21,700 research outputs found
About the Power to Enforce and Prevent Consensus by Manipulating Communication Rules
We explore the possibilities of enforcing and preventing consensus in
continuous opinion dynamics that result from modifications in the communication
rules. We refer to the model of Weisbuch and Deffuant, where agents adjust
their continuous opinions as a result of random pairwise encounters whenever
their opinions differ not more than a given bound of confidence \eps. A high
\eps leads to consensus, while a lower \eps leads to a fragmentation into
several opinion clusters. We drop the random encounter assumption and ask: How
small may \eps be such that consensus is still possible with a certain
communication plan for the entire group? Mathematical analysis shows that
\eps may be significantly smaller than in the random pairwise case. On the
other hand we ask: How large may \eps be such that preventing consensus is
still possible? In answering this question we prove Fortunato's simulation
result that consensus cannot be prevented for \eps>0.5 for large groups. %
Next we consider opinion dynamics under different individual strategies and
examine their power to increase the chances of consensus. One result is that
balancing agents increase chances of consensus, especially if the agents are
cautious in adapting their opinions. However, curious agents increase chances
of consensus only if those agents are not cautious in adapting their opinions.Comment: 21 pages, 6 figure
Special Symplectic Connections
By a special symplectic connection we mean a torsion free connection which is
either the Levi-Civita connection of a Bochner-K\"ahler metric of arbitrary
signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a
connection with special symplectic holonomy. A manifold or orbifold with such a
connection is called special symplectic.
We show that the symplectic reduction of (an open cell of) a parabolic
contact manifold by a symmetry vector field is special symplectic in a
canonical way. Moreover, we show that any special symplectic manifold or
orbifold is locally equivalent to one of these symplectic reductions.
As a consequence, we are able to prove a number of global properties,
including a classification in the compact simply connected case.Comment: 35 pages, no figures. Exposition improved, some minor errors
corrected. Version to be published by Jour.Diff.Geo
Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set Λ of arbitrary shape. Under the assumption of uniform asymptotic stability of Λ in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets Λ(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of Λ
Extrinsically Immersed Symplectic Symmetric Spaces
Let (V, \Om) be a symplectic vector space and let \phi: M \ra V be a
symplectic immersion. We show that is (locally) an
extrinsic symplectic symmetric space (e.s.s.s.) in the sense of \cite{CGRS} if
and only if the second fundamental form of is parallel.
Furthermore, we show that any symmetric space which admits an immersion as an
e.s.s.s. also admits a {\em full} such immersion, i.e., such that is
not contained in a proper affine subspace of , and this immersion is unique
up to affine equivalence.
Moreover, we show that any extrinsic symplectic immersion of factors
through to the full one by a symplectic reduction of the ambient space. In
particular, this shows that the full immersion is characterized by having an
ambient space of minimal dimension.Comment: 15 pages, version to be published by Annals of Global Analysis and
Geometr
Statistics of the General Circulation from Cumulant Expansions
Large-scale atmospheric flows may not be so nonlinear as to preclude their
statistical description by systematic expansions in cumulants. I extend
previous work by examining a two-layer baroclinic model of the general
circulation. The fixed point of the cumulant expansion describes the
statistically steady state of the out-of-equilibrium model. Equal-time
statistics so obtained agree well with those accumulated by direct numerical
simulation.Comment: 1 page paper with 4 figures that accompanies one of the winning
entries in the APS gallery of nonlinear images competitio
Meiotic recombination proteins localize to linear elements in Schizosaccharomyces pombe
Peer reviewedPostprin
Leak-rate of seals: effective medium theory and comparison with experiment
Seals are extremely useful devices to prevent fluid leakage. We present an
effective medium theory of the leak-rate of rubber seals, which is based on a
recently developed contact mechanics theory. We compare the theory with
experimental results for seals consisting of silicon rubber in contact with
sandpaper and sand-blasted PMMA surfaces.Comment: 8 pages, 11 figure
- …