An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations

Regional estimation of daily to annual regional evapotranspiration with MODIS data in the Yellow River Delta wetland

Evapotranspiration (ET) from the wetland of the Yellow River Delta (YRD) is one of the important components in the water cycle, which represents the water consumption by the plants and evaporation from the water and the non-vegetated surfaces. Reliable estimates of the total evapotranspiration from the wetland is useful information both for understanding the hydrological process and for water management to protect this natural environment. Due to the heterogeneity of the vegetation types and canopy density and of soil water content over the wetland (specifically over the natural reserve areas), it is difficult to estimate the regional evapotranspiration extrapolating measurements or calculations usually done locally for a specific land cover type. Remote sensing can provide observations of land surface conditions with high spatial and temporal resolution and coverage. In this study, a model based on the Energy Balance method was used to calculate daily evapotranspiration (ET) using instantaneous observations of land surface reflectance and temperature from MODIS when the data were available on clouds-free days. A time series analysis algorithm was then applied to generate a time series of daily ET over a year period by filling the gaps in the observation series due to clouds. A detailed vegetation classification map was used to help identifying areas of various wetland vegetation types in the YRD wetland. Such information was also used to improve the parameterizations in the energy balance model to improve the accuracy of ET estimates. This study showed that spatial variation of ET was significant over the same vegetation class at a given time and over different vegetation types in different seasons in the YRD wetlan

Understanding the performance of the electric power industry in China

© 2012 The Earth Institute at Columbia University and the Massachusetts Institute of Technology.Despite three decades of reform, China's electricity sector is still organized by a “new reformed plan” where capacity investment has been liberalized but prices and production remain controlled. This paper examines the impact of the current plan prices on end-users with reference to the OECD and how the plan price of electricity supply is formed. We argue that the plan price is set in an attempt to balance the interests of the public and the power industry. We find that China's industries do not pay a cheaper price for electricity than the West, and the plan price is formed through bargain between the firm and the state, which allows the firm to have a soft price constraint on its costs

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs

The long-term optical behavior of MRK421

All data available in B band for the BL Lac object MRK421 from 22 publications are used to construct a historical light curve, dating back to 1900. It is found that the light curve is very complicated and consists of a set of outbursts with very large duration. The brightness of MRK421 varies from 11.6 magnitude to more than 16 magnitude. Analyses with Jurkevich method of computing period of cyclic phenomena reveal in the light curve two kinds of behaviors. The first one is non-periodic with rapid, violent variations in intensity on time scales of hours to days. The second one is periodic with a possible period of $23.1\pm 1.1$ years. Another possible period of $15.3\pm 0.7$ years is not very significant. We have tested the robustness of the Jurkevich method. The period of about one year found in the light curves of MRK421 and of other objects is a spurious period due to the method and the observing window. We try to explain the period of $23.1 \pm1.1$ years under the thermal instability of a slim accretion disk around a massive black hole of mass of $2 *10^6 M_\odot$.Comment: Tex, 14 pages, 5 Postscript figures. Accepted for publication in A&A Supplement Serie

A Supersymmetric Model with the Gauge Symmetry SU(3)_1 X SU(2)_1 X U(1)_1 X SU(3)_2 X SU(2)_2 X U(1)_2

A supersymmetric model with two copies of the Standard Model gauge groups is constructed in the gauge mediated supersymmetry breaking scenario. The supersymmetry breaking messengers are in a simple form. The Standard Model is obtained after first step gauge symmetry breaking. In the case of one copy of the gauge interactions being strong, a scenario of electroweak symmetry breaking is discussed, and the gauginos are generally predicted to be heavier than the sfermions.Comment: 14 pages, revtex, 1 figure, messenger contents modified, discussion on GUTs improve