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A third-order approximate solution for surface gravity waves in the finite water depth is studied in the context of potential flow theory. This solution corresponds to the steady-state part of a multidirectional irregular wave field and provides explicit expressions for the surface elevation, free-surface velocity potential, and velocity potential. The amplitude dispersion relation is also provided. Two approaches are used to derive the third-order analytical solution, resulting in two types of approximate solutions: the perturbation solution and the Hamiltonian solution. The perturbation solution is obtained by a classical perturbation technique in which the time variable is expanded in multiscale to eliminate secular terms. The Hamiltonian solution is derived from the canonical transformation in the Hamiltonian theory of water waves. By comparing the two types of solutions, it is found that they are completely equivalent for the first- and second-order solutions and the nonlinear dispersion, but for the third-order part only the sum–sum terms are the same. Due to the canonical transformation that could completely separate the dynamic and bound harmonics, the Hamiltonian solutions break through the difficulty that the perturbation theory breaks down due to singularities in the transfer functions when the quartet resonance criterion is satisfied. Furthermore, it is also found that some time-averaged quantities based on the Hamiltonian solution, such as mean potential energy and mean kinetic energy, are equal to those in the initial state in which the sea surface is assumed to be a Gaussian random process. This is because there are associated conserved quantities in the Hamiltonian form. All of these show that the Hamiltonian solution is more reasonable and accurate to describe the third-order steady-state wave field. Finally, based on the Hamiltonian solution, some statistics are given such as the volume flux, skewness, excess kurtosis, and non-uniqueness of the induced mean flow and mean surface. [ABSTRACT FROM AUTHOR]

During the isothermal local loading forming of the large-scale integral component of titanium alloy, the underfill and streamline folding defects are prone to occur due to high ribs, a thin web, and the complex shape of the component. In this paper based on DEFORM3D software, a finite element (FE) model for the isothermal local loading forming of representative large-scale complex integral component of TA15 titanium alloy was established and the reliability and applicability of the model were validated. Then combined with theoretical analysis and an experiment, the forming quality and the common defects for this rib-web component was analyzed. Five local loading schemes were proposed to study the reasons and the corresponding solutions for underfill and folding defects and then the reasonable process condition ware proposed. According to this, the practical forming of the TA15 largescale integral component was achieved and the forging with good quality was obtained. The results obtained provide a basis for optimizing the forming process and priming a parameter selection for better complex large-scale integral component isothermal local loading forming. [ABSTRACT FROM AUTHOR]

Two piggyBac-like elements (PLEs) were identified in the cotton bollworm, Helicoverpa armigera, and were designated as HaPLE1 and HaPLE2. HaPLE1 is flanked by 16 bp inverted terminal repeats (ITRs) and the duplicated TTAA tetranucleotide, and contains an open reading frame (ORF) of 1794 bp with the presumed DDD domain, indicating that this element may be an active autonomously mobile element. HaPLE2 was found with the same ITRs, but lacks the majority of an ORF-encoding transposase. Thus, this element was thought to be a non-autonomous element. Transposable element displays and distribution of the two PLEs in individuals from three different H.  armigera populations suggest that transmobilization of HaPLE2 by the transposase of HaPLE1 may be likely, and mobilization of HaPLE1 might occur not only within the same individual, but also among different individuals. In addition, horizontal transfer was probably involved in the evolution of PLEs between H.  armigera and Trichoplusia ni. [ABSTRACT FROM AUTHOR]