Molecular dynamics in solid n-nonadecane: Experiments and computer simulations

We have undertaken a collaborative study on the molecular dynamics and the phase transition mechanisms in low-dimensional molecular crystals by combining incoherent quasielastic neutron scattering, deuterium NMR and computer simulation techniques. In this paper, we summarize the method used for deriving a dynamical model for the reorientations of n-nonadecane molecules in the rotator phase R _I of the crystal. This model has been applied successfully to interpret experimental and computational data.     

Energy–entropy dispersion relation in DNA sequences

For a number of virus- and bacterium genomes we use the concept of block entropy from information theory and compare it with the corresponding configurational energy, defined via the ionization energies of the nucleotides and a hopping term for their interactions in the sense of a tight-binding model. Additionally to the four-letter alphabet of the nucleotides we discuss a reduction to a two-letter alphabet. We find a well defined relation between block entropy and block energy for a not too large block length which can be interpreted as a generalized dispersion relation for all genome sequences. The relation can be used to look for enhanced interactions between virus and bacterium genomes. Well known examples for virus–virus and virus–bacterium interactions are analyzed along this line.     

An optimised molecular model for ammonia

Based on molecular dynamics (MD) computer simulations we investigate the dynamic behaviour of a model complex fluid suspension consisting of large (A) particles (the ‘solute’) immersed in a bath of smaller ‘solvent’ (B) particles. The goal is to identify the effect of systematic simplifications (coarse-graining) of the solvent on typical microscopic time correlation functions characterizing the single-particle and collective dynamics of the solute. As a reference system we employ a binary Lennard–Jones mixture of spherical particles with significant differences in particle sizes (σ_A>σ_B) and masses (m _A>m _B). We then replace the original B particles step by step by a reduced number of larger and heavier particles such that the mass and volume fraction of B particles is kept constant. At each step of coarse-graining, the intermolecular interactions between A particles are chosen such that the static A–A structure of the reference system is preserved. Our MD results indicate that coarse-graining has a profound influence on both the single-particle dynamics as reflected by the self-diffusion constant and the collective dynamics represented by the distinct part of the van Hove time correlation function. The latter holds only at intermediate packing fractions, whereas the collective dynamics turns out to be essentially insensitive to coarse-graining at high packing fractions.     

Effect of annealing on TiO2 nanoparticles

TiO₂ nanoparticles have been prepared by simple chemical precipitation method and annealed at different temperatures. The as-prepared TiO₂ are amorphous, and they transform into anatase phase on annealing at 450 °C, and rutile phase on annealing at 900 °C. The X-ray diffraction results showed that TiO₂ nanoparticles with grain size in the range of 21–24 nm for anatase phase and 69–74 nm for rutile phase have been obtained. FESEM images show the formation of TiO₂ nanoparticles with small size in structure. The FTIR and Raman spectra exhibited peaks corresponding to the anatase and rutile structure phases of TiO₂. Optical absorption studies reveal that the absorption edge shifts towards longer wavelength (red shift) with increase of annealing temperature.     

The wave based method: An overview of 15 years of research

The Wave Based Method is a deterministic prediction technique to solve steady-state dynamic problems and is developed to overcome some of the frequency limitations imposed by element-based prediction techniques. The method belongs to the family of indirect Trefftz approaches and uses a weighted sum of so-called wave functions, which are exact solutions of the governing partial differential equations, to approximate the dynamic field variables. By minimising the errors on boundary and interface conditions, a system of equations is obtained which can be solved for the unknown contribution factors of each wave function. As a result, the system of equations is smaller and a higher convergence rate and lower computational loads are obtained as compared to conventional prediction techniques. On the other hand, the method shows its full efficiency for rather moderately complex geometries. As a result, various enhancements have been made to the method through the years, in order to extend the applicability of the Wave Based Method. This paper gives an overview of the current state of the art of the Wave Based Method, elaborating on the modelling procedure, a comparison of the properties of the Wave Based Method and element-based prediction techniques, application areas, extensions to the method such as hybrid and multi-level approaches and the most recent developments.     

A biarc-based shape optimization approach to reduce stress concentration effects

In order to avoid stress concentration, the shape boundary must be properly designed via shape optimiza- tion. Traditional shape optimization approach eliminates the stress concentration effect by using free-form curve to present the design boundaries without taking the machin- ability into consideration. In most numerical control （NC） machines, linear as well as circular interpolations are used to generate the tool path. Non-circular curves, such as non- uniform rotational B-spline （NURBS）, need other more ad- vanced interpolation functions to formulate the tool path. Forming the circular tool path by approximating the opti- mal free curve boundary with arcs or biarcs is another op- tion. However, these two approaches are both at a cost of sharp expansion of program code and long machining time consequently. Motivated by the success of recent researches on biarcs, a reliable shape optimization approach is pro- posed in this work to directly optimize the shape boundaries with biarcs while the efficiency and precision of traditional method are preserved. Finally, the approach is validated by several illustrative examples.     

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters简

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.     

An iterative splitting approach for linear integro-differential equations

The motivation for this paper is to solve a model based on the dynamics of electrons in a plasma using a simplified Boltzmann equation. Such problems have arisen in active plasma resonance spectroscopy, which is used for plasma diagnostic techniques; see Braithwaite and Franklin (2009) [1]. We propose a modified iterative splitting approach to solve the Boltzmann equations as a system of integro-differential equations. To enable solution by fast and iterative computations, we first transform the integro-differential equations into second order differential equations. Second, we split each second order differential equations into two first order differential equations via a splitting approach. We carry out an error analysis of the higher order iterative approach. Numerical experiments with a simplified Boltzmann equation will be discussed, along with the benefits of computing with this splitting approach.     

F(z)上系统能控性PBH判据

将实数域上线性系统能控性PBH判据推广到多元有理函数域F(z).由于实数域是F(z)的子域,且为结构化矩阵,一次多项式矩阵和混合矩阵都可视为一类F(z)上矩阵,所以获得的判据适用的范围更广.给出了几个应用实例.     

Global solutions to the eikonal equation

We study structural stability of smoothness of the maximal solution to the geometric eikonal equation on (R^d,G)$({\mathbb{R}}^d,G)$, d?2$d?2$. This is within the framework of order zero metrics G. For a subclass of these metrics we show existence, stability as well as precise asymptotics for derivatives of the solution. These results are applicable to examples arising in Schrödinger operator theory.