Absolute time derivatives

Matolcsi, T.; Ván, P.

doi:10.1063/1.2719144

Cited by 12 publications

(12 citation statements)

References 39 publications

(60 reference statements)

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“…These requirements make (1) a diffeomorphism, i.e., a time-dependent flow of curvilinear coordinates 25,29,39,40,48 whose motion in space resembles in toto a physical fluid flow of classical mechanics. Einstein called these coordinate systems "reference-mollusks" 11 .…”

Section: The Conjugate Flowmentioning

confidence: 99%

Conjugate flow action functionals

Venturi

2013

Journal of Mathematical Physics

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We present a new general method to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations of the theory relative to a diffeomorphic flow of curvilinear coordinates which is assumed to be functionally dependent on the solution field. Such flow, which will be called the conjugate flow of the theory, evolves in space and time similarly to a physical fluid flow of classical mechanics and it can be selected in order to symmetrize the Gâteaux derivative of the field equations with respect to suitable local bilinear forms. This is equivalent to requiring that the governing equations of the field theory can be derived from a principle of stationary action on a Lie group manifold. By using a general operator framework, we obtain the determining equations of such manifold and the corresponding conjugate flow action functional. In particular, we study

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Section: The Conjugate Flowmentioning

confidence: 99%

Conjugate flow action functionals

Venturi

2013

Journal of Mathematical Physics

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“…If the tensor z bc is split to components according to (7), then -y is the intensive quantity related to the mass density, -yb is the intensive quantity belonging to the momentum density pb, -ybc is the intensive quantity related to the energy density tensor ebc . One can pull closer the treatment to the usual approach assuming…”

Section: Thermostatics Of Motion or Thermostatodynamicsmentioning

confidence: 99%

“…However, the space is relative also in this case, it is different for different observers: the so-called non-relativistic space-time is Galilean relativistic. With the help of the notions of special relativistic space-time, the heuristic concepts of our everyday experience can be clarified and an exact mathematical model of Galilean relativistic space-time can be formulated [1,2,3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Galilean relativistic fluid mechanics

Ván

2017

Continuum Mech. Thermodyn.

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Abstract. Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given.The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time-and spacelike components of the third order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived.It is proved, that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow.A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.

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“…• The weakly nonlocal extension of the constitutive state space is a safe procedure, because the gradient is a covector, that does not depend on the motion, e.g., does not transform by a Galilean transformation [63,64].…”

Section: The Entropy Principle In Classical Irreversible Thermodynamicsmentioning

confidence: 99%

Entropy Principle and Recent Results in Non-Equilibrium Theories

Cimmelli

Jou

Ruggeri

et al. 2014

Entropy

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We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

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Absolute time derivatives

Cited by 12 publications

References 39 publications

Conjugate flow action functionals

Conjugate flow action functionals

Galilean relativistic fluid mechanics

Entropy Principle and Recent Results in Non-Equilibrium Theories

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