Recently far infra-red (FIR) polarization of the 850μm continuum emission from T Tauri disks has been detected. The observed degree of polarization is around 3 %. Since thermal emission from dust grains dominates the spectral energy distribution at the FIR regime, dust grains might be the cause of the polarization. We explore alignment of dust grains by radiative torque in T Tauri disks and provide predictions for polarized emission for disks viewed at different wavelengths and viewing angles. In the presence of magnetic field, these aligned grains produce polarized emission in infrared wavelengths. When we take a Mathis-Rumpl-Nordsieck-type distribution with maximum grain size of 500-1000μm the degree of polarization is around 2-3 % level at wavelengths larger than ~100μm Our study indicates that multifrequency infrared polarimetric studies of protostellar disks can provide good insights into the details of their magnetic structure.

We discuss diffusion of particles in turbulent flows. In hydrodynamic turbulence, it is well known that distance between two particles imbedded in a turbulent flow exhibits a random walk behavior. The corresponding diffusion coefficient is ~ vinjlturb, where vinj is the amplitude of the turbulent velocity and lturb is the scale of the turbulent motions. It Is not clear whether or not we can use a similar expression for magnetohydrodynamic turbulence. However, numerical simulations show that mixing motions perpendicular to the local magnetic field are, up to high degree, hydrodynamical. This suggests that turbulent heat transport in magnetized turbulent fluid should be similar to that in non-magnetized one, which should have a diffusion coefficient ~ vinjlturb. We review numerical simulations that support this conclusion. The application of this idea to thermal conductivity in clusters of galaxies shows that this mechanism may dominate the diffusion of heat and may be efficient enough to prevent cooling flow formation when turbulence is vigorous.

The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful insights on many astrophysical problems. We describe a pseudo-spectral MHD code suitable for the study of incompressible turbulence. We review our recent' works on direct three-dimensional numerical simulations for MHD turbulence in a periodic box. In those works, we use a pseudo-spectral code to solve the incompressible MHD equations. We first discuss the structure and properties of turbulence as functions of scale. The results are consistent with the scaling law recently proposed by Goldreich & Sridhar. The scaling law is based on the concept of scale-dependent isotropy: smaller eddies are more elongated than larger ones along magnetic field lines. This scaling law substantially changes our views on MHD turbulence. For example, as noted by Lazarian & Vishniac, the scaling law can provide a fast reconnection rate. We further discuss how the study of incompressible MHD turbulence can help us to understand physical processes in interstellar medium (ISM) by considering imbalanced cascade and viscous damped turbulence.