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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 study aims to solve the problem of weld quality inspection, for the aluminum alloy profile welding structure of high-speed train body has complex internal shape and thin plate thickness (2–4 mm), the conventional nondestructive testing method of weld quality is difficult to implement.

In order to solve this problem, the ultrasonic creeping wave detection technology was proposed. The impact of the profile structure on the creeping wave detection was studied by designing profile structural test blocks and artificial simulation defect test blocks. The detection technology was used to test the actual welded test blocks, and compared with the results of X-ray test and destructive test (tensile test) to verify the accuracy of the ultrasonic creeping wave test results.

It is indicated that that X-ray has better effect on the inspection of porosities and incomplete penetration defects. However, due to special detection method and protection, the detection speed is slow, which cannot meet the requirements of field inspection of the welding structure of aluminum alloy thin-walled profile for high-speed train body. It can be used as an auxiliary detection method for a small number of sampling inspection. The ultrasonic creeping wave can be used to detect the incomplete penetration welds with the equivalent of 0.25 mm or more, the results of creeping wave detection correspond well with the actual incomplete penetration defects.

The results show that creeping wave detection results correspond well with the actual non-penetration defects and can be used for welding quality inspection of aluminum alloy thin-wall profile composite welding joints. It is recommended to use the echo amplitude of the 10 mm × 0.2 mm × 0.5 mm notch as the criterion for weld qualification.

The purpose of this paper is to solve the problem that the location of the initiation point cannot be measured accurately in the shallow underground space, this paper proposes a method, which is based on fusion of multidimensional vibration sensor information, to locate single shallow underground sources.

First, in this paper, using the characteristics of low multipath interference and good P-wave polarization in the near field, the adaptive covariance matrix algorithm is used to extract the polarization angle information of the P-wave and the short term averaging/long term averaging algorithm is used to extract the first break travel time information. Second, a hybrid positioning model based on travel time and polarization angle is constructed. Third, the positioning model is taken as the particle update fitness function of quantum-behaved particle swarm optimization and calculation is performed in the hybrid positioning model. Finally, the experiment verification is carried out in the field.

The experimental results show that, with root mean square error, spherical error probable and fitness value as evaluation indicators, the positioning performance of this method is better than that without speed prediction. And the positioning accuracy of this method has been improved by nearly 30%, giving all of the three tests a positioning error within 0.5 m and a fitness less than 1.

This method provides a new idea for high-precision positioning of shallow underground single source. It has a certain engineering application value in the fields of directional demolition of engineering blasting, water inrush and burst mud prediction, fuze position measurement, underground initiation point positioning of ammunition, mine blasting monitoring and so on.

Ground Penetrating Radar is a multidisciplinary Nondestructive Evaluation technique that requires knowledge of electromagnetic wave propagation, material properties and antenna theory. Under some circumstances this tool may require auxiliary algorithms to improve the interpretation of the collected data. Detection, location and definition of target’s geometrical and physical properties with a low false alarm rate are the objectives of these signal post-processing methods. Basic approaches are focused in the first two objectives while more robust and complex techniques deal with all objectives at once. This work reviews the use of Artificial Neural Networks and Machine Learning for data interpretation of Ground Penetrating Radar surveys. We show that these computational techniques have progressed GPR forward from locating and testing to imaging and diagnosis approaches.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

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 answer the following two questions: Will Saudi Arabia get older? Will its pension system be sustainable?

The methodology/approach is to forecast KSA’s population with wavelet analysis combined with the Burg model which fits a pth order autoregressive model to the input signal by minimizing (least squares) the forward and backward prediction errors while constraining the autoregressive parameters to satisfy the Levinson-Durbin recursion, then relies on an infinite impulse response prediction error filter.

Spectral analysis projections of Saudi age groups are more optimistic than the Bayesian probabilistic model sponsored by the United Nations Population Division: Saudi Arabia will not get older as fast as projected by the United Nations model. The KSA’s pension system will stay sustainable based on spectral analysis, whereas it will not based on the U.N. model.

Spectral analysis will provide better insight and understanding of population dynamics for Saudi government policymakers, as well as economic, health and pension planners.

This article introduces the Special Issue on Sustainable Management of Heritage Buildings in long-term perspective.

It starts by reviewing the gaps in knowledge and practice which led to the creation and implementation of the research project SyMBoL—Sustainable Management of Heritage Buildings in long-term perspective funded by the Norwegian Research Council over the 2018–2022 period. The SyMBoL project is the motivation at the base of this special issue.

The editorial paper briefly presents the main outcomes of SyMBoL. It then reviews the contributions to the Special Issue, focussing on the connection or differentiation with SyMBoL and on multidisciplinary findings that address some of the initial referred gaps.

The article shortly summarizes topics related to sustainable preservation of heritage buildings in time of reduced resources, energy crisis and impacts of natural hazards and global warming. Finally, it highlights future research directions targeted to overcome, or partially mitigate, the above-mentioned challenges, for example, taking advantage of no sestructive techniques interoperability, heritage building information modelling and digital twin models, and machine learning and risk assessment algorithms.

The purpose of the study is to obtain and analyze vibro-acoustic characteristics.

A unified analysis model for the rotary composite laminated plate and conical–cylindrical double cavities coupled system is established. The related parameters of the unified model are determined by isoparametric transformation. The modified Fourier series are applied to construct the admissible displacement function and the sound pressure tolerance function of the coupled systems. The energy functional of the structure domain and acoustic field domain is established, respectively, and the structure–acoustic coupling potential energy is introduced to obtain the energy functional. Rayleigh–Ritz method was used to solve the energy functional.

The displacement and sound pressure response of the coupled systems are acquired by introducing the internal point sound source excitation, and the influence of relevant parameters of the coupled systems is researched. Through research, it is found that the impedance wall can reduce the amplitude of the sound pressure response and suppress the resonance of the coupled systems. Besides, the composite laminated plate has a good noise reduction effect.

This study can provide the theoretical guidance for vibration and noise reduction.

This study aims to analyse the non-linear losses of a porous media (stack) composed by parallel plates and inserted in a resonator tube in oscillatory flows by proposing numerical correlations between pressure gradient and velocity.

The numerical correlations origin from computational fluid dynamics simulations, conducted at the microscopic scale, in which three fluid channels representing the porous media are taken into account. More specifically, for a specific frequency and stack porosity, the oscillating pressure input is varied, and the velocity and the pressure-drop are post-processed in the frequency domain (Fast Fourier Transform analysis).

It emerges that the viscous component of pressure drop follows a quadratic trend with respect to velocity inside the stack, while the inertial component is linear also at high-velocity regimes. Furthermore, the non-linear coefficient b of the correlation ax + bx² (related to the Forchheimer coefficient) is discovered to be dependent on frequency. The largest value of the b is found at low frequencies as the fluid particle displacement is comparable to the stack length. Furthermore, the lower the porosity the higher the Forchheimer term because the velocity gradients at the stack geometrical discontinuities are more pronounced.

The main novelty of this work is that, for the first time, non-linear losses of a parallel plate stack are investigated from a macroscopic point of view and summarised into a non-linear correlation, similar to the steady-state and well-known Darcy–Forchheimer law. The main difference is that it considers the frequency dependence of both Darcy and Forchheimer terms. The results can be used to enhance the analysis and design of thermoacoustic devices, which use the kind of stacks studied in the present work.