106,944 research outputs found
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
Operator for Describing Polarization States of a Photon
Based on the quantized electromagnetic field described by the
Riemann-Silberstein complex vector , we construct the eigenvector set of , which makes up an orthonormal and complete representation. In terms of we then introduce a new operator which can describe the relative ratio of the
left-handed and right-handed polarization states of a polarized photon .In
eigenvector basis the operator manifestly exhibits a behaviour
which is similar to a phase difference between two orientations of polarization
of a light beam in classical optics.Comment: This version (5 pages) will be published in the European Physical
Journal
Out of plane effect on the superconductivity of Sr2-xBaxCuO3+y with Tc up to 98K
A series of new Sr2-xBaxCuO3+y (0 x 0.6) superconductors were prepared using
high-pressure and high-temperature synthesis. A Rietveld refinement based on
powder x-ray diffraction confirms that the superconductors crystallize in the
K2NiF4-type structure of a space group I4/mmm similar to that of La2CuO4 but
with partially occupied apical oxygen sites. It is found that the
superconducting transition temperature Tc of this Ba substituted Sr2CuO3+y
superconductor with constant carrier doping level, i.e., constant d, is
controlled not only by order/disorder of apical-O atoms but also by Ba content.
Tcmax =98 K is achieved in the material with x=0.6 that reaches the record
value of Tc among the single-layer copper oxide superconductors, and is higher
than Tc=95K of Sr2CuO3+y with optimally ordered apical-O atoms. There is
Sr-site disorder in Sr2-xBaxCuO3+y which might lead to a reduction of Tc. The
result indicates that another effect surpasses the disorder effect that is
related either to the increased in-plane Cu-O bond length or to elongated
apical-O distance due to Ba substitution with larger cation size. The present
experiment demonstrates that the optimization of local geometry out of the Cu-O
plane can dramatically enhance Tc in the cuprate superconductors.Comment: 23 Pages, 1 Table, 5 Figure
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