On modeling evaporation

We develop a theoretical model for evaporation of a pure liquid drop on a thermally conductive solid substrate. We discuss a variety of effects regarding evaporation regime, the state of the liquid/gas interface and the content of gas phase. Then, we further consider two models: the one resulting from the one-sided non-equilibrium assumption and the other that assumes diffusion-limited regime and equilibrium at the liquid/gas interface. A single governing equation for the evolution of drop thickness is derived for both models. We show that although the model predicts qualitatively different temperature along liquid/gas and liquid/solid interface, the dynamics of the drops is almost the same.      

Mathematical modeling and numerical simulation of CO2 transport through hollow-fiber membranes

Chemical absorption of carbon dioxide was studied theoretically using hollow-fiber membrane contactors in this work. A 2D mathematical model was developed to study CO₂ transport through hollow-fiber membrane contactors. The model considers axial and radial diffusion in the membrane contactor. It also considers convection in the tube and shell side with chemical reaction. The finite element method (FEM) was used to solve the model equations. Modeling predictions were validated with the experimental data obtained from literature for CO₂ absorption in amine aqueous solutions as solvent. The modeling predictions were in good agreement with the experimental data for different values of gas and liquid velocities. The liquid solvents considered for this study include aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA), N-methyldiethanolamine (MDEA), 2-amino-2-methyl-1-propanol (AMP) and potassium carbonate (K₂CO₃). The simulation results indicated that amine aqueous solutions were better than K₂CO₃ aqueous solution for CO₂ absorption. Also simulation results revealed that the removal of CO₂ with aqueous solution of MEA was the highest among the amines solvents. The hollow-fiber membrane contactors showed a great potential in the area of CO₂ absorption.     

Efficient Reduced Order State Space Model Computation for a Class of Second Order Index One Systems

Simulation, design optimization and controller design of modern machine tools heavily rely on adequat numerical models. In order to achieve results in shorter computation times, reduced order models (ROMs) are applied in either of these tasks. Most modern simulation tools expect these ROMs to come in standard state space form. Structural models of the machine tool are however of second order type. In case piezo actuators are used in the device they are even differential algebraic equations (DAEs) of index one due to the coupling to the equations describing the electric potentials. This contribution is dedicated especially to those systems. We combine the ideas for balanced truncation model order reduction of large and sparse index 1 DAEs with methods developed for the efficient numerical handling of second order systems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

近似邻近点算法收敛性的一个注记

近似邻近点算法在最优化理论与方法研究中具有重要作用.在不同误差准则下,近似邻近点算法具有不同的收敛性.利用极大单调算子等工具给出了一个具体的例子,解释了在一些误差准则下近似邻近点算法的收敛性.     

关于求解随机用户均衡问题的截断拟牛顿型信赖域法研究

信赖域法是一种保证全局收敛性的优化算法,为避免Hessian矩阵的计算,基于拟牛顿校正公式构造了求解带线性等式约束的非线性规划问题的截断拟牛顿型信赖域法.首先给出了截断拟牛顿型信赖域法的构造过程及具体步骤;然后针对随机用户均衡模型中变量和约束的特点对算法进行了修正,并将多种拟牛顿校正公式下所得结果与牛顿型信赖域法的结果进行了比较,结果发现基于对称秩1校正公式的信赖域法更为合适.最后基于数值算例结果得到了一些在算法编程过程中的重要结论,对其它形式信赖域法的编程实现具有一定的参考意义.     

Solving an equilibrium model for trade of CO2 emission permits

In this paper we investigate the trade of CO₂ emission permits in the framework of a competitive economic equilibrium. For this purpose we integrate already existing regional energy-economy models (Markal-Macro) into a single multi-regional trade model. Based on two possible integration schemes we discuss two solution concepts: the first is based on pseudomonotonicity of the excess map whereas the second is a fixed point approach due to Negishi. In the latter case the overall optimization problem is decomposed. For both algorithms the regional subproblems were distributed on different computers and solved in parallel. We conclude by presenting numerical results of a model with full data sets for Switzerland, Sweden and the Netherlands.     

Comparison and correction of the drop breakup models for stochastic dilute spray flow

Spray–gas interaction is common in many industrial applications that use a liquid jet injection system. Numerous liquid drops interact with the surrounding gas as they travel through the air. During such a travel, aerodynamic interaction between a drop and the surrounding gas flattens the drop and ultimately, breaks up the drop. The TAB (Taylor Analogy Breakup) model was proposed by O’Rourke and Amsden (1987) [6] for the KIVA spray code, but the use of this model has been controversial because the original paper that proposed this model has typographical errors. Another well-known drop breakup model, such as the DDB (Drop Deformation Breakup) model of Ibrahim et al. (1993) [8], has been widely used. However, although numerical solutions of the DDB model ostensibly make it appear superior to those of other previous breakup models, they contain errors that need to be amended. This paper aims to clarify the error controversies of both models; the typographical errors and the erroneous numerical solutions. The complete mathematical derivation of the TAB model is presented, and its correct numerical solutions are compared against the experimental data. We found that the TAB model was superior to other breakup models, such as Clark (1988) [7] and DDB.     

Summarizing an Eulerian–Lagrangian model for subsea gas release and comparing release of CO2 with CH4

A subsea gas release is a concern for both safety and environment. This can be assessed by mathematical models. The development of an Eulerian–Lagrangian modelling concept to study subsea gas release has taken place over many years and the piecewise enhancements have been documented in the open literature. The model in its current state is summarized in this article. Model simulations are shown to be consistent with different experiments varying in depth from 7 to 138 m. The model can be applied to estimate how gas surfaces into the atmosphere from a subsea source. This is vital input to risk assessments. Due to recent interest in subsea CO₂ storage and transport, a comparison of CO₂- and CH₄-releases has been performed. Model results show that a much smaller fraction of released CO₂ reaches the atmosphere than CH₄ due to the high solubility of CO₂ in water.     

Supporting hydrogen based transportation: case studies with Global MARKAL Model

Steadily growing prices of oil and emissions coming from conventional vehicles, might force a switch to an alternative and less polluting fuel in the coming future. In this article we analyze the potential influence of selected factors for successful market penetration of hydrogen fuel cell vehicles in hydrogen based private transportation economy. Using a world scale, full energy system, bottom-up, optimization model (Global MARKAL Model—GMM) we address the possibility of supporting the fuel cell vehicle technology to become competitive in the markets. In a series of optimizations we evaluate the potential influence of governmental supports and the internalization of externalities related to CO₂ and local pollution emissions originating from the transportation sector, as well as preferential crediting options and demonstration projects promoting fuel cell vehicles. The results suggest that the crucial element is the price of fuel cells and their further potential to reduce costs. This reduction of costs may be triggered by governmental support such as direct subsidies to fuel cells, preferential crediting options for the buildup of hydrogen infrastructure as well as penalization of emitters of CO₂ and/or local pollutants.     

Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach

This work focuses on the simulation of CO₂ storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on CO₂ leakage. To simulate the process, a non-isothermal two-phase two-component flow system with equilibrium phase exchange is used. Since model evaluations are computationally intensive, instead of traditional Monte Carlo methods, we rely on polynomial chaos (PC) expansions for representation of the stochastic model response. A non-intrusive approach is used to determine the PC coefficients. We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies. In addition to characterizing the distributions of model observables, we compute probabilities of excess CO₂ leakage. Moreover, we consider the injection rate as a design parameter and compute an optimum injection rate that ensures that the risk of excess pressure buildup at the leaky well remains below acceptable levels. We also provide a comprehensive analysis of sensitivities of CO₂ leakage, where we compute the contributions of the random parameters, and their interactions, to the variance by computing first, second, and total order Sobol’ indices.     

Energy and CO2 emission performance in electricity generation: A non-radial directional distance function approach

This paper presents a non-radial directional distance function approach to modeling energy and CO₂emission performance in electricity generation from the production efficiency point of view. We first define and construct the environmental production technologies for the countries with and without CHP plants, respectively. The non-radial direction distance function approach is then proposed and several indexes are developed to measure energy and CO₂ emission performance of electricity generation. The directional distance functions established can be computed by solving a series of data envelopment analysis models. We then conduct an empirical study using the dataset for over one hundred countries. It is found that OECD countries have better carbon emission performance and integrated energy-carbon performance than non-OECD countries in electricity generation, while the difference in energy performance is not significant.     

Inverse complementarity in a resource deficit model

The concept of inverse complementarity for a parametric family of optimization problems is introduced. This concept is an effective tool for solving complicated applied problems arising in socioeconomic systems. As an example, a nonlinear resource deficit model is constructed in which the equilibrium is characterized by an external market value of resources coinciding with internal objectively determined resource estimates. An extraproximal method is proposed for computing an equilibrium solution. The convergence of the method is proved. Original Russian Text. A.V. Zykina, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 11, pp. 1968–1978.     

Central limit theorem for a class of one-dimensional kinetic equations

We introduce a class of kinetic-type equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with rather general properties. By establishing a connection to the central limit problem, we are able to prove long-time convergence of the equation??s solutions toward a limit distribution. For example, we prove that if the initial condition belongs to the domain of normal attraction of a certain stable law ?? _??, then the limit is a scale mixture of ?? _??. Under some additional assumptions, explicit exponential rates for the convergence to equilibrium in Wasserstein metrics are calculated, and strong convergence of the probability densities is shown.     

Semicontinuity and convergence for vector optimization problems with approximate equilibrium constraints

This paper mainly intends to present some semicontinuity and convergence results for perturbed vector optimization problems with approximate equilibrium constraints. We establish the lower semicontinuity of the efficient solution mapping for the vector optimization problem with perturbations of both the objective function and the constraint set. The constraint set is the set of approximate weak efficient solutions of the vector equilibrium problem. Moreover, upper Painlevé–Kuratowski convergence results of the weak efficient solution mapping are showed. Finally, some applications to the optimization problems with approximate vector variational inequality constraints and the traffic network equilibrium problems are also given. Our main results are different from the ones in the literature.     

Determination of storage tanks location for optimal short-term scheduling in multipurpose/multiproduct batch-continuous plants under uncertainties

A multipurpose/multiproduct plant has to deal with many combinations of tasks sequences and operation rates that lead to accumulation problems. These problems can be handled using storage tanks, but usually their location within the flowsheet is predetermined and not subject to optimization, missing the opportunity to better satisfy the customers. In this work we will determinate the optimal location of storage tanks for the short-term scheduling under uncertainty. A hybrid simulation-based optimization (SBO) strategy was developed and implemented to solve the problems combining stochastic and deterministic solution algorithms.     

The Convergence of a Levenberg–Marquardt Method for Nonlinear Inequalities

In this paper, we consider the least l ₂-norm solution for a possibly inconsistent system of nonlinear inequalities. The objective function of the problem is only first-order continuously differentiable. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a Levenberg–Marquardt algorithm is proposed to solve the parameterized smooth optimization problems. It is proved that the algorithm either terminates finitely at a solution of the original inequality problem or generates an infinite sequence. In the latter case, the infinite sequence converges to a least l ₂-norm solution of the inequality problem. The local quadratic convergence of the algorithm was produced under some conditions.     

Dual mean field annealing scheme for binary optimization under linear constraints

It is shown that certain general classes of constrained binary optimization tasks can be solved with increasing accuracy by a first order mean field approximation of the Boltzmann distribution of the associated Lagrangian as the instance size grows. The formalism is thoroughly analyzed for the quadratic and multidimensional knapsack models. In these cases analytical expressions for the convergence of the optimality gaps are given, which are experimentally verified.     

Computational modelling of bubbles,droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.