One way of mathematically modeling a dissipative system is given in the article on " wandering sets " : it involves the action of a measurable set.
22.
For example, a dissipative system involving self-assembly of nanowires has been used as a model to understand the relationship between entropy generation and the robustness of biological systems.
23.
He called these systems dissipative systems, because they are formed and maintained by the dissipative processes that exchange energy between the system and its environment, and because they disappear if that exchange ceases.
24.
It is the fact that the eigenvalues k ^ {-m } that marks this as a dissipative system : for a non-dissipative measure-preserving dynamical system, the eigenvalues of the transfer operator lie on the unit circle.
25.
If there exists a wandering set of positive measure, then the action of \ Gamma is said to be "'dissipative "', and the dynamical system ( \ Omega, \ Gamma ) is said to be a dissipative system.
26.
Prigogine called these systems dissipative systems, because they are formed and maintained by the dissipative processes which take place because of the exchange of energy between the system and its environment and because they disappear if that exchange ceases.
27.
The "'Hierarchical equations of motion "'( HEOM ) technique derived by R . Kubo and Y . Tanimura is a non-perturbative approach developed to study the evolution of a density matrix \ rho ( t ) of quantum dissipative systems.
28.
In thermodynamic terminology, human economic activity ( as well as the activity of the human life units which make it up ) may be described as a dissipative system, which flourishes by consuming free energy in transformations and exchange of resources, goods, and services.
29.
For a given field y ( x, t ) and diffusion coefficient ( or " viscosity ", as in the original fluid mechanical context ) d, the general form of Burgers'equation ( also known as "'viscous Burgers'equation "') in one space dimension is the dissipative system:
30.
A generalisation of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics ( 1788 and 1833, respectively ), it does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.
