Rogon-like solutions excited in the two-dimensional nonlocal nonlinear Schrödinger equation

We report the analytical one- and two-rogon-like solutions for the two-dimensional nonlocal nonlinear Schrödinger equation by means of the similarity transformation. These obtained solutions can be used to describe the possible physical mechanisms for rogue-like wave phenomenon. Moreover, the free function of space y involved in the obtained solutions excites the abundant structures of rogue-like wave propagations. The Hermite-Gaussian function of space y (normalized function) is, in particular, chosen to depict the dynamical behaviors for rogue-like wave phenomenon.     

Extreme Value Analysis of a Large Designed Experiment: A Case Study in Bulk Carrier Safety

The bulk carrier M.V. Derbyshire sank in 1980 when she encountered a typhoon near Japan. The most likely cause of her loss was finally explained in the report of the Re-opened Formal Investigation in 2000. The report also revealed inadequacies in safety standards for such vessels, particularly concerning regulations governing hatch cover strengths, and requested further work be undertaken to examine the sufficiency of aspects of the existing international standards for ship design. This paper describes the extreme value analysis of data from a large designed experiment intended to aid the revision of these safety standards. We highlight the importance of consistency of results over the different conditions examined, and how this can be achieved using various data pooling and regression techniques.     

Effect of a Localized Random Forcing Term on the Korteweg-De Vries Equation

In this work, we numerically investigate the influence of a white noise-type forcing on the phenomenon of forced generation of solitons by a localized moving disturbance. Our numerical method is based on finite elements and least-squares. We present numerical experiments for different values of noise amplitude and Froude number, which describe some damping effects on the emission of solitons.     

Numerical prediction of breakup mode of contracting gas filament in liquid

The breaking up of gas filament in liquid is important in many industrial and scientific applications. In this study, a transient axisymmetric model with the level set method is built up to examine the dynamics of a contracting gas filament, and to determine the effects of the aspect ratio, Ohnesorge (Oh) number, and viscosity ratio on its breakup mode. The filament undergoes no break, middle break, or end-pinching modes with increasing aspect ratio at either a low or a high Oh number, and one critical initial aspect ratio is observed for each Oh number. The fate of the filament is determined by the interaction of capillary waves on its surface, and can be predicted accurately by using the one-dimensional wave superposition method. The decreasing viscosity ratio of liquid over gas reduces the critical initial aspect ratio for the fate transition between the no break and breakup modes, and this effect is reduced at a low viscosity ratio. These findings may be helpful in fabricating gas bubbles and their breakup suppression.     

Analytical solutions for crack-like scatterers and sources in isotropic elastic plates

A common theoretical framework can be employed for modelling both active and passive approaches to structural health monitoring based on guided waves. The same fundamental solutions can be used to represent the scattered field due to crack-like damage in an active approach, or the acoustic emission due to various failure mechanisms in a passive approach. It is shown that the reciprocal theorem can be used to derive compact analytical formulae for those fundamental solutions expressed as sums over the propagating modes. The only detailed calculations that are required are those involved in determining the relevant dispersion curves and through-thickness mode functions. For clarity, the approach is first described for two-dimensional configurations. The subsequent extension to three-dimensional requires the stationary phase approximation. It is shown that the modal coefficients for crack-like sources (or scatterers) are proportional to the conjugate stress component of the corresponding mode. Furthermore, the approach can also be used for an edge crack or delamination in a semi-infinite plate, and the theoretical formulae are compared with experimentally validated computational results for that case. Further extensions are briefly noted.     

Regularity results and optimal control problems for the perturbation of boussinesq equations of the ocean

We study in this article a method which computes the variability of current, density and pressure in an oceanic domain. The equations are of Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the density. They are linearized around a given mean circulation and modified by the Boussinesq approximation: density variations are neglected except in the terms of gravity acceleration. The existence and uniqueness of a solution are proved for two sets of equations: first the three-dimensional problem and then the two-dimensional cyclic problem derived by assuming a sinusoidal x-dependence for the perturbation of mean flow. The latter corresponds to a modelization of tropical instability waves which are illustrated by the El Nino phenomenon.

The value of the pressure p on the surface of ocean is of great interest for physical interpretation. To define that quantity, it is necessary to have the regularity p ? H ¹. We have proved that the perturbation (u,ρ,p) of mean circulation is such that: u ? L ²(0T,H ²), ρ ? L ²(0,T H ²) and p ? L ² L ²(0,T H ¹), provided the perturbation of the windstress is sufficiently regular and satisfies compatibility relations. It is proved by means of an extension method, with even-odd reflection. We then develop a problem of control. The observation is the Variability of pressure on the surface of ocean. The control is the variability of windstress f, which acts as to forcing of the perturbation. We prove the existence and uniqueness of an optimal control, which is characterized by a set of equations including the direct problem and the adjoint problem. These results are valid for the three-dimensional problem and the two-dimensional cyclic problem.     

On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations

In this paper we generalize some results in the literature concerning the structure of numerical approximations to solitary wave solutions of some nonlinear, dispersive equations is studied. We prove that those time discretizations with the property of preserving, exactly or approximately up to certain order, some invariants of the problems, have a better propagation of the error and provide a more suitable simulation of the solitary waves. The generalization involves the treatment of nonlocal operators and two different kinds of equations.     

Shadow waves for pressureless gas balance laws

The pressureless gas dynamic model with body force as a source is considered. The problem is solved using the procedure used for finding delta shock type solutions to a special conservation laws known as Shadow Waves. If the body force is interpreted as the acceleration constant multiplied by the density, the solution obtained in this paper looks physically reasonable since the velocities of waves are changed accordingly with the acceleration.     

Traveling waves in porous media with phase-dependent damping

We consider a simple model for the fluid flow in a porous medium. The model consists of a hyperbolic system of balance laws, which take into account phase changes and allow for metastable states thanks to the introduction of an equilibrium pressure. A damping term is included as well, which depend not only on the velocity but also on the phase of the fluid; in particular, it vanishes in the vapor phase. The existence and uniqueness of traveling waves is proved in several important cases.