Directly modulated tunable lasers are highly desirable for constructing densewavelength division multiplexing (DWDM) access networks, owing to their advantages of low cost, compact size and low power consumption. However, the transmission distance for 10 Gbps is usually limited to about 10 km in the telecom C-band in standard single-mode fiber (SMF) due to wavelength chirp. Here we propose and demonstrate a simple technique for extending the transmission distance by detuning the wavelength of a tunable V-cavity laser with respect to DWDM multiplexers. Experiment results show that 10 Gbps signal can be transmitted error-free (BER<10 −12) over 20 km SMF with a wavelength-detuning with respect to a Gaussian-type arrayed waveguide grating (AWG) without dispersion compensation. The power penalty is only 1 dB compared to the back-to-back transmission.

In this paper a new mathematical model of secondary frost heave is presented. It is expected that the problem considered under some assumptions is well-posed. § 1 IntroductionIt is known(see [I]) that the scientific study of soil and ice segregation began in the early 1900s. By the 1900s some researchers (see [2] and [3]) had already found that ice segregation and the resultant frost heave are caused not only by freezing of in-situ water, which makes the volume of soil increase 9% (see [I]), but also by freezing of water transported toward a freezing front from the unfrozen part of soil, which makes the volume of soil increase 109°//00. From qualitative analysis, we know the water transports toward the region in which the temperature is lower(see [4]). So, although in the case of secondary frost heave the transport of water is one of the major issues in the study of soil freezing, quantative research is necessary and important. As we know in the most of papers, according to the empirical or semiempirical model, only the quasi-steady problems or wave solutions are considered (see [5~8] and references therein). In this paper, we follow the M1 model in [9] and present a new mathematical model under some assumptions. We hope it is well-posed in theory and the numerical computation by it can be used in practice.In § 2,we list the balance equations of mass and heat. Some basic assumptions and the interface and initial-boundary conditions are given in § 3 and § 4 respectively. In § 5, we present a new mathematical model which is expected to be a well-posed problem. § 2 Balance Equations of Mass and HeatWe will Consider the one-directional freezing of soil. Let the freezing process advance