Boundary Conditions Research Articles

Relativistic scalar fields canonical quantization in Einstein–Yang–Mills–Higgs’s rotating black hole space-time

The quantum theory of relativistic mechanics to deal with the scalar fields behavior in a curved space-time is represented by the Klein–Gordon equation. In this work, we will investigate the gravitationally bound states of massive and massless scalar fields around a Einstein–Yang–Mills–Higgs’s rotating black hole. After applying the standard separation of variables ansatz, we will show in detail how to obtain the novel exact solutions of the radial part of the governing Klein–Gordon equation and express the radial solution in terms of the Confluent Heun functions. By applying the bound state boundary conditions, the Confluent Heun functions are reduced to be polynomials that lead to energy quantization. We find that the scalar fields have complex-valued energy levels that indicate the decaying/growing bound states known as quasibound states. In the end, using the exact radial solution, we derive the radiation distribution function of the black hole’s outer horizon to obtain the equation of the Hawking temperature.

Upwind Summation-by-parts Finite Differences: error Estimates and WENO methodology

High order upwind summation-by-parts finite difference operators have recently been developed. When combined with the simultaneous approximation term method to impose boundary conditions, the method converges faster than using traditional summation-by-parts operators. We prove the convergence rate by the normal mode analysis for such methods for a class of hyperbolic partial differential equations. Our analysis shows that the penalty parameter for imposing boundary conditions affects the convergence rate for stable methods. In addition, to solve problems with discontinuous data, we extend the method to also have the weighted essentially nonoscillatory property. The overall method is stable, achieves high order accuracy for smooth problems, and is capable of solving problems with discontinuities.

Analysis of the Long-Term Interaction Between Molten Core and Dry Concrete at Fukushima Daiichi Unit 1

The latest investigations of Fukushima Daiichi Unit 1 have demonstrated that corium attack to the pedestal walls and pedestal floor has occurred in Fukushima Daiichi Unit 1 to a certain extent. The results of past analytical benchmarks, such as the Organisation for Economic Co-operation and Development (OECD)/Nuclear Energy Agency (NEA) Benchmark Study of the Accident at the Fukushima Daiichi Nuclear Power Plant (BSAF project), have agreed with this finding. However, the latest investigation does not show evidence of unlimited molten core–concrete interaction (MCCI), which is one of the main discrepancies from the BSAF project. More recently a MCCI benchmark has been launched in the context of the OECD/NEA project ARC-F (Analysis of Information from Reactor Building and Containment Vessels of Fukushima Daiichi Nuclear Power Station). In the benchmark, common geometry, boundary, and initial conditions have been selected among all the participants. The results show an improved agreement among different codes for what concerns overall erosion, corium temperature, and hydrogen generation, confirming that to some extent, the earlier scatter found in these variables came from differences in the MCCI scenario modeled by each partner. However, common unlimited erosion, not observed by onsite visual inspections, is still predicted. Understanding the origin of this deviation might provide insights into boundary conditions, model drawbacks, or ill-posed assumptions that might need to be revisited (e.g. interfacial temperature, effective heat transfer coefficients, concrete heat transfer). In this paper, a summary of the overall results and a discussion of modeling and boundary conditions is presented to disclose the results of the activity and the future steps to be taken in the OECD/NEA project FACE (Fukushima Daiichi Nuclear Power Station Accident Information Collection and Evaluation).

Particle scattering and fusion for the Ablowitz–Ladik chain

The Ablowitz–Ladik (AL) chain is an integrable discretized version of the nonlinear Schrödinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with 1/sinh2 pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the AL chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule.

Power versus morality: uncovering the underlying mechanisms of consumer response to perceived visual sustainability in package design

Purpose Visual sustainability has gained significant relevance for both firms and consumers. While the importance of perceived sustainability in package design is well researched, there is a research gap regarding divergent responses of consumers to perceived visual sustainability. This research aims to close this gap by providing deeper insights into the underlying mechanisms of perceived visual sustainability in package design. As a boundary condition, this work also investigates gender differences in response to a design’s visual sustainability. Design/methodology/approach To explore the mediating influences of cognitive (i.e. a product’s gentleness and power) versus emotional (i.e. moral satisfaction) attributes as well as the role of consumer gender in the perceived visual sustainability–purchase intention relationship, the authors extend previous research through three experiments. Findings Study 1 provides initial evidence supporting the main effect of perceived visual sustainability on purchase intention. Findings of Study 2 show that moral satisfaction serves as a significant driver of purchase intention for females, while power-related attributes are more influential for males. Study 3 provides additional evidence for the main effect, the interaction effect with consumer gender and underlying mechanisms. Practical implications These findings have important implications for marketers and designers aiming to design packages that appeal to different consumer groups based on their (gender-specific) values regarding visual sustainability. Originality/value This work extends the literature on green behavior by highlighting the importance of perceived visual sustainability as a factor that influences purchase intention and the role of cognitive versus affective mechanisms in shaping consumer responses to design sustainability.

The Corporate Honesty Effect and Its Boundary Conditions: B2B Firms’ Communications on Withdrawal from Russia

ABSTRACT Purpose Against the backdrop of the Russia-Ukraine conflict and ensuing industrial turmoil as well as the pressure of stakeholder sentiments, numerous U.S-based multinational B2B firms announced about their intent to withdraw from the Russian market. This study aims to probe the veracity of this form of corporate communication, exploring the corporate honesty effect by juxtaposing the stated withdrawal intentions against the actual scale of divestment. Methodology/approach We identify 241 cases of response to the Russia-Ukraine conflict pertaining to U.S-based multinational B2B corporations. This includes 34 cases of no withdrawal (i.e., no communication) and 207 cases of announcements about the firm’s intent to withdraw from Russia. For these cases, we calculate the actual scale of withdrawal (Actual Divestment Index) based on the data from Federal Tax Service of Russia and the Central Bank of the Russian Federation. Considering Actual Divestment Index as a fractional measure, we conduct fractional logit regression analysis, where the effect of the withdrawal communication on Actual Divestment Index is interpreted as the corporate honesty effect. Findings Controlling for variables such as firm size, leverage, return on assets, institutional ownership, entry mode, and industry, the analysis reveals that the scope of intended withdrawal – reflected in the stages of no action, non-essential pullout, suspension, partial core, and full core withdrawal – is positively associated with the observed level of divestment. The findings further show that firms with larger corporate resources, higher profitability, and deeper local market exposure exhibit a greater level of corporate honesty. Research implications This study builds on the MFHB framework (Cooper et al., 2023) that differentiates several distinct dimensions of corporate honesty. Our research applies these dimensions to formulate an operational definition of corporate honesty which emphasizes the fidelity to the firm’s communicated intent, situationally activated in response to external pressures and emergent socio-political sentiments, in the context of established domestic/international business relationships. Also, we contribute to the current body of knowledge on corporate honesty by introducing a method of measuring the corporate honesty effect. Practical implications Marketing managers of multinational B2B firms must endeavor to maintain the stakeholder perceptions of corporate legitimacy by constantly monitoring the level of corporate honesty effect, specifically during the time of war-induced disruptions and turmoil in B2B markets. Managers of B2B firms with larger resources, better profitability, and deeper market exposure can leverage their advantageous position to further highlight and promote their actual performance in this aspect to assuage the concerns and negative sentiments of stakeholders. Originality/value/contribution This research contributes to theories of corporate honesty by contextualizing the concept of corporate honesty within the framework of communication-action congruence. This is done in relation to the strategic divestment communications and actions undertaken by B2B multinational firms in a market embroiled in moral turmoil during a geopolitical conflict. Our alternative operationalization of corporate honesty facilitates a quantifiable assessment of this construct, offering an alternative methodology to evaluate the integrity of corporate communications vis-à-vis actual organizational action in crisis contexts. Our findings about the boundary conditions of the corporate honesty effect contributes to a nuanced understanding of the phenomenon within the domain of sociopolitical corporate activism, ethical business practices, and international market dynamics.

Global Sensitivity Analysis for Segmented Inverse Uncertainty Quantification in the Safety Analysis of Nuclear Power Plants

Within the Best Estimate Plus Uncertainty framework for the safety analysis of Nuclear Power Plants, the quantification of the uncertainties affecting the Thermal-Hydraulics (T-H) codes used is crucial. For this, Inverse Uncertainty Quantification (IUQ) methodologies are being developed for determining the probability density functions of relevant T-H codes input parameters, based on experimental data from Separate Effect Tests (SETs) experimental facilities. In practice, IUQ is challenged by the large range of variability of the experimental data in terms of Initial and Boundary Conditions (ICs & BCs), because the experimental campaigns are designed to cover the widest possible domain of conditions with the smallest number of experiments, so that same or similar ICs and BCs are seldomly repeated. To address this issue, we propose to use global sensitivity analysis, to tailor the IUQ on specific sub-regions described by segmented ICs & BCs domains. The methodology proposed is exemplified on two SETs, namely Sozzi-Sutherland and Super Moby Dick, whose experimental databases have been made available in the ATRIUM (Application Tests for Realization of Inverse Uncertainty quantification and validation Methodologies in thermal hydraulics) project promoted by the OECD/NEA/CSNI. The results obtained are superior to those of traditional IUQ methodologies for models highly sensitive to ICs & BCs.

Existence results for coupled sequential ψ-Hilfer fractional impulsive BVPs: topological degree theory approach

In this paper, the coupled system of sequential ψ-Hilfer fractional boundary value problems with non-instantaneous impulses is investigated. The existence results of the system are proved by means of topological degree theory. An example is constructed to demonstrate our results. Additionally, a graphical analysis is performed to verify our results.

Boundary value problems for a mixed-type loaded equation with a characteristic and noncharacteristic line of type change

Boundary value problems for a mixed-type loaded equation with a characteristic and noncharacteristic line of type change

The First Boundary-Value Problem for the Fokker–Planck Equation with One Spatial Variable

The First Boundary-Value Problem for the Fokker–Planck Equation with One Spatial Variable

On the feasibility of ultrasound Doppler-based personalized hemodynamic modeling of the abdominal aorta

BackgroundPersonalized modeling is a promising tool to improve abdominal aortic aneurysm (AAA) rupture risk assessment. Computed tomography (CT) and quantitative flow (Q-flow) magnetic resonance imaging (MRI) are widely regarded as the gold standard for acquiring patient-specific geometry and velocity profiles, respectively. However, their frequent utilization is hindered by various drawbacks. Ultrasound is used extensively in current clinical practice and offers a safe, rapid and cost-effective method to acquire patient-specific geometries and velocity profiles. This study aims to extract and validate patient-specific velocity profiles from Doppler ultrasound and to examine the impact of the velocity profiles on computed hemodynamics.MethodsPulsed-wave Doppler (PWD) and color Doppler (CD) data were successfully obtained for six volunteers and seven patients and employed to extract the flow pulse and velocity profile over the cross-section, respectively. The US flow pulses and velocity profiles as well as generic Womersley profiles were compared to the MRI velocities and flows. Additionally, CFD simulations were performed to examine the combined impact of the velocity profile and flow pulse.ResultsLarge discrepancies were found between the US and MRI velocity profiles over the cross-sections, with differences for US in the same range as for the Womersley profile. Differences in flow pulses revealed that US generally performs best in terms of maximum flow, forward flow and ratios between forward and backward flow, whereas it often overestimates the backward flow. Both spatial patterns and magnitude of the computed hemodynamics were considerably affected by the prescribed velocity boundary conditions. Larger errors and smaller differences between the US and generic CFD cases were observed for patients compared to volunteers.ConclusionThese results show that it is feasible to acquire the patient-specific flow pulse from PWD data, provided that the PWD acquisition could be performed proximal to the aneurysm region, and resulted in a triphasic flow pattern. However, obtaining the patient-specific velocity profile over the cross-section using CD data is not reliable. For the volunteers, utilizing the US flow profile instead of the generic flow profile generally resulted in improved performance, whereas this was the case in more than half of the cases for the patients.

Is Sustainability a Liability? Green Marketing and Consumer Beliefs About Eco-Friendly Products

Prior research has suggested that consumers believe sustainable products tend to underperform compared with those made using traditional methods, a phenomenon referred to as the “sustainability liability.” Despite early conceptual justification and evidence supporting this argument, recent research has not attempted to validate this effect and assess its practical relevance. By employing a variety of scenarios adapted from prior studies, the authors quantify the magnitude of the sustainability-liability effect and show that it is relatively small and unlikely to be meaningful. This research also estimates the boundary conditions to identify scenarios in which a significant sustainability-liability effect might occur. Using archival data, the authors demonstrate that the association between sustainability and inferior product performance has decreased over time, explaining the discrepancy between their findings and prior research. These findings have important public policy implications, providing decision makers with empirical evidence that designing and promoting eco-friendly products can benefit society without detracting from the perceived performance of the company's offerings.

Global solutions to a chemotaxis system with singular density-suppressed motility and superlinear consumption

In this paper, we consider a migration-consumption taxis system involving singular density-suppressed motility and superlinear consumption(⋆){ut=Δ(uϕ(v)),vt=Δv−uvm in a bounded smooth domain Ω⊂Rn(n≥2) with no-flux boundary conditions. Here, m≥1 is a constant. The motility function ϕ generalizes the singular prototype given by ϕ(ξ)=ξ−α(ξ>0) with α>0. In Tao and Winkler (2023) [32], Tao and Winkler studied the system (⋆) with m=1 and obtained respectively the global existence of very weak-strong and weak-strong solutions. We study the system (⋆) with m≥1 and prove that a so-called very weak-strong solution can be established for arbitrarily large initial data in W1,∞(Ω). Moreover, under the additional constraints of(⋆⋆)(6−n)α+2m(n+2)−(3n+2)>0, and with an additional assumption on ϕ′, the model (⋆) possesses a global weak-strong solution. In particular, when 2≤n≤5 and m=1, (⋆⋆) is equivalent to α>n−26−n, which consistent with the result of Tao and Winkler. However, our result contains the case n≥6. When n=6, (⋆⋆) is equivalent to m>54 without any requirement for α>0. When n>6, (⋆⋆) is equivalent to m>3n+22n+4 and 0<α<2m(n+2)−(3n+2)n−6.

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

On the solutions of a nonlinear system of q-difference equations

In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. Also, we give two examples to support our results.

Efficient determination of Born-effective charges, LO-TO splitting, and Raman tensors of solids with a real-space atom-centered deep learning approach

We introduce a deep neural network (DNN) framework called the Real-space Atomic Decomposition NETwork (radnet), which is capable of making accurate predictions of polarization and of electronic dielectric permittivity tensors in solids and aims to address limitations of previously available machine learning models for Raman predictions in periodic systems. This framework builds on previous, atom-centered approaches while utilizing deep convolutional neural networks. We report excellent accuracies on direct predictions for two prototypical examples: GaAs and BN. We then use automatic differentiation to efficiently calculate the Born-effective charges, longitudinal optical-transverse optical (LO-TO) splitting frequencies, and Raman tensors of these materials. We compute the Raman spectra, and find agreement with ab initio results. Lastly, we explore ways to generalize the predictions of polarization while taking into account periodic boundary conditions and symmetries.

Lubrication flow in grinding

In the machining process known as grinding, fluid is applied to regulate the temperature of the workpiece and reduce the risk of expensive thermal damage. The factors that influence the transport of this grinding fluid are not well understood; however, it is important to gain understanding in order to try to avoid the unnecessary cost incurred from its inefficient application. In this work, we use the method of matched asymptotic expansions to derive the multiscale system of equations that governs the flow. Under the lubrication approximation, we show that it is possible to calculate the flow rate through the grinding zone without having to solve for the flow far from the grinding zone. Additional empirically determined boundary conditions do not need to be imposed. With this lubrication model, we quantify the effect of experimental parameters on the flow field in the grinding zone and study how the flow regime responds to changes in these parameters.

A developed fatigue analysis approach for composite wind turbine blade adhesive joints using finite-element submodeling technique

The intricate shapes and complex structures of composite wind turbine blades pose significant challenges in conducting local-fatigue simulation analyses. Moreover, adhesive joints, commonly found in composite wind turbine blades, are often neglected in current finite-element methods, leading to a dearth of empirical evidence to substantiate design enhancements for these blades. To tackle these issues, this study introduces a fatigue analysis methodology based on a finite-element submodeling approach to investigate the local fatigue behavior of composite wind turbine blades, with particular emphasis on the adhesive joints. The research begins with a comprehensive fatigue simulation analysis of composite wind turbine blades to establish boundary conditions for subsequent submodeling. A specialized submodel focusing on the trailing edge, a common adhesive joint, is constructed with the inclusion of extra adhesive regions for a more accurate depiction of their actual configuration. This submodel is subsequently utilized to investigate the localized fatigue characteristics unique to the trailing edge. Moreover, an exploration into the influence of the submodeling technique and its parameters on the predicted outcomes is carried out to enhance the applicability of the proposed methodology. These results significantly advance the understanding of local static and fatigue properties in large-scale structures through finite element analysis.

The algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem

We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination method) is based on the Uzawa method by decoupling the linear system, while the second algorithm (Global inversion) is based on the overall resolution of the system by the GMRES method. A detailed implementation is proposed and some numerical tests are carried out in two and three dimensions and where the domain is multiply connected.

Impact of mixing low-reactivity gases on the mechanism of hydrogen spontaneous combustion: A ReaxFF MD study

The phenomenon of spontaneous combustion during the release of high-pressure H2 is critical to the safe storage and transportation. Besides physical methods to suppress self-ignition, the approach of mixing low-reactivity gases has gained increasing attention. Previous work has mainly focused on the flow, physical heating effects, and boundary conditions of self-ignition in mixed gases, while the intrinsic chemical reaction mechanisms of spontaneous combustion remain underexplored. To clear this issue, this work uses the ReaxFF MD simulation method to study the spontaneous combustion process of H2/CO and H2/CH4 mixtures with various concentrations. The results indicate that: (1) in pure H2, H2/CO, and H2/CH4 systems, the primary initial reaction mechanism is H2+O2HO2+H. Additionally, in some mixed systems, CO + O2CO2+O and CH4+O2CH3+HO2 may also serve as initial reaction mechanisms. (2) Under fuel-lean combustion conditions, the RIDTs of the systems decrease, supporting the viewpoint that self-ignition typically occurs first in fuel-lean regions. The addition of CO and CH4 increases the RIDTs, which helps inhibit the development of self-ignition. (3) In H2-rich environments, CO combusts to CO2 through the formation of HOCO, while CH4 undergoes dehydrogenation and oxidation processes through intermediates such as CH3, CH3O, and HCHO, leading to the formation of CO and CO2. The combustion of H2 is also influenced by these processes. (4) The addition of CO and CH4 increases the activation energy of H2 combustion, raising the reaction energy barrier that must be overcome for spontaneous combustion. This effectively helps to suppress the occurrence and development of self-ignition during the release of high-pressure gases.