2,431 research outputs found
Coupled spin models for magnetic variation of planets and stars
Geomagnetism is characterized by intermittent polarity reversals and rapid
fluctuations. We have recently proposed a coupled macro-spin model to describe
these dynamics based on the idea that the whole dynamo mechanism is described
by the coherent interactions of many small dynamo elements. In this paper, we
further develop this idea and construct a minimal model for magnetic
variations. This simple model naturally yields many of the observed features of
geomagnetism: its time evolution, the power spectrum, the frequency
distribution of stable polarity periods, etc. This model has coexistent two
phases; i.e. the cluster phase which determines the global dipole magnetic
moment and the expanded phase which gives random perpetual perturbations that
yield intermittent polarity flip of the dipole moment. This model can also
describe the synchronization of the spin oscillation. This corresponds to the
case of sun and the model well describes the quasi-regular cycles of the solar
magnetism. Furthermore, by analyzing the relevant terms of MHD equation based
on our model, we have obtained a scaling relation for the magnetism for
planets, satellites, sun, and stars. Comparing it with various observations, we
can estimate the scale of the macro-spins.Comment: 16 pages, 9 figure
The Inner Life of the Kondo Ground State: An Answer to Kenneth Wilson's Question
The Kondo ground state has been investigated by numerical and exact methods,
but the physics behind these results remains veiled. Nobel prize winner Wilson,
who engineered the break through in his numerical renormalization group theory,
commented in his review article "the author has no simple explanation ...for
the crossover from weak to strong coupling". In this article a graphical
interpretation is given for the extraordinary properties of the Kondo ground
state. At the crossover all electron states in the low energy range of
k_{B}T_{K} are synchronized. An internal orthogonality catastrophe is averted.Comment: 4 figure
Some recent developments in models with absorbing states
We describe some of the recent results obtained for models with absorbing
states. First, we present the nonequilibrium absorbing-state Potts model and
discuss some of the factors that might affect the critical behaviour of such
models. In particular we show that in two dimensions the further neighbour
interactions might split the voter critical point into two critical points. We
also describe some of the results obtained in the context of synchronization of
chaotic dynamical systems. Moreover, we discuss the relation of the
synchronization transition with some interfacial models.Comment: 8 pages, Brazilian J. of Physics (in press
Group Synchronization on Grids
Group synchronization requires to estimate unknown elements
of a compact group associated to the
vertices of a graph , using noisy observations of the group
differences associated to the edges. This model is relevant to a variety of
applications ranging from structure from motion in computer vision to graph
localization and positioning, to certain families of community detection
problems.
We focus on the case in which the graph is the -dimensional grid.
Since the unknowns are only determined up to a global
action of the group, we consider the following weak recovery question. Can we
determine the group difference between far apart
vertices better than by random guessing? We prove that weak recovery is
possible (provided the noise is small enough) for and, for certain
finite groups, for . Viceversa, for some continuous groups, we prove
that weak recovery is impossible for . Finally, for strong enough noise,
weak recovery is always impossible.Comment: 21 page
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