Bottlenecks regularity

T. Komatsuzaki and R. S. Berry, Regularity in chaotic reaction paths. II. Ar6. Energy dependence and visualization of the reaction bottleneck, Phys. Chem. Chem. Phys. 1, 1387 (1999). 

A bottleneck in all membrane processes, applied in practice, is fouling and scaling of the membranes. These processes cause a decrease in water flux through the membrane and a decrease in retention. Much attention is paid, especially in case of nanofiltration and hyperfiltration, to prevent fouling of the membrane by an intensive pretreatment and the regular removal of fouling and scaling layers by means of mechanical, physical or chemical treatment. 

Traders lacked regular supplies of good quality products and that the scale of natmal products operations may be a bottleneck as were the lack of information, lack of capital, low product quality and assurance mechanisms, difficulty in accessing financial credit and loans at reasonable rates, and poor facilities and processing equipment, and little historical investment into this sector. Furthermore, they reported from their survey of the traders themselves that the domestic markets of wholesalers and retailers are largely at low levels of commercialization in general traders have limited technical knowledge about natural products, and limited capital to expand their businesses and exploit... 

Some of the stable states are clearly regular. These include some extreme motion adiabatic states, discussed previously, that have no direct coupling to the doorway channel. In order to decay, such states must undergo multiple quantum transitions (often as many as 10), until they diffuse to the doorway channel. Figures 21 and 22 show that many of the adiabatic states are very resistant to diffusion and serve as bottlenecks for dissociation. 

The existence of Arnold diffusion is irrelevant to the properties of separatrix manifolds, which still mediate the transport of chaotic trajectories within the regions of phase space they control. However, if Arnold diffusion is present in a given multidimensional system, the possibility exists for chaotic motion initially trapped between two nonreactive (trapped) KAM layers to eventually become reactive. This would presumably manifest itself as an apparent bottleneck to the rate of population decay, as chaotic trajectories slowly leak out from the region occupied by regular KAM surfaces into the portion of phase space more directly accessible to the hypercylinders. However, transport via the Arnold diffusion mechanism typically manifests itself on time scales much larger than those that we observe in numerical simulations (Arnold diffusion usually occurs on the order of thousands of mappings, or vibrational periods), and so it seems improbable that this effect would be observed in a typical reaction dynamics simulation. It would be interesting to characterize the effect of Arnold diffusion in realistic molecular models. 

Instrumentation tools for detecting memory leaks, performance bottlenecks and soft-deadlocks are also not usually considered to be formal verification tools (since it is hard to define exact formal properties which are being verified by the non-exhaustive nature of these tools). They are also rarely utilized on regular basis as part of the continuous integration process. But again, it might be helpful to just mention them in the big picture. 

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