Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained. Since the same results test the validity of the dynamical Monte Carlo method for simulating a collisionless shock, we extend the simulation toward including an anisotropic scattering law for further developing this dynamical Monte Carlo simulation. Under this extended anisotropic scattering law, a Gaussian distribution function is used to describe the variation of scattering angles in the particle's local frame. As a result, we obtain a series of different shock structures and evolutions in terms of the standard deviation values of the given Gaussian scattering angular distributions. We find that the total energy spectral index increases as the standard deviation value of the scattering angular distribution increases, but the subshock's energy spectral index decreases as the standard deviation value of the scattering angular distribution increases.Comment: This article include 10 pages, 8 figures, and accepted by Astronomy and Astrophysic

Latency Optimal Broadcasting in Noisy Wireless Mesh Networks

In this paper, we adopt a new noisy wireless network model introduced very recently by Censor-Hillel et al. in [ACM PODC 2017, CHHZ17]. More specifically, for a given noise parameter $p\in [0,1],$ any sender has a probability of $p$ of transmitting noise or any receiver of a single transmission in its neighborhood has a probability $p$ of receiving noise. In this paper, we first propose a new asymptotically latency-optimal approximation algorithm (under faultless model) that can complete single-message broadcasting task in $D+O(\log^2 n)$ time units/rounds in any WMN of size $n,$ and diameter $D$. We then show this diameter-linear broadcasting algorithm remains robust under the noisy wireless network model and also improves the currently best known result in CHHZ17 by a $\Theta(\log\log n)$ factor. In this paper, we also further extend our robust single-message broadcasting algorithm to $k$ multi-message broadcasting scenario and show it can broadcast $k$ messages in $O(D+k\log n+\log^2 n)$ time rounds. This new robust multi-message broadcasting scheme is not only asymptotically optimal but also answers affirmatively the problem left open in CHHZ17 on the existence of an algorithm that is robust to sender and receiver faults and can broadcast $k$ messages in $O(D+k\log n + polylog(n))$ time rounds.Comment: arXiv admin note: text overlap with arXiv:1705.07369 by other author