Coupled Problems in Thermodynamics

Иванова, Е. А.; Matias, Dmitrii V.

doi:10.1007/978-3-030-30355-6_7

Cited by 7 publications

(5 citation statements)

References 55 publications

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“…This study continues and develops the research carried out in [3, 4, 18, 28–30, 38, 39]. In these works, the authors develop the Cosserat continuum models of a special type.…”

Section: Introductionmentioning

confidence: 62%

“…Models of thermal processes based on the Cosserat continuum and well consistent with the considered models of electromagnetic processes have been developed in [55–59]. In the case where it is not necessary to take into account currents and charges, the coupling of electromagnetic and thermal processes has been studied in [38, 39]. Thus, it is of interest to extend the results obtained in [38, 39] to the case of the continuum in which the currents and charges both are present.…”

Section: A Comparative Analysis Of the Linear And Two Nonlinear Theoriesmentioning

confidence: 99%

“…In the case where it is not necessary to take into account currents and charges, the coupling of electromagnetic and thermal processes has been studied in [38, 39]. Thus, it is of interest to extend the results obtained in [38, 39] to the case of the continuum in which the currents and charges both are present. The second direction of research is to add translational degrees of freedom, i.e., to consider a moving and deforming continuum.…”

Section: A Comparative Analysis Of the Linear And Two Nonlinear Theoriesmentioning

confidence: 99%

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Modeling of electrodynamic processes by means of mechanical analogies

Иванова

2020

Z Angew Math Mech

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This study continues the line of earlier research in mechanical models of electrodynamic processes suggested in previous works. The basic steps we take to construct these models are: to formulate equations of a special type Cosserat continuum, and then to suggest analogies between quantities characterizing the stress–strain state of the continuum and quantities characterizing electrodynamic processes. In addition to the previously introduced mechanical analogies of the electric field vector and the magnetic induction vector, in this paper we provide mechanical analogies of the magnetic field vector, the electric induction vector, the electric current density and the electric charge density. In the framework of the suggested model, we obtain a set of differential equations that coincide with the first Maxwell's equation (the one with the displacement current term), the Gauss law for electric field and the charge conservation law. As a debatable question, we discuss the possibility of modifying the Maxwell–Faraday equation and the Gauss law for magnetic field.

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“…This study continues and develops the research carried out in [3, 4, 18, 28–30, 38, 39]. In these works, the authors develop the Cosserat continuum models of a special type.…”

Section: Introductionmentioning

confidence: 62%

Section: A Comparative Analysis Of the Linear And Two Nonlinear Theoriesmentioning

confidence: 99%

Section: A Comparative Analysis Of the Linear And Two Nonlinear Theoriesmentioning

confidence: 99%

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Modeling of electrodynamic processes by means of mechanical analogies

Иванова

2020

Z Angew Math Mech

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“…The Gauss law for magnetic field ∇ ⋅ 𝓑 = 0 can be obtained from Equation (44) if ∇ ⋅ 𝓥 = 0 and at the initial time ∇ ⋅ 𝓑 = 0.…”

Section: Previously Suggested Analogies Of Electrodynamic Quantities ...mentioning

confidence: 99%

“…The present study continues and develops the research carried out in Refs. [2,3,17,19,28,33,34,43,44]. Below we use our mechanical model aiming to develop an original approach to describing magnetic phenomena.…”

Section: Introductionmentioning

confidence: 99%

Modeling of physical fields by means of the Cosserat continuum

Иванова

2022

Z Angew Math Mech

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We consider a special type Cosserat continuum and suggest analogies between quantities characterizing the stress-strain state of the continuum and quantities characterizing physical processes. Such an approach provides us with the ability to derive equations describing electricity, magnetism, and other physical phenomena. This study continues the line of our earlier research. In the present paper, we obtain equations that can be treated as a generalization of Maxwell's equations. The main difference between the proposed equations and classical Maxwell's equations is in the description of magnetic phenomena. In particular, we introduce the concept of a magnetic charge vector and show that this quantity, like the electric charge, satisfies the conservation law and the Gauss law. We are convinced that the magnetic charge vector is the most appropriate physical quantity to characterize the state of a magnetized body. In addition to modeling the electromagnetic field, we make assumptions about how the proposed model can describe the field corresponding to the strong interaction.

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Thence the moment of momentum

2020

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Fifty years have passed since Truesdell's seminal paper on the origin and status of the balance for the moment of momentum was published in ZAMM. It is time to take stock: Important new developments in the theory of generalized continua with internal degrees of freedom and some fascinating fundamental applications need to be pointed out. Is there new evidence from classical papers regarding its independence from the balance of linear momentum? Can micropolar theory be used to “explain” electromagnetism? How is the conservation of the moment of momentum viewed in today's physics textbooks? In this paper an attempt is made to answer these and many more interesting questions.

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Coupled Problems in Thermodynamics

Cited by 7 publications

References 55 publications

Modeling of electrodynamic processes by means of mechanical analogies

Modeling of electrodynamic processes by means of mechanical analogies

Modeling of physical fields by means of the Cosserat continuum

Thence the moment of momentum

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