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K.-h. Anthony - One of the best experts on this subject based on the ideXlab platform.
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Hamilton's action principle and thermodynamics of irreversible processes : a unifying procedure for reversible and irreversible processes
Journal of Non-newtonian Fluid Mechanics, 2001Co-Authors: K.-h. AnthonyAbstract:Abstract Thermodynamics of irreversible processes can be included into the framework of Lagrange Formalism. This Formalism presents a unified method for reversible and irreversible processes. As a remarkable fact the first and the second law of thermodynamics are derived in Lagrange Formalism by means of straightforward procedures. The whole information on the dynamics of a system is included in one function only, namely in its Lagrangian. In this paper the theory is presented in two courses. The first one offers an almost qualitative insight into the structure of the theory; the second one is concerned with the associated mathematics in some detail. The theory is illustrated by three representative examples: the style of the paper is chosen as to stimulate the discussions at a workshop and a school on the state-of-art of non-equilibrium thermodynamics of complex fluids, Oxford, 2000.
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Hamilton’s action principle and thermodynamics of irreversible processes — a unifying procedure for reversible and irreversible processes
Journal of Non-newtonian Fluid Mechanics, 2001Co-Authors: K.-h. AnthonyAbstract:Abstract Thermodynamics of irreversible processes can be included into the framework of Lagrange Formalism. This Formalism presents a unified method for reversible and irreversible processes. As a remarkable fact the first and the second law of thermodynamics are derived in Lagrange Formalism by means of straightforward procedures. The whole information on the dynamics of a system is included in one function only, namely in its Lagrangian. In this paper the theory is presented in two courses. The first one offers an almost qualitative insight into the structure of the theory; the second one is concerned with the associated mathematics in some detail. The theory is illustrated by three representative examples: the style of the paper is chosen as to stimulate the discussions at a workshop and a school on the state-of-art of non-equilibrium thermodynamics of complex fluids, Oxford, 2000.
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Lagrangian field theory of plasticity based on dislocation dynamics - Various Approaches
Journal De Physique Iv, 1998Co-Authors: K.-h. Anthony, A Azirhi, Markus ScholleAbstract:The purpose of this paper is to give a qualitative idea of a phenomenological continuum theory of plastic deformation based on dislocation dynamics. The theory works within Lagrange Formalism of fields; with regard to Thermodynamics of Irreversible Processes the fundamental field variables are mainly complex. Physically the structure of the theory follows the microstructure of dislocations and their dynamics. From the thermodynamical point of view we are dealing with internal variables, which - in contrast with tradititional approaches -really fit to the dislocation concept. Keeping in mind that plastic deformation and dislocation dynamics are running far away from thermal equilibrium Lagrange Formalism is a most appropriate tool. It further allows of taking into account dissipation which is an essential feature of plastic deformation. Finally Lagrange Formalism is the most concise form of a field theory which is most important from the practical point of view as well as from a sophisticated point of view of unification of physical theories. Our presentation aims at a structural survey of our approaches. For the details - especially for the mathematical ones - we refer to our preceding and forthcoming papers.
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NONLOCAL Lagrange Formalism IN THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES : VARIATIONAL PROCEDURES FOR KINETIC EQUATIONS
Physica A-statistical Mechanics and Its Applications, 1996Co-Authors: B. Sievers, K.-h. AnthonyAbstract:This paper is concerned with generalizations of the known local Lagrange Formalism of first order. It will be applied to kinetic equations like the Fokker-Planck equation and the Boltzmann equation. In the latter case nonlocal methods are necessary from the very beginning. Nevertheless, in the framework of Frechet's Formalism the calculations are as easy as in the classical local case.
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Dislocation dynamics by means of Lagrange Formalism of irreversible processes—Complex fields and deformation processes
International Journal of Engineering Science, 1995Co-Authors: K.-h. Anthony, A AzirhiAbstract:Abstract Conventional approaches to a phenomenological theory of plasticity suffer from the fact that they are based on the concept of a “material manifold”. In this way the dislocation dynamics are structurally eliminated from the very beginning. We propose an alternative method within the framework of Lagrange Formalism. With regard to thermodynamics of irreversible processes all degrees of freedom being involved in dissipation are associated with complex field variables. A plastically deformed crystal is modelled as a Cosserat fluid based on complex matter and vortex fields and on a real field of Cosserat triads representing the solid properties of the crystal. Using complex dislocation fields the dislocation network is described in more detail than conventionally is done by the well known dislocation density tensor. Especially the model allows for correlations within the dislocation network which is most essential for plasticity. Our model implies a methodical unification of elasticity and plasticity. The paper is mainly concerned with the mechanical aspects of the theory.
Walter Greiner - One of the best experts on this subject based on the ideXlab platform.
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extended hamilton Lagrange Formalism
2010Co-Authors: Walter GreinerAbstract:The conventional formulation of the principle of least action is based on the action functional S[q j (t)], defined using the system’s conventional Lagrangian and the set of configuration space variables as functions of time. In this formulation, the independent variable time t plays the role of the Newtonian absolute time. The clearest reformulation of the least action principle for relativistic physics is accomplished by treating the time t(s)—just like the configuration space variables q j (s)—as a dependent variable of a newly introduced independent variable, s.
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Extended Hamilton–Lagrange Formalism
Classical Mechanics, 2009Co-Authors: Walter GreinerAbstract:The conventional formulation of the principle of least action is based on the action functional S[q j (t)], defined using the system’s conventional Lagrangian and the set of configuration space variables as functions of time. In this formulation, the independent variable time t plays the role of the Newtonian absolute time. The clearest reformulation of the least action principle for relativistic physics is accomplished by treating the time t(s)—just like the configuration space variables q j (s)—as a dependent variable of a newly introduced independent variable, s.
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The Hole Theory
1990Co-Authors: Walter GreinerAbstract:Until now the solutions of the Dirac equation with negative energy have been a puzzle. Attempts similar to those we performed with the solutions of the Klein-Gordon equation, where the energy turned out to be positive (by the Lagrange Formalism) for solutions with positive and negative time evolution factors, proved unsuccessful (cf. Exercise 2.3). Solutions with negative energy appear almost everyhwere when we are concerned with processes of high energy or with strongly localized wave packets (see Exercises 8.4, 8.5). At this point we have to confront this dilemma and find a proper solution!
Peter Ostermann - One of the best experts on this subject based on the ideXlab platform.
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A Strange Detail Concerning the Variational Principle of General Relativity Theory
arXiv: General Relativity and Quantum Cosmology, 2004Co-Authors: Peter OstermannAbstract:A mathematical complication due to an unnecessary formal assumption concerning the variational principle of general relativity theory, which apparently bothered Einstein and Hilbert, is shown and cleared up. Some historical confusion seems caused by the impossibility to use the conventional Euler-Lagrange Formalism directly there, which even otherwise is nothing but one of various possible procedures to apply the superior principle of least action. Correspondingly to the absence of any direct calculation in the literature so far, only a numerical modification in parts - explicitly taken into account now after once mentioned by Hilbert without implementation - would allow to compute the fundamental Einstein tensor density from these authors' initial formulae, which must not be taken literally. Nevertheless adhering to a merely symbolic Euler-Lagrange Formalism, this needs a clear distinction between 'component differentiation' and 'tensor differentiation' defined here. Various corresponding solutions are shown including the probably most natural one. Two of them are additionally verified in the detailed supplementary material appended to the electronic edition of the note.
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A Strange Detail Concerning the Variational Principle of General Relativity Theory
arXiv: General Relativity and Quantum Cosmology, 2004Co-Authors: Peter OstermannAbstract:A mathematical complication due to an unnecessary formal assumption concerning the variational principle of general relativity theory, which apparently bothered Einstein and Hilbert, is shown and cleared up. Some historical confusion seems caused by the impossibility to use the conventional Euler-Lagrange Formalism directly there, which even otherwise is nothing but one of various possible procedures to apply the superior principle of least action. Correspondingly to the absence of any direct calculation in the literature so far, only a numerical modification in parts - explicitly taken into account now after once mentioned by Hilbert without implementation - would allow to compute the fundamental Einstein tensor density from these authors' initial formulae, which must not be taken literally. Nevertheless adhering to a merely symbolic Euler-Lagrange Formalism, this needs a clear distinction between 'component differentiation' and 'tensor differentiation' defined here. Various corresponding solutions are shown including the probably most natural one. Two of them are additionally verified in the detailed supplementary material appended to the electronic edition of the note.
Jürgen Struckmeier - One of the best experts on this subject based on the ideXlab platform.
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EXTENDED HAMILTON–Lagrange Formalism AND ITS APPLICATION TO FEYNMAN'S PATH INTEGRAL FOR RELATIVISTIC QUANTUM PHYSICS
International Journal of Modern Physics E-nuclear Physics, 2009Co-Authors: Jürgen StruckmeierAbstract:We present a consistent and comprehensive treatise on the foundations of the extended Hamilton–Lagrange Formalism — where the dynamical system is parametrized along a general system evolution parameter s, and the time t is treated as a dependent variable t(s) on equal footing with all other configuration space variables qi(s). In the action principle, the conventional classical action L1dt is then replaced by the generalized action L1ds, with L and L1 denoting the conventional and the extended Lagrangian, respectively. It is shown that a unique correlation of L1 and L exists if we refrain from performing simultaneously a transformation of the dynamical variables. With the appropriate correlation of L1 and L in place, the extension of the Formalism preserves its canonical form. In the extended Formalism, the dynamical system is described as a constrained motion within an extended space. We show that the value of the constraint and the parameter s constitutes an additional pair of canonically conjugate variables. In the corresponding quantum system, we thus encounter an additional uncertainty relation. As a consequence of the formal similarity of conventional and extended Hamilton–Lagrange Formalisms, Feynman's nonrelativistic path integral approach can be converted on a general level into a form appropriate for relativistic quantum physics. In the emerging parametrized quantum description, the additional uncertainty relation serves as the means to incorporate the constraint and hence to finally eliminate the parametrization. We derive the extended Lagrangian L1 of a classical relativistic point particle in an external electromagnetic field and show that the generalized path integral approach yields the Klein–Gordon equation as the corresponding quantum description. We furthermore derive the space–time propagator for a free relativistic particle from its extended Lagrangian L1. These results can be regarded as the proof of principle of the relativistic generalization of Feynman's path integral approach to quantum physics.
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extended hamilton Lagrange Formalism and its application to feynman s path integral for relativistic quantum physics
International Journal of Modern Physics E-nuclear Physics, 2009Co-Authors: Jürgen StruckmeierAbstract:We present a consistent and comprehensive treatise on the foundations of the extended Hamilton–Lagrange Formalism — where the dynamical system is parametrized along a general system evolution parameter s, and the time t is treated as a dependent variable t(s) on equal footing with all other configuration space variables qi(s). In the action principle, the conventional classical action L1dt is then replaced by the generalized action L1ds, with L and L1 denoting the conventional and the extended Lagrangian, respectively. It is shown that a unique correlation of L1 and L exists if we refrain from performing simultaneously a transformation of the dynamical variables. With the appropriate correlation of L1 and L in place, the extension of the Formalism preserves its canonical form. In the extended Formalism, the dynamical system is described as a constrained motion within an extended space. We show that the value of the constraint and the parameter s constitutes an additional pair of canonically conjugate variables. In the corresponding quantum system, we thus encounter an additional uncertainty relation. As a consequence of the formal similarity of conventional and extended Hamilton–Lagrange Formalisms, Feynman's nonrelativistic path integral approach can be converted on a general level into a form appropriate for relativistic quantum physics. In the emerging parametrized quantum description, the additional uncertainty relation serves as the means to incorporate the constraint and hence to finally eliminate the parametrization. We derive the extended Lagrangian L1 of a classical relativistic point particle in an external electromagnetic field and show that the generalized path integral approach yields the Klein–Gordon equation as the corresponding quantum description. We furthermore derive the space–time propagator for a free relativistic particle from its extended Lagrangian L1. These results can be regarded as the proof of principle of the relativistic generalization of Feynman's path integral approach to quantum physics.
A Azirhi - One of the best experts on this subject based on the ideXlab platform.
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Lagrangian field theory of plasticity based on dislocation dynamics - Various Approaches
Journal De Physique Iv, 1998Co-Authors: K.-h. Anthony, A Azirhi, Markus ScholleAbstract:The purpose of this paper is to give a qualitative idea of a phenomenological continuum theory of plastic deformation based on dislocation dynamics. The theory works within Lagrange Formalism of fields; with regard to Thermodynamics of Irreversible Processes the fundamental field variables are mainly complex. Physically the structure of the theory follows the microstructure of dislocations and their dynamics. From the thermodynamical point of view we are dealing with internal variables, which - in contrast with tradititional approaches -really fit to the dislocation concept. Keeping in mind that plastic deformation and dislocation dynamics are running far away from thermal equilibrium Lagrange Formalism is a most appropriate tool. It further allows of taking into account dissipation which is an essential feature of plastic deformation. Finally Lagrange Formalism is the most concise form of a field theory which is most important from the practical point of view as well as from a sophisticated point of view of unification of physical theories. Our presentation aims at a structural survey of our approaches. For the details - especially for the mathematical ones - we refer to our preceding and forthcoming papers.
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Dislocation dynamics by means of Lagrange Formalism of irreversible processes—Complex fields and deformation processes
International Journal of Engineering Science, 1995Co-Authors: K.-h. Anthony, A AzirhiAbstract:Abstract Conventional approaches to a phenomenological theory of plasticity suffer from the fact that they are based on the concept of a “material manifold”. In this way the dislocation dynamics are structurally eliminated from the very beginning. We propose an alternative method within the framework of Lagrange Formalism. With regard to thermodynamics of irreversible processes all degrees of freedom being involved in dissipation are associated with complex field variables. A plastically deformed crystal is modelled as a Cosserat fluid based on complex matter and vortex fields and on a real field of Cosserat triads representing the solid properties of the crystal. Using complex dislocation fields the dislocation network is described in more detail than conventionally is done by the well known dislocation density tensor. Especially the model allows for correlations within the dislocation network which is most essential for plasticity. Our model implies a methodical unification of elasticity and plasticity. The paper is mainly concerned with the mechanical aspects of the theory.
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dislocation dynamics by means of Lagrange Formalism of irreversible processes complex fields and deformation processes
International Journal of Engineering Science, 1995Co-Authors: K.-h. Anthony, A AzirhiAbstract:Abstract Conventional approaches to a phenomenological theory of plasticity suffer from the fact that they are based on the concept of a “material manifold”. In this way the dislocation dynamics are structurally eliminated from the very beginning. We propose an alternative method within the framework of Lagrange Formalism. With regard to thermodynamics of irreversible processes all degrees of freedom being involved in dissipation are associated with complex field variables. A plastically deformed crystal is modelled as a Cosserat fluid based on complex matter and vortex fields and on a real field of Cosserat triads representing the solid properties of the crystal. Using complex dislocation fields the dislocation network is described in more detail than conventionally is done by the well known dislocation density tensor. Especially the model allows for correlations within the dislocation network which is most essential for plasticity. Our model implies a methodical unification of elasticity and plasticity. The paper is mainly concerned with the mechanical aspects of the theory.
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Dislocation dynamics by means of Lagrange Formalism of irreversible processes—Complex fields and deformation processes
International Journal of Engineering Science, 1995Co-Authors: K.-h. Anthony, A AzirhiAbstract:Abstract Conventional approaches to a phenomenological theory of plasticity suffer from the fact that they are based on the concept of a “material manifold”. In this way the dislocation dynamics are structurally eliminated from the very beginning. We propose an alternative method within the framework of Lagrange Formalism. With regard to thermodynamics of irreversible processes all degrees of freedom being involved in dissipation are associated with complex field variables. A plastically deformed crystal is modelled as a Cosserat fluid based on complex matter and vortex fields and on a real field of Cosserat triads representing the solid properties of the crystal. Using complex dislocation fields the dislocation network is described in more detail than conventionally is done by the well known dislocation density tensor. Especially the model allows for correlations within the dislocation network which is most essential for plasticity. Our model implies a methodical unification of elasticity and plasticity. The paper is mainly concerned with the mechanical aspects of the theory.
