FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Development of the meshless finite volume particle method with exact and efficient calculation of interparticle area

The Finite Volume Particle Method (FVPM) is a meshless method based on a definition of interparticle area which is closely analogous to cell face area in the classical finite volume method. In previous work, the interparticle area has been computed by numerical integration, which is a source of error and is extremely expensive. We show that if the particle weight or kernel function is defined as a discontinuous top-hat function, the particle interaction vectors may be evaluated exactly and efficiently. The new formulation reduces overall computational time by a factor between 6.4 and 8.2. In numerical experiments on a viscous flow with an analytical solution, the method converges under all conditions. Significantly, in contrast with standard FVPM and SPH, error depends on particle size but not on particle overlap (as long as the computational domain is completely covered by particles). The new method is shown to be superior to standard FVPM for shock tube flow and inviscid steady transonic flow. In benchmarking on a viscous multiphase flow application, FVPM with exact interparticle area is shown to be competitive with a mesh-based volume-of-fluid solver in terms of computational time required to resolve the structure of an interface.     

Local artificial boundary conditions for Schrödinger and heat equations by using high-order azimuth derivatives on circular artificial boundary

The aim of the paper is to design high-order artificial boundary conditions for the Schrödinger equation on unbounded domains in parallel with a treatment of the heat equation. We first introduce a circular artificial boundary to divide the unbounded definition domain into a bounded computational domain and an unbounded exterior domain. On the exterior domain, the Laplace transformation in time and Fourier series in space are applied to achieve the relation of special functions. Then the rational functions are used to approximate the relation of the special functions. Applying the inverse Laplace transformation to a series of simple rational function, we finally obtain the corresponding high-order artificial boundary conditions, where a sequence of auxiliary variables are utilized to avoid the high-order derivatives in respect to time and space. Furthermore, the finite difference method is formulated to discretize the reduced initial–boundary value problem with high-order artificial boundary conditions on a bounded computational domain. Numerical experiments are presented to illustrate the performance of our method.     

A conservative discontinuous Galerkin scheme for the 2D incompressible Navier–Stokes equations

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier–Stokes equations. We propose an extension of Arakawa’s classical finite difference scheme for fluid flow in the vorticity–stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.     

Systematic analyses and comparison of development performance and product quality of Incremental Process and Agile Process

ContextAlthough Agile software development models have been widely used as a base for the software project life-cycle since 1990s, the number of studies that follow a sound empirical method and quantitatively reveal the effect of using these models over Traditional models is scarce.ObjectiveThis article explains the empirical method of and the results from systematic analyses and comparison of development performance and product quality of Incremental Process and Agile Process adapted in two projects of a middle-size, telecommunication software development company. The Incremental Process is an adaption of the Waterfall Model whereas the newly introduced Agile Process is a combination of the Unified Software Development Process, Extreme Programming, and Scrum.MethodThe method followed to perform the analyses and comparison is benefited from the combined use of qualitative and quantitative methods. It utilizes; GQM Approach to set measurement objectives, CMMI as the reference model to map the activities of the software development processes, and a pre-defined assessment approach to verify consistency of process executions and evaluate measure characteristics prior to quantitative analysis.ResultsThe results of the comparison showed that the Agile Process had performed better than the Incremental Process in terms of productivity (79%), defect density (57%), defect resolution effort ratio (26%), Test Execution V&V Effectiveness (21%), and effort prediction capability (4%). These results indicate that development performance and product quality achieved by following the Agile Process was superior to those achieved by following the Incremental Process in the projects compared.ConclusionThe acts of measurement, analysis, and comparison enabled comprehensive review of the two development processes, and resulted in understanding their strengths and weaknesses. The comparison results constituted objective evidence for organization-wide deployment of the Agile Process in the company.     

一步法生产涤纶FDY工艺的探讨

利用ＫＶ７３１纺丝设备一步法生产出涤纶ＦＤＹ，探讨了热辊拉伸和熔体温度对纤维质量的影响。采用高特性粘数的聚酯切片，严格控制纺丝工艺，可以在５０００ｍ／ｍｉｎ的纺丝速度下纺制高质量的细旦涤纶ＦＤＹ。     

ESTIMATION OF VAPOR PRESSURES OF ORGANIC NITROGEN AND SULFUR COMPOUNDS BY A GROUP-CONTRIBUTION METHOD

The group-contribution method for vapor pressures of hydrocarbons and organic compounds containing nitrogen or sulfur, based on the kinetic theory of fluids, is revised and extended to include new groups containing nitrogen or sulfur. Good representation is obtained for vapor pressure data in the region 1.30-270 kPa. The method may be used to estimate vapor pressures and enthalpies of vaporization for those organic fluids containing nitrogen or sulfur, where no experimental data are available.     

Surface properties of ZSM-5 modified by phosphorus

Phosphorus modification of ZSM-5 leads to extra framework P⁵⁺ and probably incorporation of +3 valence state of P in the framework. The resulting system has increased Brønsted acidity. Theoretical calculations also favour the postulate that phosphorus in +3 valence state can be incorporated into the lattice.     

A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: An NSGA-II with tuned parameters

In this research, a bi-objective vendor managed inventory model in a supply chain with one vendor (producer) and several retailers is developed, in which determination of the optimal numbers of different machines that work in series to produce a single item is considered. While the demand rates of the retailers are deterministic and known, the constraints are the total budget, required storage space, vendor's total replenishment frequencies, and average inventory. In addition to production and holding costs of the vendor along with the ordering and holding costs of the retailers, the transportation cost of delivering the item to the retailers is also considered in the total chain cost. The aim is to find the order size, the replenishment frequency of the retailers, the optimal traveling tour from the vendor to retailers, and the number of machines so as the total chain cost is minimized while the system reliability of producing the item is maximized. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimization algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. The parameters of both algorithms are first calibrated using the Taguchi approach. Then, the performances of the two algorithms are compared in terms of some multi-objective performance measures. Moreover, a local searcher, named simulated annealing (SA), is used to improve NSGA-II. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.     

Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.