Integration of the Vlasov equation along characteristics in one and two dimensions

Methods of integration of the Vlasov equation along characteristics in one and two dimensions are discussed, in connection with the problem of the formation of a charge separation at a plasma edge. Application of these methods to the problem in which the Vlasov equation is integrated in a cylindrical geometry to calculate the electric field at a plasma edge, is presented.     

Parallelization of the global extremum searching process

The parallel algorithm for searching the global extremum of the function of several variables is designed. The algorithm is based on the method of nonuniform coverings proposed by Yu.G. Evtushenko for functions that comply with the Lipschitz condition. The algorithm is realized in the language C and message passing interface (MPI) system. To speed up computations, auxiliary procedures for founding the local extremum are used. The operation of the algorithm is illustrated by the example of atomic cluster structure calculations.     

Automatic computation of the travelling wave solutions to nonlinear PDEs

Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in Maple 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases.

Program summary

Program title:TWSCatalogue identifier:AEAM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAM_v1_0.htmlProgram obtainable from:CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:1250No. of bytes in distributed program, including test data, etc.:78 101Distribution format:tar.gzProgramming language:Maple 10Computer:A laptop with 1.6 GHz Pentium CPUOperating system:Windows XP ProfessionalRAM:760 MbytesClassification:5Nature of problem:Finding the travelling wave solutions to single nonlinear PDEs.Solution method:Based on tanh-function method.Restrictions:The current version of this package can only deal with single autonomous PDEs or ODEs, not systems of PDEs or ODEs. However, the PDEs can have any finite number of independent space variables in addition to time t.Unusual features:For PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases.Additional comments:It is easy to use.Running time:Less than 20 seconds for most cases, between 20 to 100 seconds for some cases, over 100 seconds for few cases.References:[1] E.S. Cheb-Terrab, K. von Bulow, Comput. Phys. Comm. 90 (1995) 102.[2] S.A. Elwakil, S.K. El-Labany, M.A. Zahran, R. Sabry, Phys. Lett. A 299 (2002) 179.[3] E. Fan, Phys. Lett. 277 (2000) 212.[4] W. Malfliet, Amer. J. Phys. 60 (1992) 650.[5] W. Malfliet, W. Hereman, Phys. Scripta 54 (1996) 563.[6] E.J. Parkes, B.R. Duffy, Comput. Phys. Comm. 98 (1996) 288.     

Robust control of multidimensional nonstationary linear plants

Solved was the problem was of constructing a robust control system with linear nonstationary multidimensional control plant compensating the parametric and external bounded perturbations to within δ if the derivatives of the output vector are not measured and fully if the derivatives are measured.     

Collision-free spatial hash functions for structural analysis of billion-vertex chemical bond networks

State-of-the-art molecular dynamics (MD) simulations generate massive datasets involving billion-vertex chemical bond networks, which makes data mining based on graph algorithms such as K-ring analysis a challenge. This paper proposes an algorithm to improve the efficiency of ring analysis of large graphs, exploiting properties of K-rings and spatial correlations of vertices in the graph. The algorithm uses dual-tree expansion (DTE) and spatial hash-function tagging (SHAFT) to optimize computation and memory access. Numerical tests show nearly perfect linear scaling of the algorithm. Also a parallel implementation of the DTE + SHAFT algorithm achieves high scalability. The algorithm has been successfully employed to analyze large MD simulations involving up to 500 million atoms.     

Noise Immunity of High-Precision Low-Temperature Experiments

In the high-precision low-temperature experiments, noise immunity has long been an important issue. We consider the problem of measuring the slowly changing data in the presence of both white noise and sudden, short noise spikes. The Kalman filter is applied to attenuate the white noise and a spike detecting algorithm is applied to remove spikes resulting from the charged particles. Experimental data show that, with the Kalman filter, the RMS of the measurement noise in a 0.5 Hz bandwidth can be attenuated from 4 nK to 0.2 nK in the best case. A simple spike detecting algorithm worked effectively to remove spikes without increasing the random noise level.     

Burgers vector determination in deformed perovskite and post-perovskite of CaIrO3 using thickness fringes in weak-beam dark-field images

The thickness-fringe method [Ishida et al., Philosophical Magazine 42 (1980) 453] for complete determination of the character of a dislocation Burgers vector has been performed in CaIrO₃ perovskite and post-perovskite deformed at high pressures and high temperatures. By selecting several main zone axes and determining the number of terminating thickness fringes at the extremity of a dislocation from a wedge-shaped thin-foil specimen in weak-beam dark-field transmission electron microscope (TEM) images, the Burgers vectors were unambiguously determined. The results demonstrate that [1 0 0] screw and edge dislocations on the (0 1 0) slip plane are dominant in the post-perovskite phase. Curved [1 0 0] and [0 1 0] dislocations and straight 〈1 1 0〉 screw dislocations on a potential (0 0 1) slip plane were identified in the perovskite phase as well as a high density of {1 1 0} twins. Low-angle tilt boundaries consisting of different groups of parallel edge dislocations on the {1 1 0} and (0 0 1) planes indicate diffusion-assisted climb in perovskite at high temperatures. The differences in dislocation microstructures could be due to activations of limited numbers of slip systems for post-perovskite and of a large number of multiple slip systems for perovskite, which may result in the strong crystallographic preferred orientation (CPO) in post-perovskite and the lack of CPO in deformed perovskite.     

A model predictive control approach for the Italian LBE-XADS

In this paper, model predictive control (MPC) is applied to the Italian 80 MW_th experimental accelerator driven system (XADS), referring to a simple, non-linear model for the dynamic simulation of the plant, which has been developed and described in a previous work [A. Cammi, L. Luzzi, A.A. Porta, M.E. Ricotti, Prog. Nucl. Energ. 48 (2006) 578], in order to describe the interactions among the different subsystems: i.e., the accelerator-core coupling, the lead bismuth eutectic (LBE) primary system, the secondary system with diathermic oil and air coolers batteries, which reject the thermal power to the environment. Hereinafter, a model predictive controller is proposed, with the objective to minimize the difference between the average temperature of the diathermic oil and its reference value, while also minimizing the variations of the control input, which is the air coolers mass flow rate. The dynamic response of the LBE-XADS has been evaluated with reference to a reduction of 20% in the reactor power from nominal load conditions: this transient is very demanding for the overall plant, nevertheless the obtained results indicate the effectiveness of the proposed controller.     

Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection

A detailed procedure of full-electromagnetic Vlasov simulation technique is presented. Our new unsplitting conservative scheme exactly satisfies the continuity equation for charge. The implicit Finite Difference Time Domain method is also adopted for computation of electromagnetic fields, which is not restricted by the CFL condition for light. The Geospace Environment Modeling magnetic reconnection challenge problem is adopted as a benchmark test. The characteristics of the present Vlasov code are studied by varying the resolution in configuration space.