The Experts below are selected from a list of 204 Experts worldwide ranked by ideXlab platform
M. Cengiz Dökmeci - One of the best experts on this subject based on the ideXlab platform.
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Fluid–fluid and –solid interaction problems: Variational Principles revisited
International Journal of Engineering Science, 2009Co-Authors: Gülay Altay, M. Cengiz DökmeciAbstract:Abstract We systematically review some unified Variational Principles for a strong interaction problem in both a stratified fluid region and a fluid–solid region. The problem is described by a general Lagrangian formulation for an anisotropic elastic solid region, either surrounded by an incompressible non-Newtonian fluid region or surrounding the fluid region. In the first part, we express the fundamental equations of the regular fluid and solid regions in differential form. Then, we deduce the Variational Principles respectively from the principle of virtual power and the principle of virtual work for the fluid and solid regions. The physics Principles are modified through an involutory transformation together with a dislocation potential. In the second part, we similarly establish some multi-field Variational Principles for a stratified fluid of two or more distinct fluid layers of different thicknesses and mass densities. In the third part, we derive the Variational Principles for the interior and exterior interaction problems in a fluid region with a surface piercing solid, within either a rigid or an elastic structure. The Variational Principles, which operate on all the field variables lead to the fundamental equations of the regions, including the interface conditions, as their Euler–Lagrange equations. Some special cases of the Variational Principles are given.
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Variational Principles for Piezoelectric, Thermopiezoelectric, and Hygrothermopiezoelectric Continua Revisited
Mechanics of Advanced Materials and Structures, 2007Co-Authors: Gülay Altay, M. Cengiz DökmeciAbstract:In this paper some Variational Principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu Variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimento, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar Variational Principles of piezoelectricity are cited.
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Some Variational Principles for linear coupled thermoelasticity
International Journal of Solids and Structures, 1996Co-Authors: G. Aşkar Altay, M. Cengiz DökmeciAbstract:Guided by the principle of virtual work, the governing equations describing the physical behavior of a thermoelastic continuum were expressed as the Euler-Lagrange equations of certain Variational Principles. The differential Variational Principles were formulated for the thermoelastic continuum with or without an internal surface of discontinuity by introducing the dislocation potentials and Lagrange undetermined multipliers. These Principles were shown to recover some of the earlier Variational Principles as special cases, and their reciprocals were also recorded.
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Variational Principles derived for discontinuous electromagnetic fields
The Journal of the Acoustical Society of America, 1995Co-Authors: G. Aşkar Altay, M. Cengiz DökmeciAbstract:A unified procedure based on a general principle of physics (e.g., Hamilton’s principle) together with Legendre’s (or Friedrichs’s) transformation is proposed to systematically derive certain Variational Principles for discontinuous electromagnetic fields which are useful to treat electromagnetic waves and vibrations in dielectrics. The integral and differential types of Variational Principles generate Maxwell’s equations and the associated natural boundary and jump conditions as well as the initial conditions, as their Euler–Lagrange equations, for a regular finite and bounded dielectric region with or without a fixed, internal surface of discontinuity. Special cases of the Variational Principles, including a reciprocal one, are recorded which have those for time‐harmonic motions and a dielectric region within a vacuum or a perfect conductor, and they are shown to agree with and to recover some of earlier Variational Principles [e.g., M. C. Dokmeci, IEEE Trans. UFFC UFFC‐35, 775–787 (1988); UFFC‐37, 369–...
Dan Crisan - One of the best experts on this subject based on the ideXlab platform.
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semi martingale driven Variational Principles
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2021Co-Authors: Oliver D Street, Dan CrisanAbstract:Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a general framework for introducing stochasticity into Variational Principles through the concep...
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semi martingale driven Variational Principles
arXiv: Mathematical Physics, 2020Co-Authors: Oliver D Street, Dan CrisanAbstract:Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into Variational Principles through the concept of a semi-martingale driven Variational principle and constraining the component variables to be compatible with the driving semi-martingale. Within this framework and the corresponding choice of constraints, the Euler-Poincare equation can be easily deduced. We show that their corresponding deterministic counterparts are particular cases of this class of stochastic Variational Principles. Moreover, this is a natural framework that enables us to correctly characterize the pressure term in incompressible stochastic fluid models. Other general constraints can also be incorporated as long as they are compatible with the driving semi-martingale.
Oliver D Street - One of the best experts on this subject based on the ideXlab platform.
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semi martingale driven Variational Principles
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2021Co-Authors: Oliver D Street, Dan CrisanAbstract:Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a general framework for introducing stochasticity into Variational Principles through the concep...
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semi martingale driven Variational Principles
arXiv: Mathematical Physics, 2020Co-Authors: Oliver D Street, Dan CrisanAbstract:Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into Variational Principles through the concept of a semi-martingale driven Variational principle and constraining the component variables to be compatible with the driving semi-martingale. Within this framework and the corresponding choice of constraints, the Euler-Poincare equation can be easily deduced. We show that their corresponding deterministic counterparts are particular cases of this class of stochastic Variational Principles. Moreover, this is a natural framework that enables us to correctly characterize the pressure term in incompressible stochastic fluid models. Other general constraints can also be incorporated as long as they are compatible with the driving semi-martingale.
Gülay Altay - One of the best experts on this subject based on the ideXlab platform.
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Fluid–fluid and –solid interaction problems: Variational Principles revisited
International Journal of Engineering Science, 2009Co-Authors: Gülay Altay, M. Cengiz DökmeciAbstract:Abstract We systematically review some unified Variational Principles for a strong interaction problem in both a stratified fluid region and a fluid–solid region. The problem is described by a general Lagrangian formulation for an anisotropic elastic solid region, either surrounded by an incompressible non-Newtonian fluid region or surrounding the fluid region. In the first part, we express the fundamental equations of the regular fluid and solid regions in differential form. Then, we deduce the Variational Principles respectively from the principle of virtual power and the principle of virtual work for the fluid and solid regions. The physics Principles are modified through an involutory transformation together with a dislocation potential. In the second part, we similarly establish some multi-field Variational Principles for a stratified fluid of two or more distinct fluid layers of different thicknesses and mass densities. In the third part, we derive the Variational Principles for the interior and exterior interaction problems in a fluid region with a surface piercing solid, within either a rigid or an elastic structure. The Variational Principles, which operate on all the field variables lead to the fundamental equations of the regions, including the interface conditions, as their Euler–Lagrange equations. Some special cases of the Variational Principles are given.
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Variational Principles for Piezoelectric, Thermopiezoelectric, and Hygrothermopiezoelectric Continua Revisited
Mechanics of Advanced Materials and Structures, 2007Co-Authors: Gülay Altay, M. Cengiz DökmeciAbstract:In this paper some Variational Principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu Variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimento, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar Variational Principles of piezoelectricity are cited.
Masakazu Ichiyanagi - One of the best experts on this subject based on the ideXlab platform.
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Variational Principles of irreversible processes
Physics Reports, 1994Co-Authors: Masakazu IchiyanagiAbstract:Abstract This article reviews developments of Variational Principles in the study of irreversible processes during the past three decades or so. The Variational Principles we consider here are related to entropy production. The purpose of this article is to explicate that we can formulate a Variational principle which relates the transport coefficients to microscopic dynamics of fluctuations. The quantum Variational principle restricts the nonequilibrium density matrix to a class conforming to the requirement demanded by the second law of thermodynamics. These are various kinds of Variational Principles according to different stages of a macroscopic system. The three stages are known, which are dynamical, kinetic, and thermodynamical stages. The relationships among these Variational Principles are discussed from the point of view of the contraction of information about irrelevant components. Nakano's Variational principle has close similarity to the Lippmann-Schwinger theory of scattering, in which some incoming and outgoing disturbances have to be considered in a pair. It is also shown that the Variational principle of Onsager's type can be reformulated in the form of Hamilton's principle if a generalization of Hamilton's principle proposed by Djukic and Vujanovic is used. A Variational principle in the diagrammatic method is also reviewed, which utilizes the generalized Ward-Takahashi relations.
