Discrete mechanics Based on Finite Element Methods

Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.Comment: 14 pages, 0 figure

A Review of Air Pollution Control Policy Development and Effectiveness in China

Upon economic booming and rapid urbanization, China has been suffering from severe air pollution problem. While the Chinese government strives to reduce emissions through numerous laws, standards and policy measures, rapid economic and social changes challenge policy design and implementation. Over time, control policies have been largely ineffective and air quality in the majority of the nation has not been significantly improved and even worsened in many urban areas. This chapter reviews the development of the air pollution control policies in China’s nearly 70 years’ history and discusses some political and institutional factors that have resulted in the ineffectiveness of policy implementation. We examined the pollution charge system, a key policy measure used in air pollution regulation between 1980s and 2000s, and highlighted some major changes in control policies since 2000s. A comparison of pollution control policies between China and the United States is also presented. The purpose of this chapter is to inform decision makers, particularly in the developing world, with some insights of improving policy designs and environmental governance in the control of air pollution

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron transfer rate processes

In this work, we revisit the electron transfer rate theory, with particular interests in the distinct quantum solvation effect, and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theore. & Comput. Chem. {\bf 5}, 685 (2006). Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier-crossing to tunneling, and from barrierless to quantum barrier-crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.Comment: 13 pages, 10 figures, submitted to J. Phys. Chem.

Scaling in directed dynamical small-world networks with random responses

A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems. The interplay of these ingredients results in collective dynamical evolution of a spin-like variable S(t) of the whole network. In the present model, global average spreading length \langel L >_s and average spreading time _s are found to scale as p^-\alpha ln N with different exponents. Meanwhile, S behaves in a duple scaling form for N>>N^*: S ~ f(p^-\beta q^\gamma t'_sc), where p and q are rewiring and external parameters, \alpha, \beta, \gamma and f(t'_sc) are scaling exponents and universal functions, respectively. Possible applications of the model are discussed.Comment: 4 pages, 6 Figure

Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field

The Lorentz symmetry of gravity is spontaneously broken when the non-minimally coupled Kalb-Ramond field acquires a nonzero vacuum expectation value. In this work, we present exact solutions for static and spherically symmetric black holes in the framework of this Lorentz-violating gravity theory. In order to explore the physical implications of Lorentz violation, we analyze the thermodynamic properties of the obtained solutions and evaluate its impact on some classical gravitational experiments within the Solar System. Furthermore, the Lorentz-violating parameter is constrained by using the measured results of these experiments.Comment: 21 pages and 1 figur