On the accuracy of simulations of turbulence

The widely recognized issue of adequate spatial resolution in numerical simulations of turbulence is studied in the context of two-dimensional magnetohydrodynamics. The familiar criterion that the dissipation scale should be resolved enables accurate computation of the spectrum, but fails for precise determination of higher-order statistical quantities. Examination of two straightforward diagnostics, the maximum of the kurtosis and the scale-dependent kurtosis, enables the development of simple tests for assessing adequacy of spatial resolution. The efficacy of the tests is confirmed by examining a sample problem, the distribution of magnetic reconnection rates in turbulence. Oversampling the Kolmogorov dissipation scale by a factor of 3 allows accurate computation of the kurtosis, the scale-dependent kurtosis, and the reconnection rates. These tests may provide useful guidance for resolution requirements in many plasma computations involving turbulence and reconnection

Universality of the edge tunneling exponent of fractional quantum Hall liquids

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $\nu = 1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.Comment: 5 pages, 3 figure

Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $\nu = 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.Comment: 4 pages, 3 figures. New version shortened for PRL. Corrected typo

Design of a 2.4 GHz High-Performance Up-Conversion Mixer with Current Mirror Topology

In this paper, a low voltage low power up-conversion mixer, designed in a Chartered 0.18 μm RFCMOS technology, is proposed to realize the transmitter front-end in the frequency band of 2.4 GHz. The up-conversion mixer uses the current mirror topology and current-bleeding technique in both the driver and switching stages with a simple degeneration resistor. The proposed mixer converts an input of 100 MHz intermediate frequency (IF) signal to an output of 2.4 GHz radio frequency (RF) signal, with a local oscillator (LO) power of 2 dBm at 2.3 GHz. A comparison with conventional CMOS up-conversion mixer shows that this mixer has advantages of low voltage, low power consumption and high-performance. The post-layout simulation results demonstrate that at 2.4 GHz, the circuit has a conversion gain of 7.1 dB, an input-referred third-order intercept point (IIP3) of 7.3 dBm and a noise figure of 11.9 dB, while drawing only 3.8 mA for the mixer core under a supply voltage of 1.2 V. The chip area including testing pads is only 0.62×0.65 mm2