On Multiple Criteria Decision Support for Suppliers on the Competitive Electric Power Market

As an active participant of a competitive energy market, the generator (the energy supplier) challenges new management decisions being exposed to the financial risk environment. There is a strong need for the decision support models and tools for energy market participants. This paper shows that the stochastic short-term planning model can be effectively used as a key analytical tool within the decision support process for relatively small energy suppliers (price-takers). A self-scheduling method for the thermal units on the energy market is addressed. A schedule acquired for given preferences can be used as a desired pattern for bidding process. The uncertainty of the market prices is modeled by a set of possible scenarios with assigned probabilities. Several risk criteria are introduced leading to a multiple criteria optimization problem. The risk criteria are well appealing and easily computable (by means of linear programming) but they meet the formal risk aversion standards. The aspiration/reservation based interactive analysis applied to the multiple criteria problem allows us to find an efficient solution (generation scheme) well adjusted to the generator preferences (risk attitude).     

广义连续流场论中新的功能及功率能率原理

提出极性和非局部极性连续统场论中具有交叉项的新的功能及功率能率原理,并据此和广义的Piola定理一次性地而且无需其它要求地推导出所有相应的运动方程和边界条件以及新的能量和能率均衡方程。同时,建立起广义连续统力学中的新的能量和能率均衡原理。给出的新的功能及能率原理纠正了现有文献中所有有关不带交叉项的能量和能率原理的不完整性。     

Stochastic Stability of Some Mechanical Systems

We discuss the behavior, for large values of time, of two linear stochastic mechanical systems. The systems are similar mathematically in that they contain a white noise in their parameters. The initial data may be random as well but are independent of white noise. The expected energy is calculated in both cases. It is well known that for free nonstochastic mechanical systems with viscous damping, the energy approaches zero as time increases. We check that this behavior takes place for the stochastic systems under consideration in the case when the initial data are random but the parameters are not. When the parameters contain a random noise the expected energy may be infinite, approach zero, remain bounded, or increase with no bound. This regime is similar to but more interesting than the known regime for the solutions of differential equations with time dependent periodic coefficients that describes the behavior of a mechanical system with characteristics that are periodic functions of time. We give necessary and sufficient conditions for stability of both systems in terms of the structure of the set of roots of an auxiliary equation.     

广义连续统场论中新的增率型功率和能率原理

目的是建立广义连续统场论的增率型功率和能率原理.通过组合具有交叉项的增率型虚速度和虚角度原理以及虚应力和虚偶应力原理提出了微极连续统场论中具有交叉项的增率型功率和能率原理,并借助广义Piola定理同时而且无需其它附加要求地推导出微极和非局部微极连续统场论的所有增率型运动方程和边界条件以及能率方程.类似地可以推导出微态连续统的相应结果.文中给出的结果是新的,并可作为建立广义连续统力学相关的增率型有限元方法的理论基础.     

A multicriteria approach to sustainable energy supply for the rural poor

Despite significant progress in energy technology, about two billion people worldwide, particularly the poor in rural areas of developing countries, have no access to electricity. Decision-making concerning the most appropriate energy technology for supplying these areas has been difficult; existing energy decision-support tools have been useful but are mostly incomplete. Trade-offs, as well as impacts that can be positive or negative, may emerge as a result of implementing modern forms of energy. These can affect both community’s livelihoods as well as the confidence of decision-makers in relation to alternative technologies. The paper discusses a newly designed multicriteria approach and its novel robustness analysis for selecting energy generation systems for the improvement of livelihoods in rural areas. The proposed methodology builds upon a sustainable rural livelihoods framework to address multiple interactions and calculate trade-offs aimed at boosting decision-makers’ confidence in the selected technologies. The methodology is tested via a case study in Colombia.     

Galerkin methods in time for semi-discrete viscoelastodynamics

In semi-discrete nonlinear elastodynamics, higher order energy and momentum conserving time stepping schemes turned out to be well suited for computing long time motions [1]. In comparison to standard ODE integrators, conserving schemes exhibit superior stability properties which are of utmost importance in a nonlinear .nite element framework. We show that conserving schemes are particularly well suited as starting point for the development of energy consistent schemes for dissipative dynamical systems. In particular, viscoelastic material behaviour is considered. A key advantage of energy consistent schemes lies in the fact that the equilibrium state of viscoelastic systems can be de.nitely reached, independent of the material parameters. In the paper, we compare two Galerkin methods for the temporal discretisation of semi-discrete nonlinear viscoelastodynamics: the standard continuous Galerkin (cG) method and an enhanced continuous Galerkin (eG) method which ful.ls the total energy balance exactly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A complete-damage problem at small strains

Damage of a linearly-responding material that can completely disintegrate is addressed at small strains. Using time-varying Dirichlet boundary conditions we set up a rateindependent evolution problem in multidimensional situations. The stored energy involves the gradient of the damage variable. This variable as well as the stress and energies are shown to be well defined even under complete damage, in contrast to displacement and strain. Existence of an energetic solution is proved, in particular, by detailed investigating the Γ-limit of the stored energy and its dependence on boundary conditions. Eventually, the theory is illustrated on a one-dimensional example.     

A complete-damage problem at small strains

Damage of a linearly-responding material that can completely disintegrate is addressed at small strains. Using time-varying Dirichlet boundary conditions we set up a rateindependent evolution problem in multidimensional situations. The stored energy involves the gradient of the damage variable. This variable as well as the stress and energies are shown to be well defined even under complete damage, in contrast to displacement and strain. Existence of an energetic solution is proved, in particular, by detailed investigating the Γ-limit of the stored energy and its dependence on boundary conditions. Eventually, the theory is illustrated on a one-dimensional example.      

Motion by weighted mean curvature is affine invariant

Suppose curves are moving by curvature in a plane, but one embeds the plane in R³ and looks at the plane from an angle. Then circles shrinking to a round point would appear to be ellipses shrinking to an “elliptical point,” and the surface energy would appear to be anisotropic as would the mobility. The result of this paper is that if one uses the apparent surface energy and the apparent mobility, then the motion by weighted curvature with mobility in the apparent plane is the same as motion by curvature in the original plane but then viewed from the angle. This result applies not only to the isotropic case but to arbitrary surface energy functions and mobilities in the plane, to surfaces in 3-space, and (in the case that the surface energy function is twice differentiable) to the case of motion viewed through distorted lenses (i.e., diffeomorphisms) as well. This result is to be contrasted with an earlier result [4], which states that for area-preserving affine transformations of the plane where the energy and mobility are not also transformed, motion by curvature to the power 1/3 (rather than 1) is invariant.     

Hamilton系统的连续有限元法

利用常微分方程的连续有限元法,对非线性Hamilton系统证明了连续一次、二次有限元法分别是2阶和3阶的拟辛格式,且保持能量守恒;连续有限元法是辛算法对线性Hamilton系统,且保持能量守恒．在数值计算上探讨了辛性质和能量守恒性,与已有的辛算法进行对比,结果与理论相吻合．     

Numerical simulation of shear band formation in hyperelastic material by energy relaxation

A theorical framework for the analysis of localized failure in hyperealstic material is presented based on the energy minimization principles associated with micro-structure developments. The theory is predicated upon the assumptions that the thickness of shear band represented by its volume fraction tends to zero as well as that the energy inside shear band is a function of the norm of the deformation gradient. Shear bands are treated as laminates of first order. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. An application of the proposed formulation to Neo-Hookean material is presented. Numerical simulation is shown in order to evaluate the performance of the proposed energy relaxation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Frederick Justin Almgren, 1933–1997

Suppose curves are moving by curvature in a plane, but one embeds the plane in R³ and looks at the plane from an angle. Then circles shrinking to a round point would appear to be ellipses shrinking to an “elliptical point,” and the surface energy would appear to be anisotropic as would the mobility. The result of this paper is that if one uses the apparent surface energy and the apparent mobility, then the motion by weighted curvature with mobility in the apparent plane is the same as motion by curvature in the original plane but then viewed from the angle. This result applies not only to the isotropic case but to arbitrary surface energy functions and mobilities in the plane, to surfaces in 3-space, and (in the case that the surface energy function is twice differentiable) to the case of motion viewed through distorted lenses (i.e., diffeomorphisms) as well. This result is to be contrasted with an earlier result [4], which states that for area-preserving affine transformations of the plane where the energy and mobility are not also transformed, motion by curvature to the power 1/3 (rather than 1) is invariant.     

Energetic modelling for carbon fibre reinforced carbon

In this contribution an energetic model for multi-phase materials is developed describing the influence of microstructure on different length scales as well as the evolution of phase changes. Restrictions on the energy functional are discussed. In such a non-convex framework, interfacial contributions serve for relaxing the total energy. Such models can be applied to describe the macroscopic material properties of carbon fibre reinforced carbon where phase transitions between regions of different texture of the carbon matrix are observed on nanoscale as well as columnar microstructures on microscale [2]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Natural networks as thermodynamic systems

Natural networks are considered as thermodynamic systems that evolve from one state to another by consuming free energy. The least-time consumption of free energy is found to result in ubiquitous scale-free characteristics. The network evolution will yield the scale-independent qualities because the least-time imperative will prefer attachment of nodes that contribute most to the free-energy consumption. The analysis of evolutionary equation of motion, derived from statistical physics of open systems, reveals that evolution of natural networks is a path-dependent and nondeterministic process. Despite the noncomputability of evolution, many mathematical models of networks can be recognized as approximations of the least-time process as well as many measures of networks can be appreciated as practical assessments of the system's thermodynamic status. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

带裂纹层合板能量释放率分析

为了进一步了解裂纹尖端应力场的特性,本文对复合材料层合板的界面裂纹作了分析.文中强调了能量释放率分量存在的条件,并给出能量释放率分量和应力强度因子间的关系式.结合经典板理论的分析结果,根据外荷作用及某些几何参数和材料多数,导出了一般复合材料层合板的应力强度因子的封闭形式解.为了得到在一般荷载条件下能量释放率的分量,必须分别确定模型混合参数Ω,文中讨论了确定参数Ω的方法,最后,应用本文方法于几种不同种类的复合材料层合板,证明其结果可应用于工程实践.     

A variational arbitrary Lagrangian-Eulerian finite element formulation for standard dissipative solids at finite strains

A novel Arbitrary Lagrangian-Eulerian (ALE) finite element formulation for standard dissipative media at finite strains is presented. In contrast to previously published ALE approaches accounting for dissipative phenomena, the proposed scheme is fully variational. Consequently, no error estimates are necessary and thus, linearity of the problem and the corresponding Hilbert-space are not required. Hence, the resulting Variational Arbitrary Lagrangian-Eulerian (VALE) finite element method can be applied to highly nonlinear phenomena as well. In case of standard dissipative solids, so-called variational constitutive updates provide a variational principle. Based on these updates, the deformation mapping follows from minimizing an incrementally defined (pseudo) potential, i.e., energy minimization is the overriding criterion that governs every aspect of the system. Therefore, it is natural to allow the variational principle to drive mesh adaption as well. Thus, in the present paper, the discretizations of the deformed as well as the undeformed configuration are optimized jointly by minimizing the respective incremental energy of the considered mechanical system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times

The long-time behaviour of spectral semi-discretisations of weakly non-linear wave equations is analysed. It is shown that the harmonic actions are approximately conserved for the semi-discretised system as well. This permits to prove that the energy of the wave equation along the interpolated semi-discrete solution remains well conserved over long times and close to the Hamiltonian of the semi-discrete equation. Although the momentum is no longer an exact invariant of the semi-discretisation, it is shown to be approximately conserved. All these results are obtained with the technique of modulated Fourier expansions. Dedicated to Professor Arieh Iserles on the Occasion of his Sixtieth Birthday.     

Energy drift in molecular dynamics simulations

In molecular dynamics, Hamiltonian systems of differential equations are numerically integrated using the Störmer–Verlet method. One feature of these simulations is that there is an unphysical drift in the energy of the system over long integration periods. We study this energy drift, by considering a representative system in which it can be easily observed and studied. We show that if the system is started in a random initial configuration, the error in energy of the numerically computed solution is well modeled as a continuous-time stochastic process: geometric Brownian motion. We discuss what in our model is likely to remain the same or to change if our approach is applied to more realistic molecular dynamics simulations.     

基于SD的煤炭矿区节能减排仿真与调控

煤炭矿区在生产煤炭能源的同时,会产生大量的能耗和排放,而降低煤炭产量必然会影响矿区的经济效益.如何协调经济发展与能源消耗、污染排放之间的矛盾,是煤炭矿区亟待解决的难点问题.通过分析煤炭生产各环节节能与减排要素、煤炭矿区节能减排系统的复杂结构和系统内部的动态反馈机制,建立了煤炭矿区节能减排系统动力学模型,并对煤炭矿区不同的发展方案进行了仿真模拟.结果表明,矿区总投资、煤炭生产投资、环保投资、各种吨煤能耗量等因素在煤炭矿区节能减排系统中发挥了重要的影响作用;可以通过增加矿区总投资,优化煤炭生产投资与环保投资比例,降低吨煤能耗量来达到矿区经济与节能减排协调发展的状态.     

Modeling of functionally graded circular energy harvesters due to flexoelectricity

Flexoelectric effect can be enhanced in micro/nano scale due to its size-dependency, making it particularly suitable for energy harvesting. In this work, a theoretical model is built to characterize the functionally graded circular flexoelectric energy harvesters based on the Kirchhoff thin plate hypothesis. Using Hamilton's principle, both the force balance equation and current balance equation are obtained. Approximated closed-form solutions of the energy harvesting performances are achieved through the assumed-mode method. Numerical analysis results demonstrate that the clamped circular energy harvesters with the ratio of the electrode radius to the plate radius be 0.64 will generate the maximum electrical output. The volume fraction coefficient has a significant impact on the resonant frequency, electrical output as well as the optimal load resistance. Meanwhile, shrinking the thickness of the circular energy harvester from 10µm to 0.1µm will lead to a remarkable increase of the optimal energy conversion efficiency from 10⁻⁶ to 10⁻². Furthermore, the strain gradient effect is examined to result in a higher resonant frequency while suppress the electrical output particularly if the length scale parameter is relatively large.