0.3truecm

**Dynamic Phases in a Spring-block System
0.01truecm**

When a block is pulled via a spring across a surface, there appear to be
several different dynamic phases. These can be characterized by the
pulling velocity and a dynamic velocity
where is the acceleration
of gravity, is the mass of the block, and is the spring constant.
For sufficiently small , the block displays stick-slip (relaxation) motion.
Then as a function of decreasing , this stick-slip motion is first
nearly periodic, then aperiodic with approximately
an exponential slip size distribution,
then aperiodic with possibly a power-law slip size distribution. When is
increased, the block eventually ceases to stick and just slides across the
surface. The motion can then be adequately described by a Langevin model.
-0.1truecm *A. Johansen, P. Dimon, C. Ellegaard, J.S. Larsen, and H.H. Rugh
0.3truecm*

**Studies of Granular Flow
0.01truecm**

When small beads flow through a narrow channel, there will be
fluctuations in the flow rate around the mean.
We are studying the nature of the these fluctuations as a function
of the various parameters which we can control, such as the ratio
of the bead size to the channel width, and the tilt of the channel.
-0.1truecm *C. Veje and P. Dimon
0.3truecm*

**Study of Fragmentation
0.01truecm**

The measured mass distributions of fragments from various objects show
evidence of obeying a scaling law.
The scaling exponent is found to depend on the dimensionality of the object
but otherwise not on its morphology or composition.
A cube, for example, has the same exponent as a sphere.
-0.1truecm *(L. Oddershede), (J. Bohr), and P. Dimon
0.3truecm*

**Colored Activity in Self Organized Critical Interface Dynamics
0.01truecm**

We study roughening interfaces that become self organized critical
by a rule similar to that of invasion percolation.
We demonstrate that there is a fundamental
difference between transient and critical
dynamical exponents. The exponents break the Galilean invariance
and temporal multiscaling is observed.
We show that the activity along the interface
exhibits non trivial power law correlations in both space
and time even though only quenched Gaussian noise is applied.
The results are compared with simulations where
spatial power law correlated noise are used as input.
-0.1truecm *K. Sneppen and M.H. Jensen
0.3truecm*

**Multidiffusion in Critical Dynamics of Strings and Membranes
0.01truecm**

We study dynamical roughening of strings which
do not break the symmetry neither parallel nor
vertical to the overall suspension.
The suggested non local dynamics enforces a build
up of long range correlations
and the system becomes self organized critical
with a new universality class which exhibits
nontrivial temporal scalings and power law
correlated activity along the string, even though
only localized Gaussian noise is applied.
We observe multiscaling of the temporal behaviour
both perpendicular and parallel (multidiffusion)
to the evolving string at criticality.
-0.1truecm *K. Sneppen and M.H. Jensen
0.3truecm*

**Random Fractals, Phase Transitions, and Negative Dimension Spectra
0.01truecm**

We introduce an exactly soluble model of a random fractal
where the corresponding dimension spectrum ,
as a consequence of finite size effects in ensemble averaging,
exhibits negative values of corresponding to
the strongest singularities of the probability measure,
i.e. at the left part where .
The right part of the spectrum,
which corresponds to the regular part of the measure,
is not well defined as the scaling length .
These two effects are related to the fact that
the generalized dimensions exhibit:
1) a first order phase transition at and
2) a non-existing thermodynamic limit for .
We show that the scaling properties of the model can be
understood as the thermodynamic limit of
versus .
The connections to fractal aggregates is briefly discussed.
-0.1truecm *M.H. Jensen, (G. Paladin), (A. Vulpiani), and (W. v.d. Water)
0.3truecm*

**Punctuated Equilibrium and the Critical Edge of an Evolving Ecosystem
0.01truecm**

We study a dynamic model for an evolving
ecology of interacting species.
The species are constrained by barriers in an
underlying fitness landscape that parametrize
the reproduction stability of each species
and its potential mutants in the environment.
A central element of the model is a variability
in the couplings between species, which form
a metric of the ecosystem that is self organized
and subject to dynamic changes.
This is obtained by a fine graining of the ecosystem
into possible dependencies between species.
In the limit of very rarely mutating species,
the ecology expands its genetic space always keeping
the system on the edge of generic scale invariance.
Furthermore, an ecosystem governed by local
punctuations within individual species morphology,
will during its evolution show collective behaviour
in terms of global punctuations,
involving many simultaneous local punctuations.
The expanding ecology increases the
diversity of life which in turn opens for an
enhanced complexity of the individual species.
-0.1truecm *K. Sneppen, M.H. Jensen, (P. Bak), and (H. Flyvbjerg)
0.3truecm*

**Inflation Rule for Canonical-cell Tilings
0.01truecm**

Despite the fact that quasicrystals were first discovered
a decade ago, the atomic structures for all but a handful
of them have yet to be determined. In other words,
physicists have been measuring the properties of a class of
solid-state material for ten years, but they still do not
know what it is, exactly, they have been measuring the
properties of. This must set some sort of record.
I am presently trying to formulate the geometrical framework
of an atomic model for icosahedral quasicrystals. This
endeavour involves the search for an inflation rule, whereby
quasiperiodic ``canonical-cell'' tilings can be generated.
Such tilings, once decorated with atoms, specify the atomic
structures of model quasicrystals; these structures
should accurately approximate the structures of real
quasicrystals. I have not yet found any such inflation
rule.
-0.1truecm *M. Oxborrow
0.3truecm*

**Self-Organized Critical Dynamics of Fronts:
Intermittency and Multiscaling.
0.01truecm**

We present recent work on punctuated
dynamics of fronts.
This kind of dynamics drives the evolving front to a
critical state with temporal
multiscaling of the interface profile
due intermittent activity characterized by
avalanches which connect regions of recent local activity.
This activity pattern exhibits
non trivial power law correlations in both space and time.
We present numerical results in both 1+1 and 2+1 dimensions and
generalize a theory for the critical exponents to all dimensions.
-0.1truecm *(J. Falk), K. Sneppen, and M.H. Jensen
0.3truecm*

**Punctuated Equilibrium and Criticality
in a Simple Model of Evolution
0.01truecm**

A simple and robust model of biological evolution
of an ecology of interacting species is introduced. The model
self-organizes into a critical steady state with intermittent co-
evolutionary avalanches of all sizes, i. e. it exhibits "punctuated
equilibrium" behavior. This collaborative evolution is much
faster than non-cooperative scenarios since no large and
coordinated, and hence prohibitively unlikely, mutations are
involved.
-0.1truecm *K. Sneppen and (P. Bak)
0.3truecm*

**Mean Field Theory for a Simple Model of Evolution
0.01truecm**

A simple dynamical model for Darwinian evolution
on its slowest time-scale is analyzed.
Its mean-field theory is formulated and solved.
A random neighbor version of the model is simulated,
as is a one-dimensional version.
In one dimension, the dynamics can be described in terms of
a "repetitious random walker"
and anomalous diffusion with exponent 0.4.
In all cases the model self-organizes to a robust critical attractor.
-0.1truecm *K. Sneppen, (H. Flyvbjerg), and (P. Bak)
0.3truecm*

**Self-Organization in Simple Models of the Brain
0.01truecm**

One of the most important goals in neuroscience is to understand the way the brain manage to undertake a diversity of tasks. The processing units are the neurons and their connections. On the neural level the underlying network dynamics is not task specific, and a realistic attempt to explain the brains ability to function must take this into account. In sharp contrast, the traditional artificial neural networks are heavily constrained, and the a priori knowledge of the task is crucial. Based on this, the system is trained to construct an appropriate input-output function, which is then used in different but similar situations. The brain is not hard-wired at birth, with all its connections coded into the DNA. Evolution is efficient, but not that efficient. The amount of information contained in DNA is vastly insufficient to specify all neural connections. The structure has to be self-organized rather than by design. Thus to understand the brain, we must understand the principles by which is organizes itself through interactions with the environment.

Recently, we have introduced a new class of adaptive networks that by
construction are able to function in an changeable environment. Their
performance is intimately connected with the adaptive nature, where
information flows through a variety of ever changing paths. We denote
this adaptive performance to emphasize that the dynamics cannot
be divided into a learning mode and a retrieving mode as known from
traditional artificial neural networks.
Studies on the performing networks can follow one of two directions.
Either a study on the relations to physiology and phycology, or a study
on industrial applications. On the medical side, the point is to
extract some important principles for brain functioning associated with
the proposed network dynamics. This include a study of the chemistry
and the `electronics' involved when a neuron fires. On the network
level, we would like to understand the processes of conditioning, and
the behaviors like habituation and sensitization. Moreover, there is
a growing interest in the variety of timescales present in recorded EEG
signals. On the industrial side, there are a multitude of possible
candidates in the literature, from control and robotics to analysis
and diagnosis. Initial tests are carried out on computer, but electronic
`neurons' have been build for further testing.
-0.1truecm *P. Alstrøm, (P. Bak) and (D. Stassinopoulos)
0.3truecm*

**Intermittent Dynamics and Self Organized Depinning
in Propagating Fronts
0.01truecm**

We study the roughening dynamics of a 2 dimensional
front where advances are made at minimal pinning sites,
while slopes of the front are kept finite by additional
lateral growth.
The interface self organizes toward a critical state
with long range correlations in space and time.
The dynamics is governed by intermittent
burst which give rise to a scale invariant
avalanche distribution and
multiscaling of the temporal roughening.
Generalizing a recently proposed theory for the
1-d case, we demonstrate that the multiscaling
can be explained by the static roughness exponent alone.
The correlation between subsequent deposition
activities exhibits the same power law as in the
one dimensional case. The implication of such
dimensional independence is discussed.
-0.1truecm *(J. Falk), M.H. Jensen, and K. Sneppen
0.3truecm*

**Critical Punctuations and Metastability for Evolving Strings, Interfaces
0.01truecm**

We study the dynamics of interfaces
that become self organized critical by a rule similar
to that of invasion percolation. In the critical state
we observe temporal multiscaling of the interface
profile and an activity pattern that exhibits
non trivial power law correlations in both space
and time even though only quenched Gaussian noise is applied.
One way to characterize this intermittent activity is through
avalanches consistent of connected regions of recent local activity.
These avalanches display scale invariance, thus
reflecting both small and large scale properties of the dynamics.
An extension of the presented concepts to evolving strings
leads to a new universality class with other scalings.
Possible systems governed by the investigated
algorithms are discussed.
-0.1truecm *K. Sneppen and M.H. Jensen
0.3truecm*

**Scaling Behaviour in Daily Air Humidity Fluctuations
0.01truecm**

We show that the daily average air humidity fluctuations exhibit
non-trivial behaviour which is different from
the spectral properties of other meteorological quantities.
This feature and the fractal spatial structure found in
clouds make it plausible to regard air humidity fluctuations as a
manifestation of self-organized criticality.
We give arguments why the dynamics of air humidity
can be similar to dynamics of sandpile models of SOC.
-0.1truecm *G. Vattay and A. Harnos
*

*
*

Mon Feb 6 10:24:27 MET 1995