Recently, Hennebelle and Chabrier (2008) derived an analytical theory for the mass spectrum of non self-gravitating clumps associated with overdensities in molecular clouds and for the initial mass function of gravitationally bound prestellar cores, as produced by the turbulent collapse of the cloud. In this companion paper, we examine the effects of the non-isothermality of the flow, of the tu...

Massive stars define the upper limits of the star formation process, dominate the energetics of their local environs, and significantly affect the chemical evolution of galaxies. Their role in starburst galaxies and the early Universe is likely to be important, but we still do not know the maximum mass that a star can possess, i.e.“the upper mass cutoff.” I will discuss results from a program t...

The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ method. This results in modest-size systems of nonlinear algebraic equations which can be efficiently continued by standard continuation software such as AUTO and...

Observations indicate that the central portions of the Present-Day Prestellar Core Mass Function (hereafter CMF) and the Stellar Initial Mass Function (hereafter IMF) both have approximately log-normal shapes, but that the CMF is displaced to higher mass than the IMF by a factor F ∼ 4±1. This has lead to suggestions that the shape of the IMF is directly inherited from the shape of the CMF – and...

We review recent advances in our understanding of the origin of the initial mass function (IMF). We emphasize the use of numerical simulations to investigate how each physical process involved in star formation affects the resulting IMF. We stress that it is insufficient to just reproduce the IMF, but that any successful model needs to account for the many observed properties of star forming re...

This paper presents a study for solving unsaturated flow in heterogeneous porous media using the meshless method with radial basis function (RBF). For modeling nonlinear hydrological process zone, an exponential model is introduced Richards equation such that we may obtain linearized equation. We adopt multiquadric as RBF simulating problems layered soils, flux and head must satisfy continuity ...

Multiquadric method is employed for solving the two dimensional depth-integrated water quality model and the eutrophication model in marine environments. The models simulate the spatial and temporal variations of nutrients in the Tolo Harbour of Hong Kong by taking considerations of the tidal current, wind stress, growth dynamics of phytoplankton and the transformation rate of nutrients. The ph...

Abstract In this paper, a new approach to improve univariate multiquadric operators is surveyed. The presented scheme is obtained by using Hermite interpolating polynomials where the function is approximated by generalized LB quasi-interpolation operator. Error analysis shows that the convergence rate depends on the shape parameter c. Thus, our operators could provide the desired smoothness and...