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Dynamics of Dissipative Systems with Hamiltonian Structures
International Journal of Bifurcation and Chaos, 2021In this work, we study a class of dissipative, nonsmooth [Formula: see text] degree-of-freedom dynamical systems. As the dissipation is assumed to be proportional to the momentum, the dynamics in such systems is conformally symplectic, allowing us to use some of the Hamiltonian structure.
Xiaoming Zhang +4 more
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Theory of Dissipative Structures
1973One of the main reasons to develop thermodynamics beyond the equilibrium range lies in the need for a physico-chemical basis of biological order. Not only would one like to explain the maintenance of low entropy situations and subtle metabolic regulation processes but also one wants to provide a physico-chemical basis of evolution towards structures of
Prigogine, Ilya, Lefever, René
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Thermodynamics, Structure and Dissipation
1971It is well known that classical thermodynamics is mainly concerned with equilibrium situations. However it was relatively recently recognized in many important fields of research that a state of true equilibrium is only attained under exceptional conditions.
Prigogine, Ilya, Lefever, René
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On the formation of unique dissipative structures
Biosystems, 1982We consider a simple model for the formation of dissipative structures. In general there exists a multitude of stable final states. We show, however, that when the diffusion constant increases during the development of the system, a stationary state is reached which does not depend on the choice of initial conditions.
D S, Chernavskii, T W, Ruijgrok
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On the Entropy of Dissipative and Turbulent Structures
Annalen der Physik, 1986The authors have studied the Klimontovich entropy statement with the help of selfoscillations of nonlinear oscillators and laminar and turbulent flows in tubes. In Klimontovich's S-theorem the entropy decreases with the increase in distance from equilibrium.
Ebeling, W. +2 more
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Attractors of dissipative structure in three dissipative fluids
Physical Review E, 1994A theory to find attractors of dissipative structure is developed by using autocorrelations for distributions. It is shown that the realization of coherent structures in dissipative dynamical systems is equivalent to that of self-organized states with the minimum change rate of autocorrelations for their instantaneous values, which usually represent ...
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Dissipative structures in two dimensions
Biophysical Chemistry, 1975Some further results on dissipative structures for one- and, more particularly, for two-dimensional bounded systems are presented. A model chemical network involving reactions and diffusion is investigated. The influence of the boundary conditions (no fluxes or fixed concentrations), the geometrical shape of the limits (circular or rectangular) and the
Erneux, Thomas, Kaufman, Marcelle
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Eigenfunction for dissipative dynamic operators and the attractor of the dissipative structure
Physical Review E, 1993This study shows that the states with the minimum dissipation rate in general dissipative dynamic systems are expressed by the eigenfunctions for the dissipative dynamic operators. These eigenfunctions are shown to constitute the self-organized and self-similar decay phase as the attractor of the dissipative structure.
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