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Articles 1 - 30 of 130
Full-Text Articles in Non-linear Dynamics
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
Horizontal Well’S Path Planning: An Optimal Switching Control, Zhaohua Gong, Kok Lay Teo, Chongyang Liu, Enmin Feng
Horizontal Well’S Path Planning: An Optimal Switching Control, Zhaohua Gong, Kok Lay Teo, Chongyang Liu, Enmin Feng
Chongyang Liu
In this paper, we consider a three-dimensional horizontal well’s path planning problem, where the well’s path evolves as a combination of several constant-curvature smooth turn segments. The problem is formulated as an optimal switching control problem subject to continuous state inequality constraints. By applying the time-scaling transformation and constraint transcription in conjunction with local smooth approximation technique, the optimal switching control problem is approximated by a sequence of optimal parameter selection problems with only box constraints, each of which is solvable by gradient-based optimization techniques. The optimal path planning problems of the wells Ci-16-Cp146 and Jin27 in Liaohe oil field …
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.
Criterion For An Oscillatory Charged Jet During The Bubble Spinning Process, Ji-Huan He, H.Y. Kong
Criterion For An Oscillatory Charged Jet During The Bubble Spinning Process, Ji-Huan He, H.Y. Kong
Ji-Huan He
The oscillatory diameter of the charged jet during the bubble electrospinning results in beads on the obtained nanofibers. We demonstrate that the applied voltage and the initial flow rate of the jet are the crucial parameters that are necessary to control morphology of the nanofibers. We also find that there is a criterion for production of smooth nanofibers without beads. The theory developed in this paper can be extended to the classical electrospinning and the blown bubble-spinning.
Variational Iteration Method For Bratu-Like Equation Arising In Electrospinning, Ji-Huan He, Hai-Yan Kong, Rou-Xi Chen, Ming-Sheng Hu, Qiao-Ling Chen
Variational Iteration Method For Bratu-Like Equation Arising In Electrospinning, Ji-Huan He, Hai-Yan Kong, Rou-Xi Chen, Ming-Sheng Hu, Qiao-Ling Chen
Ji-Huan He
This paper points out that the so called enhanced variational iteration method (Colantoni & Boubaker, 2014) for a nonlinear equation arising in electrospinning and vibration-electrospinning process is the standard variational iteration method. An effective algorithm using the variational iteration algorithm-II is suggested for Bratu-like equation arising in electrospinning. A suitable choice of initial guess results in a relatively accurate solution by one or few iteration.
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 …
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 …
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 …
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.
On The Semi-Inverse Method And Variational Principle, Xue-Wei, Li, Ya Li, Ji-Huan He
On The Semi-Inverse Method And Variational Principle, Xue-Wei, Li, Ya Li, Ji-Huan He
Ji-Huan He
In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.’s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.
Exp-Function Method For Fractional Differential Equations, Ji-Huan He
Exp-Function Method For Fractional Differential Equations, Ji-Huan He
Ji-Huan He
A fractional nonlinear wave equation is used as an example to elucidate how to solve fractional differential equations with local fractional derivatives via the fractional complex transform and the exp-function method.
Fractal Approach To Heat Transfer In Silkworm Cocoon Hierarchy, Dong-Dong Fei, Fu-Juan Liu, Qiu-Na Cui, Ji-Huan He
Fractal Approach To Heat Transfer In Silkworm Cocoon Hierarchy, Dong-Dong Fei, Fu-Juan Liu, Qiu-Na Cui, Ji-Huan He
Ji-Huan He
Silkworm cocoon has a complex hierarchic structure with discontinuity. In this paper, heat transfer through the silkworm cocoon is studied using fractal theory. The fractal approach has been successfully applied to explain the fascinating phenomenon of cocoon survival under extreme temperature environment. A better understanding of heat transfer mechanisms for the cocoon could be beneficial to the design of biomimetic clothes for special applications.
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
Xiao-Jun Yang
Fractional calculus is an important method for mathematics and engineering [1-24]. In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional differential equation with fractal conditions \[ D^\alpha x\left( t \right)=f\left( {t,x\left( t \right)} \right),t\in \left[ {0,T} \right], x\left( {t_0 } \right)=x_0 , \] where $0<\alpha \le 1$ in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.
Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski
Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski
Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski
Wojciech Budzianowski
This article provides an analysis of processes for separation CO2 by using carbonic anhydrase enzyme with particular emphasis on reactive-membrane solutions. Three available processes are characterised. Main challenges and prospects are given. It is found that in view of numerous challenges practical applications of these processes will be difficult in near future. Further research is therefore needed for improving existing processes through finding methods for eliminating their main drawbacks such as short lifetime of carbonic anhydrase or low resistance of reactive membrane systems to impurities contained in flue gases from power plants.
An Exercise With The He’S Variation Iteration Method To A Fractional Bernoulli Equation Arising In A Transient Conduction With A Non-Linear Boundary Heat Flux, Jordan Hristov
Jordan Hristov
Surface temperature evolution of a body subjected to a nonlinear heat flux involving counteracting convection heating and radiation cooling has been solved by the variations iteration method (VIM) of He. The surface temperature equations comes as a combination of the time-fractional (half-time) subdiffusion model of the heat conduction and the boundary condition relating the temperature field gradient at the surface through the Riemann-Liouville fractional integral. The result of this equation is a Bernoulli-type ordinary fractional equation with a nonlinear term of 4th order. Two approaches in the identification of the general Lagrange multiplier and a consequent application of VIM have …
Integral-Balance Solution To The Stokes’ First Problem Of A Viscoelastic Generalized Second Grade Fluid, Jordan Hristov
Integral-Balance Solution To The Stokes’ First Problem Of A Viscoelastic Generalized Second Grade Fluid, Jordan Hristov
Jordan Hristov
Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes’ first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a parabolic profile with an unspecified exponent allowing optimization through minimization of the norm over the domain of the penetration depth. The closed form solution explicitly defines two dimensionless similarity variables and , responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. The solution was developed with three forms of the governing equation through its two dimensional forms …
Thermal Impedance At The Interface Of Contacting Bodies: 1-D Example Solved By Semi-Derivatives, Jordan Hristov
Thermal Impedance At The Interface Of Contacting Bodies: 1-D Example Solved By Semi-Derivatives, Jordan Hristov
Jordan Hristov
Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances of two bodies with different initial temperatures contacting at the interface ( ) at . The approach is purely analytic and uses only semi-derivatives (half-time) and semi-integrals in the Riemann-Liouville sense. The example solved clearly reveals that the fractional calculus is more effective in calculation the thermal resistances than the entire domain solutions
Variational Iteration Method For Q-Difference Equations Of Second Order, Guo-Cheng Wu
Variational Iteration Method For Q-Difference Equations Of Second Order, Guo-Cheng Wu
G.C. Wu
Recently, Liu extended He's variational iteration method to strongly nonlinear q-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.
The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun
The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun
Xiao-Jun Yang
The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.
Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun
Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun
Xiao-Jun Yang
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.