211,568 research outputs found
The complexity of random ordered structures
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Spatio-temporal stochastic resonance induces patterns in wetland vegetation dynamics
Water availability is a major environmental driver affecting riparian and
wetland vegetation. The interaction between water table fluctuations and
vegetation in a stochastic environment contributes to the complexity of the
dynamics of these ecosystems. We investigate the possible emergence of spatial
patterns induced by spatio-temporal stochastic resonance in a simple model of
groundwater-dependent ecosystems. These spatio-temporal dynamics are driven by
the combined effect of three components: (i) an additive white Gaussian noise,
accounting for external random disturbances such as fires or fluctuations in
rain water availability, (ii) a weak periodic modulation in time, describing
hydrological drivers such as seasonal fluctuations of water table depth, and
(iii) a spatial coupling term, which takes into account the ability of
vegetation to spread and colonize other parts of the landscape. A suitable
cooperation between these three terms is able to give rise to ordered
structures which show spatial and temporal coherence, and are statistically
steady in time.Comment: 9 pages, 7 figure
Statics and Dynamics of Yukawa Cluster Crystals on Ordered Substrates
We examine the statics and dynamics of particles with repulsive Yukawa
interactions in the presence of a two-dimensional triangular substrate for
fillings of up to twelve particles per potential minimum. We term the ordered
states Yukawa cluster crystals and show that they are distinct from the
colloidal molecular crystal states found at low fillings. As a function of
substrate and interaction strength at fixed particle density we find a series
of novel crystalline states that we characterize using the structure factor.
For fillings greater than four, shell and ring structures form at each
potential minimum and can exhibit sample-wide orientational order. A disordered
state can appear between ordered states as the substrate strength varies. Under
an external drive, the onsets of different orderings produce clear changes in
the critical depinning force, including a peak effect phenomenon that has
generally only previously been observed in systems with random substrates. We
also find a rich variety of dynamic ordering transitions that can be observed
via changes in the structure factor and features in the velocity-force curves.
The dynamical states encompass a variety of moving structures including
one-dimensional stripes, smectic ordering, polycrystalline states, triangular
lattices, and symmetry locking states. Despite the complexity of the system, we
identify several generic features of the dynamical phase transitions which we
map out in a series of phase diagrams. Our results have implications for the
structure and depinning of colloids on periodic substrates, vortices in
superconductors and Bose-Einstein condensates, Wigner crystals, and dusty
plasmas.Comment: 14 pages, 17 postscript figure
Descriptive Complexity of Deterministic Polylogarithmic Time and Space
We propose logical characterizations of problems solvable in deterministic
polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We
introduce a novel two-sorted logic that separates the elements of the input
domain from the bit positions needed to address these elements. We prove that
the inflationary and partial fixed point vartiants of this logic capture
PolylogTime and PolylogSpace, respectively. In the course of proving that our
logic indeed captures PolylogTime on finite ordered structures, we introduce a
variant of random-access Turing machines that can access the relations and
functions of a structure directly. We investigate whether an explicit predicate
for the ordering of the domain is needed in our PolylogTime logic. Finally, we
present the open problem of finding an exact characterization of
order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science
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