Open Access. Powered by Scholars. Published by Universities.®
Numerical Analysis and Computation Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Control Theory (8)
- Non-linear Dynamics (8)
- Computer Sciences (5)
- Dynamic Systems (5)
- Engineering (5)
-
- Numerical Analysis and Scientific Computing (5)
- Ordinary Differential Equations and Applied Dynamics (5)
- Physics (5)
- Biological and Chemical Physics (4)
- Catalysis and Reaction Engineering (4)
- Chemical Engineering (4)
- Chemistry (4)
- Civil and Environmental Engineering (4)
- Complex Fluids (4)
- Computational Engineering (4)
- Computer-Aided Engineering and Design (4)
- Dynamical Systems (4)
- Dynamics and Dynamical Systems (4)
- Energy Systems (4)
- Engineering Mechanics (4)
- Engineering Physics (4)
- Engineering Science and Materials (4)
- Environmental Chemistry (4)
- Environmental Engineering (4)
- Environmental Sciences (4)
- Fluid Dynamics (4)
- Heat Transfer, Combustion (4)
- Keyword
-
- Informacje dla studentów (in Polish) (4)
- APM20133 (1)
- Air permeability (1)
- COAP2014 (1)
- Fractal medium (1)
-
- Fractional Navier-Stokes equations (1)
- Fractional derivative (1)
- Fractional differential equations (1)
- Fractional heat conduction (1)
- Homotopy perturbation method (1)
- Homotopy perturbation method; Duffing equation; Periodic solution (1)
- JFI2013 (1)
- JOTA2014 (1)
- Multistage system (1)
- Nonlinear optimization (1)
- Nonlinear time-delay system; Sensitivity analysis; Parameter identification; Optimization algorithm; Fed-batch fermentation (1)
- Parameter identification (1)
- Pseudorandom number generator (1)
- SCL2014 (1)
- Switched system; Time-delay system; Switching times; Numerical optimization (1)
- Time-delay system (1)
- Time-delay system; Optimal control; Free terminal time; Control parameterization; Nonlinear optimization (1)
- Time-delayed switched system; Optimal control; Switching instants; Smoothing approximation; Fed-batch process (1)
- Variational iteration method (1)
Articles 1 - 12 of 12
Full-Text Articles in Numerical Analysis and Computation
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.