A meshfree-based local Galerkin method with condensation of degree of freedom

Condensation technique of degree of freedom is firstly proposed to improve the computational efficiency of meshfree method with Galerkin weak form. In present method, scattered nodes without connectivity are divided into several subsets by cells with arbitrary shape. The local discrete equations are established over each cell by using moving kriging interpolation, in which the nodes that located in the cell are used for approximation. Then, the condensation technique can be introduced into the local discrete equations by transferring equations of inner nodes to equations of boundary nodes based on cell. In the scheme of present method, the calculation of each cell is carried out by meshfree method with Galerkin weak form, and local search is implemented in interpolation. Numerical examples show that the present method has high computational efficiency and convergence, and good accuracy is also obtained.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Gas-phase reactions of aryl radicals with 2-butyne : an experimental and theoretical investigation employing the N-methyl-pyridinium-4-yl radical cation

Aromatic radicals form in a variety of reacting gas-phase systems, where their molecular weight growth reactions with unsaturated hydrocarbons are of considerable importance. We have investigated the ion-molecule reaction of the aromatic distonic N-methyl-pyridinium-4-yl (NMP) radical cation with 2-butyne (CH3C CCH3) using ion trap mass spectrometry. Comparison is made to high-level ab initio energy surfaces for the reaction of NMP and for the neutral phenyl radical system. The NMP radical cation reacts rapidly with 2-butyne at ambient temperature, due to the apparent absence of any barrier. The activated vinyl radical adduct predominantly dissociates via loss of a H atom, with lesser amounts of CH3 loss. High-resolution Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry allows us to identify small quantities of the collisionally deactivated reaction adduct. Statistical reaction rate theory calculations (master equation/RRKM theory) on the NMP + 2-butyne system support our experimental findings, and indicate a mechanism that predominantly involves an allylic resonance-stabilized radical formed via H atom shuttling between the aromatic ring and the C-4 side-chain, followed by cyclization and/or low-energy H atom beta-scission reactions. A similar mechanism is demonstrated for the neutral phenyl radical (Ph center dot)+2-butyne reaction, forming products that include 3-methylindene. The collisionally deactivated reaction adduct is predicted to be quenched in the form of a resonance-stabilized methylphenylallyl radical. Experiments using a 2,5-dichloro substituted methyl-pyridiniumyl radical cation revealed that in this case CH3 loss from the 2-butyne adduct is favoured over H atom loss, verifying the key role of ortho H atoms, and the shuttling mechanism, in the reactions of aromatic radicals with alkynes. As well as being useful phenyl radical analogues, pyridiniumyl radical cations may form in the ionosphere of Titan, where they could undergo rapid molecular weight growth reactions to yield polycyclic aromatic nitrogen hydrocarbons (PANHs).

A meshfree-based local Galerkin method with condensation of degree of freedom for elastic dynamic analysis

Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dynamic analysis. In the present method, scattered nodes without connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approximation. Then local discrete equations can be simplified by condensation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by assembling all local discrete equations and are solved by using the standard implicit Newmark’s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is implemented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.

A novel ambiguity acceptance test threshold determination method with controllable failure rate

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood, although it is one of the most important topics in ambiguity validation. Currently, there are two threshold determination methods in the ambiguity validation procedure: the empirical approach and the fixed failure rate (FF-) approach. The empirical approach is simple but lacks of theoretical basis. The fixed failure rate approach has a rigorous probability theory basis, but it employs a more complicated procedure. This paper focuses on how to determine the threshold easily and reasonably. Both FF-ratio test and FF-difference test are investigated in this research and the extensive simulation results show that the FF-difference test can achieve comparable or even better performance than the well-known FF-ratio test. Another benefit of adopting the FF-difference test is that its threshold can be expressed as a function of integer least-squares (ILS) success rate with specified failure rate tolerance. Thus, a new threshold determination method named threshold function for the FF-difference test is proposed. The threshold function method preserves the fixed failure rate characteristic and is also easy-to-apply. The performance of the threshold function is validated with simulated data. The validation results show that with the threshold function method, the impact of the modelling error on the failure rate is less than 0.08%. Overall, the threshold function for the FF-difference test is a very promising threshold validation method and it makes the FF-approach applicable for the real-time GNSS positioning applications.

Molecular complexes of metallo tetraphenyl porphyrins with 2,4,5,7-tetranitro fluorenone

The interactions of mesotetraphenyl porphyrin and its metallo derivatives with 2,4,5,7-tetra nitrofluorenone have been studied using spectroscopic methods. The association constants (K) for 1:1 complexes in Ch2Cl2Cl2 follow the order Pd+2>Co+2> Cu+2>VO+2>Ni+2>Zn+2. The values of K are accounted in terms of stereochemistry of MTPPs and the electronic configuration of the metal ions. The magnitude and direction of the proton NMR shifts of the acceptor and donor in the complexes and their ESR parameter furnish information as to the possible structures of these complexes in solution.

Complexes of lanthanide nitrates with 2-N-(6-picoIyl)-benzamide

New complexes of lanthanide nitrates with 2-N-(6-picolyl)-benzamide of the formulae Ln2[6-pic-BA], [NO3l6 (Ln = Y and La-Yb) have been prepared and characterised by chemical analysis, infrared, molar conductance and electronic spectral data. Molar conductance data along with IR data point to the presence of co-ordinated nitrate groups. IR spectra prove the bidentate co-ordination of the ligand to the metal ion, through the oxygen of the secondary amide and the nitrogen of the heterocyclic ring. Electronic spectral studies in the visible region suggest an eight co-ordinate geometry around the metal ions.

Complexes of lanthanide perchlorates with 2-N-(pyridyl)benzamide

New complexes of lanthanide perchlorates with 2-N-(pyridyl) benzamide (PyBA) of the type Ln(PyBA)3(ClO4)3 where Ln = Y and La---Yb have been synthesised and characterised by analyses, conductance, IR, 13C NMR (for diamagnetic complexes only) and electronic spectra. The molar conductance and IR data point to the ionic nature of the perchlorate groups in the complexes. IR data along with the 13C NMR data unequivocally proves that the coordination of the ligand to the metal ions taken place in a bidentate fashion through the oxygen of the benzamide group and the nitrogen of the heterocyclic ring. From a comparison of the visible electronic spectral shapes of the Nd3+, Ho3+ and Er3+ complexes with those reported in the literature, a 6-coordinate geometry around the metal ion has been assigned in all the complexes.

Molecular-complexes of metallo tetraphenyl porphyrins with 2,4,5,7-tetranitro fluorenone

The interactions of mesotetraphenyl porphyrin and its metallo derivatives with 2,4,5,7-tetra nitrofluorenone have been studied using spectroscopic methods. The association constants (K) for 1:1 complexes in Ch2Cl2Cl2 follow the order Pd+2>Co+2> Cu+2>VO+2>Ni+2>Zn+2. The values of K are accounted in terms of stereochemistry of MTPPs and the electronic configuration of the metal ions. The magnitude and direction of the proton NMR shifts of the acceptor and donor in the complexes and their ESR parameter furnish information as to the possible structures of these complexes in solution.

Extraordinary synergy in the mechanical properties of polymer matrix composites reinforced with 2 nanocarbons

One of the applications of nanomaterials is as reinforcements in composites, wherein small additions of nanomaterials lead to large enhancements in mechanical properties. There have been extensive studies in the literature on composites where a polymer matrix is reinforced by a single nanomaterial such as carbon nanotubes. In this article, we examine the significant synergistic effects observed when 2 different types of nanocarbons are incorporated in a polymer matrix. Thus, binary combinations of nanodiamond, few-layer graphene, and single-walled nanotubes have been used to reinforce polyvinyl alcohol. The mechanical properties of the resulting composites, evaluated by the nanoindentation technique, show extraordinary synergy, improving the stiffness and hardness by as much as 400% compared to those obtained with single nanocarbon reinforcements. These results suggest a way of designing advanced materials with extraordinary mechanical properties by incorporating small amounts of 2 nanomaterials such as graphene plus nanodiamond or nanodiamond plus carbon nanotube.