Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces

The well-known translation between the power law of the energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems

A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators

We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern number, even if it is defined for a non-conserved quantity such as spin in the case of the spin Hall effect, one can always infer the existence of gapless edge states under certain twisted boundary conditions that allow tunneling between edges. This relation is robust against disorder and interactions, and it provides a unified topological classification of both the quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it reconciles the apparent conflict between the stability of bulk topological order and the instability of gapless edge states in systems with open boundaries (as known happening in the spin Hall case). The consequences of time reversal invariance for bulk topological order and edge state dynamics are further studied in the present framework.Comment: A mistake corrected in reference

On the application of the depth-averaged random walk method to solute transport simulations

Most numerical studies on the solute transport problems relies on mesh-based methods, and complicated schemes have been developed to enhance numerical stability and reduce artificial diffusion. This paper systematically studies the depth-averaged random walk scheme, which is a meshfree method with the merits of being highly robust and free of numerical diffusion. Firstly, the model is used to solve an instantaneous release problem in uniform flows. Extensive parametric studies are carried out to investigate the influences of the number of particles and the size of time steps. The predictions are found to be independent of time steps but are sensitive to the particle numbers. Secondly, the model is applied to the solute transport along a tidal estuary subject to extensive wetting and drying during tidal oscillations. Finally, the model is applied to investigate the wind-induced chaotic mixing in a shallow basin. The effect of diffusion on the chaotic mixing is investigated. This study proposes a generic sampling method to interpret the output of the random walk method and highlights the importance of accurately taking diffusion into account in studying the mixing phenomena. The sampling technique also offers a guideline for estimating the total number of particles needed in the application.Royal Academy of Engineering UK-China Urban Flooding Research Impact Programme (UUFRIP\100051), the 111 Project (B17015), China Scholarship Counci

Error Performance of Double Space Time Transmit Diversity Systems

The theoretical error performance of double space time transmit diversity (DSTTD) system with optimum combining receiver is analyzed in this paper. by employing both spatial multiplexing and transmit diversity in one system, DSTTD provides practical tradeoff between system spectral efficiency and diversity gain. We derive exact analytical expressions to describe the symbol error rate for DSTTD systems. The effects of both diversity gain and antenna interference introduced by spatial multiplexing are quantified in the results. In addition, the performance of DSTTD system with successive interference cancellation is also investigated. Simulation results are in excellent agreement with the theoretical results obtained in this paper

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page

Transition Metal-free Methylation of Amines with Formaldehyde as the Reductant and Methyl Source

A simple transition metal-free procedure using formal dehyde for the N,N-dimethylation and N-methylation of primary and secondary anilines is reported. The reaction showed limitations on sterically hindered and electron-withdrawing anilines, but is successful on amines with electron-donating substituents. Formaldehyde acts as both the reducing agent and the carbon source in the reaction