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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.

The purpose of this paper is to determine both analytically and numerically the solution to a new one-dimensional equation for the propagation of small-amplitude waves in shallow waters that accounts for linear and nonlinear drift, diffusive attenuation, viscosity and dispersion, its dependence on the initial conditions, and its linear stability.

An implicit, finite difference method valid for both parabolic and second-order hyperbolic equations has been used to solve the equation in a truncated domain for five different initial conditions, a nil initial first-order time derivative and relaxation times linearly proportional to the viscosity coefficient.

A fast transition that depends on the coefficient of the linear drift, the diffusive attenuation and the power of the nonlinear drift are found for initial conditions corresponding to the exact solution of the generalized regularized long-wave equation. For initial Gaussian, rectangular and triangular conditions, the wave’s amplitude and speed increase as both the amplitude and the width of these conditions increase and decrease, respectively; wide initial conditions evolve into a narrow leading traveling wave of the pulse type and a train of slower oscillatory secondary ones. For the same initial mass and amplitude, rectangular initial conditions result in larger amplitude and velocity waves of the pulse type than Gaussian and triangular ones. The wave’s kinetic, potential and stretching energies undergo large changes in an initial layer whose thickness is on the order of the diffusive attenuation coefficient.

A new, one-dimensional equation for the propagation of small-amplitude waves in shallow waters is proposed and studied analytically and numerically. The equation may also be used to study the displacement of porous media subject to seismic effects, the dispersion of sound in tunnels, the attenuation of sound because of viscosity and/or heat and mass diffusion, the dynamics of second-order, viscoelastic fluids, etc., by appropriate choices of the parameters that appear in it.

We examine the roles of sample initial conditions and unobserved individual effects in consistent estimation of the dynamic binary response panel data model. Different specifications of the model are estimated using female welfare and labor force participation data from the Survey of Income and Program Participation. These include alternative random effects (RE) models, in which the conditional distributions of both the unobserved heterogeneity and the initial conditions are specified, and fixed effects (FE) conditional logit models that make no assumptions on either distribution. There are several findings. First, the hypothesis that the sample initial conditions are exogenous is rejected by both samples. Misspecification of the initial conditions results in drastically overstated estimates of the state dependence and understated estimates of the short- and long-run effects of children on labor force participation. The FE conditional logit estimates are similar to the estimates from the RE model that is flexible with respect to both the initial conditions and the correlation between the unobserved heterogeneity and the covariates. For female labor force participation, there is evidence that fertility choices are correlated with both unobserved heterogeneity and pre-sample participation histories.

The purpose of this chapter is to review our findings related to the question “Do outcomes related to dynamic assessment on a cognitive measure predict reading growth?” Our discussion related to the predictive validity of such procedures focused on outcomes related to a battery of memory and reading measures administered over a three-year period to 78 children (11.6 years) with and without reading disabilities (RD). Working memory (WM) tasks were presented under initial, gain, and maintenance testing conditions. The preliminary results suggested that maintenance testing conditions were significant moderators of comprehension and vocabulary growth, whereas probe scores and gain testing conditions were significant moderators of nonword fluency growth. Overall, the results suggested that the dynamic assessment of WM added significant variance in predicting later reading performance.

The purpose of this study is to demonstrate the effect of initial international joint ventures (IJV) structural conditions on two main equity-based instability facets: change of IJV ownership structure and acquisition of the IJV by one of the IJV partners. Drawing on the transaction cost theory, the authors examine three key initial structural conditions: IJV formation mode, number of partners and IJV’s ownership structure.

The authors apply the “Event history analysis” technique to test the hypotheses using a data set of 140 French-foreign JVs.

The findings show that the mode of an acquisitive IJV and unequal equity positions held by partners increase the likelihood of a change of IJV’s ownership structure and its eventual acquisition by one of the partners. In addition, the findings show that while an increase in the number of IJV partners is directly related to the change of IJV ownership structure, it has a statistically insignificant effect on IJV acquisition.

Drawing on “transaction costs” arguments, this study advances the literature by offering fine-grained results related to the effects of initial structural conditions on aspects of unintended instability in French-foreign JVs.

This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions.

Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations.

Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots.

Shallow water equations with crisp and fuzzy initial conditions have been solved.

“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.

The purpose of this study is to develop a simulation method to calculate non-stationary distributions of the chemical potential of oxygen in a solid oxide fuel cell (SOFC) under operation.

The initial-boundary value problem was appropriately formulated and the appropriate boundary conditions were implemented so that the problem of non-stationary behavior of SOFC can be solved in accordance with actual operational and typical experimental conditions. The dependencies of the material properties on the temperature and partial pressure of oxygen were also elaborately introduced to realize actual material responses. The capability of the proposed simulation method was demonstrated under arbitrary operating conditions.

The steady state calculated with the open circuit voltage condition was conformable with the analytical solution. In addition, the transient states of the spatial distributions of potentials and currents under the voltage- and current-controlled conditions were successfully differentiated, even though they eventually became the same steady state. Furthermore, the effects of dense materials assumed for interconnects and current collectors were found to not be influential. It is thus safe to conclude that the proposed method enables us to simulate any type of transient simulations regardless of controlling conditions.

Although only uniaxial models were tested in the numerical examples in this paper, the proposed method is applicable for arbitrary shapes of SOFC cells.

The value of this paper is that adequate numerical simulations by the proposed method properly captured the electrochemical transient transport phenomena in SOFC under various operational conditions, and that the applicability was confirmed by some numerical examples.

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.