Boundary Conditions Research Articles

Exploring run-and-tumble movement in confined settings through simulation.

Motion in bounded domains is a fundamental concept in various fields, including billiard dynamics and random walks on finite lattices, and has important applications in physics, ecology, and biology. An important universal property related to the average return time to the boundary, the Mean Path Length Theorem (MPLT), has been proposed theoretically and experimentally confirmed in various contexts. We investigated a wide range of mechanisms that lead to deviations from this universal behavior, such as boundary effects, reorientation, and memory processes. This study investigates the dynamics of run-and-tumble particles within a confined two-dimensional circular domain. Through a combination of theoretical approaches and numerical simulations, we validate the MPLT under uniform and isotropic particle inflow conditions. This research demonstrates that although the MPLT is generally applicable for different step length distributions, deviations occur for non-uniform angular distributions, non-elastic boundary conditions, or memory processes. These results underline the crucial influence of boundary interactions and angular dynamics on the behavior of particles in confined spaces. Our results provide new insights into the geometry and dynamics of motion in confined spaces and contribute to a better understanding of a broad spectrum of phenomena ranging from the motion of bacteria to neutron transport. This type of analysis is crucial in situations where inhomogeneity occurs, such as multiple real-world scenarios within a limited domain.

Spirit at work: a panacea for ethical problems caused by marketing managers’ love of money

Purpose Limited research has investigated how spirit at work, functioning as a “good barrel,” fosters ethical decision-making (EDM) even in the presence of unethical managerial behavior (“bad apples”). Therefore, this study aims to investigate the spirit at work, a situational variable, as a moderating variable in the relationship between the love of money (LoM), an individual-level factor, and EDM. Design/methodology/approach A time-lagged survey of the members of the Marketing Association of Pakistan was conducted. The data were analyzed using partial least square structural equation modeling. Findings Adding to much of the existing research, which finds that LoM can influence ethical intention directly, this research finds that LoM influences ethical intention only through ethical judgment. Moreover, the spirit at work tempers the negative relationship between LoM and ethical judgment, thereby mitigating LoM’s detrimental effects not only on ethical judgment but also its downstream effects on ethical intention. Practical implications Organizations, by planting the seeds of spirit at work, can institutionalize good barrels, which can alleviate the negative effects of the marketing managers’ LoM, the root cause of unethical behavior. This way, this study establishes a business case for spirit at work. Originality/value The novelty of this study is the development and investigation of a holistic conceptual framework for EDM of marketing professionals that incorporates LoM as an antecedent, ethical judgment as an underlying mechanism, ethical intention as an outcome variable and spirit at work as a boundary condition.

An empirical investigation of ethnic-cultural procedural fairness effects and their boundary conditions among three societal groups in South Africa

ABSTRACT Ethnic-cultural procedural fairness refers to the perception that societal actors use fair and unbiased procedures to make decisions vis-à-vis one’s ethnic-cultural group. Prior research using ethnic-cultural minority samples has convincingly shown that such perceptions are associated with a range of desirable outcomes. Yet, this body of evidence has so far limited its scope to European and North American samples. Moreover, more research is needed on the underlying psychological processes. Therefore, the central aim of the present study was to investigate ethnic-cultural procedural fairness effects among three societal groups in South Africa. In Study 1 (N = 326 black South Africans), we observed relationships between ethnic-cultural fairness perceptions and positive institutional and intergroup attitudes. Institutional and social trust respectively mediated these associations. Study 2 (N = 747) replicated these findings among white (n = 595), but not among coloured South Africans (n = 152). Notably, across both studies, we also obtained evidence for moderation. That is, procedural fairness effects on institutional attitudes were significantly smaller among socioeconomically burdened black participants, and procedural fairness effects on intergroup attitudes were fully curbed among white participants who reported high levels of perceived group discrimination. Taken together, our results call for enhanced attention to procedural fairness obstacles outside of typical WEIRD settings.

Numerical solution of nonclassical boundary value problems

AbstractWe provide a new approach to obtain solutions of linear differential problems set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the solutions. We show by numerical tests that these schemes are numerically robust and computationally efficient.

A robust septic hermite collocation technique for dirichlet boundary condition Heat conduction equation

Abstract In the current manuscript, approximate solution for 1D heat conduction equation will be sought with the Septic Hermite Collocation Method (SHCM). To achieve this goal, by means of the roots of both Chebyschev and Legendre polynomials used at the inner collocation points, the pseudo code of the method is found out and applied using Matlab which is one of the widely utilized symbolic programming platforms. The unconditional stability of the scheme is shown by the traditional von-Neumann stability technique. To illustrate the accuracy and effectiveness of this newly current numerical scheme, a comparison among analytical and the computed numerical results is presented in tabular forms. It has been illustrated that the scheme is both accurate and effective one and at the same time can be used in a successful way for finding out numerical solutions of several nonlinear problems as well as linear ones.

Analytical solutions for the advective–diffusive ice column in the presence of strain heating

Abstract. A thorough understanding of ice thermodynamics is essential for an accurate description of glaciers, ice sheets and ice shelves. Yet there exists a significant gap in our theoretical knowledge of the time-dependent behaviour of ice temperatures due to the inevitable compromise between mathematical tractability and the accurate description of physical phenomena. In order to bridge this shortfall, we have analytically solved the 1D time-dependent advective–diffusive heat problem including additional terms due to strain heating and depth-integrated horizontal advection. Newton's law of cooling is applied as a Robin-type top boundary condition to consider potential non-equilibrium temperature states across the ice–air interface. The solution is expressed in terms of confluent hypergeometric functions following a separation of variables approach. Non-dimensionalization reduces the parameter space to four numbers that fully determine the shape of the solution at equilibrium: surface insulation, effective geothermal heat flow, the Péclet number and the Brinkman number. The initial temperature distribution exponentially converges to the stationary solution. Transient decay timescales are only dependent on the Péclet number and the surface insulation, so higher advection rates and lower insulating values imply shorter equilibration timescales, respectively. In contrast, equilibrium temperature profiles are mostly independent of the surface insulation parameter. We have extended our study to a broader range of vertical velocities by using a general power-law dependence on depth, unlike prior studies limited to linear and quadratic velocity profiles. Lastly, we present a suite of benchmark experiments to test numerical solvers. Four experiments of gradually increasing complexity capture the main physical processes for heat propagation. Analytical solutions are then compared to their numerical counterparts upon discretization over unevenly spaced coordinate systems. We find that a symmetric scheme for the advective term and a three-point asymmetric scheme for the basal boundary condition best match our analytical solutions. A further convergence study shows that n≥15 vertical points are sufficient to accurately reproduce the temperature profile. The solutions presented herein are general and fully applicable to any problem with an equivalent set of boundary conditions and any given initial temperature distribution.

Marginal stability analyses for thermochemical convection and its implications for the dynamics of continental lithosphere and core-mantle boundary regions

Summary Significant compositional differences may exist in the lithospheric mantle and above the core-mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modeling. We investigated both the instabilities in lithospheric mantle (i.e., lithospheric instability) and the mantle above the CMB (i.e., plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e., two oscillatory convection modes and one layered convection regime) as that with no-slip boundary condition reported in Jaupart et al., (2007). However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modeling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.

Solvability of a sixth‐order boundary value problem with multi‐point and multi‐term integral boundary conditions

This paper aims to investigate the existence and uniqueness of solutions for a sixth‐order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The existence result of at least one nontrivial solution is obtained by applying the Krasnoselskii–Zabreiko fixed point theorem. Moreover, we also establish the existence of unique solution to the considered problem via Hölder and Minkowski inequalities and Rus's theorem. Finally, two numerical examples are included to show the applicability of our main results.

Transverse resonance technique for analysis of a symmetrical open stub in a microstrip transmission line

Open stubs in a strip (microstrip) transmission line are one of the most common elements of planar circuits used in numerous devices in the various types of wireless systems. Therefore, the urgent problem is to develop an analyzing method for discontinuities in the form of the open stub in a microstrip transmission line at frequencies at which the high-frequency effects must be considered. In the paper, a technique of scattering characteristics calculating on a symmetrical microstrip open stub by transverse resonance method is presented. Boundary value problems for a rectangular volume resonator based on a microstrip transmission line with a symmetric open stub are solved for the three options boundary conditions in the symmetry plane and on the longitudinal boundaries. The intersection of the spectral curves obtained by the numerical solution of the “electric” and “magnetic” boundary value problems determines the minima of a reflection or transmission coefficients of fundamental wave on discontinuities. To algebraize the boundary value problems for the eigen frequencies of volume resonator with discontinuity, the corresponding two-dimensional functions of the magnetic potential are constructed, through which the components of the current density on the strip are determined. The functions of magnetic potential were defined by decomposing them into expansion by Fourier series, which ensures stable convergence of the series and numerical calculation algorithm. The developed technique has been tested by calculating the eigenfrequency spectra of an open microstrip stub using the transverse resonance method on the example of an open stub in a microstrip transmission line with a resonant frequency of about 3.0 GHz. Also, a technique for numerical solutions of “electric” and “magnetic” boundary-value problems for resonators with two electrodynamically coupled symmetric open stubs in a microstrip transmission line is developed.

Continuous Time Randon Walks with Resetting in a Bounded Chain

The model of classical random walks with Poissonian resetting in a one-dimensional lattice is analyzed in detail in its general version. A special emphasis is made on the resetting effects that emerge due to the variety of arbitrary initial and boundary conditions. A quantum analog of the model is also discussed.

Nonexistence for a system of time‐fractional diffusion equations in an exterior domain

A system of time‐fractional diffusion equations posed in an exterior domain of ( ) under homogeneous Dirichlet boundary conditions is investigated in this paper. The time‐fractional derivatives are considered in the Caputo sense. Using nonlinear capacity estimates specifically adapted to the nonlocal properties of the Caputo fractional derivative, the geometry of the domain, and the boundary conditions, we obtain sufficient conditions for the nonexistence of a weak solution to the considered system.

Requirements for the Development and Operation of a Freeze-Up Ice-Jam Flood Forecasting System

This article provides a comprehensive overview of ice-jam flood forecasting methodologies applicable to rivers during freezing. It emphasizes the importance of understanding river ice processes and fluvial geomorphology for developing a freeze-up ice-jam flood forecasting system. The article showcases a stochastic modelling approach, which involves simulating a deterministic river ice model multiple times with varying parameters and boundary conditions. This approach has been applied to the Exploits River at Badger in Newfoundland, Canada, a river that has experienced several freeze-up ice-jam floods. The forecasting involves two approaches: predicting the extent of the ice cover during river freezing and using an ensemble method to determine backwater flood level elevations. Other examples of current ice-jam flood forecasting systems for the Kokemäenjoki River (Pori, Finland), Saint John River (Edmundston, NB, Canada), and Churchill River (Mud Lake, NL, Canada) that are operational are also presented. The text provides a detailed explanation of the processes involved in river freeze-up and ice-jam formation, as well as the methodologies used for freeze-up ice-jam flood forecasting. Ice-jam flood forecasting systems used for freeze-up were compared to those employed for spring breakup. Spring breakup and freeze-up ice-jam flood forecasting systems differ in their driving factors and methodologies. Spring breakup, driven by snowmelt runoff, typically relies on deterministic and probabilistic approaches to predict peak flows. Freeze-up, driven by cold temperatures, focuses on the complex interactions between atmospheric conditions, river flow, and ice dynamics. Both systems require air temperature forecasts, but snowpack data are more crucial for spring breakup forecasting. To account for uncertainty, both approaches may employ ensemble forecasting techniques, generating multiple forecasts using slightly different initial conditions or model parameters. The objective of this review is to provide an overview of the current state-of-the-art in ice-jam flood forecasting systems and to identify gaps and areas for improvement in existing ice-jam flood forecasting approaches, with a focus on enhancing their accuracy, reliability, and decision-making potential. In conclusion, an effective freeze-up ice-jam flood forecasting system requires real-time data collection and analysis, historical data analysis, ice jam modeling, user interface design, alert systems, and integration with other relevant systems. This combination allows operators to better understand ice jam behavior and make informed decisions about potential risks or mitigation measures to protect people and property along rivers. The key findings of this review are as follows: (i) Ice-jam flood forecasting systems are often based on simple, empirical models that rely heavily on historical data and limited real-time monitoring information. (ii) There is a need for more sophisticated modeling techniques that can better capture the complex interactions between ice cover, water levels, and channel geometry. (iii) Combining data from multiple sources such as satellite imagery, ground-based sensors, numerical models, and machine learning algorithms can significantly improve the accuracy and reliability of ice-jam flood forecasts. (iv) Effective decision-support tools are crucial for integrating ice-jam flood forecasts into emergency response and mitigation strategies.

Local geometric properties of conductive transmission eigenfunctions and applications

Abstract The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$ , $n=2,3$ . Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [26] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [26] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [26] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.

Assessing the effects of sustainable supply chain management practices on operational performance: the role of business regulatory compliance and corporate sustainability culture

PurposeThis study examines the mediating and moderating effects of business regulatory compliance (BRC) on the association between sustainable supply chain management practices (SSCMP) and operational performance (PERFOP), and how corporate sustainability culture (CSC) serves as a boundary condition to BRC.Design/methodology/approachThis research draws data from 245 firms operating in multiple industries in Ghana. Ordinary Least Square (OLS) was employed to test the direct effects, while Hayes Process Macros was employed to test the indirect and conditional effects among the study variables using a structural equation modelling approach.FindingsThe results showed that SSCMP has a direct positive effect on PERFOP. The study further revealed that BRC mediates the relationship between SSCMP and PERFOP. This study found that BRC negatively moderates the association between SSCMP and PERFOP, suggesting that high levels of BRC generate unintended adverse effect on the SSCMP- PERFOP link. However, the results revealed that CSC serves as a boundary condition to BRC.Originality/valueTo the best of our knowledge, this is the first study that emphasizes how the resource-based view and regulatory focus theory interact to explain how different degrees of CSC and BRC impact SSCMP performance outcomes. This study advances research in the sustainability literature, in response to calls for further research in this domain. This study draws decision-makers attention on the need to make sustainability practices an integral part of corporate culture in order to set a business tone that stimulates easy compliance to sustainability requirements.

Is Beauty the Key to Market Entry? Evaluating Influencer Beauty Through Computer Vision and Multimodal Machine Learning

ABSTRACT Purpose Livestreaming commerce is becoming increasingly frequent, and this rapid development has benefited from ever-increasing numbers of influencers joining businesses. Given this context, the purpose of this study is to examine the nonlinear effect of influencers’ beauty on viewer purchases. Methodology Based on the unstructured data of 2,597 livestreaming clips from TikTok, we first leverage a computer vision-based API interface, Face++, to calculate influencer beauty. Economic models are used to investigate this relationship. Second, the Sobel test is used to test the mediating effects of LSTM-based influencer trustworthiness. Finally, two moderators, product category and influencer type, are verified to clarify the boundary conditions. Findings First, there is an inverted U-shaped relation between influencer beauty and sales rate. Second, influencer trustworthiness mediates the impact of influencer beauty on sales rate. Finally, we find that compared with newcomer influencer selling experience products, veteran influencer beauty has a greater impact on sales when selling search products. Implications First, to the best of our knowledge, this is one of the few empirical studies evaluating influencer beauty through video data. More broadly, our research contributes to the rich influencer marketing literature by taking advantage of the abundant visual information provided by the new business context of livestreaming. The second is the new method of computer vision and multimodal machine learning. The combination of these new methods provides a scalable toolkit for unstructured data mining for academia and a realistic reference for livestreaming commerce for industry. The third contribution is content validity. We depend on hard archival data, which reflect changes in influencer beauty and viewers’ purchases in real time. This study extends the external validity of past studies and has greater reference value for real livestreaming businesses.

Influence of seawater loading on the thermal history of underlying strata in an oceanic basin—an example from the eastern Gulf of Papua

The eastern Gulf of Papua, at the easternmost end of the Papuan Basin, has been subjected to extended seawater loading during the Cenozoic, allowing an investigation into the influence of seawater loading on the thermal development of the underlying rock layers in the oceanic basin. Utilising paleontological, lithologic and paleobathymetric data, along with present-day temperature fields, this study reconstructed the burial history, thermal history and maturity of the eastern Papuan Basin using PetroMod2012.2 1D software. Burial history curves for the virtual wells were employed to trace the evolutionary stages in different regions, revealing a positive relationship between predicted vitrinite reflectance (R o) and modelled thermal history. R o values displayed a gradual decrease from northeast to southwest, with higher R o values observed in areas unaffected by seawater loading. The presence of seawater loading had a notable impact on thermal history, particularly influencing the upper boundary condition and the sediment–water interface temperature of the temperature field. This research enhances our understanding of the Meso-Cenozoic thermal history of the eastern Papuan Basin and reveals the factors influencing stratigraphic thermal evolution.

Effect of displacement loading rate on dynamic mechanical characteristics of fault stick-slip under constant normal stiffness conditions

The role of the displacement loading rate in fault activation and evolution is of utmost importance, yet most existing studies have primarily focused on its effect under constant normal load (CNL) conditions. However, in reality, the rock mass surrounding the earthquake source at the deep part of the fault provides normal stiffness conditions. Therefore, the influence of the displacement loading rate on the dynamic mechanical characteristics of fault stick-slip under constant normal stiffness (CNS) conditions remains uncertain. To bridge this research gap, we conducted an experimental investigation on simulated faults in granite under constant normal stiffness (CNS) conditions. Our analysis focused on the influence of the displacement loading rate on the spatial and temporal evolution of local stresses along the fault and the size of the fault nucleation zone. The findings revealed the following: Under the CNS condition, the equivalent shear stress is larger compared to the CNL condition, while the shear stress drop is smaller. The recovery of normal stress under CNS conditions depends more on the displacement loading rate. The nucleation location of the fault is influenced by the normal boundary conditions, with a larger nucleation zone observed in the CNS condition than in the CNL condition. In the early stage of friction, the local stress and stress drop of the fault exhibit a positive correlation with the displacement loading rate, whereas in the later stage, they display a negative correlation. Moreover, at the same location, the order of local stress drop rates for the fault is v3 > v1 > v2, where v1 represents the local normal stress drop rate, v2 represents the local shear stress drop rate and v3 represents the local friction coefficient drop rate. These research results contribute to a further understanding of the deep fault-slip mechanical behavior.

A modeling method for thermal steady-state simulation of the four-layer printed circuit board.

Thermal simulation of a Printed Circuit Board (PCB) can help identify potential overheating risks in the circuit. The proposed modeling method combines analytical temperature solutions and numerical approximations. Only Fourier-series analytical solutions related to the prepreg-layer surfaces need to be calculated, rather than the entire structure. Heat transfer through the lateral sides of a PCB is approximately considered as part of the compensated heat flux of the insulating-layer surface boundaries. Heat diffusion within or between metal layers is numerically approximated using the finite volume method. The core layer is treated as "thermally-thick". Temperature-dependent boundary conditions are considered through iterations. A test solver was developed based on the method. The modeling accuracy was validated by comparison with COMSOL Multiphysics for a four-layer structure with a moderate degree of discretization. Additionally, a PCB for generating DC 3.3V was designed, tested, and modeled, with the modeling results confirmed by the thermal images. The electro-thermal analysis of the distribution of electric potential and Joule heating in traces and vias was integrated into the PCB model. The layout maps of the PCB were further adjusted to reduce Joule heating in the output circuit, and the improvement on reducing the IR drop and hotspot temperature was examined.

Self-consistent modelling of radio frequency sheath in 3D with realistic ICRF antennas

Abstract Ion Cyclotron Resonant Frequency (ICRF) induced impurity production has raised many concerns since ITER proposed to change the first wall material from beryllium to tungsten. Enhanced DC plasma potential (VDC) due to RF sheath rectification is well known as one of the most important mechanisms behind the RF induced impurities. Our previous work (L. Lu et.al, Plasma Phys. Control. Fusion 60 (2018) 035003) considered the impact of both the slow wave and the fast wave on the RF sheath rectification in a 2D geometry. It can barely recover the double-hump structure of the VDC poloidal distribution observed in various machines when only the slow wave is modelled using the multi-2D approach which intrinsically assumes the poloidal wavenumber kz is zero. The fast wave on the other hand is found to be more sensitive to a finite kz and may need to be tackled in 3D. This work reports our recent progress on the 3D RF sheath modelling. In this new code, the latest RF sheath boundary conditions (J. R. Myra, J. Plasma Phys. 87 (2021) 905870504) and the realistic 3D ICRF antennas are implemented. Compared to the 2D results, the 3D code could well recover the double-hump poloidal distribution of VDC even with the fast wave included, which confirms our speculation on the necessity of treating the fast wave in 3D. While the double-hump pattern is robust in the simulation, the amplitude of VDC is found to be affected by the magnetic tilt angle and the antenna geometry. This emphasizes the importance of adopting a realistic antenna geometry in the RF sheath modelling. The double-hump VDC poloidal structure breaks as the magnetic tilt angle increases. This is explained by the gyrotropic property of the cold plasma dielectric tensor. The spatial proximity effect we identified in the previous 2D simulations is still valid in 3D. Finally, simulation shows the slow wave dominates the RF sheath excitation in the private SOL, while the fast wave gradually takes over when moving to the far SOL region. This code could be a new tool to provide numerical support for ITER impurity assessment and ICRF antenna design.

Turing–Hopf Bifurcation Coinduced by Diffusion and Delay in Gierer–Meinhardt Systems

This paper investigates the impact of gene expression time delay and diffusion on the dynamic behavior of a class of Gierer–Meinhardt systems under Neumann boundary conditions. It provides necessary and sufficient conditions for the emergence of Hopf, Turing, and Turing–Hopf bifurcations. Utilizing the normal form of the Turing–Hopf bifurcation, the spatiotemporal dynamics close to the bifurcation point are categorized into six types, encompassing spatially inhomogeneous and homogeneous periodic solutions, as well as spatially homogeneous and inhomogeneous steady states, along with their transitions. Notably, it’s observed that the systems may lack stable spatially inhomogeneous periodic solutions under specific parameters, despite the emergence of Turing–Hopf bifurcation. These findings are supported by numerical simulations.