Solution of counter diffusion problem with position dependent diffusion coefficent by using variational methods

Unsteady state counter diffusion problem with position dependent diffusion coefficient can be modeled using Fick’s second law. A mathematical model was constructed and solved to quantitatively describe the dynamic behavior of solute diffusion through non-homogeneous materials where diffusion coefficient is a function of position. The eigenfunction expansion approach was utilized to solve the model. The eigenvalues and eigenfunction of the system were obtained using a variational method. It has been shown that position dependency of the material can be neglected if the thickness of the material is relatively small. Mathematical models were solved for different thicknesses and different diffusion coefficient functions.     

一类区域经济发展的系统动力学模型

本文针对区域经济发展过程中的相互作用问题 ,运用微分动力系统的理论与方法 ,建立了一类区域经济发展的系统动力学模型 ,并就实际问题进行分析 ,得到了相应比较好的结果     

A dynamic wind farm aggregate model for the simulation of power fluctuations due to wind turbulence

An important aspect related to wind energy integration into the electrical power system is the fluctuation of the generated power due to the stochastic variations of the wind speed across the area where wind turbines are installed. Simulation models are useful tools to evaluate the impact of the wind power on the power system stability and on the power quality. Aggregate models reduce the simulation time required by detailed dynamic models of multiturbine systems.In this paper, a new behavioral model representing the aggregate contribution of several variable-speed-pitch-controlled wind turbines is introduced. It is particularly suitable for the simulation of short term power fluctuations due to wind turbulence, where steady-state models are not applicable.The model relies on the output rescaling of a single turbine dynamic model. The single turbine output is divided into its steady state and dynamic components, which are then multiplied by different scaling factors. The smoothing effect due to wind incoherence at different locations inside a wind farm is taken into account by filtering the steady state power curve by means of a Gaussian filter as well as applying a proper damping on the dynamic part.The model has been developed to be one of the building-blocks of a model of a large electrical system, therefore a significant reduction of simulation time has been pursued. Comparison against a full model obtained by repeating a detailed single turbine model, shows that a proper trade-off between accuracy and computational speed has been achieved.     

Real time disruption management for a two-stage batch production–inventory system with reliability considerations

In this research, a two-stage batch production–inventory system is introduced. In this system, the production may be disrupted, for a given period of time, either at one or both stages. In this paper, firstly, a mathematical model has been developed to suggest a recovery plan for a single occurrence of disruption at either stage. Secondly, multiple disruptions have been considered, for which a new disruption may or may not affect the recovery plan of earlier disruptions. We propose a new approach that deals with a series of disruptions over a period of time, which can be implemented for disruption recovery on a real time basis. In this approach, the model formulated for single disruption has been integrated to generate initial solutions for individual disruptions and the solutions have been revised for multiple dependent disruptions with changed parameters. With the proposed approach, an optimal recovery plan can be obtained in real time, whenever the production system experiences either a sudden disruption or a series of disruptions, at different points in time. Some numerical examples and a real-world case study are presented to explain the benefits of our proposed approach.     

Fractional-step <Emphasis Type="Italic">θ</Emphasis>-method for solving singularly perturbed problem in ecology

We consider a predator-prey model arising in ecology that describes a slow-fast dynamical system. The dynamics of the model is expressed by a system of nonlinear differential equations having different time scales. Designing numerical methods for solving problems exhibiting multiple time scales within a system, such as those considered in this paper, has always been a challenging task. To solve such complicated systems, we therefore use an efficient time-stepping algorithm based on fractional-step methods. To develop our algorithm, we first decouple the original system into fast and slow sub-systems, and then apply suitable sub-algorithms based on a class of θ-methods, to discretize each sub-system independently using different time-steps. Then the algorithm for the full problem is obtained by utilizing a higher-order product method by merging the sub-algorithms at each time-step. The nonlinear system resulting from the use of implicit schemes is solved by two different nonlinear solvers, namely, the Jacobian-free Newton-Krylov method and the well-known Anderson’s acceleration technique. The fractional-step θ-methods give us flexibility to use a variety of methods for each sub-system and they are able to preserve qualitative properties of the solution. We analyze these methods for stability and convergence. Several numerical results indicating the efficiency of the proposed method are presented. We also provide numerical results that confirm our theoretical investigations.     

Mechatronic Subsystem Studied of Approximate Method Modeled by Hypergraph

The transverse vibrating mechatronic subsystem is considered. Integral parts of this system are: a continuous beam with known boundary conditions and a transducer, extorted by harmonic voltage excitation, to be perfectly bonded to the beam surface. Findings this article are dynamical characteristics of the discussed mechatronic and mechanical system to model them by hypergraphs. Research limitation is that the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered, however for this kind of systems the approach is sufficient. Practical implications of this researches was that global approach is presented, that means in the domain of frequency spectrum analysis. The methods of analysis and obtained results can be base of design and investigation for this type of mechatronic systems. Originality of this paper is that the mechatronic system created from mechanical and electric subsystems with electromechanical bondage has been considered. This approach is different from those considered so far because is it relies on application approximate methods of analysis of mechatronic subsystem and modeling the one by hypergraph [1-7]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integrable nonholonomic deformation of modified Volterra lattice equation

The modified Volterra lattice equation with nonholonomic constrain has been considered in this paper. The integrability of the deformed model has been demonstrated by providing a Lax pair. Applying the gauge transformation to the Lax pair, we establish Darboux transformation theorem for the nonholonomic deformation equation. Some analytic solutions of the system are obtained via the one-fold and two-fold Darboux transformations. The deformation on explicit solutions exhibits different curvy profiles and propagation trajectories that were not found in modified Volterra lattice equation.     

Fractional (space–time) diffusion equation on comb-like model

In this work, a directed connection between the fractal structure and the fractional calculus has been achieved. The fractional space–time diffusion equation is derived using the comb-like structure as a background model. The solution of the obtained equation will be established for three different interesting cases.     

Towards 'Knowledge-based' Systems for Global Optimization

A system has been designed to tackle the global optimizationproblem using parameters based on an internal model of the objectivefunction which represent the system's ‘knowledge’about the function. Examples of such a system have been usedon both the one-dimensional and the multidimensional problem,and the results obtained are encouraging for further work.     

Frequency characteristics of flexibly vibration discrete-continuous mechatronic system

The purpose of this paper is formulating of problem of flexibly vibrating mechatronic system. The main approach of the subject was to formulate the problem in the form of set of differential equation of motion and state equation of considered mechatronic model of object. The considered flexibly vibrating mechanical system is a continuous beam, clamped at one of its end. Integral part of mechatronic system is a transducer, extorted by harmonic voltage. In the paper the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered. The methods of analysis and obtained results can be base on design and investigation for this type of mechatronic systems. The mechatronic system formed from mechanical and electric subsystems with electromechanical bondage has been considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An integrated material handling system for a truck assembly plant

The paper attempts to develop a more comprehensive analytical framework for examining the relative merits of alternative material handling and inventory strategies for a truck assembly plant. This model can be used to minimise handling in delivering requirements from the warehouse to the assembly line and from the unpacking area to the warehouse. The model is also designed to look at arrangements of the storage areas to increase the efficiency of material management. This model is based on extensions of the Vehicle Routing Problem. Solutions to the model have been obtained by an implementation of a Genetic Algorithm. The historical demand data of the plant are used to simulate and analyse the different strategies to statistically determine the best material handing and inventory strategies for the truck assembly plant. As a result of implementation, the efficiency of the current system has been increased by about 30%.     

A model of fluid injection into the spinal disc

This paper presents an analytical model of the stress–strain response of intervertebral disc to fluid injection. The disc has nonlinear properties and collagen fibres play a significant role in sustaining strain. Each fibre is modeled as a flexible, helical string inclined at ∼30° to the horizontal plane. The tensile stress in the fibres is obtained from a nonlinear stress–strain law that has been determined by experiment. An asymptotic approximation of the model equations based on the ratio of the fluid injected to the initial volume of fluid in the disc is developed and its solution obtained. Some quantitative predictions are made by considering a hypothetical value of the amount of fluid injected and some material values of discs at different levels of the spine. Numerical simulations show that the model compare reasonably well with some experimental observations for discs of the lumbar region.     

Non-equilibrium gas-liquid transition model

A new rigorous mathematical model for evaporation/condensation, including boiling, has been proposed. A problem of phase transition and in particular evaporation/condensation is one of the most acute problems of modern technology with numerous applications in industry, such as: in refrigeration, distillation in chemical industry. It is very common to use equilibrium evaporation model, which assumes that concentrations of species in the gas phase is always at saturated condition. Such kind of approach can lead to significant errors, resulting in negative concentrations in complex computer simulations. In this work two analytical solution of simplified differential-algebraic system have been obtained. One of them was deduced using assumption that the process is isothermal and gas volume fraction is constant. In the second solution the assumption about gas volume fraction has been removed. The code for numerical solution of differential-algebraic system, using conservative scheme, has been developed. It was designed to solve both systems of equations with boiling and without. Numerical calculations of ammonia-water system with various initial conditions, which correspond to evaporation and/or condensation of both components, have been performed. It has been shown that, although system quickly evolves to quasi equilibrium state (the differences between current and equilibrium concentrations are small) it is necessary to use non-equilibrium evaporation model, to calculate accurately evaporation/condensation rates, and consequently all other dependent variables. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Closed-form control oriented model of highly flexible manipulators

This paper first presents a highly flexible 3D manipulator with links of arbitrary shape, then develops a closed-form dynamic model that best describes it. The model is based on a Newton–Euler formulation and the substructuring method is used to account for large deformations. The formulation of the motion equations starts from a data set which can be either analytically or numerically computed by finite elements(FE) codes. Simulation has been used to validate the model and compare the results with those of two different multibody software and one experimental, which was obtained from the Multi-Elastic-Link Robot Identification Dataset (MERIt), developed by the TU Dortmund. Then, thanks to the approach here adopted, an integral manifold model is derived, suitable for advanced control system design.     

A model of the relay valve used in an air brake system

The mathematical model governing the response of the relay valve in an air brake leads to a hybrid system in which different governing equations apply to different phases of the response of the air brake. To accurately describe the brake’s response characteristics it is imperative to take into account this hybrid structure, and it is to this aspect of the problem that this paper is addressed. The safe operation of any vehicle on the road depends, amongst other things, on a properly operating brake system. Most commercial vehicles such as trucks, tractor–trailers, buses, etc., are equipped with an air brake system. Any defect in a brake system can degrade its performance seriously and can lead to accidents. It is desirable and also important to develop systems that can control and diagnose air brake systems in order to both sustain and improve their performance. One approach to develop such systems is by obtaining a model of the air brake system and then using the same in the design process. The air brake system currently used in commercial vehicles can be broadly divided into a pneumatic subsystem and a mechanical subsystem. One of the main components in the pneumatic subsystem is the relay valve which operates the brakes on the rear axles of a tractor and the axles of a trailer. A relay valve has different modes of operation and the pressure response of the relay valve can be naturally described as the response of a hybrid system. In this article, we develop a hybrid dynamical model to predict the pressure response of the relay valve. An air brake testing facility has been set up at Texas A&M University and this model will be corroborated against experimental data obtained from the same.     

On an incompressible Navier–Stokes/Cahn–Hilliard system with degenerate mobility

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain by allowing for a degenerate mobility. The model has been developed by Abels, Garcke and Grün for fluids with different densities and leads to a solenoidal velocity field. It is given by a non-homogeneous Navier–Stokes system with a modified convective term coupled to a Cahn–Hilliard system, such that an energy estimate is fulfilled which follows from the fact that the model is thermodynamically consistent.     

A numerical solution of a one-dimensional blood flow model—moving grid approach

We consider a one-dimensional blood flow model suitable for larger arteries. It consists of a hyperbolic system of two coupled nonlinear equations. The model has already been successfully used in practice. Its numerical solution is usually achieved by means of an explicit Taylor–Galerkin scheme. We have proposed a different approach. The system can be transformed to characteristic directions emphasizing the physical nature of the problem. We solved this system by using an operator splitting on a moving grid.     

Coexistence of competing predators in a coral reef ecosystem

An analysis is made using a four-dimensional mathematical model where there is a constant rate of flow of input nutrient. An organism is introduced in the model which is growing by taking in that nutrient. Two other predators on that organism are also introduced. The predators at the second and third trophic levels belong to the same species, though of different age groups. The predator at the third trophic level exhibits a distinct cannibalistic attitude to the predator of the second trophic level. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the species associated with the system cannot thrive even in the absence of competition. Local stability of the system is obtained when one or more of the predators go extinct. Under appropriate circumstances a positive rest point of the system is obtained. Computer simulations have been carried out to illustrate different analytical results.     

Inexact de Novo programming for water resources systems planning

This study presents an interval de Novo programming (IDNP) approach for the design of optimal water-resources-management systems under uncertainty. The model is derived by incorporating the existing interval programming and de Novo programming, allowing uncertainties represented as intervals within the optimization framework. The developed IDNP approach has the advantages in constructing optimal system design via an ideal system by introducing the flexibility toward the available resources in the system constraints. A simple numerical example is introduced to illustrate the IDNP approach. The IDNP is then applied to design an inexact optimal system with budget limit instead of finding the optimum in a given system with fixed resources in a water resources planning case. The results demonstrate that the developed method efficiently produces stable solutions under different objectives. Optimal supplies of good-quality water are obtained in considering different revenue targets of municipal–industrial–agricultural competition under a given budget.     

Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm optimization

ABSTRACT

In this paper, a two-warehouse inventory problem has been investigated under inflation with different deterioration effects in two separate warehouses (rented warehouse, RW, and owned warehouse, OW). The objective of this investigation is to determine the lot-size of the cycle of the two-warehouse inventory system by minimizing the average cost of the system. Considering different inventory policies, the corresponding models have been formulated for linear trend in demand and interval valued cost parameters. In OW, shortages, if any, are allowed and partially backlogged with a variable rate dependent on the duration of the waiting time up to the arrival of the next lot. The corresponding optimization problems have been formulated as non-linear constrained optimization problems with interval parameters. These problems have been solved by an efficient soft computing method, viz. practical swarm optimization. To illustrate the model, a numerical example has been solved with different partially backlogging rates. Then to study the effect of changes of different system parameters on the optimal policy, sensitivity analyses have been carried out graphically by changing one parameter at a time and keeping the others at their original values. Finally, a fruitful conclusion has been reached regarding the selection of an appropriate inventory policy of the two-warehouse system.