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The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.

In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.

The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.

This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.

In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.

To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.

The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.

The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

The “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.

Finite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.

The results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.

To the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

This paper studies the Digital Service Innovation (DSI) concept by systematically reviewing earlier studies from various scholarly communities. This study aims to recognize how recent advances in DSI literature from different research streams complement and can be incorporated into the growing digital servitization literature to define better and understand DSI.

After systematically identifying 123 relevant articles, this study employed complementary methods, such as author bibliographic coupling, linguistic text mining/textual analysis and qualitative content analyses.

This paper first maps the intellectual structure and boundaries of the DSI-related communities and qualitatively assesses their characteristics. These communities are (1) Innovation for digital servitization, (2) Service innovation in the digital age and (3) Adoption of novel e-services enabled by information system development. Next, the composition of the DSI concept is examined and depicted to comprehend the notion's critical dimensions. The findings discuss the range of theories and methods in the existing research, including antecedents, processes and outcomes of DSI.

This study reviews, extends the understanding of origins and critically evaluates DSI-related research. Moreover, the paper redefines and clarifies the structure and boundaries of the DSI-concept. In doing so, it elaborates on the substance of DSI and identifies the essential themes for its understanding and conceptualization. Thus, the study helps the future development of the concept and allows knowledge accumulation by bridging adjacent research communities. It helps researchers and managers navigate the foggy emerging research landscape.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

The vibration of the rails is a significant source of railway rolling noise, often forming the dominant component of noise in the important frequency region between 400 and 2000 Hz. The purpose of the paper is to investigate the influence of the ground profile and the presence of the train body on the sound radiation from the rail.

Two-dimensional boundary element calculations are used, in which the rail vibration is the source. The ground profile and various different shapes of train body are introduced in the model, and results are observed in terms of sound power and sound pressure. Comparisons are also made with vibro-acoustic measurements performed with and without a train present.

The sound radiated by the rail in the absence of the train body is strongly attenuated by shielding due to the ballast shoulder. When the train body is present, the sound from the vertical rail motion is reflected back down toward the track where it is partly absorbed by the ballast. Nevertheless, the sound pressure at the trackside is increased by typically 0–5 dB. For the lateral vibration of the rail, the effects are much smaller. Once the sound power is known, the sound pressure with the train present can be approximated reasonably well with simple line source directivities.

Numerical models used to predict the sound radiation from railway rails have generally neglected the influence of the ground profile and reflections from the underside of the train body on the sound power and directivity of the rail. These effects are studied in a systematic way including comparisons with measurements.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

This conceptual, multi-voiced paper aims to collectively explore and theorize family entrepreneuring, which is a research stream dedicated to investigating the emergence and becoming of entrepreneurial phenomena in business families and family firms.

Because of the novelty of this research stream, the authors asked 20 scholars in entrepreneurship and family business to reflect on topics, methods and issues that should be addressed to move this field forward.

Authors highlight key challenges and point to new research directions for understanding family entrepreneuring in relation to issues such as agency, processualism and context.

This study offers a compilation of multiple perspectives and leverage recent developments in the fields of entrepreneurship and family business to advance research on family entrepreneuring.

This study examines how accounting tools and techniques are used to create and support membership and reporting boundaries for a multi-entity sustainability scheme. It also considers whether boundary setting for this initiative helps to connect corporate activity with planetary boundaries and the SDGs.

A case study of a national agrifood sustainability scheme, analysing extensive documentary data and multi-entity sustainability reports. The concept of partial organising is used to frame the analysis.

Accounting, in the form of planning, verification, target setting, annual review and reporting, can be used to create a membership and a reporting boundary. Accounting tools and techniques support the scheme's standard-setting and monitoring elements. The study demonstrates that the scheme offers innovation in how sustainability reporting is managed. However, it does not currently provide a cumulative assessment of the effect of the sector's activity on ecological carrying capacity or connect this activity to global sustainability indicators.

Future research can build on this study's insights to further develop our understanding of multi-entity sustainability reporting and accounting's role in organising for sustainability. The authors identify several research avenues including: boundary setting in ecologically significant sectors, integrating global sustainability indicators at sectoral and organisational levels, sustainability controls in multi-entity settings and the potential of multi-entity reporting to provide substantive disclosure.

This paper provides insight into accounting's role in boundary setting for a multi-entity sustainability initiative. It adds to our understanding of the potential of a multi-entity reporting boundary to support connected measurement between corporate activity and global sustainability indicators. It builds on work on partial organising and provides insight into how accounting can support this form of organising for sustainability.

The purpose of this paper is to demonstrate the impact of the welding sequence on the substrate plate distortion during the wire and arc additive manufacturing (WAAM) process. This paper also aims to show the capability of finite element simulations in the prediction of those thermally induced distortions.

An experiment was conducted in which solid aluminum blocks were manufactured using two different welding sequences. The distortion of the substrates was measured at predefined positions and converted into bending and torsion values. Subsequently, a weakly coupled thermo-mechanical finite element model was created using the Abaqus simulation software. The model was calibrated and validated with data gathered from the experiments.

The results of this paper showed that the welding sequence of a part significantly affects the formation of thermally induced distortions of the final part. The calibrated simulation model was able to capture the different distortion behavior attributed to the welding sequences.

Within this work, a simulation model was developed capable of predicting the distortion of WAAM parts in advance. The findings of this paper can be used to improve the design of WAAM welding sequences while avoiding high experimental efforts.