Dissipative structures macro

Dissipative structures arise only in strongly nonequilibrium systems, with the states described by nonhnear equations for internal macro parameters. The emergence of the Benard cells in fluids can be described using non hnear differential equations of hydrodynamics coupled with Lyapunov s analysis of the instability of the respective solutions. It is shown that the solution of hydrodynamic equations related to a resting fluid and normal heat transfer becomes unstable at AT > AT, and a new stable convection mode is established in the fluid. 

At the formation of the structure of crosslinked polymers one can observe the formation of dissipative structures (DS) of two levels - micro- and macro-DS. Micro-DS are local order domains (clusters) and their formation is due to the high viscosity of the reactive medium in the gelation period. As it is known [47], this results in turbulence of viscous media and subsequent formation of ordered regions. 

We conclude that the growth of a new phase is controlled by the rate of dissipation at a moving kink. This dissipation is taking place at the microlevel and must be prescribed in order for the macro-description to be complete. The incompleteness of the continuum model manifests itself through the sensitivity of the solution to the singular (measure-valued) contributions describing fine structure of the subsonic jump discontinuities (kinks). 

As has been discussed above, molecular clusters produced in a supersonic expansion are preferred model systems to study solvation-mediated photoreactions from a molecular point of view. Under such conditions, intramolecular electron transfer reactions in D-A molecules, traditionally observed in solutions, are amenable to a detailed spectroscopic study. One should note, however, the difference between the possible energy dissipation processes in jet-cooled clusters and in solution. Since molecular clusters are produced in the gas phase under collision-free conditions, they are free of perturbations from many-body interactions or macro-molecular structures inherent for molecules in the condensed phase. In addition, they are frozen out in their minimum energy conformations which may differ from those relevant at room temperature. Another important aspect of the condensed phase is its role as a heat bath. Thus, excess energy in a molecule may be dissipated to the bulk on a picosecond time-scale. On the other hand, in a cluster excess energy may only be dissipated to a restricted number of oscillators and the cluster may fragment by losing solvent molecules. 

In practice, tack experiments, translation tribometry, and atomic force microscopy (AFM) are used to quantify adhesion and friction at the macro- and nanoscales. In order to record dissipation phenomena, the influence of structural parameters (degree of crosshnking and presence of free chains) and experimental factors (friction speed, normal force) is analyzed. 

Fig. 3. Landscape transformation. From a state A1 of lower order through increasing dissipation, a system reaches a critical threshold and, after a branching point, it arrives at the state A2 of higher order. The old organisational state is a rural landscape an increased flux of energy produces macro fluctuations of the local organisation and then some instabilities. These instabilities cause an increased dissipation of energy, the system becomes difficult to maintain when a threshold is reached (e.g. a prevailing of urban structures over the former rural ones) a new organisational state results (from Ingegnoli, 2002).

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