Electroviscoelasticity of Liquid/Liquid Interfaces: Fractional Order Van der Pol Model – New Results
Само за регистроване кориснике
2007
Конференцијски прилог (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. The behavior of e.g., liquid/liquid interfaces is based on three forms of «instabilities», these are rigid,elastic and plastic. Three possible mathematical formalisms have been considered related to this physical formalism,i.e. to the theory of electroviscoelasticity: the first is tension tensor model, the second is Van der Pol derivative model and the third model is fractional order Van der Pol derivative model. The third model presents an effort to generalize the previous Van der Pol equation using fractional integro-differential operators (fractional calculus).
In this paper, central parts of presentation will be solution using Caputo definition of fractional operators to obtain a (non)homogeneous solution of a (nonlinear)/linearized equation of fractional order Van der P...ol model that represents the initial electromagnetic oscillation at the electroviscoelastic liquid/liquid interface.Specially, it will be discussed a case of low fractionality i.e the order of fractional derivative p slightly deviates from an integer value n. Finally, it is proposed numerical algorithm using a predictor-corrector approach for calculating corresponding homogeneous solution of nonlinear differential equation of the Van der Pol type.
Кључне речи:
electroviscoelasticity / fractional-order model / finely dispersed systems / numerical evaluationИзвор:
Proceedings of 1st International Congress of Serbian Society of Mechanics,10- 13, April,Kopaonik, 2007, 2007, 109-118Издавач:
- Belgrade: Serbian Society of Mechanics
Финансирање / пројекти:
- Фини дисперзни системи: микро-, нано-, ато-инжењерство (RS-MESTD-MPN2006-2010-142034)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Lazarević, Mihailo AU - Spasić, Aleksandar PY - 2007 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5330 AB - A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. The behavior of e.g., liquid/liquid interfaces is based on three forms of «instabilities», these are rigid,elastic and plastic. Three possible mathematical formalisms have been considered related to this physical formalism,i.e. to the theory of electroviscoelasticity: the first is tension tensor model, the second is Van der Pol derivative model and the third model is fractional order Van der Pol derivative model. The third model presents an effort to generalize the previous Van der Pol equation using fractional integro-differential operators (fractional calculus). In this paper, central parts of presentation will be solution using Caputo definition of fractional operators to obtain a (non)homogeneous solution of a (nonlinear)/linearized equation of fractional order Van der Pol model that represents the initial electromagnetic oscillation at the electroviscoelastic liquid/liquid interface.Specially, it will be discussed a case of low fractionality i.e the order of fractional derivative p slightly deviates from an integer value n. Finally, it is proposed numerical algorithm using a predictor-corrector approach for calculating corresponding homogeneous solution of nonlinear differential equation of the Van der Pol type. PB - Belgrade: Serbian Society of Mechanics C3 - Proceedings of 1st International Congress of Serbian Society of Mechanics,10- 13, April,Kopaonik, 2007 T1 - Electroviscoelasticity of Liquid/Liquid Interfaces: Fractional Order Van der Pol Model – New Results EP - 118 SP - 109 UR - https://hdl.handle.net/21.15107/rcub_machinery_5330 ER -
@conference{ author = "Lazarević, Mihailo and Spasić, Aleksandar", year = "2007", abstract = "A new, recently developed, theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems, and is based on a new constitutive model of liquids. The behavior of e.g., liquid/liquid interfaces is based on three forms of «instabilities», these are rigid,elastic and plastic. Three possible mathematical formalisms have been considered related to this physical formalism,i.e. to the theory of electroviscoelasticity: the first is tension tensor model, the second is Van der Pol derivative model and the third model is fractional order Van der Pol derivative model. The third model presents an effort to generalize the previous Van der Pol equation using fractional integro-differential operators (fractional calculus). In this paper, central parts of presentation will be solution using Caputo definition of fractional operators to obtain a (non)homogeneous solution of a (nonlinear)/linearized equation of fractional order Van der Pol model that represents the initial electromagnetic oscillation at the electroviscoelastic liquid/liquid interface.Specially, it will be discussed a case of low fractionality i.e the order of fractional derivative p slightly deviates from an integer value n. Finally, it is proposed numerical algorithm using a predictor-corrector approach for calculating corresponding homogeneous solution of nonlinear differential equation of the Van der Pol type.", publisher = "Belgrade: Serbian Society of Mechanics", journal = "Proceedings of 1st International Congress of Serbian Society of Mechanics,10- 13, April,Kopaonik, 2007", title = "Electroviscoelasticity of Liquid/Liquid Interfaces: Fractional Order Van der Pol Model – New Results", pages = "118-109", url = "https://hdl.handle.net/21.15107/rcub_machinery_5330" }
Lazarević, M.,& Spasić, A.. (2007). Electroviscoelasticity of Liquid/Liquid Interfaces: Fractional Order Van der Pol Model – New Results. in Proceedings of 1st International Congress of Serbian Society of Mechanics,10- 13, April,Kopaonik, 2007 Belgrade: Serbian Society of Mechanics., 109-118. https://hdl.handle.net/21.15107/rcub_machinery_5330
Lazarević M, Spasić A. Electroviscoelasticity of Liquid/Liquid Interfaces: Fractional Order Van der Pol Model – New Results. in Proceedings of 1st International Congress of Serbian Society of Mechanics,10- 13, April,Kopaonik, 2007. 2007;:109-118. https://hdl.handle.net/21.15107/rcub_machinery_5330 .
Lazarević, Mihailo, Spasić, Aleksandar, "Electroviscoelasticity of Liquid/Liquid Interfaces: Fractional Order Van der Pol Model – New Results" in Proceedings of 1st International Congress of Serbian Society of Mechanics,10- 13, April,Kopaonik, 2007 (2007):109-118, https://hdl.handle.net/21.15107/rcub_machinery_5330 .