J. Plasma Fusion Res. SERIES, Yol.2 (1999) 3-7

Simulation ScienceSATO Tetsuya
National Institute for Fusion Science, Toki 509-5292, Japan(Received: 19 February 1999

/ Accepted: 9 June 1999)

Abstract
The strategy of Simulation Science at NIFS is described. In contrast with the strategy of the Santa
Fe Institute where an artificial rule is given to a personal computer and a pattern evolution governed by

the rule is obtained to apply it to the sort of real world phenomenon, our strategy is such that bigsimulations are carried out for various complex phenomena in the real world by a world-largest
supercomputer at hand to extract a global rule common to complex systems with different many-bodyinteracting forces. Having once obtained such a universal rule, then one may be able to predict how acomplex system evolves globally.

Keywords:
simulation science, science of complexity, Santa Fe Institute, self-organization

1. Beyond the Age of Nonlinear Solver
Creating a new paradigm beyond the Modern

interactions at an arbitrary instantaneous moment, arethrown into trash cans, despite the fact that we are

Science is highly invoked. The Modern Science has
been governing the fundamental thought of humanconcerned with the long time evolution. It may happen,

beings for more than three hundreds years since
Descartes and Newton. In doing Science, one breaks apiece out of the whole and defines its boundary

stabilized in a rather short time scale by mutual mode
coupling effects among those modes or by changing thebackground structure, while smaller growth rate modes
keep growing, though slowly, without being affectedmuch by the nonlinear stabilization of the larger modes.
Then it becomes quite possible that an initially tiny
growth rate mode eventually becomes the ruler of theworld of interest and reigns it. Of course, this new world

definitely, thereby the outside world being considered asa known and unaffected background. Any consistentback reaction to the outside world is ignored, notbecause we are not interested in it but simply because
we do not have a clear paradigm to include it.
The most successful and reliable tool that humanbeings have invented for comprehending the universe is
the mathematics. Mathematics has convinced us. after
three hundred years exploration, that at least non-human(non-living) phenomena are reasonably to becomprehended. However, any single identity or
phenomenon in nature cannot stand as it is, but isslightly or deeply related to numerous other agencies
that existed or happened in the past through highly
tangled causal chains. In Modern Science, any tinyinteractions, when so judged compared with otherthough, that the larger (linear) growth rate modes can becould after some time be destroyed by other modes.
Such a change of the ruler might continue forever.

In nature there are uncountable number of events
that cannot be explained by the conventionalperturbational treatment introducing small parameters.
Nature is not that simple. Most phenomena in naturechange repeatedly their spatio-temporal behaviors inrather instantaneous fashions, no matter how the system

may be considered to be well represented by a small

parameter expansion at an arbitrary moment and@1999 by The Japan Society of Plasma

C orre s p ondin g autho r' s e - mail : s ato @ tc s c.nifs. ac.j p

Science and Nuclear Fusion Research

Sato T., Simulation Scienceposition. Biological evaluation is such a typicalThe strategy is the following. First, one gives a simple

example.

artificial rule that might govern the behavior of an
artificial complex system and simulates its evolution
according to the artificial rule by, say, a personal
computer. Secondly, one compares the spatial or

In the meantime, computer appeared, and it now
becomes possible to solve any individual complex
phenomenon by it. Therefore, the present day computer
may well be called the age of "Nonlinear Solver".
However as far as we are satisfied only with solving aseemingly complex single phenomenon, computer
simulation would act only as a passive role in Scienceand never open up a new paradigm of Science. The
ability of "supercomputer" has currently grown up sothat almost any highly tangled phenomena, now called"complex phenomena", can individually be solved. It is
now time to go beyond this simple passive stage as theage of Nonlinear Solver, and certainly this can now bedone. In this paper proposed is a new scientificmethodology for the 2l" century that would go beyond
the age of Nonlinear Solver. This new age of computer
simulation may well be called the age of "Simulation
Science".

temporal pattern obtained by the simulation with that
occurring in the real world. Then, one hypothesizes thatthe given artificial rule be the rule of the real world (see,Fig.l) .

In contrast with this approach, our strategy ofSimulation Science takes an opposite way in the sensethat we directly deal with complex phenomena
happening in the real world [2-5]. By fully utilizing
advanced technologies such as a supercomputer andperiphery visualization devices, we reveal the dynamical
evolutions of various complex phenomena of whichgoverning laws are already disclosed by the ModernScience. Then we seek for a universal rule commonly
appearing among the revealed complex phenomena andconstruct a working hypothesis on how order is createdin a many-body system, i.e., a self-organization
2. The Strategy of Simulation Sciencehypothesis. Having this working hypothesis in mind, weThe Santa Fe Institute is now widely known as theCenter of Excellence that challenges the Complexity [].

< $tnategr of n$imulrtion Scienen >(fha Santa fe Strategy for Cotplexity)
Ar-t-i f .ici aj.. Ilor-.ld

Bnal.. Ilcr-.ld

Pattertr Forution ard

Etnlution ofllany-body SyrteE

Givsn Art if icial

hrls+Easic fule of aReal ilorldTFig. 1 The Santa Fe Institute Strategy towards theScience of Complexity.

Fig.2 The NIFS Strategy towards the Science ofComplexity (Simulation Science).

Sato T., Simulation Science

predict certain behaviors for other many-body systems

external excitation, namely, sudden excitation andwith different interaction forces with the hope toendorse or upgrade it. Repeating this process, we hopethat the hypothesis will eventually be sublimated into auniversal law governing the behaviors of many-bodycontinuous excitation. For various examples where theinteraction forces (nonlinearity) are different, we have
performed simulations.

systems (see, Fig.2).

Two typical dynamical evolutions for sudden
excitation are shown in Fig.3, which represent thestepwise relaxation toward the minimum energy state

3. Self-Organization Hypothesis[6,7]. Also, shown in Fig. 4 are five examples for

We make a working hypothesis that "openness"and "nonlinearity" are the fundamentals of complexity.
Openness implies that the system is subject to"excitation" from an external world and "exhaust" into
an external world. Subject to an external excitation, acontinuous excitation which exhibit intermittent burstlike evolutions [8-1 l].
The final examples, Fig.5, shows how the exhaust

nonlinear system is non-equilibrated, unless theequilibration rate of the system such as the diffusion rateof disorderliness reflects upon the self-organizedstructure Il].

Finally, we note that the production rate ofdisorderliness is maximized when order is most actively

is large enough. When the non-equilibration goesbeyond a certain threshold, the system suffers fromdeformation (instability). As the deformation grows, thedeformation (potential) energy stored by acting against
the restoring force to the original structure also grows.
Usually a complex system allows discrete structures
corresponding to the largeness of excitation energy.
Therefore, the deformation of the original structure can
not last unlimitedly, but eventually exceeds the bound of
the deformation (catastrophic or bifurcation point) andgoes into a new state.
Here we turn our eyes to the "exhaust". Excitationis the principal agency of causing self-organization. On
the other hand, the exhaust appears to be passive in selforganization. However, it actually plays an importantrole. In fact, disorderliness or superfluity is inevitably
created during the process of order creation. If thedisorderliness (so-called entropy in the equilibriumdynamics) is kept in the system, the discreteness may be
obscured or may happen to disappear. Thus, it is said
that expulsion of disorderliness from the system islargely infl uential on self-organization.

4. Self-Organization Scenario
Since the scenario is given elsewhere [2-5], we will
only present the summary of the simulation results

which endorse the scenario. In this work we will not beinterested in the spatial pattern itself because it isdependent upon details of the nonlinearity of the system.
In other words, the pattern is by large an internalfeature. Instead, we are more concerned with theuniversality irrespective of nonlinearity of the system, or
the type of nonlinear interactions such as the long range
force or the short range force.

First. we shall examine two extreme cases ofl

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energy state for a sudden excitation: (a)magnetohydrodynamic self-organization when
the system is suddenly excited to a higher energy
level [6], (b) polymer crystalization when the heatbath temperature is suddenly decreased [71.

Sato T., Simulation ScienceE,atX-pdil
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Fig. 4 Intermittent self-adaptive excursions between local maxima and local minima for a continuous excitation: (a)Topological transitions of a continuously twisted flux tube I8l, (b) energy releases of a continuously driven
magnetic reconnction [9], (c) dipole and octapole reversals of a dynamo problem [10], and {d) formations of giant(super) double layers in a current driven plasma system [111.
created, though the quantitative evidences are omitted"normal"Fdl:
eohere because of the limit of space.

15. Summary
We have presented our strategy of opening up anew paradigm for the 21't Century Science by means ofadvanced supercomputer and visualization technologies.

(4,otc1F=t1go"super"10U

0400-5800 1023

xl ADo)Fig. 5 Difference in the self-organized structure between

the disorderliness-reserved system anddisorderliness-expulsed system for double layer

formation I11l: (a) double layer for thedisorderliness-reserved case and (b) giant double
layer for the disorderliness-expulsed case.

which we name "Simulation Science".
One important successful output derived from thisstrategy was demonstrated. A universal rule is derived
that self-organization evolves in an intermittent fashion

for a continuous excitation from an external world,
while it relaxes towards a minimum energy state in a
stepwise fashion for a sudden excitation. It is also
demonstrated that depending upon whetherdisorderliness is expulsed or not, the self-organizedstructure exhibits a qualitatively different one.

Acknowledgements
This work is an integration of the works done bythe Complexity Simulation Group of NIFS.

Sato T., Simulation ScienceReferences[1] See, for example, J.L. Casti, Would-be worlds: how
simulation is changing the frontiers of science(John Wiley & Sons, Inc., 1997).
l2l T.Sato and the Complexity Simulation Group,Phys. Plasmas 3, 2135 (1996).

t3l T.Sato, J. Korean Phys. Soc.31, sl09 (1997).
[4] T. Sato, Chinese Phys. Lett., in print.
t5l T. Sato, Pftysics of lonized Gases (Plenum, 1999)
p.449.

[6] S.-P. Zhu, R. Horiuchi and T. Sato, Phys. Rev. Esr,6047 (1995).

[7] S. Fujiwara and T. Sato, Phys. Rev. Lett. 80, 991(1998).

t8l H. Amo, T. Sato and A Kageyama, Phys. Rev. E
51, 3838 (199s).
t9l H. Kitahara, T. Hayashi and T. Sato, J. Phys. Soc.
Jpn.65,3208 (1996).

ll0l M.M. Ochi, A. Kageyama and T. Sato, Phys.
Plasmas 3,777 (1999).

I l] T. Sato and H. Takamaru, Phys. Plasmas 2,3609(1995).