We present Chapman–Enskog and Hilbert expansions applied to the O(v/c) Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman–Enskog or Hilbert expansions with react...

Abstract An in-house Direct Simulation Monte Carlo (DSMC) code has been developed using an object-oriented interface for the purpose of eventually modelling gas and plasma microflows in micromechanical systems, by coupling it with existing Particle-In-Cell (PIC) solver. The is validated canonical flow problems such as micro-Couette micro-Poiseuille flows. Since emphasis on supersonic highly com...

Care (Dr Patel) and Medicine (Drs Chapman, Luo, Woodruff, and Arora), University of Chicago, Chicago, Illinois. Correspondence:Dr Arora, Department of Medicine, University of Chicago, 5841 S Maryland Ave, MC 2007, AMB W216, Chicago, IL 60637 ([email protected] .edu). Author Contributions: Drs Patel and Arora had full access to all of the data in the study and take responsibility for ...

Children and adolescents with Down syndrome show an emerging profile of speech and language characteristics that is typical of the syndrome (Chapman & Hesketh, 2000; Chapman, 2003; Abbeduto & Chapman, 2005) and different from typically developing children matched for nonverbal mental age, including expressive language deficits relative to comprehension that are most severe for syntax, and, in a...