Waves induced by a submerged moving dipole in a two-layer fluidof finite depth

The waves induced by a moving dipole in a two-fluid system are analytically and experimentally investigated. The velocity potential of a dipole moving horizontally in the lower layer of a two-layer fluid with finite depth is derived by superposing Greens functions of sources (or sinks). The far-field waves are studied by using the method of stationary phase. The effects of two resulting modes, i.e. the surface- and internal-wave modes, on both the surface divergence field and the interfacial elevation are analyzed. A laboratory study on the internal waves generated by a moving sphere in a two-layer fluid is conducted in a towing tank under the same conditions as in the theoretical approach. The qualitative consistency between the present theory and the laboratory study is examined and confirmed.

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates. Based on the stationary phase method, the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.

Analytical structure of Hermite Gaussian beam in far field

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.

Gravity Wave Generated by Initial Axisymmetric Disturbance at the Surface of an Ice‑covered Ocean with Porous Bed

This paper is concerned with the generation of gravity waves due to prescribed initial axisymmetric disturbances created at the surface of an ice sheet covering the ocean with a porous bottom.The ice cover is modeled as a thin elastic plate,and the bottom porosity is described by a real parameter.Using linear theory,the problem is formulated as an initial value problem for the velocity potential describing the motion.In the mathematical analysis,the Laplace and Hankel transform techniques have been used to obtain the depression of the ice-covered surface in the form of a multiple infnite integral.This integral is evaluated asymptotically by the method of stationary phase twice for a long time and a large distance from the origin.Simple numerical computations are performed to illustrate the efect of the ice-covered surface and bottom porosity on the surface elevation,phase velocity,and group velocity of the surface gravity waves.Mainly the far-feld behavior of the progressive waves is observed in two diferent cases,namely initial depression and an impulse concentrated at the origin.From graphical representations,it is clearly visible that the presence of ice cover and a porous bottom decreases the wave amplitude.Due to the porous bottom,the amplitude of phase velocity decreases,whereas the amplitude of group velocity increases.

Generation of shaping nondiffracting structured caustic beams on the basis of stationary phase principle

On the basis of the stationary phase principle,we construct a family of shaping nondiffracting structured caustic beams with the desired morphology.First,the analytical formula of a nondiffracting astroid caustic is derived theoretically using the stationary phase method.Then,several types of typical desired caustics with different shapes are numerically simulated using the obtained formulas.Hence,the key optical structure and propagation characteristics of nondiffracting caustic beams are investigated.Finally,a designed phase plate and an axicon are used to generate the target light field.The experimental results confirm the theoretical prediction.Compared with the classical method,the introduced method for generating nondiffracting caustic beams is high in light-energy utilization;hence,it is expected to be applied conveniently to scientific experiments.

Wellposedness of some quasi-linear Schrdinger equations

This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.