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Francois Renard
Forsker ved Univ. i Grenoble, Frankrike
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Sammendrag:
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.
© viten.com 2000
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