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Bernhard Maschke - One of the best experts on this subject based on the ideXlab platform.
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on the passivity based control of Irreversible Processes
Automatica, 2016Co-Authors: Hector Ramirez, Yann Le Gorrec, Bernhard Maschke, F CouenneAbstract:Irreversible port-Hamiltonian systems (IPHS) have recently been proposed for the modelling of Irreversible thermodynamic systems. On the other hand, a classical result on the use of the second law of thermodynamics for the stabilization of Irreversible Processes is the celebrated thermodynamic availability function. These frameworks are combined to propose a class of Passivity Based Controller (PBC) for Irreversible Processes. An alternative formulation of the availability function in terms of internal energy is proposed. Using IPHS a matching-condition, which is interpreted in terms of energy-shaping, is derived and a specific solution that permits to assign a desired closed-loop structure and entropy rate is proposed. The approach can be compared with Interconnection and Damping Assignment-PBC, this method however leads in general to thermodynamically non-coherent closed-loop systems. In this paper a system theoretic approach is employed to derive a constructive method for the control design. The closed-loop system is in IPHS form, hence it can be identified with a thermodynamic system and the control parameters related with thermodynamic variables, such as the reaction rates in the case of chemical reactions. A generic non-linear non-isothermal continuous stirred tank reactor is used to illustrate the approach.
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an entropy based formulation of Irreversible Processes based on contact structures
Chemical Engineering Science, 2010Co-Authors: Audrey Favache, Denis Dochain, Bernhard MaschkeAbstract:In this paper we propose an analytical formulation of the dynamical behaviour of complex and open physical systems which is formulated on the total thermodynamic phase space using the contact form associated with Gibbs' relation. Starting from balance equations we construct control contact systems by using the entropy function to represent the thermodynamic properties. The contact Hamiltonian function generating the dynamical behaviour has then the units of an entropy variation. We consider complex thermodynamic systems, described by compartmental systems, and we construct the associated control contact system by composing the control contact formulation of every compartment. The contact Hamiltonian functions generating the dynamical behaviour are discussed with respect to two alternative formalisms used for describing coupled sets of reversible and Irreversible Processes, namely the GENERIC formulation and the Matrix formulation. This analysis is then illustrated on the elementary example of a coupled mechanical and thermodynamic system. (C) 2010 Elsevier Ltd. All rights reserved.
Miltiadis Papalexandris - One of the best experts on this subject based on the ideXlab platform.
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a two phase model for compressible granular flows based on the theory of Irreversible Processes
Journal of Fluid Mechanics, 2004Co-Authors: Miltiadis PapalexandrisAbstract:In this article we introduce a new two-phase model for compressible viscous flows of saturated mixtures consisting of a carrier fluid and a granular material. The mixture is treated as a multicomponent fluid, with a set of thermodynamic variables assigned to each of its constituents. The volume fraction occupied by the granular phase and its spatial gradient are introduced as additional degrees of freedom. Then, by applying the classical theory of Irreversible Processes we derive algebraic expressions for the viscous stresses and heat flux vectors, the momentum and energy exchanges between the two phases, as well as a parabolic partial differential equation for the volume fraction. In our model, thermal non-equilibrium between the two phases emerges as a source term of the evolution equation for the volume fraction, in contrast with earlier models.
F P Devecchi - One of the best experts on this subject based on the ideXlab platform.
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Irreversible Processes in inflationary cosmological models
Physical Review D, 2002Co-Authors: Gilberto M Kremer, F P DevecchiAbstract:By using the thermodynamic theory of Irreversible Processes and Einstein general relativity, a cosmological model is proposed where the early universe is considered as a mixture of a scalar field with a matter field. The scalar field refers to the inflaton while the matter field to the classical particles. The irreversibility is related to a particle production process at the expense of the gravitational energy and of the inflaton energy. The particle production process is represented by a non-equilibrium pressure in the energy-momentum tensor. The non-equilibrium pressure is proportional to the Hubble parameter and its proportionality factor is identified with the coefficient of bulk viscosity. The dynamic equations of the inflaton and the Einstein field equations determine the time evolution of the cosmic scale factor, the Hubble parameter, the acceleration and of the energy densities of the inflaton and matter. Among other results it is shown that in some regimes the acceleration is positive which simulates an inflation. Moreover, the acceleration decreases and tends to zero in the instant of time where the energy density of matter attains its maximum value.
Byung Chan Eu - One of the best experts on this subject based on the ideXlab platform.
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thermodynamic theory of Irreversible Processes
2016Co-Authors: Byung Chan EuAbstract:In this work, we are interested in a molecular theory (i.e., statistical mechanics) of time- and space-dependent nonequilibrium (Irreversible) Processes in matter regarded as composed of many discrete particles.
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generalized thermodynamics the thermodynamics of Irreversible Processes and generalized hydrodynamics
2006Co-Authors: Byung Chan EuAbstract:Preface. 1. Introduction. 2. The Zeroth Law of Thermodynamics. 3. The First Law of Thermodynamics. 4. The Second Law of Thermodynamics. 5. Thermodynamics of Global Irreversible Processes. 6. Conservation Laws and Evolution Equations. 7. Local Form of the Second Law of Thermodynamics. 8. Local Irreversible Thermodynamics. 9. Thermodynamics of Linear Irreversible Processes. 10. Irreversible Thermodynamics of Steady States. 11. Variational Principles. 12. Contact Form in Thermodynamics. Index.
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Thermodynamics of Irreversible Processes
Chemical Engineering Science, 1995Co-Authors: Byung Chan EuAbstract:The thermodynamics of Irreversible Processes is a continuum theory of Processes in matter with no reference to its molecular constitution. The reductionist tradition of natural philosophy, however, inevitably requires molecular theoretical foundations in the form of a particulate theory of matter based on the concept of particles (e.g., atoms and molecules) currently held in science. The kinetic theory of fluids has been primarily developed to provide macroscopic phenomena and thermodynamics of reversible and Irreversible Processes in continuum matter with molecular theoretical foundations. In such a theory a suitable kinetic equation is used for the distribution function of the system in the phase space or the Hilbert space, but in practice the solution of the kinetic equation is sought in such a way as to help understand at the thermodynamic level of description the macroscopic phenomena which we experience or observe in nature and in the laboratory. Therefore the solution is a particular solution corresponding to our thermodynamic level of understanding of the natural phenomena of interest. It is then inevitable that we examine what is really meant by the thermodynamic level of description in the first place. In the course of our scientific training we have been taught thermodynamics of reversible Processes, and a great deal of our scientific reasoning and thinking Processes is molded and influenced by equilibrium thermodynamics, especially when we are concerned with macroscopic phenomena in continuum matter, but the subject is not very useful for us when we face Irreversible macroscopic Processes. Consequently our first task in attempting to study the kinetic theory of matter is in establishing a theoretical formalism for macroscopic phenomena in continuum matter on the foundations of the laws of thermodynamics as we know of at present in the forms proposed by their formulators. We then develop a solution procedure for the kinetic equation for the distribution function of matter in the phase space or the Hilbert space depending on whether the classical or quantum mode of description is adopted for the development of the theory, in such a way that the thermodynamics of Irreversible Processes is described from the molecular viewpoint. We are thus motivated to develop first a thermodynamic theory of Irreversible Processes without using the molecular picture of matter. In this endeavor we take the position that the first task is to develop a logical structure within the framework of the original form of the laws of thermodynamics as phrased by their formulators. Since the most difficult and unsettled part of the theory is concerned with the mathematical representation of the second law of thermodynamics, we will devote close attention to it, but will be brief with the representation of the first law of thermodynamics and other conservation laws as well as the zeroth law regarding the temperature, since there is nothing new for us to add to them at present. Applications of the theory developed for Irreversible Processes will be deferred to a later chapter. We will assume that the substance does not have an intrinsic angular momentum. We also assume that the system consists of an r-component non-reactive mixture. Therefore the case of chemical reactions is excluded, but it is easy to modify the theory to include the case of chemical reactions. After completing the formulation of the theory under the assumptions taken, we will point out where the necessary modifications must be made to include chemical reactions. Since the kinetic theory part of this work does not deal with fluids with an angular momentum, we will not consider the Irreversible thermodynamics of such fluids.
F Calogero - One of the best experts on this subject based on the ideXlab platform.
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spontaneous reversal of Irreversible Processes in a many body hamiltonian evolution
New Journal of Physics, 2008Co-Authors: F Calogero, F LeyvrazAbstract:Recently a technique has been introduced to -modify a Hamiltonian so that the -modified Hamiltonian thereby produced is isochronous: all its solutions are periodic in all degrees of freedom with the same period ˜ T = 2/ . In this paper—after briefly reviewing this approach— we focus in particular on the -modified version of the most general realistic many-body problem whose behavior, over time intervals much shorter than the isochrony period ˜ T , differs only marginally from the thermodynamically Irreversible evolution of the corresponding, unmodified and realistic many-body system. We discuss the (apparently paradoxical) periodic recurrence of the Irreversible Processes occurring in this -modified model, implying a periodic reversal of its Irreversible behavior. We then discuss the equilibrium statistical mechanics of this -modified model, including the compatibility of standard thermodynamic notions such as entropy with the peculiar phenomenology featured by its time evolution. The theoretical discussion is complemented by numerically simulated examples of the molecular dynamics yielded by the (standard and classical) Hamiltonian describing (many) particles interacting pairwise via potentials of Lennard-Jones type and via harmonic potentials in two-dimensional space, and by its -modified version. In the latter case, the simulation displays (approximate) returns to configurations away from thermodynamic equilibrium after relaxation to equilibrium had occurred.
