Models of unidirectional propagation in heterogeneous excitable media

Two differential equation models of excitable media (threshold and recovery kinetics) with solutions that exhibit unidirectional propagation are presented. It is shown that unidirectional propagation in heterogeneous excitable media with non-oscillatory kinetics can be initiated from homogeneous initial data. Simulations on a reaction-diffusion model with FitzHugh-Nagumo kinetics and spatially heterogeneous parameters yields a rotating wave on a one-dimensional circular spatial domain. An ordinary differential equation model with four semi-coupled excitable cells and heterogeneous parameters is analyzed to determine a critical parameter region over which unidirectional propagation may occur.     

Three-dimensional modelling of NOx and particulate traps using CFD: A porous medium approach

Lean burn after-treatment systems are the current focus for reducing emissions from diesel exhaust. The trend is for commercial CFD packages to use a single channel modelling approach. Due to computational demands, this necessitates specification of representative channels for modelling, implying prior knowledge of the flow field. This paper investigates a methodology for applying the porous medium approach to lean burn after-treatment systems. This approach has proved successful for three-way catalysis modelling and has the advantage that the flow field is predicted. Chemical kinetic rates for NO_x trapping and regeneration in the model are based on information available in the open literature. Similarly, filtration information based on mass accumulation and soot combustion kinetics are also readily available. Modification of the source terms in a commercial CFD package enables prediction of trapping and release of NO_x. This is an effective way to model a NO_x trap after-treatment system and provides simultaneous 3D modelling of the flow field. With diesel, particulate filtration is required. In the case of particulate traps, however, because of channel geometry, some assumptions are necessary for use of the porous medium approach and these are discussed in this paper. Both models produce qualitatively correct output and have parameters that can be tuned to conform to experimental data. Data to validate the NO_x trap model is to be measured. The particulate trap model, on the other hand, is a feasibility study for modelling the complete diesel after-treatment system using the porous medium approach.     

Relaxation model of piezoelectric materials

Polarization switching inside grains is time dependent. When external applied loading is not quasi-static, macroscopic properties of piezoelectric materials changes with the rate of loading. In this paper, a 2-D micromechanical model is proposed in order to simulate the rate dependent properties of certain perovskite type tetragonal piezoelectric materials based on linear constitutive, nonlinear domain switching, intergranular effects and kinetics models. The material is electrically loaded with an alternating voltage of various frequencies. For the onset of domain switching, energy equation is implemented. Propagation of the domain wall during domain switching in grains is modeled by means of exponential kinetics relation after domain nucleation. Mechanical strain butterfly loops under different frequencies (0.01Hz–1Hz) are simulated. The model gives important insights into the rate dependency of the piezoelectric materials that have been observed in some experiments reported in the literature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin [S.H. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. Theor. Biol. 60 (1976) 449–457] to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction–diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.     

A mathematical model of infectious diseases

In the formulation of models for the spread of communicable diseases which include removal and population dynamics, it is necessary to distinguish between removal through recovery with immunity and removal by death due to disease. This distinction must be made because of the difference in the effect on the population dynamics of the different kinds of removal and because there are significant differences in the behavior of the models. We have formulated a class of models which allow recovery with immunity for a fraction of the infective and permanent removal by death from disease for the remainder. Earlier models of this type have postulated an increased death rate for infective, but such models are restricted to exponentially distributed-infective periods. Because of the differences in behavior between models with recovery and models with permanent removal do not arise when the infective period is exponentially distributed, we have chosen to formulate a different type of model which is sufficiently general to admit qualitative differences.     

Start-up of multi-species anaerobic digestion systems: extrapolation of the single species approach

This paper presents a brief evaluation of a start-up strategy for multi-species anaerobic digestion systems modelled as two-step reaction systems, where acidogenesis is described by Monod kinetics while the methanogenesis is described by Haldane kinetics. The start-up policy has been developed originally for single species systems with the aim of maximizing the biogas outflow rate. It consists of switching the dilution rate from minimum to maximum and then to the optimal value (bang-bang control) in order to bring the system from an arbitrary initial condition to the optimal set-point. This start-up strategy is applied to the multi-species system using an averaged model, which is usually the only model that can be identified for a multi-species system, as measuring individual biomasses is almost impossible in practice. Even the development of an accurate averaged model, fully characterizing the system dynamics based on the variation of the species proportions is difficult. The averaged models used in this study are built based on a more or less accurate knowledge of the species proportions and their kinetics at the start-up instant and used as such in the application of the start-up policy. It is shown that the start-up policy leads to an efficient ecosystem, characterized by high outflow rate of biogas, which is very close to the maximum even in the case of an inaccurate averaged model. The influence of the model accuracy on the system stability and its productivity is discussed. This study can also be viewed as a robustness evaluation with respect to model inaccuracy of the single species start-up strategy, as the process changes from the averaged kinetics to the kinetics of the winning species during species selection.     

M?ssbauer study on Sn-doped (Lal1-x,Srx)2Cu1-x,Snx,O4 superconductors under a new concept

¹¹⁹Sn M?ssbauer research is carried out on (La_1-xSr_x),Cu_1-xSn_xO₄(x = 0.075 and 0.110) superconductors which are designed under a new concept. The M?ssbauer spectra results show that Sn occupies Cu position in Sn⁴⁺ state, and there is no Sn²⁺ ion occupying La position. The local lattice deformation near Sn⁴⁺ site is small, but displays an increasing tendency with Sn doping. For La₂CuO₄ matrix, the simultaneous dopings of Sr/Sn induce holes and electrons on CuO₂ layer in a new mechanism which influences superconductivity. Under a new mechanism of extra oxygen, the extra oxygen effect of Sn-doping on superconductivity is discussed     

Modeling of microstructural pattern formation in crystal plasticity

The mechanical behavior of most materials is dictated by a present or emergent underlying microstructure which is a direct result of different, even competing physical mechanisms occurring at lower length scales. In this work, energetic microstructure interaction via different non-convex contributions to the free energy in metals is modeled. For this purpose rate dependent gradient extended crystal plasticity models at the glide-system level are formulated. The non-convex energy serves as the driving force for the emergent microstructure. The competition between the kinetics and the relaxation of the free energy is an essential feature of the model. Non-convexity naturally arises in finite-deformation single-slip crystal plasticity and the results of the gradient model for this case are compared with an effective laminate model based on energy relaxation. Similarities as well as essential differences are observed and explained. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

马氏调制强度的传染模型下CDS的CVA计算

本文考虑了具有马氏调制强度的传染模型下,信用违约互换(CDS)的双边信用估值调整(CVA).在我们考虑的模型中,利率、回收率以及CDS的买方、卖方和参照实体三方的违约强度均受宏观经济环境的影响,该经济状况由一连续时间状态的齐次马氏链所刻画.利用测度变换和累积强度的Laplace变换,我们给出了CDS合同的双边CVA的表达公式,该公式可以表示为线性常微分方程组的基本解的形式.利用所得到的公式,我们数值分析了马氏调制和违约相关性对双边CVA的影响.     

Development and analysis of some versions of the fractional-order point reactor kinetics model for a nuclear reactor with slab geometry

In this paper, we report the development and analysis of some novel versions and approximations of the fractional-order (FO) point reactor kinetics model for a nuclear reactor with slab geometry. A systematic development of the FO Inhour equation, Inverse FO point reactor kinetics model, and fractional-order versions of the constant delayed neutron rate approximation model and prompt jump approximation model is presented for the first time (for both one delayed group and six delayed groups). These models evolve from the FO point reactor kinetics model, which has been derived from the FO Neutron Telegraph Equation for the neutron transport considering the subdiffusive neutron transport. Various observations and the analysis results are reported and the corresponding justifications are addressed using the subdiffusive framework for the neutron transport. The FO Inhour equation is found out to be a pseudo-polynomial with its degree depending on the order of the fractional derivative in the FO model. The inverse FO point reactor kinetics model is derived and used to find the reactivity variation required to achieve exponential and sinusoidal power variation in the core. The situation of sudden insertion of negative reactivity is analyzed using the FO constant delayed neutron rate approximation. Use of FO model for representing the prompt jump in reactor power is advocated on the basis of subdiffusion. Comparison with the respective integer-order models is carried out for the practical data. Also, it has been shown analytically that integer-order models are a special case of FO models when the order of time-derivative is one. Development of these FO models plays a crucial role in reactor theory and operation as it is the first step towards achieving the FO control-oriented model for a nuclear reactor. The results presented here form an important step in the efforts to establish a step-by-step and systematic theory for the FO modeling of a nuclear reactor.     

Linear time-periodic dynamical systems: an H2 analysis and a model reduction framework

Linear time-periodic (LTP) dynamical systems frequently appear in the modelling of phenomena related to fluid dynamics, electronic circuits and structural mechanics via linearization centred around known periodic orbits of nonlinear models. Such LTP systems can reach orders that make repeated simulation or other necessary analysis prohibitive, motivating the need for model reduction. We develop here an algorithmic framework for constructing reduced models that retains the LTP structure of the original LTP system. Our approach generalizes optimal approaches that have been established previously for linear time-invariant (LTI) model reduction problems. We employ an extension of the usual H₂ Hardy space defined for the LTI setting to time-periodic systems and within this broader framework develop an a posteriori error bound expressible in terms of related LTI systems. Optimization of this bound motivates our algorithm. We illustrate the success of our method on three numerical examples.     

Unilateral counterparty risk valuation of CDS using a regime-switching intensity model

We consider the unilateral credit valuation adjustment (CVA) of a credit default swap (CDS) under a contagion model with regime-switching interacting intensities. The model assumes that the interest rate, the recovery, and the default intensities of the protection seller and the reference entity are all influenced by macro-economy described by a homogeneous Markov chain. By using the idea of “change of measure” and some formulas for the Laplace transforms of the integrated intensity processes, we derive the semi-analytical formulas for the joint distribution of the default times and the unilateral CVA of a CDS.     

One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations

The ? ₁-synthesis model and the ? ₁-analysis model recover structured signals from their undersampled measurements. The solution of the former is a sparse sum of dictionary atoms, and that of the latter makes sparse correlations with dictionary atoms. This paper addresses the question: when can we trust these models to recover specific signals? We answer the question with a condition that is both necessary and sufficient to guarantee the recovery to be unique and exact and, in the presence of measurement noise, to be robust. The condition is one–for–all in the sense that it applies to both the ? ₁-synthesis and ? ₁-analysis models, to both constrained and unconstrained formulations, and to both the exact recovery and robust recovery cases. Furthermore, a convex infinity–norm optimization problem is introduced for numerically verifying the condition. A comprehensive comparison with related existing conditions is included.     

Mathematical modelling and optimisation of a waste water treatment plant by combined oxygen electrode and biological waste water treatment model

Structured mathematical models of oxygen electrode and biological waste water treatment were combined to optimise the position of electrode in the bioreactor. Parameters sensibility testing of mathematical model has shown that the model was most sensitive to the change of these parameters (in decreasing order of significance): oxygen consumption per unit of BOD_5, specific consumption rate of adsorbed BOD₅, volumetric coefficient of oxygen transfer rate (k_La), and waste water inflow. Two positions of electrode were tested: in the bioreactor and in the bioreactors syphon outlet shaft. Results obtained for the exchange of the oxic/anoxic phase and sludge recycling plant indicated that a reduction of electrical power for the aeration could be achieved if O₂ electrode is placed in the bioreactor tank, compared to position in outlet shaft. Better positioning of electrode has resulted in shortening of the oxic/anoxic cycle by 13% and the daily working time of aerators for 0.5 h per day, respectively. In the same time, the number of oxic/anoxic cycles per day was increased by 29%. In addition, results obtained by mathematical modelling indicated no debasement of chemical composition in out coming purified water if new position will be used.     

Global dynamics of delay‐distributed HIV infection models with differential drug efficacy in cocirculating target cells

In this paper, we investigate the dynamical behaviors of three human immunodeficiency virus infection models with two types of cocirculating target cells and distributed intracellular delay. The models take into account both short‐lived infected cells and long‐lived chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different. The incidence rate of infection is given by bilinear and saturation functional responses in the first and second models, respectively, while it is given by a general function in the third model. Lyapunov functionals are constructed and LaSalle invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. We have derived the basic reproduction number R₀ for the three models. For the first two models, we have proven that the disease‐free equilibrium is globally asymptotically stable (GAS) when R₀≤1, and the endemic equilibrium is GAS when R₀>1. For the third model, we have established a set of sufficient conditions for global stability of both equilibria of the model. We have checked our theoretical results with numerical simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

政府补贴下考虑规模效应的动力电池梯次利用闭环供应链决策与协调

针对零售商主导的考虑政府补贴和规模效应的动力电池闭环供应链,研究成员最优决策及协调问题。分别在无补贴、补贴零售商、补贴制造商、补贴第三方回收商四种情形下,分析了补贴对象、规模效应、再制造动力电池比例对成员最优决策及利润的影响,并实现了闭环供应链的协调。研究表明:政府补贴能够降低零售价,提高回收率以及各成员利润;补贴第三方回收商相比补贴零售商和补贴制造商而言,回收率以及第三方回收商利润提高更为明显,补贴零售商和补贴制造商相比补贴第三方回收商而言,零售价降低、制造商和零售商利润提高更为明显;可用于再制造的废旧动力电池比例增大能够降低动力电池销售价格,提高动力电池回收率;第三方回收商规模效应的增大有利于降低零售价格,提高动力电池产品回收率及闭环供应链各成员收益。     

Differences in microstructure of Pd77.5Au6Si16.5 alloy solidified under microgravity and gravity conditions

The microstructure of Pd_77.5Au₆Si_16.5alloy solidified both on board a Chinese Retrievable Satellite and on the earth is studied. Postmortem analyses of microstructure presented that the same types of phases, primary phase (Pd₃Si) and eutectics (Pd₃Si + Pd solid solution) were formed in both cases. But the phase morphologies were quite different. It was dendritic for the primary phase and lamellar for the eutectics under normal gravity condition. However, under microgravity condition the primary phase was granular and the eutectic was peculiar network. Detailed analysis showed that the differences in morphologies of the microstructure were due to the existence of gravity-induced buoyancy convection on the earth which increased the mass transport abilities and decreased the thickness of the solute boundary in front of the solid-liquid interface during solidification under normal gravity condition.     

基于Stackelberg博弈的闭环供应链回收模式选择及其优化研究

从闭环供应链视角,分别构建了包含制造商、零售商、线上回收商和线下回收商等不同主体参与的四种闭环供应链回收模式,并通过Stackelberg博弈分析,求解了各模式中回收主体的均衡利润以及供应链总利润,得出了闭环供应链的最佳回收模式。在此基础上,进一步引入碳交易机制对最佳回收模式进行了优化分析,最后,运用Matlab 2017a软件仿真验证了模型分析的合理性和优化作用的有效性。研究结果表明:由线上和线下回收商、零售商、制造商组成的多回收主体模式(即O/U/R/M-M模式)能够使得包括各回收主体在内的供应链整体利润最大化,因而是现实中应该优先选择的回收模式;回收再制造比例值的变化与各模式下供应链各成员的利润值高低直接相关;而碳交易机制的引入能有效提升最佳回收模式中的制造商利润及供应链总利润。