Nonlinear stability of convection induced by inclined thermal and solutal gradients

The energy method, giving the sufficient condition for stability, is developed for the convection problem induced by inclined thermal and solutal gradients in a horizontal layer of a saturated porous medium. The boundaries are taken to be perfectly conducting and Darcy's law is employed to represent the porous medium. A nonlinear stability analysis is performed and compound matrix method is employed for numerical calculations. The optimal stability bound is computed and numerical results are compared with the linear theory for different parameter values.     

Exergoeconomic optimal performance of an irreversible closed Brayton cycle combined cooling,heating and power plant

A combined cooling, heating and power (CCHP) plant model composed of an irreversible closed Brayton cycle and an endoreversible four-heat-reservoir absorption refrigeration cycle is established by using finite time thermodynamics. The irreversibilities considered in the CCHP plant include heat-resistance losses in the hot-, cold-, thermal consumer-, generator-, absorber-, condenser- and evaporator-side heat exchangers as well as non-isentropic losses in the compression and expansion processes. Equations of exergy efficiency and profit rate of the CCHP plant are derived. Based on the finite time exergoeconomic analysis method, profit rate optimization is carried out by searching the optimal compressor pressure ratio and the optimal heat conductance distributions of the seven heat exchangers for a fixed total heat exchanger inventory and with the help of Powell arithmetic. The effects of some design parameters, including compressor and gas turbine efficiencies, ratio of heat demanded by the thermal consumer to power output, heat reservoir temperature ratios and price ratios on the optimal heat conductance distributions, optimal compressor pressure ratio, maximum profit rate and finite time exergoeconomic performance bound of the CCHP plant are discussed by numerical examples. The results obtained may provide some theoretical guidelines for the designs and operations of the practical CCHP plants.     

On the duals of geometric Goppa codes from norm-trace curves

In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric approach is performed and applied to study in particular the dual codes of one-point and two-point codes arising from norm-trace curves through Goppaʼs construction, providing in many cases their minimum distance and some bounds on the number of their minimum-weight codewords. The results are obtained by showing that the supports of the minimum-weight codewords of the studied codes obey some precise geometric laws as zero-dimensional subschemes of the projective plane. Finally, the dimension of some classical two-point Goppa codes on norm-trace curves is explicitely computed.     

Enumeration of Pareto optimal multi-criteria spanning trees – a proof of the incorrectness of Zhou and Gen's proposed algorithm

The minimum spanning tree (MST) problem is a well-known optimization problem of major significance in operational research. In the multi-criteria MST (mc-MST) problem, the scalar edge weights of the MST problem are replaced by vectors, and the aim is to find the complete set of Pareto optimal minimum-weight spanning trees. This problem is NP-hard and so approximate methods must be used if one is to tackle it efficiently. In an article previously published in this journal, a genetic algorithm (GA) was put forward for the mc-MST. To evaluate the GA, the solution sets generated by it were compared with solution sets from a proposed (exponential time) algorithm for enumerating all Pareto optimal spanning trees. However, the proposed enumeration algorithm that was used is not correct for two reasons: (1) It does not guarantee that all Pareto optimal minimum-weight spanning trees are returned. (2) It does not guarantee that those trees that are returned are Pareto optimal. In this short paper we prove these two theorems.     

Comparison of analytical and numerical solution for optimal vortex diffuser design

The contribution deals with optimization of wing tip devices, so called vortex diffusers. A comparison is given between an analytical approach for obtaining the optimal circulation loading and the results of a numerical investigation using a lifting line method. The purpose of most wing tip devices is to reduce the induced drag of the main wing by converting vortex energy into thrust. In order to achieve an optimal design, a variational formulation originally proposed by Betz and Prandtl for air screws is applied to the circulation distribution of the diffuser blades. In extension to the inviscid formulation, a viscous correction is applied in order to account for frictional forces. In an effort to validate the analytical results, a comparison is given with numerical solutions from a lifting line method. The loading of the diffuser blades is parametrized and optimized with respect to resulting thrust by use of a quasi-Newton gradient method. Comparison shows that, knowing the velocity distribution in the near wake of the wing, considerable decrease of induced drag may be achieved making use of vortex diffusers. Although actual circulation loading may differ between the analytical and numerical estimation, resulting thrust agrees within a few percent. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numeric modeling of thermal pollution in Plomin bay area

In order to analyze the thermal pollution of the Plomin bay induced by the used cooling water released from Plomin 1 and Plomin 2 thermal power plants, flow simulations and temperature field analysis were conducted. The measurements of the bay surface temperature field were carried out as well as the corresponding 3D water flow simulations on the realistically modeled bay. The accuracy of the simulation results was evaluated by the comparison of computed and measured surface temperatures. Furthermore, numerical meshes of different density were used in order to determine model sensitivity where the results showed a significant effect of the mesh density on the simulation results. Although the simulations obtained with a denser mesh yield more accurate results and allow for the reconstruction of heated water surface flow with better reliability, the sparser mesh provided sufficiently accurate results as well. The overall temperature field obtained with the numerical model agrees well with the measured temperature values, which demonstrates the successful application of the 3D flow numerical model on the Plomin bay thermal pollution problem.      

Min-weight double-tree shortcutting for Metric TSP: Bounding the approximation ratio

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e. the minimum-weight double-tree shortcutting. Previously, we gave an efficient algorithm for this problem, and carried out its experimental analysis. In this paper, we address the related question of the worst-case approximation ratio for the minimum-weight double-tree shortcutting method. In particular, we give lower bounds on the approximation ratio in some specific metric spaces: the ratio of 2 in the discrete shortest path metric, 1.622 in the planar Euclidean metric, and 1.666 in the planar Minkowski metric. The first of these lower bounds is tight; we conjecture that the other two bounds are also tight, and in particular that the minimum-weight double-tree method provides a 1.622-approximation for planar Euclidean TSP.     

Statistical identification and optimal control of thermal power plants

Statistical system identification and its use for the optimal control of thermal power plants are discussed. The analysis of the plant dynamics and derivation of the state-space representation are performed by fitting a multivariate AR model to the plant data obtained by an experiment. The basic concept of the power plant control and the motivation that necessitated the statistical approach are explained in the introduction. Practical procedure for the implementation of the method is described in detail with examples obtained from actual plants. The main items discussed are the selection of system variables by means of relative power contribution analysis, determination of the state equation and adjustment of the optimal feedback gain by digital simulation technique. Finally, excellent performance of the proposed control system is demonstrated by the operating records of 500 MW and 600 MW supercritical plants.     

Generalized model and optimum performance of an irreversible thermal Brownian microscopic heat pump

A generalized model of an irreversible thermal Brownian microscopic heat pump is established in this paper. It is composed of Brownian particles which are moving in a periodic sawtooth potential with external forces and contacting with alternating hot and cold reservoirs along the space coordinate. The generalized irreversible Brownian heat pump model incorporates heat flows driven by both the potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs. This paper derives the expressions for heating load, power input and coefficient of performance (COP) of the Brownian heat pump. The optimum performance of the generalized heat pump model is analyzed by using the theory of finite time thermodynamics (FTT). Effects of the design parameters, i.e., the external force, the heat leakage coefficient, barrier height of the potential, asymmetry of the sawtooth potential and heat reservoir temperature ratio on the performance of the Brownian heat pump are discussed in detail. The performance of the Brownian heat pump depends strictly on the design parameters. Through the proper choice of these parameters, the Brownian heat pump can operate in the optimal regimes. The optimum COP performance and the fundamental optimal relations between COP and heating load are studied by detailed numerical examples. It is shown that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, both the heating load and COP performances of the Brownian heat pump will decrease. The effective ranges of the external force and barrier height of the potential in which the Brownian motor system can operate as a heat pump are further determined.     

QMC Rules of Arbitrary High Order: Reproducing Kernel Hilbert Space Approach

In this paper we consider numerical integration of smooth functions lying in a particular reproducing kernel Hilbert space. We show that the worst-case error of numerical integration in this space converges at the optimal rate, up to some power of a log?N factor. A similar result is shown for the mean square worst-case error, where the bound for the latter is always better than the bound for the square worst-case error. Finally, bounds for integration errors of functions lying in the reproducing kernel Hilbert space are given. The paper concludes by illustrating the theory with numerical results.     

Minimum-weight design of continuous beams under displacement and stress constraints

Explicit optimality conditions for minimum-weight design of elastic sandwich beams with segmentwise constant structural stiffness, subject to displacement and mean-square stress constraints, are obtained. An iterative procedure that combines the use of the optimality conditions with finite-element analysis is proposed and is illustrated by numerical examples. These examples suggest that very few iterations are necessary to obtain a good approximation to the optimal design. It is shown that, for practical purposes, the optimization problem may be simplified by using the optimality conditions derived for statically determinate beams instead of those valid for statically indeterminate beams.This research was sponsored by the U.S. Army Research Office, Durham, North Carolina. The authors are grateful to Professor W. Prager for helpful comments.     

A nonlinear optimal control problem for the nonsteady temperature of a layer with constraints on the thermal stress

We propose a numerical method of constructing the optimal heating regime for a thermally stressed unbounded layer with constraints on the control and thermal stresses. Solving the nonlinear optimization problem for rapidity is reduced to solving the inverse problem of thermoelasticity. The results of numerical studies are presented. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Minimum-weight design of elastic sandwich beams with deflection constraints

In this paper, minimum-weight design of an elastic sandwich beam with a prescribed deflection constraint at a given point is investigated. The analysis is based on geometrical considerations using then-dimensional space of discretized specific bending stiffness. Since the present method of analysis is different from the method based on the calculus of variations, the conditions of piecewise continuity and differentiability on specific bending stiffness can be relaxed. Necessary and sufficient conditions for optimality are derived for both statically determinate and statically indeterminate beams. Beams subject to a single loading and beams subject to multiple loadings are analyzed. The degree to which the optimality condition renders the solution unique is discussed. To illustrate the method of solution, two examples are presented for minimum-weight designs under dual loading of a simply supported beam and a beam built in at both ends. The present analysis is also extended to the following problems: (a) optimal design of a beam built in at both ends with piecewise specific stiffness and a prescribed deflection constraint and (b) minimum-cost design of a sandwich beam with prescribed deflection constraints.The results presented in this paper were obtained in the course of research supported partly by the US Army Research Office, Durham, North Carolina, Research Grant No. DA-ARO-31-G1008, and partly by the Office of Naval Research, Contract No. N00014-67-A-0109-0003, Task No. NR 064-496. The authors wish to express their thanks to Professor H. Halkin for pointing out the applicability of optimal control theory to the present problem and to Professor W. Prager for his valuable suggestions.     

Maximum neutron flux in thermal research reactors

This paper deals with the determination of the space distribution of fuel concentration in thermal reactors for the purpose of obtaining maximum neutron flux. With some approximations, this problem is reduced to a nonclassical variational problem, which is solved by using Pontryagin's maximum principle. It is shown that the optimal fuel configuration of the reactor core consists of a reflector in its center, a zone of constant (permissible) power density, a zone of constant (maximum) fuel concentration, and a peripheral reflector of infinite thickness.     

一类非线性Schrodinger方程的差分／Legendre谱元法

考察一类带幂次非线性项的Schrodinger方程的Dirichlet初边值问题，提出了一个有效的计算格式，其中时间方向上应用了一种守恒的二阶差分隐格式，空间方向上采用Legendre谱元法．对于时间半离散格式，证职了该格式具有能量守恒性质，并给出了L^2误差估计，对于全离散格式，应用不动点原理证明了数值解的存在唯一性，并给出了L^2误差估计．最后，通过数值试验验证了结果的可信性．     

Optimal operation for a bi-fuel thermal power plant by mathematical programming

This study is an attempt to provide the management of the Electricity Generating Authority of Thailand with an effective tool for determining the best operation of thermal units. A bi-fuel thermal power plant at North Bangkok, consisting of three thermal units, is considered. One of these units is adaptable to both lignite and fuel oil use, while the others use only fuel oil. A general optimization model, applicable to most power plants, is developed and a simplified version is applied to the North Bangkok Power Plant. A 0–1 mixed integer linear programming technique is used to find a method of operating the thermal units, which minimizes total fuel costs. Comparing the optimal solutions with actual operating strategies shows that savings in costs can be realised by implementing the model solution. Moreover, since the framework developed is quite general, it may be usefully applied to other power plant studies.     

A generalized model of an irreversible thermal Brownian refrigerator and its performance

A generalized model of an irreversible thermal Brownian refrigerator, which consists of Brownian particles moving in a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate, is established in this paper. The heat flows driven by both potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs are taken into account. The optimum performance of the generalized model is analyzed using the theory and method of finite time thermodynamics. The analytical expressions for cooling load, coefficient of performance (COP) and power input of the Brownian refrigerator are derived. It is shown by numerical examples that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, the Brownian refrigerator is always irreversible and the COP can never attain the Carnot COP. The influences of the heat leakage, the external force, barrier height of the potential, asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs on the performance of the Brownian refrigerator are also investigated in detail. The effective regions of external force and barrier height of the potential in which the Brownian motor can operate as a refrigerator are determined. It is found that the performance of the Brownian refrigerator depends strictly on the design parameters. If these design parameters are properly chosen, the Brownian refrigerator can be controlled to operate in the optimal regimes. The results obtained herein about the general Brownian refrigerator model include those obtained in many previous literatures.     

Economic dispatch of thermal power systems using geometric programming

In this paper the economic dispatch of thermal power systems under consideration of transmission line losses is investigated. Using a well-known transmission-loss-formula derived by Kirchmayer and others the problem is formulated as a signomial geometric program. A sensitivity analysis with respect to small changes in the system load is discussed. A simple numerical example is provided.     

Stochastic immersed boundary method incorporating thermal fluctuations

We give a brief introduction to the stochastic immersed boundary method which allows for simulation of small length-scale physical systems in which elastic structures interact with a fluid flow in the presence of thermal fluctuations. The conventional immersed boundary method is extended to account for thermal fluctuations by introducing stochastic forcing terms in the fluid equations. This gives a system of stiff SPDE's for which standard numerical approaches perform poorly. We discuss a numerical method derived using stochastic calculus to overcome the stiff features of the equations. We then discuss results which indicate that the method captures physical features predicted by statistical mechanics for small length-scale systems. The stochastic immersed boundary method holds promise as a numerical approach in simulating microscopic mechanical systems in which thermal fluctuations play a fundamental role. A more detailed discussion of this work is given in [1, 2, 3]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaotic artificial immune approach applied to economic dispatch of electric energy using thermal units

The economic dispatch problem (EDP) is an optimization problem useful in power systems operation. The objective of the EDP of electric power generation, whose characteristics are complex and highly non-linear, is to schedule the committed generating unit outputs so as to meet the required load demand at minimum operating cost while satisfying system constraints. Recently, as an alternative to the conventional mathematical approaches, modern heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in EDPs. As special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used as optimization technique in EDPs. Based on the chaos theory, this paper discusses the design and validation of an optimization procedure based on a chaotic artificial immune network approach based on Zaslavsky’s map. The optimization approach based on chaotic artificial immune network is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. Simulation results and comparisons show that the chaotic artificial immune network approach is competitive in performance with other optimization approaches presented in literature and is also an attractive tool to be used on applications in the power systems field.