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Inertial Manifold
In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponential growth, exponentially quickly. Since an inertial manifold is Dimension (vector space), finite-dimensional even if the original system is infinite-dimensional, and because most of the dynamics for the system takes place on the inertial manifold, studying the dynamics on an inertial manifold produces a considerable simplification in the study of the dynamics of the original system.R. Temam. Inertial manifolds. ''Mathematical Intelligencer'', 12:68–74, 1990 In many physical applications, inertial manifolds express an interaction law between the small and large wavelength structures. Some say that the small wavelengths are enslaved by the large (e.g. Synergetics (Haken), synergetics). Inertial manifolds may also ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dissipative
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to a final form, where the capacity of the final form to do thermodynamic work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the second law of thermodynamics, the entropy varies with temperature (reduces the capacity of the combination of the two bodies to do work), but never decreases in an isolated system. These processes produce entropy at a certain rate. The entropy production rate times ambient temperature gives the dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |