基于蚁群算法的桁架结构布局离散变量优化方法

提出的布局优化方法是将桁架结构的截面变量、拓扑变量及形状变量统一为离散变量.将离散变量转化为适应于蚁群算法求解TSP问题的离散变量,应用MATLAB语言编写求解桁架结构布局优化程序,最终实现对问题的分析与求解.通过对几个经典的平面、空间桁架结构布局优化算例的验算表明:本文设计的基于蚁群算法的桁架结构布局离散变量优化方法较单独处理截面优化、拓扑优化及形状优化问题具有更大的效益,相对于其他布局优化方法也展现出更好的优化效果.“基于蚁群算法的桁架结构布局离散变量优化方法”在程序设计、求解速度、求解空间及其方法通用性等方面都表现出良好的性能,并且简单、实用,适应于实际工程应用.     

Pressure dependence of two-level systems in disordered atomic chain

The dependence of two-level systems in disordered atomic chain on pressure, both positive and negative was studied numerically. The disorder was produced through the use of interatomic pair potentials having more than one energy minimum. It was found that there exists a correlation between the energy separation of the minima of two-level systems Δ and the variation of this separation with pressure. The correlation may have either positive or negative sign, implying that the asymmetry of two-level systems may in average increase or decrease with pressure depending on the interplay of different interactions between atoms in disordered state. The values of Δ depend on the sign of pressure.     

Theoretical analysis of porous radiant burners under 2-D radiation field using discrete ordinates method

This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners (PRBs). In the present work, a 2-D rectangular model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. The gas and the solid phases are considered in non-local thermal equilibrium and combustion in the porous medium is modeled by considering a non-uniform heat generation zone. The homogeneous porous media, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. The radiation effect in the gas flow is neglected but the conductive heat transfer is taken into account. In order to analyze the thermal characteristics of porous burners, the coupled energy equations for the gas and porous medium in steady condition are solved numerically and the discrete ordinates method (DOM) is used to obtain the distribution of radiative heat flux in the porous media. Finally, the effects of various parameters on the performance of porous radiant burners are examined. The present results are compared with some reported theoretical and experimental results by other investigators and good agreement is found.     

The Application of Discrete Variational Identity on Semi-Direct Sums of Lie Algebras

With non-semisimple Lie algebras, the trace identity was generalized to discrete spectral problems. Then the corresponding discrete variational identity was used to a class of semi-direct sums of Lie algebras in a lattice hierarchy case and obtained Hamiltonian structures for the associated integrable couplings of the lattice hierarchy. It is a powerful tool for exploring Hamiltonian structures of discrete soliton equations.     

二维环状无限深势阱中的朗道能级

对于带电粒子在磁场中的运动,在各种教科书上都有详细的阐述,但是对于限制在二维无限深势阱的带电粒子,现在流行的各种量子力学教科书上都没有阐述.本文主要讨论二维无限深势阱中的能级和朗道能级.     

NUMERICAL INVERSION OF MULTIDIMENSIONAL LAPLACE TRANSFORMS USING MOMENT METHODS

This paper develops a numerical method to invert multi-dimensional Laplace transforms. By a variable transform, Laplace transforms are converted to multi-dimensional Hansdorff moment problems so that the numerical solution can be achieved. Stability estimation is also obtained. Numerical simulations show the efficiency and practicality of the method.     

On the discrete adjoints of adaptive time stepping algorithms

We investigate the behavior of adaptive time stepping numerical algorithms under the reverse mode of automatic differentiation (AD). By differentiating the time step controller and the error estimator of the original algorithm, reverse mode AD generates spurious adjoint derivatives of the time steps. The resulting discrete adjoint models become inconsistent with the adjoint ODE, and yield incorrect derivatives. To regain consistency, one has to cancel out the contributions of the non-physical derivatives in the discrete adjoint model. We demonstrate that the discrete adjoint models of one-step, explicit adaptive algorithms, such as the Runge–Kutta schemes, can be made consistent with their continuous counterparts using simple code modifications. Furthermore, we extend the analysis to cover second order adjoint models derived through an extra forward mode differentiation of the discrete adjoint code. Several numerical examples support the mathematical derivations.     

Application of the GALI method to localization dynamics in nonlinear systems

We investigate localization phenomena and stability properties of quasiperiodic oscillations in N$N$ degree of freedom Hamiltonian systems and N$N$ coupled symplectic maps. In particular, we study an example of a parametrically driven Hamiltonian lattice with only quartic coupling terms and a system of N$N$ coupled standard maps. We explore their dynamics using the Generalized Alignment Index (GALI), which constitutes a recently developed numerical method for detecting chaotic orbits in many dimensions, estimating the dimensionality of quasiperiodic tori and predicting slow diffusion in a way that is faster and more reliable than many other approaches known to date.     

Community facilitation of problem structuring and decision making processes: Experiences from the EU LEADER+ programme

This paper reports on the work carried out supporting a rural community in Denmark under the LEADER+ programme. This is a programme that supports development in particularly vulnerable rural regions of the European countries members of EU. It supports creative and innovative projects that can contribute to long-term and sustainable development in these regions. The main tasks have been the organisation and facilitation of conferences and workshops to structure the problematic situation of identifying and designing innovative projects for the development of the community and to support decision making processes related to the agreement on action plans. Learning to design, plan, manage and facilitate conferences and workshops have also being another central activity. The main purpose of these conferences and workshops was not only problem structuring and decision making in connection with community development but also the transfer of facilitation skills and appropriate methods to the community.     

Prospective elementary teachers use of representation to reason algebraically

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment. The use of isomorphic tasks promoted their ability to justify their generalizations and to understand the relationship of the coefficient and y-intercept to the models constructed with pattern blocks. Based on critical events in the teaching experiment, we developed a scale to map changes in preservice teachers’ understanding. Features of the tasks emerged that contributed to this understanding.