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Based on a recent L 2 -L 1 framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to the Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.

Abstract. We outline a relationship between three slowly varying characteristics of the coupled ocean-atmosphere system in the tropical Pacific: (i) quasi-periodicity, (ii) extended predictability, and (iii) approximate low dimensionality. The Southern Oscillation Index (SOI) and Nifio-3 sea surface temperatures characterize climatic variations in the tropical Pacific; these two time series are usually anticorrelated. This low-dimensional characterization suggests that much of the system's seasonal-to-interannual predictability depends on the regular behavior of the two scalar time series under consideration. The predictive skill of two idealized models is studied, showing the strong connection between regularity and predictability. E1-Nifio/Southern-Oscillation (ENSO) predictability is then assessed for current forecast models. When the periodic component of the ENSO signal is strong, it results in higher forecast skill. This skill decreases when the anticorrelation between SOI and Nifio-3 temperature anomalies is lost, as it has been in the first half of this decade.

We propose and demonstrate a novel physical secure high-speed optical communication scheme based on synchronous chaotic spectral phase encryption (CSPE) and decryption (CSPD). The CSPE is performed by a module composed of two dispersion components and one phase modulator (PM) between them, and the CSPD is carried out by a twin module with reverse dispersions and inverse PM driving signals. The PM driving signals of the CSPE and CSPD modules are privately-synchronized chaotic signals that are independently generated by local external-cavity semiconductor lasers subject to common injection. The numerical results indicate that with the CSPE, the original message can be encrypted as a noiselike signal, and the timing clock of original message is efficiently hidden in the encrypted signal. Based on the private synchronization of the chaotic PM driving signals, only the legal receiver can decrypt the message correctly, while the eavesdropper is not able to intercept useful message. Moreover, the proposed scheme can also support secure symmetric bidirectional high-speed WDM transmissions. This work shows a prospective way to implement high-speed secure optical communications at physical layer.

We study the Ericksen-Leslie's hyperbolic incompressible liquid crystal model. Under some constraints on the Leslie coefficients which ensure the basic energy law is dissipative, we prove the local-in-time existence and uniqueness of the classical solution to the system with finite initial energy. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the unique global classical solution can be established.

We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case [20] and some techniques from compressible Navier-Stokes equations, we prove the local-in-time existence of the classical solution to the system with finite initial energy, under some constraints on the Leslie coefficients which ensure the basic energy law is dissipative. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the global classical solution can be established.

We revisit the classical work of Caflisch [C] for compressible Euler limit of the Boltzmann equation. By using a new L 2 -L ∞ method, we prove the validity of the Hilbert expansion before shock formathions in the Euler system with moderate temperature variation.

The global classical solution to the incompressible Navier-Stokes-Fourier equation with small initial data in the whole space is constructed through a zero Knudsen number limit from the solutions to the Boltzmann equation with general collision kernels. The key point is the uniform estimate of the Sobolev norm on the global solutions to the Boltzmann equation.