Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different 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 the FADE.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Stability and change

This special feature section of Journal of Management & Organization (Volume 17/1 - March 2011) sets out to widen understanding of the processes of stability and change in today's organizations, with a particular emphasis on the contribution of institutional approaches to organizational studies. Institutional perspectives on organization theory assume that rational, economic calculations, such as the maximization of profits or the optimization of resource allocation, are not sufficient to understand the behavior of organizations and their strategic choices. Institutionalists acknowledge the great uncertainty associated with the conduct of organizations and suggest that taken-for-granted values, beliefs and meanings within and outside organizations also play an important role in the determination of legitimate action.

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.

Synthesis and thermal stability of hydrotalcites based upon gallium

Hydrotalcites based upon gallium as a replacement for aluminium in hydrotalcite over a Mg/Al ratio of 2:1 to 4:1 were synthesised. The d(003) spacing varied from 7.83 A ° for the 2:1 hydrotalcite to 8.15 A ° for the 3:1 gallium containing hydrotalcite. A comparison is made with the Mg Al hydrotalcite in which the d(003) spacing for the Mg/Al hydrotalcite varied from 7.62 A ° for the 2:1Mg hydrotalcite to 7.98 A ° for the 4:1 hydrotalcite. The thermal stability of the gallium containing hydrotalcite was determined using thermogravimetric analysis. Four mass loss steps at 77, 263–280,485 and 828 degrees C with mass losses of 10.23, 21.55, 5.20 and 7.58% are attributed to dehydration, dehydroxylation and decarbonation. The thermal stability of the galliumcontaining hydrotalcite is slightly less than the aluminium hydrotalcite.

A descriptive approach for power system stability and security assessment

Power system dynamic analysis and security assessment are becoming more significant today due to increases in size and complexity from restructuring, emerging new uncertainties, integration of renewable energy sources, distributed generation, and micro grids. Precise modelling of all contributed elements/devices, understanding interactions in detail, and observing hidden dynamics using existing analysis tools/theorems are difficult, and even impossible. In this chapter, the power system is considered as a continuum and the propagated electomechanical waves initiated by faults and other random events are studied to provide a new scheme for stability investigation of a large dimensional system. For this purpose, the measured electrical indices (such as rotor angle and bus voltage) following a fault in different points among the network are used, and the behaviour of the propagated waves through the lines, nodes, and buses is analyzed. The impact of weak transmission links on a progressive electromechanical wave using energy function concept is addressed. It is also emphasized that determining severity of a disturbance/contingency accurately, without considering the related electromechanical waves, hidden dynamics, and their properties is not secure enough. Considering these phenomena takes heavy and time consuming calculation, which is not suitable for online stability assessment problems. However, using a continuum model for a power system reduces the burden of complex calculations

Thermal stability of the ‘cave’ mineral ardealite Ca2(HPO4)(SO4)•4H2O

Thermogravimetry combined with evolved gas mass spectrometry has been used to characterise the mineral ardealite and to ascertain the thermal stability of this ‘cave’ mineral. The mineral ardealite Ca2(HPO4)(SO4)•4H2O is formed through the reaction of calcite with bat guano. The mineral shows disorder and the composition varies depending on the origin of the mineral. Thermal analysis shows that the mineral starts to decompose over the temperature range 100 to 150°C with some loss of water. The critical temperature for water loss is around 215°C and above this temperature the mineral structure is altered. It is concluded that the mineral starts to decompose at 125°C, with all waters of hydration being lost after 226°C. Some loss of sulphate occurs over a broad temperature range centred upon 565°C. The final decomposition temperature is 823°C with loss of the sulphate and phosphate anions.