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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 paper aims to study the energy ratios of plane waves on an imperfect interface of elastic half-space (EHS) and orthotropic piezothermoelastic half-space (OPHS).

The dual-phase lag (DPL) theory with memory-dependent derivatives is employed to study the variation of energy ratios at the imperfect interface.

A plane longitudinal wave (P) or transversal wave (SV) propagates through EHS and strikes at the interface. As a result, two waves are reflected, and four waves are transmitted, as shown in Figure 2. The amplitude ratios are determined by imperfect boundaries having normal stiffness and transverse stiffness. The variation of energy ratios is computed numerically for a particular model of graphite (EHS)/cadmium selenide (OPHS) and depicted graphically against the angle of incidence to consider the effect of stiffness parameters, memory and kernel functions.

The energy distribution of incident P or SV waves among various reflected and transmitted waves, as well as the interaction of waves for imperfect interface (IIF), normal stiffness interface (NSIF), transverse stiffness interface (TSIF), and welded contact interface (WCIF), are important factors to consider when studying seismic wave behavior.

The present model may be used in various disciplines, such as high-energy particle physics, earthquake engineering, nuclear fusion, aeronautics, soil dynamics and other areas where memory-dependent derivative and phase delays are significant.

In a variety of technical and geophysical scenarios, wave propagation in an elastic/piezothermoelastic medium with varying magnetic fields, initial stress, temperature, porosity, etc., gives important information regarding the presence of new and modified waves.

The objective of this study is to model the propagating front in the interaction of gases in an aircraft fuel tank. To this end, we introduce a nonlinear parabolic operator, for which solutions are shown to be regular.

The authors provide an analytical expression for the propagating front, that shifts any combination of oxygen and nitrogen, in the tank airspace, into a safe condition to avoid potential explosions. The analytical exercise is validated with a real flight.

According to the flight test data, the safe condition, of maximum 7% of oxygen, is given for a time t = 45.2 min since the beginning of the flight, while according to our analysis, such a safe level is obtained for t = 41.42 min. For other safe levels of oxygen, the error between the analytical assessment and the flight data was observed to be below 10%.

The interaction of gases in a fuel tank has been little explored in the literature. Our value consists of introducing a set of nonlinear partial differential equations to increase the accuracy in modeling the interaction of gasses, which has been typically done via algebraic equations.

Currently, many studies have shown an increasing interest in owner-dynamic capabilities (ODCs). Existing studies mainly focus on the dynamic capability basis and capability development within the owner organization, whereas they rarely analyze the capability mobilization within the network of participants in megaprojects. Therefore, this study aims to explain the interaction and evolution of the mobilization strategies of ODCs and the cooperative strategies of other participants.

This study develops a tripartite evolutionary game model to analyze the evolutionarily stable strategy of the owner, the reciprocal participants and the general participants. Results are numerically simulated with a validation case. The asymptotic stability of multiple group strategies is discussed under the replicator dynamic system.

This study suggests that resource complementarity significantly reduces the difficulty of mobilization. Moreover, these strategies are only effective with sufficient ODCs. The results indicate that reciprocal participants are more sensitive to the change in resource complementarity.

This study provides strategic guidance for mobilizing ODCs in megaprojects to better embrace uncertainty and stress, contributing to the dynamic capability literature with an evolutionary game approach. And new insight for the study of reciprocity preference in megaprojects is also provided.