It is mentioned in page 166, of the book Experimental techniques in low-temperature physics by Guy Kendall White, Philip J. Meeson

"Most properties of materials are categorised in terms of the phonon system, the electron system and the spin system (i.e. the nuclear or electronic magnetic moments)."

Three subsystems that make up for most of the properties of materials, the physical and chemical properties, matter organised into the macroscopic system of the physical world, determine how the physical world behaves.

"These different subsystems, although intimately mixed together in any one material, can be separated in the imagination and analysed as independent systems."

Determine physical behaviour as the embedded sub-systems are intimately mixed, which brings into mind attractors and synchronization, attractors achieved by the ever so slight tweaking of relevant parameters, the electron-phonon interactions synchronized, by even the transient fluctuation enhancement referred to as peculiar to macroscopic systems, triggered by the exposure to additional parametres brought in, by the other embedded sub-systems.

These three subsystems separated and analysed independently? Their connections severed, each one imagined on itself? An approach which can be followed on all subsystems, lower-dimensional systems embedded in higher dimensional systems, the macroscopic systems? Understanding the relationships between embedded and embedding systems, all systems in all realms, portable via the self-similarity principle of chaos.

And all the while, each sub-system being dynamic, ever so 'touchy' to any changes introduced by either sub-system, via the electron-phonon interaction.

"Consider for example the separation of the phonon system from the electron system in a metal. This proceeds from the knowledge that the phonon system is 'heavy' arising from the motion of ions in the lattice whilst electrons are light. The mass difference (and differing statistics) influences the available energy levels in each system and ultimately limits the flow of momentum and energy between the two systems."

The phonon system 'heavy', the electron system 'light' a matter of size. The phonon system arises from the motion of ions, the electron system from electrons. This mass difference limits the flow of momentum and energy between the two systems, practically isolated from one another, each system with its own agent, phonon electron, interactions between their agents determine their behaviour.

Accordingly, it can be assumed that any introduction of extra agents, like nanoparticles upsets this balance, the flow of momentum and energy, between the two systems, as the mass of the nanoparticles being similar in size, could introduce novel interactions, leading to the emergence of properties, alien to the subsystems. The observation of novel chemical and physical properties in nanoparticles, when introduced into the nanoscales, indicative of this process.

"This 'adiabatic' or Born-Oppenheimer approximation regards the two subsystems as separate but interacting via an electron-phonon interaction."

Embedded sub-systems separate but interacting via an electron-phonon interaction? Interacting as sub-systems? Preserving their integrity, their independence of a sort. An adiabatic boundary, a barrier that prevents the direct flow of energy and momentum from an embedded system to another or even the embedding macroscopic system apart from the electron-phonon interaction, each sub-system the 'whole' by itself and as a whole interacts.

Embedded sub-systems adiabatic. Embedding systems, by virtue of being embedded themselves, sub-systems to higher dimensional systems, adiabatic too. All systems adiabatic. Biological, emotional, psychological, social systems adiabatic? Understanding systems by using the adiabatic system property?

## Tuesday, 25 August 2009

## Thursday, 20 August 2009

### Low-dimensional systems embedded in macroscopic systems. Enhanced fluctuations?

I feel I have stumbled once again onto something which will augment my knowledge, my perspective. It will drag me away from my current endeavours to bring me back enhanced and ready for new challenges.

Writing unhindered by any considerations deemed irrelevant for my pursuits. Enough introduction, back to the point.

Šil'nikov phenomena, are referred to, in this paper titled 'Poincaré versus Boltzmann in Šil'nikov phenomena'. It was the climax of my google searching, following terms like, subordinate Šil'nikov bifurcations, Sil'nikov-saddle-node interaction, Šil'nikov phenomena, Sil'nikov chaos.

Analyse the terms and deepen my knowledge by examining the effects, the mentioned concepts had on the knowledge already held in my reverberated neural nets and in the process ascend whatever fragments are there, and emerge in new knowledge, new ways of looking at things.

In the abstract of the paper, 'Poincaré versus Boltzmann in Šil'nikov phenomena', it mentions

"By suitable adjustment of the control parameters in a CO2 laser with feedback we show experimental evidence of Sil'nikov chaos, ..."

... control parameters, as in parameters and variables. Parameters, of which their values are considered if not unchanged, changing within a very narrow limiting and limited range, as in any fractal-making program, what you tweak ever so slightly, to get all kinds, versions of the initial fractal. Suitably adjusting the parameters, deemed as controlling in the CO2 laser. Feedback providing the iteration part, the recursiveness in function, for chaos coming.

Experimental evidence of Sil'nikov chaos? What kind of chaos is this?

It further mentions,

".. characterized by intensity pulses almost equal in shape, but irregularly separated in time."

Intensity pulses irregularly separated in time, their experimental setup signature of chaos. Irregularity signifying chaos.

"The times of return to a Poincare section are statistically spread,.."

Poincare sections traversing its flow in time, incisions right through its fractal space, revealed statistically spread times of return, the order hidden amidst chaos. Chaos generating order.

Chaos as described in mathematics, measuring fluctuations in the intensity of forces, stresses, pressures plotted into graphs or even plain mathematical functions, self-referential, iterated loosing themselves into chaos. Translated into all kinds of forces exhibited in all systems possible. Physical, mental, emotional, psychological, social, spiritual systems analysed in the very same way as mathematical chaos.

"... however their iteration map is one-dimensional and in close agreement with that arising from Sil'nikov theory."

The map of the iterated points is one-dimensional? All falling onto a single line? Or the map, being a function and the one-dimensional referred to, its mathematical property. And all this, .. 'in close agreement with that arising from Sil'nikov theory'.

"Thus, the iteration map of the time intervals becomes the most appropriate indicator of this chaos."

An appropriate indicator of this chaos? Sil'nikov chaos. The one-dimensional iteration map of the time intervals?

"The residual width of the experimentally measured maps is due to a transient fluctuation enhancement peculiar to macroscopic systems, which is absent in low-dimensional chaotic dynamics."

Macroscopic systems distinct from low-dimensional chaotic dynamics? Underlying systems different than systems above? Chaotic dynamics of underlying systems, systems embedded within systems above, low-dimensional as embedded systems are bound to have less dimensions, than the system they are embedded in, embedding system which includes more than one low-dimensional systems.

The transient fluctuation enhancement peculiar to macroscopic systems? Due to the influence of additional parametres a low-dimensional system is exposed to, by the other low-dimensional system(s) that together comprise the macroscopic system they are embedded in?

Each low-dimensional system compensating for the introduced parameters, tweaked. Embedded low-dimensional systems integrated and together now determine the properties, attributes, the behaviour of the macroscopic system.

My very own thoughts developing in a similar process. All systems possible, physical psychological, social developing likewise.

Writing unhindered by any considerations deemed irrelevant for my pursuits. Enough introduction, back to the point.

Šil'nikov phenomena, are referred to, in this paper titled 'Poincaré versus Boltzmann in Šil'nikov phenomena'. It was the climax of my google searching, following terms like, subordinate Šil'nikov bifurcations, Sil'nikov-saddle-node interaction, Šil'nikov phenomena, Sil'nikov chaos.

Analyse the terms and deepen my knowledge by examining the effects, the mentioned concepts had on the knowledge already held in my reverberated neural nets and in the process ascend whatever fragments are there, and emerge in new knowledge, new ways of looking at things.

In the abstract of the paper, 'Poincaré versus Boltzmann in Šil'nikov phenomena', it mentions

"By suitable adjustment of the control parameters in a CO2 laser with feedback we show experimental evidence of Sil'nikov chaos, ..."

... control parameters, as in parameters and variables. Parameters, of which their values are considered if not unchanged, changing within a very narrow limiting and limited range, as in any fractal-making program, what you tweak ever so slightly, to get all kinds, versions of the initial fractal. Suitably adjusting the parameters, deemed as controlling in the CO2 laser. Feedback providing the iteration part, the recursiveness in function, for chaos coming.

Experimental evidence of Sil'nikov chaos? What kind of chaos is this?

It further mentions,

".. characterized by intensity pulses almost equal in shape, but irregularly separated in time."

Intensity pulses irregularly separated in time, their experimental setup signature of chaos. Irregularity signifying chaos.

"The times of return to a Poincare section are statistically spread,.."

Poincare sections traversing its flow in time, incisions right through its fractal space, revealed statistically spread times of return, the order hidden amidst chaos. Chaos generating order.

Chaos as described in mathematics, measuring fluctuations in the intensity of forces, stresses, pressures plotted into graphs or even plain mathematical functions, self-referential, iterated loosing themselves into chaos. Translated into all kinds of forces exhibited in all systems possible. Physical, mental, emotional, psychological, social, spiritual systems analysed in the very same way as mathematical chaos.

"... however their iteration map is one-dimensional and in close agreement with that arising from Sil'nikov theory."

The map of the iterated points is one-dimensional? All falling onto a single line? Or the map, being a function and the one-dimensional referred to, its mathematical property. And all this, .. 'in close agreement with that arising from Sil'nikov theory'.

"Thus, the iteration map of the time intervals becomes the most appropriate indicator of this chaos."

An appropriate indicator of this chaos? Sil'nikov chaos. The one-dimensional iteration map of the time intervals?

"The residual width of the experimentally measured maps is due to a transient fluctuation enhancement peculiar to macroscopic systems, which is absent in low-dimensional chaotic dynamics."

Macroscopic systems distinct from low-dimensional chaotic dynamics? Underlying systems different than systems above? Chaotic dynamics of underlying systems, systems embedded within systems above, low-dimensional as embedded systems are bound to have less dimensions, than the system they are embedded in, embedding system which includes more than one low-dimensional systems.

The transient fluctuation enhancement peculiar to macroscopic systems? Due to the influence of additional parametres a low-dimensional system is exposed to, by the other low-dimensional system(s) that together comprise the macroscopic system they are embedded in?

Each low-dimensional system compensating for the introduced parameters, tweaked. Embedded low-dimensional systems integrated and together now determine the properties, attributes, the behaviour of the macroscopic system.

My very own thoughts developing in a similar process. All systems possible, physical psychological, social developing likewise.

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