Superconductivity and the Self Organisation of the Universe
New states can arise from far from equilibrium, possessing an extraordinary degree of order, whereby trillions of molecules coordinate their actions in space and time. Prigogine coined the term “dissipative structures” to describe them, since they result from the exchange of matter and energy between system and environment, together with the production of entropy (dissipation) by the system. The complex and mutually dependent processes leading to the formation of structures, collectively called “self organisation”…in such a universe, irreversible non-equilibrium thermodynamics allows for the possibility of self organisation leading to structures ranging from planets and galaxies to cells and organisations. R Highfield and P Coveney 2015.
According to Masser (2006), it would be appropriate to represent the Big Bang not as a single event, but as an on going process of gradual formation out of chaos. In other words the evolution of the universe is a continuous self organisation process that has led to its currently observed structure with a host of galaxies, galaxy clusters and planetary systems.
In some materials, the strong electron-electron correlations to other degrees of freedom with the complex many body quantum system lead to new, emergent properties that are controlled by a competition of fluctuation effects, characterised by phase transitions at critical temperature, where correlations lead to coordination with a macroscopic region – resulting in the breaking of a symmetry of the system.
Below the transition temperature, a new broken-symmetry ground state is found, which can possess a variety of novel, emergent properties that are macroscopically observed. In condensed-matter physics, the complex interaction of many degrees of freedom, such as electrons, ions and spins leads to the formation of properties such as superconductivity, magnetism, charge density waves and orbitally ordered states.
In current physics, from a theoretical perspective, insights from black hole physics and string theory indicate that our ‘macroscopic’ notions of spacetime and gravity are emergent from an underlying microscopic description in which they have no a priori meaning.
Self Organisation and Patterning
This posts further considers how the concept of self organisation might support an emergent universe. Particular consideration is giving to patterning and how this might inform our understanding of phase transitions.
Nonequilibrium patterns in open systems are ubiquitous in nature. A theoretical foundation that explains the basic features of a large class of patterns was given by Turing in the context of chemical reactions and the biological process of morphogenesis. These patterns can include stripes, hexagonal arrangement of spots, and superlattices (Y Lang 2006). Overall 7 patterns of reaction diffusion have been evidenced. N Tompkins 2014. Analogs of Turing patterns have also been studied in optical systems where diffusion of matter is replaced by diffraction of light.
Reaction diffusion type patterns can also be found in semiconductors (V Ardizzone 2015) and superconductors. Stripes formation occurs in type 1 superconducting film. In two gap superconductors, superconducting vortices accommodation themselves by forming stripes fluxed patterns. Physicists have also found that the bubble-like arrangement of magnetic domains in superconducting lead exhibits patterns that are very similar to everyday froths. In type II superconductor systems, a magnetic field can penetrate a sample in a tube-like configuration. The magnetic flux (superconducting vortices) arrange in the lattice with hexagonal symmetry. Competition between superconducting and non superconducting phases can result in a formation of a hexagonal pattern. (Y Holovatch 2015)
As in the case of reaction diffusion modelling – periodic oscillations may play a role in this. Applied magnetic field produce interesting effects in nanostructured superconductors e.g they may induce different types of periodic responses. A G Guiterrez 2014).
Vortices and Superconductors
“Vortices control the current carrying ability of all superconductors. At the same time, these objects can mimic cosmic strings, elucidating concepts that address fundamental features of the evolution of our universe…in a decreasing magnetic field, individual vortices sequentially detach from the giant vortex and eventually escape from the lead samples. Most importantly, the behavior of these vortices strictly obey the Abelian Higgs model of quantum field theory. I Lukanchuk 2015.
Vacuum superconductivity may have supported by sufficiently strong magnetic fields in the early universe, and the subsequent super-currents might have seeded the mysterious large-scale magnetic fields seen across the universe today. As a background of a very strong magnetic field a quantum vacuum may turn into a new phase characterized by anisotropic electromagnetic superconductivity. M N Chernodub 2012.
There are a number of materials e.g high temperature cuprates, that are beyond BCS theory, and it has been shown that the AdS/CFT correspondence can provide solvable models of strong coupling superconductivity Rong-Gen Cai 2015.
Reaction Diffusion and Superconductors
Perhaps the reason that reaction diffusion forms appear in superconductors is because they offer the best topology for conduction.
A universe arising through emergence could potentially generate superconducting channels through reaction-diffusion. A reaction diffusion type of process could also impose space-time, and provide the basis for holographic data. In holographic data storage technology, holographic data can be encoded onto a signal beam using a spatial light modulator. This translates electronic 0’s and 1’s into an optical checkboard pattern of light and dark pixels. A hologram is formed in the light sensitive storage medium at the point where a reference beam and signal beam intersect. Chemical reactions occur causing the light distribution to be recorded as a permanent polymerisation pattern.
Below is an image of superconducting disk and next to it is a computer generated reaction diffusion shape.
The Coupling of Quantum and Classical Chaos
In addition, the relationship between reaction diffusion patterning and superconducting may be related to the finding that a map of entanglement entropy of a superconducting qubit that, over time, comes to strongly resemble that of classical dynamics—the regions of entanglement in the quantum map resemble the regions of chaos on the classical map. The islands of low entanglement in the quantum map are located in the places of low chaos on the classical map. “And, it turns out that thermalization is the thing that connects chaos and entanglement. It turns out that they are actually the driving forces behind thermalization’. S Fernandez 2016.
Vortices and Emergence
Scientists have already observed self-replication in non-living systems. Vortices in turbulent fluids spontaneously replicate themselves by drawing energy from shear in the surrounding fluid. Theoretical models and simulations of microstructures that self-replicate have been presented. These clusters of specially coated microspheres dissipate energy by roping nearby spheres into forming identical clusters. Besides self-replication, greater structural organization is another means by which strongly driven systems ramp up their ability to dissipate energy.
Similar wave patterns to those found in the BZ or the Predator Prey model appear in many other reaction diffusions systems having the same dynamical behavior. For some values of the parameters, the BZ reaction and PP models also behave as excitable systems. The main feature of this kind of systems is the way in which they respond to perturbations. Typically there exists a threshold value such that if the perturbation goes above it the system reaches the fixed point only after a long excursion in the phase space… The threshold property is characteristic of cubic nonlinearities in the reaction term, as exemplified by the Fitzhugh-Nagumo (FN) equations. The propagation of the excitation through neighboring points, coupled diffusively, generates traveling pulses. In two dimensions, when a propagating pulse is broken at a point, it begins to rotate around the ends, producing spiral waves. However, the phenomenology can be much more complicated. For example, target patterns can also be formed in an extended excitable medium if the pulses are emitted periodically, and spiral waves can be formed by breaking target waves by stirring the medium, or by noise-induced effects. Massimo Cencini et al 2003. In the case of excitable bistable media, fronts can connect to each other, so that dissipative solitons or more complicated structures such as 3D rings or knots are created (A Liehr 2013).
Dynamics of quark hadron transition is one of the most important issues in relativistic heavy-ion collisions, as well as in the universe…..lattice results showed that the quark-hadron transition is not first order, rather it is most likely a cross-over for low chemical potential. This cross-over is believed to govern the dynamics of transition in relativistic heavy-ion collisions at high energies…..For the dynamics of the phase transition, the most important difference between a first order transition and a cross-over (or a continuous transition) is the presence of a phase boundary for the former case which separates the two phases. The transition for a first order case is completed by nucleation of bubbles which expand. The moving bubble walls (phase boundaries) lead to physical phenomena, such as non-trivial scattering of quarks, local heating, specific types of fluctuations, etc., which are qualitatively different from the case of cross-over or a continuous transition…It turns out that the presence of moving interfaces more generic, and not necessarily restricted to the case of first order transitions. Such situations routinely arise in the study of so called reaction-diffusion equations. P Bagchi – 2015.
Vortices in a flow have a significant effect on one dimensional front propagation. In particular, a moving vortex tends to pin and drag a front. If a chain of vortices oscillates periodically mode locking often occurs. Mode locking is often found in oscillating systems that are forced periodically by an external perturbation. If the amplitude of the perturbation is large enough, the natural oscillation of the system may change and lock to the external perturbation, with the two oscillating with frequencies that are rationally related. Reaction fronts are found to mode-lock for a wide range of frequencies, and the mode locking results in faceted fronts that line up along the general direction of the underlying vortex array. Self sustaining trigger waves are found composed of large scale spiral and spiral pair patterns, similar to the patterns in an RD (no flow) limit, but with significantly larger typical length and with clear anisotropy which reflects the vortex array. J. R. Boehmer and T. H. Solomon 2008.
Superconductivity, Magnetism and QCD
QCD implies color superconductivity of quark matter at high density.
One of the fundamental processes involved in nonequilibrium pattern formation is the spatial propagation of interfaces or fronts. Front propagation usually emerges when a local reaction dynamics interplays with diffusion in space of the reacting agents and has been observed in a wide range of physical, chemical, and biological systems. One of the most prominent models which displays propagating fronts is the Fisher-Kolmogorov-PetrovskyPiscounov (FKPP) equation. The FKPP equation can also potentially support quantum – classical correspondence and could be at the heart of visible matter formation.
This equation brings together:
- The propagation of unstable non linear wave fronts/population dynamics. Pulled fronts are extremely sensitive to noise in the leading edge. Fluctuations arise when the underlying physical substrate consists of discrete constituents interacting on a lattice (intrinsic noise), or when there are external environmental perturbations (extrinsic noise). P Bressloff. 2011.
- dynamo theory and the azimuthal magnetic field (which can be reduced to the FKPP equation). S Fedotov et al 2003. An important area of research in dynamo theory is the determination of the speed at which magnetic fronts propagate in a turbulent electrically conducting fluid. This problem is usually studied on the basis of a mean-field dynamo equation for a large scale magnetic field, and has been used to explore the formation of magnetic fields in galactic disks.
- If the classical treatment of the FKPP equation due to Freidlin is expanded to include the phenomenon of anisotropic diffusion with a finite velocity, in the long-time large-distance asymptotic limit the Hamiltonian dynamical system associated with the anisotropic reaction–diffusion equation has a structure identical to that of general relativity theory. The function determining the position of the reaction front and its speed is nothing else but the action functional for a particle in both gravitational and electromagnetic fields….. It is well known that the macroscale equations for turbulent heat/mass transport involve effective anisotropic transport processes with a finite velocity S Fedotov et al 2000
- The same FKPP (reaction diffusion) type of equation appears in various fields of statistical physics and, recently, in the domain of Quantum Chromodynamics (QCD), the interaction theory of quarks and gluons, where it models the evolution of the gluon momenta in the wave-function of a hadron or a nucleus when the energy increases..
- Higher order corrections to the Colour Glass Condensate evolution equations, include the BK and JIMWLK equations (the BK equation lies in the university class of the FKPP equation and correspondences to a spin glass phase of FKPP ). The correspondence between the BK and FKPP equations, clarifies the properties of saturation fronts in QCD in analogy with known properties of reaction–diffusion processes. A crucial property is the emergence of traveling waves.Reaction–diffusion processes exhibit an extreme sensitivity to particle number fluctuations, generated by gluon splittings, which produce correlations among pairs of gluons. F Gleis 2010
- In addition the sFKPP equation (which could provide insights into impact parameters dependent fluctuations in high energy QCD beyond the BK equation. For traveling waves in the diffusive approximation of the QCD evolution equations, the traveling waves go to zero before the transition point of the sFKPP analoguous equation due to a shift of the speed (at least for the leading order kernel in αs). The maximal noise-strength occurs in the region related by duality with a coalescence, which is accessible to exact noisy traveling wave solutions….. For large enough QCD fudge factor, it may be reached even in the perturbative QCD regime. Otherwise, it may indicate the slowing down of rapidity evolution expected from the nonperturbative QCD regime…..The dual particle process becomes the diffusion-controlled reaction in the strong noise (or weak growth) limit of the stochastic FKPP equation….Front motion in higher spatial dimensions is of great interest for a variety of growth processes. In higher spatial dimensions even an initially smooth or flat front can develop structure in the transverse direction(s) and fluctuations may play an even more dramatic role in the dynamics. . Robi Peschanski 2008. Charles R. Doering.
- It has also been recognised that there is a strong similarity between the FKPP, BK and the Banfi, Marchesini, and Smye (BMS) evolution equation for non-global jet observables that exhibits a remarkable analogy with the BK equation used in the small x context. It has been suggested that these are essentially identical equations that can be viewed either in terms of the probability, or amplitude, of something not happening or in terms of the nonlinear terms setting unitarity limits Giuseppe Marchesini 2015. The analogy can be used to generalize the former beyond the leading Nc approximation. The result shows striking analogy with the JIMWLK equation describing the small x evolution of the color glass condensate. H Weigert 2004.
Collisions through the Large Hadron Collider have resulted in a form of matter called a colour glass condensate (CGC), which is a liquid like wave of gluons. The vast bulk of visible matter is an emergent phenomena arising from the dynamics of the QCD vacuum and the interactions of the fundamental quark and gluon constituents of QCD).
The CGC RG equations indicate that – at fixed impact parameter – a proton and heavy nucleus become indistinguishable at high energy. The physics of saturated gluons is universal and independent of the details of the fragmentation region. The universal dynamics have a correspondence with the reaction-diffusion processes in statistical physics. In particular, it may lie in a spin glass universality class. F Gleis 2010 . The CGC is recognised as having properties similar to Bose Condensates and spin glasses.
A Self Organising Universe Using Reaction Diffusion
The following brings together various findings on how the emergence of the universe might resemble reaction-diffusion systems.
Star and Galaxy Formation
The spectra coming from accretion disks suggests that the formation of stars and galaxies is driven by a feedback process specific for stable non equilibrium systems… Analysis of a model of star formation process system, shows that prolonged stationary star formation in localised area and repetitive bursting star formation events can be understood as different behaviour models of galactic dissipative structures. Young Stellar associates with their H11 regions and molecular clouds are manifestations of the ordered distribution of matter participating in the star formation process G Bodifee 1986
It has been suggested that galaxies are dissipative systems, and the spatial and time structure of the interstellar medium and young stars is governed by reaction-diffusion equations JV Feitzinger – 1985, and galactic disks are reaction-diffusion systems. Lee Smolin 1996 and Nozakura, T. & Ikeuchi, S 1988.
Interstellar dust emitted from the atmosphere of earlier condensed stars enhances the probability that the condense of new stars, whereas the heating of interstellar dust by developed stars inhibits the occurance of further condensate processes. This is thought to explain the formation of spiral galaxies of the Sc type (A Liehr 2013).
Shu noticed, that a certain degree of spiral structure must be present in every mode of oscillation which contain stars in resonance. Stars, unlike gas, can resonate with the oscillating gravity field without any continual shattering due to collisions. (Shu 1970a, b; Lin & Shu 1971). I I Pasha 2004. Also see A Toomre 1969.
The coherent galactic oscillations of star formation self-organized in spiral waves, previously detected by numerical simulations (Seiden, Schulman, Feitzinger, 1982) could analytically described by the concept of a limit cycle. Analytical work on self-propagating stochastic star formation was also done by Kaufman (1979), Shore (1981, 1982) and Cowie and Rybicki (1982). J. V. Feitzinger
Kondoh, et al., applied nonlinear density wave theory to the spiral structure of galaxies. Their spiral arms are characterized by a soliton and explained as a pattern of a propagating nonlinear density wave….Luo, et al., discussed the spiral magnetohydrodynamic density waves with a tangential shear force and the stability of density waves. discussed also the resonantly excited nonlinear density waves in disk systems . Cartin, et al (1999 and 2001), applied the spiral galaxy as a self-regulated system far from equilibrium to look at a reaction-diffusion model for the formation of spiral structures in certain types of galaxies. YF Chang – 2009
Evidence suggests that the superficially chaotic process of galaxy formation is underlined by a temporal self-organization up to at least one gigayear. In view of this it is tempting to suggest that, given the known existence of spatial fractals (such as the power-law two-point function of galaxies), there is a joint spatio-temporal self-organization in galaxy formation….This spatial regularity is not inherited from the linear power spectrum but must be a result of cooperation between nonlinear evolution and galaxy formation. In self-gravitating systems, such as galaxies, the temporal and spatial structures may be related. R Cen 2014.
Simulations of the gas flow in a variety of two-dimensional barred spiral galaxies have shown that vortices in the gas appear. It has been suggested that vortices may promote the formation of planetesimals (Bodo 2007). It is well established that in self gravitating protoplanetary discs, vortices are dynamically coupled with density waves due to the disc’s differential rotation, or shear. On the other hand, density waves play a central role in the theory of self-gravitating discs and their coupling with vortices implies that the latter can also be subject to self-gravity effects, thus taking active part in defining overall dynamics of self-gravitating discs G. R. Mamatsashvili1 2013.
Investigating the relativistic self-interacting gas in the field of an external pp gravitational wave, A B Balakin 2003 found features that are similar to those which one encounters in phenomena of self-organization in many-particle systems.
The black-hole-like phenomena might take place in the nonlinear Schrodinger type equation, where black holes of a constant curvature spacetime have been related to the soliton-like solutions for dissipative version of the NLS in the form of the Reaction-Diffusion system. These solutions called dissipatons, characterize completely the black hole horizon, the Hawking temperature and the causal structure. Ok Pashaev – 2001
One of the basic problems in the theory of pattern formation is, even in the presence of the instability, how do initially disordered structures emerging from small random fluctuations give rise to regular and highly precise structures in the course of development? It is well known that uncontrolled growth of patterns usually produces an array of topological defects that only slowly disappear through mutual repulsion or attraction and annihilation. However, specific feedback control mechanisms can significantly accelerate this process. LS Tsimring – 2014. A clock system could provide such a feedback mechanism.
At biological clock level, oscillations can be modelled as phase transitions and reaction diffusion, raising questions of whether biology is reflecting the wider universe. Clock rhythms have been modelled as (a) limit cycles, (b) periodic orbits, (c) a temporal organisation that appears beyond a critical point of instability of a non-equilibrium steady state, (d) a sustained oscillations of the limited cycle can be viewed as temporary dissipative structures, a kind of phase transition of bifurcation or self synchronisation transition (Y Kuramoto 1984), and reaction and reaction-diffusion
These types of interactions might lead to the creation of structures at different scales at a cosmic level. Cyclic or oscillating models have been suggested for the universe that use infinite or self sustaining cycles. The idea of an oscillatory universe has been mooted for decades e.g Tolman, Graham et al 2011 and 2014 A T. Mithani 2015.
Cosmic Clocks and the Creation of Memory – is the Universe Made Up of Aligned Clocks?
Clock rhythms are found throughout the cosmos.
Millisecond pulsars are nature’s most precise clocks, with long-term, sub-microsecond stability that rivals human-made atomic clocks.
The CoRoT and Kepler space missions have detected oscillations in hundreds of Sun-like stars and thousands of field red-giant stars. These stars could potentially be used as as accurate clocks and rulers for Galactic studies.
It has also been suggested that the solar cycle is timed by a clock. Dicke (1978) has argued that the phase of the solar cycle appears to be coupled to an internal clock: shorter cycles are usually followed by longer ones, as if the Sun remembers the correct phase. The data set is really too short to demonstrate the presence of a phase memory, but phase and amplitude of the cycle are strongly correlated for 300 yr or more. It is shown that this memory effect can be explained by mean field theory in terms of fluctuations in α, which induce coherent changes in the frequency and amplitude of a dynamo wave. P Hoyng – 1996
Magnetic wave components appearing in pairs, originating in two different layers in the Sun’s interior. They both have a frequency of approximately 11 years, although this frequency is slightly different, and they are offset in time. Over the cycle, the waves fluctuate between the northern and southern hemispheres of the Sun.
Yeates et al. (2008) have shown that the dynamical memory of the solar dynamo mechanism governs predictability and this memory is different for advection- and diffusion-dominated solar convection zones. By utilizing stochastically forced, kinematic dynamo simulations, it has been demonstrated that the inclusion of downward turbulent pumping of magnetic flux reduces the memory of both advection- and diffusion-dominated solar dynamos to only one cycle; stronger pumping degrades this memory further. Bidya Binay Karak et al 2012.
Nonlinear systems that have periodic orbits include circadian rhythms and when it occurs in constant environment conditions, periodic behaviour provides the clearest sign that the chemical system operates beyond a point of non-equilibrium instability.
Periodic orbits play an important role in celestial mechanics. An orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers.
In additional period orbits can have a role in quantum tunnelling. The principle of regularisation of quantum tunnelling by chaos can be understood by using a prototypical system which consists of two symmetrical cavities connected by a one dimensional potential barrier along the line of symmetry. Choosing the geometry of the cavity such that the classical dynamics become chaotic can greatly enhance and regularise quantum tunnelling… when the potential barrier is infinite, each cavity is a close system with an infinite set of eigenenergies and eigenstates. Many eigenstates are concentrated on classical periodic orbits forming quantum scars. For a classically integrable cavity, some stable or marginally stable periodic orbits can persist even when the potential barrier become finite, so that each cavity system is effectively a quantum system. Many surviving eigenstates correspond to classical periodic orbits whose trajectories do not encounter the potential barriers, generating extremely low tunnelling rates, even when the energy is comparable with, or larger, than the height of the potential barrier. The eigenstates corresponding to classical orbits that interact with the potential barrier however, can lead to relatively strong tunnelling. Ying Cheng Lai 2012.
Directed Percolation and Galaxies (Phase Transition)
It has been suggested that spiral galaxies arises from a percolation phase transition that underlies the phenomenon of propagating star formation. According to this view, the appearance of spiral arms is a consequence of the differential rotation of the galaxy and the characteristic divergence of correlation lengths for continuous phase transitions. Other structural properties of spiral galaxies, such as the distribution of the gaseous components and the luminosity, arise directly from a feedback mechanism that pins the star formation rate close to the critical point of the phase transition.
Galaxies may have the ingredients needed for star formation-gas, proper temperatures, and densities-but, if left alone, nothing happens. However, if a shock wave from a supernova passes through the gas, there is a good chance a molecular cloud will form so that stars may condense…A cell having a new cluster is allowed to initiate activity in its neighbors as before. However, the probability for molecular cloud formation is now taken as proportional to the density of atomic hydrogen since it is from this gas that the molecular clouds are formed. Once the gas has become a molecular cloud, it is unavailable for the creation of new clouds. The molecular clouds begin to form stars, the energetic processes of which eventually destroy the cloud . A small percentage of the cloud is condensed into stars, but the rest of the cloud is dispersed into atomic hydrogen, allowing the process to repeat. This process leads to the feedback mechanism, which is responsible for keeping the galaxy near the critical point of the percolation phase transition. L S Schulman 2012
Clustering – Cosmic Lattices
An analysis of thousands of galaxies finds that they are strung like pearls on a necklace, even on relatively small scales. Elmo Tempel and his student Maarja Bussov at Tartu Observatory in Estonia and their colleagues have found a small-scale pattern in cosmic structure. The pair wrote an algorithm to identify the ones that lie within 1.5 million light years of a filament in the large-scale cosmic web. That turned up 68,373 galaxies and 35,158 groups residing within relatively narrow cylinders. When they compared the distances between those individual galaxies and groups, they found these cosmic objects tended to lie either about 30 million light years, or less frequently, about 18 million light years from each other. New Scientist 21 Nov 2014
When looking at the distribution of galaxies on scales of billions of light-years, astronomers have found that galaxies aren’t evenly distributed: They form a web of filaments and clump around huge galaxy-scarce voids. This arrangement of material is known as the large-scale structure. The large scale organization of the universe comes from different sources: catalogues of galaxy redshifts; absorption lines in quasar spectra; the cosmic background radiation; studies of the distribution of hot ionized gas in clusters of galaxies; measurements of large scale peculiar velocities
Large scale cosmic structures include superclusters, galaxy filaments and large quasar groups (LQG’s). It has been found that the rotation axes of the central supermassive black holes in a sample of quasars are parallel to each other over distances of billions of light-years. Findings indicate that the rotation axes of quasars tend to be parallel to the large-scale structures that they inhabit. That means that if the quasars are in a long filament, then the spins of their central black holes will point along the filament. According estimates, there’s only a one percent probability that these alignments are simply the result of chance.
Further Questions: A Holographic Universe
Is the holographic universe based on diffusion reaction memory i.e memory can be stored in:
- reaction diffusion like systems (such systems can create chemical memory).
- interference when waves collide. This also offers the potential for the recording of holographic information.
- Vortices in which the solitons could be stored
- solitons (as quibits)
This post have focused on self organisation at cosmic level, however a mechanism for generating spontaneous fractal patterns (spatial structure) on many scales means that this approach could be used at any scale – potentially creating an infinite universe/open system e.g Dissipative processes can also be used to explore the formation of biological matter e.g J Tabony 1999. N Glade – 2004 , J. D. Goddard 2014 however this is not explored in depth within this posting. This also reflects self organised criticality theory.
2015-2016. This article merely joins up other peoples work into an overall system. These works have been referenced so it is clear that others have provided the individual pieces of evidence that have been used to shape a specific systems approach.