clinical practice (such as signal-to-noise ratio (SNR), artifacts, boundaries, and enhancement). The aim of the study was to determine the impact of image quality on clinically significant prostate cancer (csPCa) detection, positive predictive value (PPV) and radiologist's diagnosis in different sequences and prostate zones. This retrospective study included 306 patients who underwent prostate MRI with definitive pathological reports from February 2021 to December 2022. All histopathological specimens were evaluated according to the recommendations of the International Society of Urological Pathology (ISUP). An ISUP Grade Group ≥ 2 was considered as csPCa. Three radiologists from different centers respectively performed a binary classification assessment of image quality in the following ten aspects: (1) T2WI in the axial plane: SNR, prostate boundary conditions, the presence of artifacts; (2) T2WI in the sagittal or coronal plane: prostate boundary conditions; (3) DWI: SNR, delineation between the peripheral and transition zone, the presence of artifacts, the matching of DWI and T2WI images; (4) DCE: the evaluation of obturator artery enhancement, the evaluation of dynamic contrast enhancement. Fleiss' Kappa was used to determine the inter-reader agreement. Wilson's 95% confidence interval (95% CI) was used to calculate PPV. Chi-square test was used to calculate statistical significance. A p-value < 0.05 was considered statistically significant. High-quality images had a higher csPCa detection rate (56.5% to 64.3%) in axial T2WI, DWI, and DCE, with significant statistical differences in SNR in axial T2WI (p 0.002), the presence of artifacts in axial T2WI (p 0.044), the presence of artifacts in DWI (p < 0.001), and the matching of DWI and T2WI images (p < 0.001). High-quality images had a higher PPV (72.5% to 78.8%) and showed significant statistical significance in axial T2WI, DWI, and DCE. Additionally, we found that PI-RADS 3 (24.0% to 52.9%) contained more low-quality images compared to PI-RADS 4-5 (20.6% to 39.3%), with significant statistical differences in the prostate boundary conditions in axial T2WI (p 0.048) and the presence of artifacts in DWI (p 0.001). Regarding the relationship between csPCa detection and image quality in different prostate zones, this study found that significant statistical differences were only observed between high- (63.5% to 75.7%) and low-quality (30.0% to 50.0%) images in the peripheral zone (PZ). Prostate MRI quality may have an impact on the diagnostic performance. The poorer image quality is associated with lower csPCa detection rates and PPV, which can lead to an increase in radiologist's ambiguous diagnosis (PI-RADS 3), especially for the lesions located at PZ.

Time Optimal and PID Controller for Armed Manipulator Robots

This paper is fourfold. First, three different time-optimal control problems for simulating the manipulator robots with one, two, and three arms are mathematically formulated. Corresponding to the related dynamical systems, the nonlinear system of ordinary differential equations is derived. It has been found that these problems are time-free and have distinct initial and boundary conditions, making them hard to solve. To find the minimum time with different payloads, a successful numerical method based on the finite difference and the three-stage Lobatto formula is proposed. Secondly, the related torquecontrolling problems are simulated, and then for one, two, and three armed manipulator robots, they are solved using the PID controller method. Thirdly, it is shown that, compared to the time-optimal controlling problem, the optimal PID torque controller solution takes more time to do the job than was expected. However, the solution in the PID controller method shows less oscillation than the time-optimal control problem. Fourthly, mathematical theories are used, and the numerical results for both methods and different payloads are compared.

Multiple solutions for fractional elliptic systems

Abstract This paper investigates the existence and multiplicity of solutions to fractional elliptic systems on conical spaces. Specifically, we focus on the challenges posed by complex geometric configurations, including cones with rough bases, and their implications for the treatment of lateral boundary conditions. By utilizing the fibering map approach and iterative method, we aim to address these challenges and provide new insights into the field. Notably, these issues have not been previously explored in existing literature, highlighting the originality and significance of our study.

How do work-family practices influence employee work-family conflict? Moderations of commitment-based HRM and human capital

PurposeThe paper aims to clarify the relationship between organizational work-family practices and employee work-family conflict in light of the boundary conditions of commitment-based human resource management (HRM) and employee human capital.Design/methodology/approachThe paper opted for a multi-source, multi-level design and surveyed 1,717 individuals (including CEOs, HR managers and employees) from 159 firms in China. The model was tested using hierarchical linear modeling.FindingsThe paper provides empirical insights that the effect of work-family practices on work-family conflict is indispensably dependent on the adoption of commitment-based HRM. In addition, employee human capital further moderated this interaction in that the effect of work-family practices on reducing work-family conflict was most salient with high-education employees who were embedded in a high-commitment HRM system.Research limitations/implicationsTesting the hypotheses in the Chinese context has both its merits and drawbacks. Specific results are pursuant to the Chinese context. Therefore, a cross-cultural comparative study is called upon.Practical implicationsThe paper includes implications for organizations striving to minimize employee work-family conflict.Originality/valueThis paper primarily applies the resource-building perspective to examine the synergistic effects of organizational resources (targeting work-family practices together with general commitment-based HRM) and individual intellectual resources (human capital) on employee work family conflict.

Substantive or symbolic ? The strategic choice of sustainable environmental strategy for enterprises induced by the new environmental protection law

AbstractThe new “Environmental Protection Law” (abbreviated as NEPL) holds milestone significance for the construction of China's ecological legal system. However, evidence regarding the impact of NEPL on sustainable environmental strategy (abbreviated as SES) still lacks empirical analysis. This study aims to examine the mechanisms and boundary conditions through which the NEPL influences SES. Utilizing a difference‐in‐differences approach, an empirical analysis is conducted on the data of listed companies on the Shanghai and Shenzhen A‐shares from 2008 to 2021. The findings are as follows: (1) NEPL has significantly promoted both the substantive environmental strategy (abbreviated as SUB) and symbolic environmental strategy (abbreviated as SYM) of heavily polluting enterprises. Compared with SYM, the impact of NEPL on SUB is more significant. (2) Analyst coverage plays a significantly positive moderating role in the relationship between NEPL and SUB, while managerial myopia plays a significantly positive moderating role in the relationship between NEPL and SYM. (3) Environmental legitimacy pressure exerts a mediating effect on the relationship between NEPL and SES. The research findings enrich existing theories related to strategic choice and environmental policy under government intervention and provide policy recommendations for enterprises to achieve sustainable development in the context of NEPL.

Every cloud has a silver lining: Understanding how hotel employees’ counterproductive work behavior may shape their pro-environmental behavior

Drawing upon moral cleansing theory, we investigate why and when employees’ counterproductive work behavior (CWB) may lead to their pro-environmental behavior (PEB) by pinpointing felt guilt and moral deficit as two parallel conduits and moral identity as an important boundary condition. To test our proposed model, 72 employees affiliated to three hotels in a chain were selected via experience sampling method. Data were collected through sending online survey links via WeChat, an instant communication app in China. Results reveal that employees performing CWB elicits feelings of guilt and a sense of moral deficit to themselves, which in turn triggers them to engage further in PEB. Moreover, findings suggest that moral identity strengthens the positive association of CWB with felt guilt and moral deficit and intensifies the indirect effects towards PEB. We therefore craft a dual-pathway framework that illuminates why and when CWB conducted by employees may, paradoxically, lead to PEB.

Flame propagation behavior inside a closed duct upstream of a flame arrester housing

A possible way to introduce hydrogen into the energy matrix would be to enrich traditional fuels like natural gas and propane with hydrogen. Therefore, the study of the flame propagation behavior of these hydrogen enriched fuels becomes important to future industrial applications. In the present work the aim was to experimentally study the effect of hydrogen enrichment of propane and natural gas. However, in order to achieve more generality, the studied mixtures were characterized through the Lewis (Le), Zeldovich (Ze) and the reaction Damköler (Da°) numbers. A total of six mixtures were considered, in which the Ze varied from 4.94 to 8.45, the Le varied from 0.71 to 1.36 and the Da° varied from 14.56 to 36.11. In addition, the obtained results were compared to previous work to assess the effect of the experimental boundary conditions on the flame propagation velocity. The experimental results show that, for mixtures with similar Le numbers, the lower the Ze number the higher the flame propagation velocity. The maximum propagation velocities obtained in the first propagation section of the module are between 18.60 m/s and 57.11 m/s. Therefore, these flames can be considered as weakly accelerating flames. Moreover, the maximum flame propagation velocities showed a good correlation with the product Le × Ze. Regarding the presence of the flame arrester housing without an arrester element, it was observed that it causes an increase in flame propagation velocity. However, when compared to a previous work in which a flame arrester element was inside the housing, the velocity was higher for the present work.

Seismic Performance of Cross-Shaped Partially Encased Steel–Concrete Composite Columns: Experimental and Numerical Investigations

Special-shaped partially encased steel–concrete composite (PEC) columns could not only improve the aesthetic effect and room space use efficiency, but also exhibit good mechanical performance under static load when used in multi-story residential and office buildings. However, research on the seismic performance of special-shaped PEC columns is insufficient and urgently needed. To investigate the seismic performance of cross-shaped partially encased steel–concrete composite (CPEC) columns, three CPEC columns were designed and tested under combined constant axial load and lateral cyclic load. The test results show that the CPEC columns had good load capacity and ductility, and that the columns failed because of concrete crushing and steel flange buckling after the yielding of the steel flange. The plump hysteresis loops indicated that the CPEC column also had good energy dissipation capacity. Due to the constraint of hydraulic jacks, increasing the load ratio would decrease the effective length, thereby increasing the load capacity of the CPEC column and decreasing the ductility. A finite element model was also established to simulate the response of the CPEC columns, and the simulated results agree well with the experimental results. Thereafter, an extensive parametric analysis was performed to study the influences of different parameters on the seismic performance of CPEC columns. For the CPEC column with an ideal hinged boundary condition at the top, its lateral load capacity gradually decreases with the growth of the load ratio and link spacing and increases with the rise of the steel yield strength, concrete compressive strength, flange and web thickness, and sectional aspect ratio. This research could provide a basis for future theoretical analyses and engineering application.

Local existence and global boundedness for a chemotaxis system with gradient dependent flux limitation

In this paper, we investigate the following Keller–Segel system with flux limitation [Formula: see text] under no-flux boundary conditions in a ball [Formula: see text]), where [Formula: see text] is positive and [Formula: see text] with [Formula: see text]. It is proved that the problem (⋆) possesses a unique classical solution that can be extended in time up to a maximal [Formula: see text]. Moreover, it is shown that the above solution is global and bounded when either [Formula: see text] if [Formula: see text] and [Formula: see text], or [Formula: see text] if [Formula: see text] and [Formula: see text]. We point out that when [Formula: see text], our result is consistent with that of [N. Bellomo and M. Winkler, Comm. Partial Differential Equations 42 (2017) 436–473].

Free Vibration of Ogival Circular Arch

This study aims to analyze the free vibration of an ogival arch in which two symmetrical arched shapes are discontinuously met at the mid-arc. Differential equations governing the free vibration of an ogival circular arch were derived, where the rotatory inertia and shear deformation effects are included. The governing equations were numerically solved to calculate natural frequencies and mode shapes. In numerical solution methods, the symmetric and anti-symmetric boundary conditions at the mid-arc were focused rather than the boundary conditions of supported end due to the discontinuity of the mid-arc. For the first time, the free vibration problem for discontinuous arches, such as ogival arches, is solved in this study. Calculation results of this study for natural frequencies are compared well with those of the finite element method. The effects of various arch parameters on natural frequencies were highlighted and discussed in detail.

On the wavefunction cutoff factors of atomic hydrogen confined by an impenetrable spherical cavity

AbstractThe Schrödinger equation for the hydrogen atom enclosed by an impenetrable spherical cavity is solved through a Finite‐Differences approach to gain an insight on the actual nature and structure of the ansatz wavefunction cutoff factor widely used in an ad hoc manner in corresponding variational calculations to comply with the Dirichlet boundary conditions. The results of this work provide a theoretical foundation for the choice of the appropriate analytical cutoff functions that fulfill the boundary conditions. We find three different regions for the behavior of the cutoff functions. Small cavity radius where the cutoff function has a parabolic behavior, an intermediate region where the cutoff function is quasi‐linear, and a large cavity region where the cutoff function is a step‐like function. We deduce the traditional linear and quadratic cutoff functions used in the literature as well as its validity region for the confining radius. Finally, we provide a mathematical deduction of the exact cutoff function in terms of the nodal structure of the free hydrogenic wavefunctions and a relation to the Laguerre polynomials for some cavity radii where the free atomic energy level coincides with a confined energy level. We find that the cutoff function transit over several unconfined solutions in terms of its nodal structure as the system is compressed.

Dynamic response strength of integrated foundation for multiple wind turbines

The focus of this paper is on the conceptual design of offshore multi wind turbine integrated floating foundation (MWF) and the strength analysis method of floating structures considering motion response. Firstly, the maximum environmental load and ultimate motion attitude of MWF were used as boundary conditions to solve the problem of imprecise constraint loads in traditional analysis methods. Then, a stress solving equation based on motion state and inertia release was established to solve the equivalent accuracy problem of floating body motion state. Finally, through theoretical analysis, numerical simulation, and experimental testing, it was found that the stress solution method considered the motion state of the floating body in this paper to be more accurate and reliable, with an error of less than 10% compared to the stress results of experimental testing. Improved calculation accuracy by 30%. These studies provide more accurate analytical methods and theoretical references for predicting the strength of floating structures in actual oceans.