Underlying Boundary Conditions Research Articles

How and when is boundary-spanning behaviour related to innovative behaviour: role of intrinsic motivation and organisational support

PurposeThis study aimed to investigate the underlying boundary conditions under which boundary-spanning behaviour has a positive or negative effect on innovative behaviour.Design/methodology/approachA multi-wave and multi-source research design was adopted to collect data. Data were analysed using the multilevel structural equation modelling and latent moderated structural equation approach.FindingsThe results showed that boundary-spanning behaviour was significantly and negatively associated with employees' innovative behaviour via ego depletion when employees' intrinsic motivation or organisational support was low. Additionally, boundary-spanning behaviour was significantly and positively associated with employees' innovative behaviour via ego depletion when employees' intrinsic motivation or organisational support was high.Originality/valueThis research suggests that the consequences of boundary-spanning behaviour are conditional, explaining the contrasting conclusions in this regard.

How and when higher climate change risk perception promotes less climate change inaction

Climate change has been positioned as one of the most severe environmental threats facing us today. To address climate change, enhancing climate change risk perception and reducing climate change inaction are both critical. However, little research has touched on the issue of whether climate change risk perception is linked to climate change inaction in a negative manner. Moreover, there is still much unknown about the complex process behind this relationship, and the boundary conditions of this process awaits clarification. To address these gaps in the literature, two studies were conducted to first confirm the possible negative association between climate change risk perception and climate change inaction and, second, explore through a parallel mediational model whether climate change belief and environmental efficacy mediate simultaneously the relation between climate change risk perception and climate change inaction. Finally, a moderated sequential mediational model was used to investigate whether climate change risk perception is associated with climate change inaction through the sequential mediation of climate change belief and environmental efficacy, and to clarify underlying boundary conditions by analyzing the moderation of mindfulness as well. The results showed that, as expected, higher levels of climate change risk perception were related to less climate change inaction, and this relation was mediated by enhanced climate change belief and heightened environmental efficacy in a sequential manner. Furthermore, the sequential mediating effect of climate change belief and environmental efficacy was stronger among those who had a higher level of mindfulness. These findings advance the emerging research on climate change inaction by elucidating the mechanisms underlying the effect of climate change risk perception. Moreover, they extend the Domain-Context-Behavior (DCB) model and Gateway belief model (GBM). In practice, climate change education and climate change inaction interventions can be designed and implemented to nudge clean production, green supply chain and green consumption, which finally contribute to sustainable development and the ‘green transformation’ of society.

Methods to Extract Underlying Boundary Conditions from Transient Metal Effectiveness Measurements

Metal effectiveness measurements (or overall cooling effectiveness measurements) are becoming increasingly used to understand complex coupled systems in gas turbine experimental research. Unlike traditional techniques in which individual boundary conditions are measured in isolation and superposed using a thermal model, metal effectiveness measurements give the final result of a complex coupled system. In correctly scaled experiments this allows aerothermal performance at near-engine conditions to be evaluated directly, and is thus powerful both as a research technique and for derisking engine development programs. The technique is particularly useful for evaluating the thermal performance of internally cooled turbine components, because of the complexity and degree of interaction of the underlying boundary conditions. An intrinsic limitation of metal effectiveness measurement data is that the individual boundary conditions (e.g., the internal and external heat transfer coefficients) cannot be directly obtained from the final measurement. Decoupling of these boundary conditions would allow deeper understanding of the systems that are the subject of experiments. The objective of this paper is to present methods to extract the individual underlying boundary conditions from data available in typical metal effectiveness experimental measurements, and to assess the uncertainty associated with decoupling techniques. Although we reference experimental data from advanced facilities for metal effectiveness research throughout, much of the analysis is performed using a low-order heat transfer model to allow the impact of experiment design and measurement errors to be clearly separated at each stage of the analysis.

Caribbean cyclone activity: an annually-resolved Common Era record

Tropical cyclones (TC) represent a substantial threat to life and property for Caribbean and adjacent populations. The prospective increase of TC magnitudes, expressed in the 15th chapter of the IPCC AR5 report, entails a rising probability of ecological and social disasters, which were tragically exemplified by several severe Caribbean TC strikes during the past 20 years. Modern IPCC-grade climate models, however, still lack the required spatial and temporal resolution to accurately consider the underlying boundary conditions that modulate long-time TC patterns beyond the Instrumental Era. It is thus necessary to provide a synoptic mechanistic understanding regarding the origin of such long-time patterns, in order to predict reliable changes of TC magnitude and frequency under future climate scenarios. Caribbean TC records are still rare and often lack the necessary continuity and resolution to overcome these limitations. Here, we report on an annually-resolved sedimentary archive from the bottom of the Great Blue Hole (Lighthouse Reef, Belize). The TC record encompasses 1885 years and extends all existing site-specific TC archives both in terms of resolution and duration. We identified a likely connection between long-term TC patterns and climate phenomena responses to Common Era climate variations and offer a conceptual and comparative view considering several involved tropospheric and oceanographic control mechanisms such as the El-Niño-Southern-Oscillation, the North Atlantic Oscillation and the Atlantic Multidecadal Oscillation. These basin-scaled climate modes exercise internal control on TC activity by modulating the thermodynamic environment (sea-surface temperature and vertical wind shear stress dynamics) for enhanced/suppressed TC formation both on millennial (primary) and multi-decadal (secondary) time scales. We interpret the beginning of the Medieval Warm Period (MWP) as an important time interval of the Common Era record and suspect that the southward migration of the intertropical convergence zone (ITCZ) caused, in combination with extensive hydro-climate changes, a shift in the tropical Atlantic TC regime. The TC activity in the south-western Caribbean changed in general from a stable and less active stage (100–900 CE) to a more active and variable state (1,100 CE-modern).

Fully Legendre Spectral Galerkin Algorithm for Solving Linear One-Dimensional Telegraph Type Equation

In this paper, we analyze and implement a new efficient spectral Galerkin algorithm for handling linear one-dimensional telegraph type equation. The principle idea behind this algorithm is to choose appropriate basis functions satisfying the underlying boundary conditions. This choice leads to systems with specially structured matrices which can be efficiently inverted. The proposed numerical algorithm is supported by a careful investigation for the convergence and error analysis of the suggested approximate double expansion. Some illustrative examples are given to demonstrate the wide applicability and high accuracy of the proposed algorithm.

Uniqueness results on phaseless inverse acoustic scattering with a reference ball

This paper is devoted to the uniqueness in inverse acoustic scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a single incident plane wave. In this paper, based on adding a reference ball as an extra artificial impenetrable obstacle (resp. penetrable homogeneous medium) to the inverse obstacle (resp. medium) scattering system and then using superpositions of a fixed plane wave and some point sources as the incident waves, we rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of far-field patterns. The reference ball technique in conjunction with the superposition of incident waves brings in several salient benefits. First, the framework of our theoretical analysis can be applied to both the inverse obstacle and medium scattering problems. Second, for inverse obstacle scattering, the underlying boundary condition could be of a general type and be uniquely determined. Finally, only a single frequency is needed.

Equivalent core concept for large-scale structural-level applications

This study examined the applicability of the equivalent core concept, which replaces a discrete core with a homogenized solid core representing its elastic properties, on a large-scale structure. To this end, numerical verifications were performed for corrugated core structures at two levels, the specimen level and structural level. Before the verifications, analytical equations were gathered from previous reports to obtain the homogenized elastic properties of corrugated cores. At the specimen-level verifications, the maximum deflections of the corrugated core panel specimens subject to three-point bending were calculated with sandwich beam theory, finite element models with discretely modeled cores and equivalent cores. For the structural-level verifications, the maximum deflection and natural frequency were computed from a discrete finite element model and an equivalent model of a railway car body structure. The results revealed that the equivalent models gave excellent agreement with the theoretical values if the same underlying boundary conditions were used; however, greater discrepancies were observed with the discrete models. In addition, for the structural-level verifications the equivalent core model reasonably approximated the discrete model with marginal accuracy. Therefore, employing the equivalent core concept can be expected to save computational costs in the initial design stage of large-scale structures.

New Spectral Solutions for High Odd-Order Boundary Value Problems via Generalized Jacobi Polynomials

In this article, some new efficient and accurate algorithms are developed for solving linear and nonlinear odd-order two-point boundary value problems. The algorithm in linear case is based on the application of Petrov–Galerkin method. For implementing this algorithm, two certain families of generalized Jacobi polynomials are introduced and employed as trial and test functions. The trial functions satisfy the underlying boundary conditions of the differential equations, and the test functions satisfy the dual boundary conditions. The developed algorithm leads to linear systems with band matrices which can be efficiently inverted. These special systems are carefully investigated, especially their complexities. Another algorithm based on the application of the typical collocation method is presented for handling nonlinear odd-order two-point boundary value problems. The use of generalized Jacobi polynomials leads to simplified analysis and very efficient numerical algorithms. Numerical results are presented for the sake of testing the efficiency and applicability of the two proposed algorithms.

Surface–Volume–Surface Electric Field Integral Equation for Magneto-Quasi-Static Analysis of Complex 3-D Interconnects

A novel single-source surface–volume–surface integral equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new equation originates in the volume integral equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface integral equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductor's boundary. As no approximation is utilized and all underlying boundary conditions and pertinent equations are satisfied in the reduction, the new integral equation is rigorously equivalent to the solution of the traditional volume electric field integral equation. The rigorous nature of the proposed single-source surface integral equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface integral equation is also presented. Numerical solution of the proposed surface integral equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.

New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method

Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient.

Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made.

A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix

In this paper, a well-conditioned collocation method is constructed for solving general $p$th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the number of collocation points, and the underlying boundary conditions are imposed exactly. Moreover, the new basis leads to an exact inverse of the pseudospectral differentiation matrix of the highest derivative (at interior collocation points), which is therefore called the pseudospectral integration matrix (PSIM). We show that PSIM produces the optimal integration preconditioner and stable collocation solutions with even thousands of points.

Red light, blue light, Feynman and a layer of glass: the causal propagator

A propagator–description approach of the propagation of EM waves is provided, in complex situations with underlying boundary conditions. To this end, the so-called Schwinger–Feynman causal propagator is explicitly derived, and spelled out, for the first time, for transmission of a photon through, and reflection off, a layer of glass of flat parallel surfaces. In a very general context, the corresponding transition amplitudes of a polarized or unpolarized photon are obtained, and the conservation of probabilities, and the underlying consistency conditions of the results, are established. Inspired by Feynman’s intuitive and well-publicized non-technical treatment of such a problem with red and blue light, one, in a quantum view-point, is interested in the probabilities of the events just described in determining the fate of a photon. This analysis provides an alternative way of looking at the problem in question, through propagation of photons, as a physically more appealing approach, in Feynman’s spirit, than by matching plane waves at boundaries as we often do. It also shows how a propagator may be derived, in more complex situations with specific boundary conditions, than just simply in infinite extended spaces. Finally, it is hoped that this work will be stimulating and of interest to practitioners with different emphases on EM wave propagation.

The innovation potential of new infrastructure development: An empirical study of Heathrow airport's T5 project

We propose a conceptual framework to analyze technology adoption in mega infrastructure projects, and assess their potential to innovating large socio-technical systems. Drawing on an in-depth empirical analysis of Heathrow airport's Terminal 5 project, we find that innovation hinges on technology adoption decisions that are governed systematically by two intertwined determinants – assessment of expected profitability and development of absorptive capacity, both of which are distributed across various interdependent actors. On an ad hoc basis, technological decisions are also affected by other factors, namely attitudes toward risk, politics, and (lack of) established standards. We reveal how a schedule-driven project framing creates an underlying boundary condition that constrains the longitudinal process of building a ‘whole collective’ with capacity to absorb new technologies. The innovation potential of mega projects is thus subjected to a fundamental, unifying tension: on the one hand, they offer a one-off opportunity to invest in cutting-edge technologies and innovate socio-technical systems; on the other hand, project stakeholders have limited time to develop capacity to absorb novel technologies and negotiate differences on assessments of profitability and risk. Stakeholders may therefore be compelled to agree to adopt proven technologies upfront to reduce uncertainty and mitigate risks, thus limiting the innovation potential of new infrastructure development.

Structural analysis of composite bolted joints using the complex potential method

Abstract The problem of a pin-loaded hole in a symmetric composite plate with finite dimensions is considered within the scope of the classical laminate theory. The analysis is performed by means of the Lekhnitskii complex potential method. For the given problem, an appropriate power series expansion of the complex potentials is stipulated, where the coefficients are determined from the underlying boundary conditions. The present approach provides an efficient method for the calculation of stresses and displacements in the neighbourhood of the hole where failure is likely to occur.

A composite view on Windenburg's problem: Buckling and minimum stiffness requirements of compressively loaded orthotropic plates with edge reinforcements

Abstract This paper discusses the buckling behaviour of orthotropic composite plates under uniform uniaxial compression with one free reinforced unloaded edge. A typical application example for use of such a mechanical model is the web of stiffeners and frames attached to the fuselage skin of an aircraft. The considered plates are rectangular and simply supported at the loaded transverse edges. One of the longitudinal unloaded edges is also simply supported, while the second unloaded edge is not supported at all but is reinforced by a flange of arbitrary cross-section. At first, an exact solution for the elastic buckling problem is derived from the governing differential equation by imposing the underlying boundary conditions. Thereafter, two approximate closed-form solutions for the buckling load are derived, which can be conveniently used for practical application purposes. Generic buckling curves using characteristic non-dimensional quantities are also presented. Finally, the question of the required bending stiffness EI min of the flange is treated, to ensure that the flange withstands buckling and provides simply supported boundary conditions to the free reinforced plate edge.

Efficient spectral ultraspherical-dual-Petrov–Galerkin algorithms for the direct solution of (2 n + 1)th-order linear differential equations

Some efficient and accurate algorithms based on ultraspherical-dual-Petrov–Galerkin method are developed and implemented for solving (2 n + 1)th-order linear elliptic differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a spectral discretization. The key idea to the efficiency of our algorithms is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results are presented to demonstrate the efficiency of our proposed algorithms.

Explicit local buckling analysis of stiffened composite plates accounting for periodic boundary conditions and stiffener–plate interaction

Abstract The present contribution is devoted to the closed-form analysis of orthotropic plates under uniaxial uniform compressive load. The plates under consideration are stiffened by open-profile stiffeners in the longitudinal direction which represents a structural situation that is typical, e.g. for many aircraft parts such as tailplanes, wing covers or, at least in an approximate sense, fuselage sections. The analysis method explicitly accounts for periodicity properties of the given structural situation as well as for stiffener–plate interaction and is based on adequate displacement shapes for both the plate as well as the stiffeners in the form of simple polynomials and trigonometric functions. While the plates and the stiffener webs are treated as shear-rigid Kirchhoff-type plates, the stiffener flanges are modeled as Bernoulli-type beam elements in order to allow for a feasible solution of the problem. Using a Ritz-type approach, explicit expressions for the buckling loads are achieved which allow for a straightforward, efficient and yet reliable buckling analysis of stiffened composite panels. The excellent accuracy of the derived analysis method is established through comparison with the results by other authors and with results generated from the exact transcendental elasticity solution that is derived from the governing partial differential equations and the underlying boundary conditions. The characteristic buckling behaviour of stiffened composite plates is discussed for several representative plate-stiffener configurations.

Transient Surface Strains and the Deconvolution of Thermoelastic States and Boundary Conditions

Abstract Thermoelastic states as they pertain to thermal-shock are difficult to determine since the underlying boundary conditions must be known or measured. For direct problems where the boundary conditions such as temperature or flux, are known a priori, the procedure is mathematically tractable with many analytical solutions available. Although this is more practical from a measurement standpoint, the inverse problem where the boundary conditions must be determined from remotely determined temperature and/or flux data are ill-posed and therefore inherently sensitive to errors in the data. Moreover, the limited number of analytical solutions to the inverse problem rely on assumptions that usually restrict them to timeframes before the thermal wave reaches the natural boundaries of the structure. Fortunately, a generalized solution based on strain-histories can be used instead to determine the underlying thermal excitation via a least-squares determination of coefficients for generalized equations for strain. Once the inverse problem is solved and the unknown boundary condition on the opposing surface is determined, the resulting polynomial can then be used with the generalized direct solution to determine the thermal- and stress-states as a function of time and position. For the two geometries explored, namely a thick-walled cylinder under an internal transient with external convection and a slab with one adiabatic surface, excellent agreement was seen with various test cases. The derived solutions appear to be well suited for many thermal scenarios provided that the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature. While polynomials were employed for the current analysis, transcendental functions and/or combinations with polynomials can also be used.

Closed-form buckling analysis of compressively loaded composite plates braced by omega-stringers

In this contribution, the stability problem of composite plates braced by longitudinal omega-stringers under compression is treated in a closed-form analytical manner. Given that no global buckling modes of both plate and stringers occur and further assuming certain periodicity properties of the occurring local plate buckling modes, the given situation is reduced to the bifurcation buckling problem of an elastically restrained plate wherein the edge restraints depend on the geometric and material properties of the stringers and are calculated via the principle of virtual work. The buckling modes of the plate itself are approximated using an interpolation scheme consisting of rather simple trigonometric functions which allows for a closed-form analytical description of both the buckling modes as well as of the buckling loads of the elastically restrained composite plates. Accompanying detailed finite element computations show that the closed-form analytical approach is in very satisfying agreement with the numerical results and as such can be used with confidence in day-to-day engineering practice. Furthermore, the exact elasticity solution for the buckling problem of a compressively loaded elastically restrained composite plate is shortly discussed which can be derived from the governing partial differential equation in conjunction with the underlying boundary conditions of the plate. The closed-form approach can be shown to be in excellent agreement with the exact results which are generated in a numerical manner. Lastly, based on non-dimensional characteristic quantities, the exact elasticity solution is used to generate generic buckling curves which may be useful for practical engineering analysis and design purposes.