Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.Comment: 25 pages, 9 figure

Density functional theory of inhomogeneous liquids. I. The liquid-vapor interface in Lennard-Jones fluids

A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of the homogeneous fluid, obtained, e.g., from thermodynamic perturbation theory. Comparison to the DCF obtained from simulation of a Lennard-Jones fluid shows this to be a surprisingly good approximation for a wide range of densities. The model is used to construct a density functional theory for inhomogeneous fluids which is applied to the problem of calculating the surface tension of the liquid-vapor interface. The numerical values found are in good agreement with simulation

Security of Streaming Media Communications with Logistic Map and Self-Adaptive Detection-Based Steganography

Voice over IP (VoIP) is finding its way into several applications, but its security concerns still remain. This paper shows how a new self-adaptive steganographic method can ensure the security of covert VoIP communications over the Internet. In this study an Active Voice Period Detection algorithm is devised for PCM codec to detect whether a VoIP packet carries active or inactive voice data, and the data embedding location in a VoIP stream is chosen randomly according to random sequences generated from a logistic chaotic map. The initial parameters of the chaotic map and the selection of where to embed the message are negotiated between the communicating parties. Steganography experiments on active and inactive voice periods were carried out using a VoIP communications system. Performance evaluation and security analysis indicates that the proposed VoIP steganographic scheme can withstand statistical detection, and achieve secure real-time covert communications with high speech quality and negligible signal distortion

Potential Symmetry Studies on a Rotating Fluid System

A rotational fluid model which can be used to describe broad vortical flows ranging from large scale to the atmospheric mesoscale and the oceanic submesoscale is studied by the symmetry group theory. After introducing one scalar-, two vector-, and two tensor potentials, we find that the Lie symmetries of the extended system include many arbitrary functions of z and {z,t}. The obtained Lie symmetries are used to find some types of exact solutions. One of exact solutions can be used to qualitatively describe the three-dimensional structure of hurricanes