For macroscopic systems this opens possibilities for synthesis of new materials and creating new types of propulsion systems.
Chaos only exists in nonlinear systems (at least for classical macroscopic systems; see sec. 6 for subtitles regarding quantum chaos).
For the first example, we shall examine a macroscopic system of 10 books that is not subjected to thermodynamic effects.
So far, the entanglement sharing and quantum teleportation was reported for cold atoms [16 18], and even for macroscopic systems [19].
However, for macroscopic systems it is possible to directly approximate the time evolution of the stochastic state variables by the chemical Langevin equation [ 10, 11], which reads (8) d x i (t ) = ∑ j = 1 M n i j a j (x (t ) ) + ∑ j = 1 M n i j a j (x (t ) ) d W j, i = 1,..., N when rewritten using the Wiener process [ 74] for easier numerical treatment.
The scientific concept of this program is to study the elemental technology in macroscopic system integration for advanced fusion blankets based on an understanding of the relevant mechanics at the microscopic level.
However, despite the progress there remains an enormous challenge in bridging the vast range of distances and time scales between de novo atomistic simulations and the quantitative continuum models for the macroscopic systems essential in industrial design and operations.
The results are expected to be particularly relevant in the analysis of the nonlinear dynamics of suspended beam micro- and nanoresonators, but are not restricted to these particular devices, being valid for similar macroscopic systems.
A still unsolved challenge for fully exploiting CNT superior mechanical properties for reinforcement of macroscopic systems is control of the interfacial interaction across multiple length scales to favor load transfer.
Finally, the collapse theories account in a completely satisfactory way for the classical behavior of macroscopic systems.
