# Pak Shing Li

## Contact Details

NamePak Shing Li |
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## Pubs By Year |
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## Pub CategoriesSolar and Stellar Astrophysics (6) Astrophysics of Galaxies (4) Astrophysics (2) Physics - Fluid Dynamics (1) Physics - Computational Physics (1) Mathematics - Classical Analysis and ODEs (1) Mathematics - Combinatorics (1) Instrumentation and Methods for Astrophysics (1) |

## Publications Authored By Pak Shing Li

Stellar feedback from high-mass stars can strongly influence the surrounding interstellar medium and regulate star formation. Our new ALMA observations reveal sequential high-mass star formation taking place within one sub-virial filamentary clump (the G9.62 clump) in the G9. Read More

The intermittent dissipation of interstellar turbulence is an important energy source in the diffuse ISM. Though on average smaller than the heating rates due to cosmic rays and the photoelectric effect on dust grains, the turbulent cascade can channel large amounts of energy into a relatively small fraction of the gas that consequently undergoes significant heating and chemical enrichment. In particular, this mechanism has been proposed as a solution to the long-standing problem of the high abundance of CH+ along diffuse molecular sight lines, which steady-state, low temperature models under-produce by over an order of magnitude. Read More

The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman observations analyzed by Crutcher et al. (2010). We show that their finding that the 3D magnetic field scales approximately as density$^{0. Read More

We conjecture that the balanced complete bipartite graph $K_{\lfloor n/2 \rfloor,\lceil n/2 \rceil}$ contains more cycles than any other $n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer $k$. Read More

We study the extension problem on the Sierpinski Gasket ($SG$). In the first part we consider minimizing the functional $\mathcal{E}_{\lambda}(f) = \mathcal{E}(f,f) + \lambda \int f^2 d \mu$ with prescribed values at a finite set of points where $\mathcal{E}$ denotes the energy (the analog of $\int |\nabla f|^2$ in Euclidean space) and $\mu$ denotes the standard self-similiar measure on $SG$. We explicitly construct the minimizer $f(x) = \sum_{i} c_i G_{\lambda}(x_i, x)$ for some constants $c_i$, where $G_{\lambda}$ is the resolvent for $\lambda \geq 0$. Read More

The temperature of the gas in molecular clouds is a key determinant of the characteristic mass of star formation. Ambipolar diffusion (AD) is considered one of the most important heating mechanisms in weakly ionized molecular clouds. In this work, we study the AD heating rate using 2-fluid turbulence simulations and compare it with the overall heating rate due to turbulent dissipation. Read More

Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma $\beta_0$ of 0. Read More

Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma \beta=0. Read More

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. Read More

Ambipolar diffusion is important in redistributing magnetic flux and in damping Alfven waves in molecular clouds. The importance of ambipolar diffusion on a length scale $\ell$ is governed by the ambipolar diffusion Reynolds number, $\rad=\ell/\lad$, where $\lad$ is the characteristic length scale for ambipolar diffusion. The logarithmic mean of the AD Reynolds number in a sample of 15 molecular clumps with measured magnetic fields (Crutcher 1999) is 17, comparable to the theoretically expected value. Read More

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein (2006). Read More

The Padoan and Nordlund model of the stellar initial mass function (IMF) is derived from low order statistics of supersonic turbulence, neglecting gravity (e.g. gravitational fragmentation, accretion and merging). Read More