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En selv-organiserende planet

Mye av kompleksiteten som finnes i levende organismer og i ikke-levende systemer kan beskrives av fysiske og kjemiske lover. Men er det mulig å finne fellestrekk og mekanismer som kan gi informasjon om systemer av så forskjellig art som bakterier, været neste uke, og børssvingninger?

Selv-organisering beskriver utviklingen av en mønsteraktig fordeling av stoff og energi i et system, uten at denne fordelingen blir styrt av eksterne forhold. På en måte så bryter selv-organisering den vanlige oppfatningen av at alt påvirkes av ytre forhold. Resultatet av selv-organisering på en planet som Jorden er fantastiske mønstre som varierer både i rom, tid, og skala. Mønstre som oppstår i naturen kan vise overraskende regelmessighet, men kan også være uforutsigbare og kaotiske.

Naturlige systemer forandres med tid i forhold til hvordan omgivelsene forandres. Dynamikken til slike systemer kan beskrives matematisk (differensial-likninger), og utviklingen av teorier som beskriver slike systemer var en av de store bragdene i fysikk på 1900-tallet. Disse systemer er ikke i likevekt, og har egenskaper som kan beskrives som komplekse og ustabile. Med utgangspunkt i to nesten identiske tilstander, kan systemet utvikle seg helt forskjellig med tid. Denne følsomheten for utvikling med tid er bakgrunnen for vanskelighetene med å forutsi været, jordskjelv, og økonomiske svingninger.

I denne artikkelen kan du lese om forskjellige typer av selv-oraniserte systemer, og hvordan disse kan forstås ved hjelp av fysiske og kjemiske lover. Eksemplene varierer fra fysikk og geografi, til økonomi og trafikksystemer.

Resten av artikkelen er på Engelsk:

What is Self-Organization ?
There are many dramatic examples wherein spatial or temporal patterns of mass and energy arise without having been imposed by the surroundings. The heart beats with a cyclicity unrelated to any periodic disturbance imposed on the living system by its surroundings. Animal coat patterns, mineralization banding in rocks and regular arrays of sand dunes are examples of spatial patterns that emerge without external templates. Delineating the mechanisms underlying such self-generated patterns is the key to understanding the origin of the complexity manifested in natural environments. A self-organized pattern breaks the symmetry imposed by the surroundings on the system. For example, a regularly beating heart can reside in an environment that is time-independent; the heartbeat breaks the monotony (time invariance) of the surroundings.

The classic example of spatial self-organization is Bénard cellular convection, named after of a French scientist who studied this problem. It arises when a layer of fluid is heated from below. Assume that the temperature at the top of the layer is constant and that at the bottom is a higher constant value. If the temperature difference imposed across the horizontal layer is small, then at a fixed depth, the temperature in the layer is unchanging in the horizontal direction; the system reflects the translational invariance of the surroundings in the horizontal direction. If the temperature difference between the bottom and the top increases sufficiently, the fluid near the bottom can become lighter than that at the top. Because of gravitation forces, such a system is so top-heavy that fluid tends to overturn, i.e., the denser, cooler fluid at the top tends to fall to the bottom, displacing the hotter, lighter fluid there. In this state, a pattern of alternating up- and down-drafts emerges spontaneously. This pattern breaks the monotony of the constant temperature at the bottom of the layer and the (lower) constant temperature at the top. Thus, Bénard patterns self-organize.

Bénard convection cells arising in a fluid layer heated from below. Energy dissipation occurs through convection in hexagonal-shaped cells. The cell containing the liquid is several centimeters wide.

Convection lines in the fluid in a cross-section of the Bénard experiment.

In the example cited above, self-organization results in "dissipative structure"; such structures require a continuous exchange of energy and/or matter between the surroundings and the system. These structures are thus sustained only when a system is sufficiently far from thermodynamic equilibrium. In this example, thermodynamic equilibrium corresponds to an immobile fluid with temperature constant everywhere. From these beginnings, the study of self-organization and far from equilibrium systems has expanded into many fields including physics, chemistry, biology, geology, sociology and economics.

A few general principles guide in the search for self-organization phenomena that occurs dissipative energy conditions. Dissipative structures only exist when the system is maintained sufficiently far from equilibrium. They correspond to a type of coherent behaviour and, they are not a property of an individual atom, molecule or their lattice arrangement. For example, when a sand dune moves across a desert, the grains in the dune are continually being replaced by other grains. Thus, the dune is not a property of any set of grains but rather a property of the interaction of wind and sand grains. To develop or sustain a dissipative structure, a system must be maintained sufficiently far from equilibrium. Thus, the system must be fed by a continuous influx of energy and reactants and purged of product chemical species and heat.

Self-Organization and the Earth
Self-organization takes place in a wide range of systems. Spiral patterns exist on time scales from seconds to billions of years and on length scales from microns (DNA molecules) to light years (galaxies). If there are underlying universal principles, they must transcend much of the details of the physics and chemistry of these systems. Some of the simplest phenomena are described below.

The Length of Coastlines
When systems of many degrees of freedom are driven very far from equilibrium, one might expect that so many dissipative structures are available to the system that a "crisis" of uncertainty is created. Such a system fluctuates among these behaviours and thereby displays an overall behaviour that is overwhelmingly complex and seemingly unpredictable. The question arises as to what, if anything, one can do to characterize these self-organized states. Fractals and self-organized criticality are promising concepts developed since 1960 that have led to the characterization of such systems.

Fractals are objects with scaling properties and whose structure persists at all levels of magnification. Fractals were first conceived of in the context of measuring the length of shorelines. It is found that the measurement of a coastline depends on the refinement of the measurement device. As the latter increases, one accounts for more and more small-scale features and hence the measured shore-length increases. These concepts have been greatly refined due to the work of Benoît Mandelbrot who introduced the term fractal. Mandelbrot and later workers showed that the apparent divergence of shoreline net length with measurement refinement could be interpreted in terms of the dimension of the fractal. The area of a smooth object can be related to the square of its overall size. In contrast, for a fractal surface, its area is related to its overall size by a power greater than two. This power is an example of the fractal dimension of an object. Such concepts help to rationalize large sets of results covering a wide range of scales and are found in many scientific areas.

Avalanches and Earthquakes
In many complex systems, there is a large number of subsystems whose individual dynamics are relatively simple. However, when these subsystems are strongly coupled, their dynamics can be complex and analysed in the context of the so-called theory of self-organized criticality.
br> An experiment on the stability of a growing sand pile can be carried out to illustrate the notion of self-organized criticality. In this experiment, a sand pile is created by adding grains and waiting for the stabilization of the pile before adding new grains. As the pile grows, sand grains begin to slide off the edges of the base. When an additional sand grain is added, an avalanche whose size is not predictable may occur. The number of avalanches of a given size follows a simple distribution relating the frequencies of avalanches to their size (many tiny avalanches and few big ones).

The most striking feature of this self-organized state is its lack of characteristic length and time scales. As in the case of the fractal, no particular avalanche size stands out from any others. Remarkably, in this critical self-organized state, two avalanches are equally likely to act together, whether or not they occur close to each in space.

Natural examples of self-organized criticality include earthquakes, landslides and snow avalanches. The general theme is that, while each of the many degrees of freedom (or grain of sand for the avalanche) has a small response when driven independently, the coupled system can exhibit dramatic avalanche-like behaviour, manifesting a coherent behaviour where the many individual responses are correlated on a long range. Critical dynamics properties are not the consequence of the physical nature of the individual coupling but more the result of the statistical characteristics of their organization and its large-scale consequences.

Sand pile experiment: Sand is added at a constant rate and the total weight of the sand pile is recorded as a function of time. b-c) Resultant time dependence of the total mass of sand. The chaotic avalanche dynamics is expressed on all time scales.

Self-Organization at the Planet scale
Natural environments for which one can expect self-organization to emerge should have the properties of dissipative systems through which energy or matter flow continuously. At the scale of the earth, large-scale transfers are known promoting the conditions for the formation of complexity. The earth as a whole can also be considered as a dissipative system as it receives energy from its internal layers and from the sun. This energy is transformed into heat and released into space through an infrared radiation. This cycle of energy drives most of the self-organized processes at the earth surface, including life.

The earth can be viewed as a dissipative system driven far from equilibrium by its internal heat and by the sun's radiation. Energy dissipates through infrared radiation in space

As suggested in the experiment with the fluid convection cells, systems in contact with both an energy source and a heat sink can support dissipative structure. Such situations commonly occur on the earth where vast amounts of energy are continually invading the interior and outer surfaces of the crust (solar heat, volcanoes, ...). Life exists also as forms of dissipative structure; organisms cease to function unless they can consume nutrients and expel waste. In this way, life is continuously out of equilibrium, organized around the energy that constantly streams from the sun. However, viruses, bacteria and even mammal embryos can stay frozen indefinitely under proper conditions. This latter state of suspended animation is only a way of slowing the inevitable kinetics of their thermal decomposition. Like glasses or other metastable phases, life in such states will eventually revert to lower energy substances such as water or carbon dioxide. Nonetheless, one is struck by the stability that allows for long-time inanimate states of life.

Much has been made to explain the unique circumstances that allow life to exist on earth. Life requires the great richness of molecular configurations that underlie its structures and the memory needed for sufficient evolutionary experimentation over geological time scales. This implies limitations on planet thermal regime, size and elemental diversity. Planet size plays a key role: low gravity does not retain fluids and thus cannot sustain the reactive chemical environment they supply. Excessive gravity, on the other hand, destroys structure. If a planet is too hot, the self-organization of molecules and crystals becomes rapidly disrupted by thermal disturbances. If it is too cold, the time scale for molecular (genetic) experimentation is too long. Thus, the genesis and evolution of life can only take place on a planet of moderate temperature.

Thermal moderation also is necessary for the coexistence of the three essential phases of matter-solid, liquid and gas. Solids (and similarly, macromolecules) allow for the memory of spatial configurations of matter that adds continuity to the evolution of organisms. Liquids and gases provide a rapidly fluctuating molecular environment that promotes chemical change and the resulting creation of diversity. It is the balance of memory and change that underscores continual evolution to states of greater and greater complexity.

Society Organization
The same physical principles that describe inanimate systems can be applied to understand some behaviours of society. A classic example of self-organized population oscillations is the predator-prey system. The prey population increases due to reproduction fostered by available food resources and decreases either due to predation or other non-predator causes. This system can exhibit an oscillatory population dynamic in time and space. Suppose there is an excess of prey. The predator population increases in response to this time of plenty. However, the greatly increased predator population erodes the prey population. Predator starvation sets in and the predator population decreases significantly. This provides an opportunity for the prey population to increase, completing one cycle.

Stock Market
The world of business and economics is replete with variations in success and failure. The stock market is perhaps the most familiar illustration of the forces at work that lead to oscillatory behaviour. Suppose the price of a share rises. Then many investors take note and, wishing to make a profit, want to buy that stock. Supply and demand thereby force the price upward. Even more investors want to participate in this rally. Then some analysts note that the price has gone out of line with the "true" value. Some investors immediately sell and the price tends to drop. This induces panic selling and the stock price drops significantly below true value. After a period, panic subsides and the stock at the low price is viewed as a good bargain. Buying starts again and the cycle repeats. This exuberance/depression cyclicity is pervasive throughout the world of economics.

Traffic Jams
Computer models of self-organization can be applied to understand how traffic jam behaves and under which conditions they form. Simple models consider a lattice; which represents a motorway. Each site of the lattice is either empty or contains a car with very simple rules of displacement: moving to the up, moving to the right. An up car can shift right with a certain probability if it is blocked ahead by other cars. By increasing the number of cars on the motorway, a limit is reached for which some cars become blocked and a traffic jam develops. Complexity of the system can be increased by allowing the cars to have different velocities, by adding an accident that stops the traffic or by taking into account the behaviour of drivers when they see an accident.

The Future of the Self-Organization Theory
A necessary condition for the existence of self-organization is that the system be driven sufficiently far from equilibrium. To develop and sustain these phenomena, a continuous dissipation of energy must be expended through the exchanges of mass and energy between the system and its surroundings. Even at a planetary scale, when a planet exchanges mass and energy with its surroundings or between its constituent parts, it fulfils a necessary condition for self-organization. And in every subsystem, even in living organisms, conditions are such that matter and energy are flowing, leading to self-organization. One cannot give the "final word" on self-organization at the present time. Scientists realize that we are just at the beginning of a rich era for future research.

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