New generalized method to construct new non-travelling wave solutions and travelling wave solutions of K–D equations

With the aid of computerized symbolic computation, we obtain new types of general solution of a first-order nonlinear ordinary differential equation with six degrees of freedom and devise a new generalized method and its algorithm, which can be used to construct more new exact solutions of general nonlinear differential equations. The (2+1)-dimensional K–D equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain non-travelling wave solutions and travelling wave solutions.     

基于Authorware的wave音频播放器的设计

介绍了如何使用Authorware开发一个播放wave音频文件的播放器。通过这一设计,意在抛砖引玉,帮助大家在多媒体软件开发中,提高对包括声音在内的多媒体信息的处理能力和软件交互性的设计能力。     

Locally distributed control of wave equations with variable coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of control will yield the exact controllability property by using piecewise multiplier method and Riemannian geometry method. Some examples are presented.     

基于Shock wave Flash控件实现Delphi与Flash交互

随着计算机的普及,客户对软件界面的要求越来越高,基于Delphi、VC的界面控件尽管非常丰富,但是若让Flash作为显示界面,会给软件带来更好的效果。以Delphi 2007和Flash CS3为例,探讨如何使Flash和Delphi之间进行完美融合。     

Population-based microbial computing: a third wave of synthetic biology?

Synthetic biology is an emerging research field, in which engineering principles are applied to natural, living systems. A major goal of synthetic biology is to harness the inherent “biological nanotechnology” of living cells for the purposes of computation, production or diagnosis. As the field evolves, it is gradually developing from a single-cell approach (akin to using standalone computers) to a distributed, population-based approach (akin to using networks of connected machines). We anticipate this eventually representing the “third wave” of synthetic biology (the first two waves being the emergence of modules and systems, respectively, with the second wave still yet to peak). In this paper, we review the developments that are leading to this third wave, and describe some of the existing scientific and technological challenges.     

Sudden bed changes and wave–current interactions in coastal regions

Mean bottom evolutions due to currents and wind waves, even due to wave–current interactions, are easily computed by averaging mean quantities over one or more wave cycles. However, dealing with fine processes, like breaking waves and bar formations in coastal regions, great quantities of sediment are transported and, as a consequence, considerable erosion and deposition can occur quite rapidly. Other phenomena normally associated with earthquakes, like volcanic eruptions, landslides, etc. occur frequently in various coastal regions of the terrestrial globe. Those problems can only be tackled by using a more complete set of equations with improved wave dispersion characteristics, and taking into account time–bed-level changes. Other characteristic non-linearity phenomena in shallow water regions and wave–current interaction become important factors that have to be considered. From the sedimentary point of view, particularly in terms of the wave and current fields, it is not known whether the existing sand transport models are generally valid.The applicability of a computational structure, based on extended Boussinesq-type equations, and two existing sediment transport models are discussed and confirmed through published data. Numerical results obtained at Ria Formosa, Algarve, in the ambit of the European Union INDIA Project are shown.     

Solving metamaterial Maxwell’s equations via a vector wave integro-differential equation

In this paper, we discuss the time-domain metamaterial Maxwell’s equations. One major contribution of this paper is that after some effort we find that the metamaterial Maxwell’s equations can be beautifully reduced to a vector wave integro-differential equation involving just one unknown, which is quite similar to that obtained from the standard Maxwell’s equations in vacuum. Then we study the existence and uniqueness of this new modeling equations, and propose a fully-discrete finite element method to solve this model. Numerical results justifying our analysis are presented. This discovery shall make simulation of metamaterials much more efficient than the previous works.     

Radar measurement of directional ocean wave spectra at low incidence angles†

Abstract

There exist several techniques for the measurement of directional ocean wave spectra. The most conventional technique is the employment of pitch-roll buoys but a disadvantage of this technique is that it measures at a fixed point. Another promising technique is the use of airborne or spaceborne radars. We present here results of a comparison between the data from an airborne radar, which is measuring near vertical incidence, and measurements of directional wave spectra obtained by means of a pitch-roll buoy and processed by using the Long-Hasselmann iterative algorithm. Although preliminary, these results constitute a step towards the employment of the airborne radar based on the Radar Ocean Wave Spectrometer (ROWS) principle as defined by Jackson (1981), as a validation tool for spaceborne synthetic aperture radars.     

Solitary wave solutions for a generalized KdV–mKdV equation with variable coefficients

In this work, a generalized time-dependent variable coefficients combined KdV–mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type solitary waves, kink type solitary waves, and combined type solitary waves solutions for the considered model. Importantly, the results show that there exist combined solitary wave solutions in inhomogeneous KdV-typed systems, after proving their existence in the nonlinear Schrödinger systems. It should be noted that, the characteristics of the obtained solitary wave solutions have been expressed in terms of the time-dependent coefficients. Moreover, we give the formation conditions of the obtained solutions for the considered KdV–mKdV equation with variable coefficients.     

A stabilized MITC element for accurate wave response in Reissner–Mindlin plates

Residual based finite element methods are developed for accurate time-harmonic wave response of the Reissner–Mindlin plate model. The methods are obtained by appending a generalized least-squares term to the mixed variational form for the finite element approximation. Through judicious selection of the design parameters inherent in the least-squares modification, this formulation provides a consistent and general framework for enhancing the wave accuracy of mixed plate elements. In this paper, the mixed interpolation technique of the well-established MITC4 element is used to develop a new mixed least-squares (MLS4) four-node quadrilateral plate element with improved wave accuracy. Complex wave number dispersion analysis is used to design optimal mesh parameters, which for a given wave angle, match both propagating and evanescent analytical wave numbers for Reissner–Mindlin plates. Numerical results demonstrates the significantly improved accuracy of the new MLS4 plate element compared to the underlying MITC4 element.     

Generating gaits for snake robots: annealed chain fitting and keyframe wave extraction

Snake robots have many degrees of freedom, which makes them both extremely versatile and complex to control. They are often controlled with gaits, coordinated cyclic patterns of joint motion. Using gaits simplifies the design of high-level controllers, but shifts the complexity burden to designing the gaits. In this paper, we address the gait design problem by introducing two algorithms: Annealed chain fitting and Keyframe wave extraction. Annealed chain fitting efficiently maps a continuous backbone curve describing the three-dimensional shape of the robot to a set of joint angles for a snake robot. Keyframe wave extraction takes joint angles fit to a sequence of backbone curves and identifies parameterized periodic functions that produce those sequences. Together, they allow a gait designer to conceive a motion in terms three-dimensional shapes and translate them into easily manipulated wave functions, and so unify two previously disparate gait design approaches. We validate the algorithms by using them to produce rolling and sidewinding gaits for crawling and climbing, with results that match previous empirical investigations.     

Scattering cross sections for composite surfaces with large mean square slopes—full wave analysis

Abstract

In this work the full wave approach to rough surface scattering is applied to composite models of rough surfaces with large mean square slopes. It is shown that both specular point scattering as well as Bragg scattering are accounted for in the analysis and the results are compared with earlier solutions based on a combination of physical optics and perturbation theories. Using the full wave approach it is not essential to decompose the rough surface into individual surfaces with different roughness scales unless it is desired to separate the specular point contribution from the Bragg contribution to the scattering cross sections. Shadowing is accounted for in the analysis.     

Compacton-like and kink-like waves for a higher-order wave equation of Korteweg–de Vries type

In this paper, the bifurcation method of the dynamical and numerical approach to differential equations to study higher order wave equations of Korteweg–de Vries (KdV) type is used. With this methodology we obtain the compacton-like and kink-like wave solutions of the high order KdV type equation. Their implicit expressions are given and their planar graphs are simulated. The results show that the numerical integrations are identical with the theoretical derivations.     

A hybrid genetic algorithm–adaptive network-based fuzzy inference system in prediction of wave parameters

An important issue in application of fuzzy inference systems (FISs) to a class of system identification problems such as prediction of wave parameters is to extract the structure and type of fuzzy if–then rules from an available input–output data set. In this paper, a hybrid genetic algorithm–adaptive network-based FIS (GA–ANFIS) model has been developed in which both clustering and rule base parameters are simultaneously optimized using GAs and artificial neural nets (ANNs). The parameters of a subtractive clustering method, by which the number and structure of fuzzy rules are controlled, are optimized by GAs within which ANFIS is called for tuning the parameters of rule base generated by GAs. The model has been applied in the prediction of wave parameters, i.e. wave significant height and peak spectral period, in a duration-limited condition in Lake Michigan. The data set of year 2001 has been used as training set and that of year 2004 as testing data. The results obtained by the proposed model are presented and analyzed. Results indicate that GA–ANFIS model is superior to ANFIS and Shore Protection Manual (SPM) methods in terms of their prediction accuracy.     

Periodic and solitary wave solutions of the attractive and repulsive nonlinear Schrödinger equation

By means of symbolic computation, the first integral method is presented to obtain novel exact solutions of the nonlinear evolution equation. The obtained results include periodic and solitary wave solutions. The power of this manageable method is confirmed and the availability of symbolic computation is demonstrated.     

Homotopy analysis method for solving multi-term linear and nonlinear diffusion–wave equations of fractional order

In this paper we have used the homotopy analysis method (HAM) to obtain solutions of multi-term linear and nonlinear diffusion–wave equations of fractional order. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented.     

Chaotic vibration of the one-dimensional linear wave equation with a van der Pol nonlinear boundary condition

The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations. It characterizes the nonisotropic chaotic vibration by means of the total variation theory. Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.     

Sensing liquid density using resonant flexural plate wave devices with sol–gel PZT thin films

This study presents the design, fabrication and possible applications in liquid density sensing and biosensing of a flexure plate wave (FPW) resonator using sol–gel-derived lead zirconate titanate (PZT) thin films. The resonator has a two-port structure with a reflecting grating on a composite membrane of PZT and SiN_x. The design of the reflecting grating is derived from a SAW resonator model using COM theory to generate a sharp resonant peak. A comparison between the theoretical mass and the viscosity effects reveals the applications and the constraints of the proposed device in liquid sensing. Multiple coatings of sol–gel-derived PZT films are employed because of the cost advantage and the strong electromechanical coupling effect over other piezoelectric films. Issues of fabrication of the proposed material structure are addressed. Theoretical estimates of the mass and the viscosity effects are compared with the experimental values. The resonant frequency relates quite linearly to the density of low-viscosity liquids, revealing the feasibility of the proposed device. An erratum to this article can be found at     

Exact wave solutions for a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation

In this work, we investigate a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation. Based on the simplified Hirota bilinear method, we first construct its soliton solutions. Meanwhile, we correct the formula of N-soliton solution for this equation. On the basis of these solitons we further calculate its lump solutions, periodic waves. Meanwhile, rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method. Some figures are given to display the behavior of these solutions.