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Articles 1 - 30 of 146
Full-Text Articles in Physical Sciences and Mathematics
C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski
Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski
Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Procesy Cieplne I Aparaty (Lab), Wojciech M. Budzianowski
Inżynieria Chemiczna Lab., Wojciech M. Budzianowski
Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu
Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu
Chongyang Liu
In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together with those of …
On Combining Neighbouring Extremals With Control Parameterization, Chongyang Liu, Qun Lin, Ryan Loxton, Kok Lay Teo
On Combining Neighbouring Extremals With Control Parameterization, Chongyang Liu, Qun Lin, Ryan Loxton, Kok Lay Teo
Chongyang Liu
In this paper, we consider the neighbouring extremals for a class of optimal control problems with control constraints. We first solve the optimal control problem using control parameterization method to obtain the optimal open-loop control and the optimal reference state. Then, a neighbouring feedback control law is derived for small state perturbations caused by changes on reference state at switching times.
Nonlinear State-Dependent Impulsive System In Fed-Batch Culture And Its Optimal Control, Bangyu Shen, Xiaojing Wang, Chongyang Liu
Nonlinear State-Dependent Impulsive System In Fed-Batch Culture And Its Optimal Control, Bangyu Shen, Xiaojing Wang, Chongyang Liu
Chongyang Liu
In this paper, a nonlinear impulsive controlled system, in which the volume of feeding is taken as the control function, is proposed to formulate the fed-batch fermentation process.In the system, both impulsive moments and jumps size of state are state-dependent. Some important properties of the system are investigated. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system is presented.The optimal control problem is subject to the continuous state inequality constraint and the control constraint. The existence of optimal control is also obtained. In order to derive the …
Inżynieria Chemiczna Ćw., Wojciech M. Budzianowski
Tematyka Prac Doktorskich, Wojciech M. Budzianowski
Tematyka Prac Doktorskich, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He
Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He
Ji-Huan He
A homotopy perturbation method with two expanding parameters is suggested. The method is especially effective for a nonlinear equation with two nonlinear terms, which might have different effects on the solution. A nonlinear oscillator is used as an example to elucidate the solution procedure.
Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li
Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional …
Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong
Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong
Chongyang Liu
The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control …
Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu
Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu
Chongyang Liu
Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a …
Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo
Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo
Chongyang Liu
In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the …
A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo
A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo
Chongyang Liu
This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time-delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system …
Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo
Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo
Chongyang Liu
In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary …
A New Class Of Scalable Parallel Pseudorandom Number Generators Based On Pohlig-Hellman Exponentiation Ciphers, Paul Beale
Paul Beale
Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes. We propose a new scalable class of parallel pseudorandom number generators based on Pohlig--Hellman exponentiation ciphers. The method generates uniformly distributed floating point pseudorandom streams by encrypting simple sequences of integer \textit{messages} into \textit{ciphertexts} by exponentiation modulo prime numbers. The advantages of the method are: the method is trivially parallelizable by parameterization with each pseudorandom number generator derived from an independent prime modulus, the method is fully scalable on massively parallel computing clusters due to the large number of primes available …
Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski
Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski
Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski
Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Mechanika Płynów Lab., Wojciech M. Budzianowski
Mechanika Płynów Lab., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Variational Iteration Method For The Burgers' Flow With Fractional Derivatives—New Lagrange Multipliers, Guo-Cheng Wu, Dumitru Baleanu
Variational Iteration Method For The Burgers' Flow With Fractional Derivatives—New Lagrange Multipliers, Guo-Cheng Wu, Dumitru Baleanu
G.C. Wu
The flow through porous media can be better described by fractional models than the classical ones since they include inherently memory effects caused by obstacles in the structures. The variational iteration method was extended to find approximate solutions of fractional differential equations with the Caputo derivatives, but the Lagrange multipliers of the method were not identified explicitly. In this paper, the Lagrange multiplier is determined in a more accurate way and some new variational iteration formulae are presented.
Application Of The Local Fractional Series Expansion Method And The Variational Iteration Method To The Helmholtz Equation Involving Local Fractional Derivative Operators, Yang Xiaojun
Xiao-Jun Yang
We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.
Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng
Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng
Chongyang Liu
The main control goal in fed-batch fermentation is to maximize yield of target product and reduce operation costs. In this paper, we propose a controlled nonlinear time-delay system, in which the flow rate of glycerol is taken as the control function and the terminal time of the fermentation as the optimization variable, to model the 1,3-propanediol (1,3-PD) production in fed-batch process. Taking the mass of 1,3-PD per unit time as the performance index, we formulate a constrained optimal control model with free terminal time to optimize the production process. Using a time-scale transformation, the optimal control problem is equivalently transcribed …
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Xiao-Jun Yang
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for...
Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation, Abdulghafor M. Al-Rozbayani Ph.D., Mohammed O. Al-Amr M.Sc.
Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation, Abdulghafor M. Al-Rozbayani Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the discrete Adomian decomposition method (DADM) is applied to a fully implicit scheme of the generalized Burger’s–Huxley equation. The numerical results of two test problems are compared with the exact solutions. The comparisons reveal that the proposed method is very accurate and effective for this kind of problems.
Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang
Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang
Xiao-Jun Yang
The local fractional Schr¨odinger equations in the one-dimensional Cantorian systemare investigated.The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.
A Numerical Method For Solving Systems Of Fredholm Integral Equations By Collocation Linear Legendre Multi-Wavelets, Sa Edalatpanah, E Abdolmaleki
A Numerical Method For Solving Systems Of Fredholm Integral Equations By Collocation Linear Legendre Multi-Wavelets, Sa Edalatpanah, E Abdolmaleki
SA Edalatpanah
In this paper continuous Legendre multi-wavelets on the interval [0, 1) are utilized as a basis in collocation method to approximate the solutions of the Fredholm integral equations system. To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Finally, numerical results are given which support the theoretical results.
Convergence Analysis For Double Splitting Of Matrices, Hs Najafi, Sa Edalatpanah
Convergence Analysis For Double Splitting Of Matrices, Hs Najafi, Sa Edalatpanah
SA Edalatpanah
For single splittings of matrices, there are well-known convergence and comparison theorems. However, there are a few convergence theorems for double splitting. In this paper, we study this class of iterative methods. Furthermore, this paper gives new convergence results for double splitting of matrices.