256,521 research outputs found
Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters
It is shown how different globally coupled map systems can be analyzed under
a common framework by focusing on the dynamics of their respective global
coupling functions. We investigate how the functional form of the coupling
determines the formation of clusters in a globally coupled map system and the
resulting periodicity of the global interaction. The allowed distributions of
elements among periodic clusters is also found to depend on the functional form
of the coupling. Through the analogy between globally coupled maps and a single
driven map, the clustering behavior of the former systems can be characterized.
By using this analogy, the dynamics of periodic clusters in systems displaying
a constant global coupling are predicted; and for a particular family of
coupling functions, it is shown that the stability condition of these clustered
states can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR
Single Scale Analysis of Many Fermion Systems. Part 1: Insulators
We construct, using fermionic functional integrals, thermodynamic Green's
functions for a weakly coupled fermion gas whose Fermi energy lies in a gap.
Estimates on the Green's functions are obtained that are characteristic of the
size of the gap. This prepares the way for the analysis of single scale
renormalization group maps for a system of fermions at temperature zero without
a gap.Comment: 42 page
Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences
Symbolic sequences generated by coupled map lattices (CMLs) can be used to
model the chaotic-like structure of genomic sequences. In this study it is
shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a
shift of 4 symbols) very closely reproduce the multifractal spectrum of
human genomic sequences for coupling constant if .
The presence of rare configurations causes deviations for , which
disappear if the rare event statistics of the CML is modified. Such rare
configurations are known to play specific functional roles in genomic sequences
serving as promoters or regulatory elements.Comment: 7 pages, 6 picture
Mapping functional traits: comparing abundance and presence-absence estimates at large spatial scales
Efforts to quantify the composition of biological communities increasingly focus on functional traits. The composition of communities in terms of traits can be summarized in several ways. Ecologists are beginning to map the geographic distribution of trait-based metrics from various sources of data, but the maps have not been tested against independent data. Using data for birds of the Western Hemisphere, we test for the first time the most commonly used method for mapping community trait composition – overlaying range maps, which assumes that the local abundance of a given species is unrelated to the traits in question – and three new methods that as well as the range maps include varying degrees of information about interspecific and geographic variation in abundance. For each method, and for four traits (body mass, generation length, migratory behaviour, diet) we calculated community-weighted mean of trait values, functional richness and functional divergence. The maps based on species ranges and limited abundance data were compared with independent data on community species composition from the American Christmas Bird Count (CBC) scheme coupled with data on traits. The correspondence with observed community composition at the CBC sites was mostly positive (62/73 correlations) but varied widely depending on the metric of community composition and method used (R2: 5.6×10−7 to 0.82, with a median of 0.12). Importantly, the commonly-used range-overlap method resulted in the best fit (21/22 correlations positive; R2: 0.004 to 0.8, with a median of 0.33). Given the paucity of data on the local abundance of species, overlaying range maps appears to be the best available method for estimating patterns of community composition, but the poor fit for some metrics suggests that local abundance data are urgently needed to allow more accurate estimates of the composition of communities
Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model
We use the nested loop approach to investigate loop models on random planar
maps where the domains delimited by the loops are given two alternating colors,
which can be assigned different local weights, hence allowing for an explicit
Z_2 domain symmetry breaking. Each loop receives a non local weight n, as well
as a local bending energy which controls loop turns. By a standard cluster
construction that we review, the Q = n^2 Potts model on general random maps is
mapped to a particular instance of this problem with domain-non-symmetric
weights. We derive in full generality a set of coupled functional relations for
a pair of generating series which encode the enumeration of loop configurations
on maps with a boundary of a given color, and solve it by extending well-known
complex analytic techniques. In the case where loops are fully-packed, we
analyze in details the phase diagram of the model and derive exact equations
for the position of its non-generic critical points. In particular, we
underline that the critical Potts model on general random maps is not self-dual
whenever Q \neq 1. In a model with domain-symmetric weights, we also show the
possibility of a spontaneous domain symmetry breaking driven by the bending
energy.Comment: 44 pages, 13 figure
Reduced Density-Matrix Approach to Strong Matter-Photon Interaction
We present a first-principles approach to electronic many-body systems
strongly coupled to cavity modes in terms of matter-photon one-body reduced
density matrices. The theory is fundamentally non-perturbative and thus
captures not only the effects of correlated electronic systems but accounts
also for strong interactions between matter and photon degrees of freedom. We
do so by introducing a higher-dimensional auxiliary system that maps the
coupled fermion-boson system to a dressed fermionic problem. This reformulation
allows us to overcome many fundamental challenges of density-matrix theory in
the context of coupled fermion-boson systems and we can employ conventional
reduced density-matrix functional theory developed for purely fermionic
systems. We provide results for one-dimensional model systems in real space and
show that simple density-matrix approximations are accurate from the weak to
the deep-strong coupling regime. This justifies the application of our method
to systems that are too complex for exact calculations and we present first
results, which show that the influence of the photon field depends sensitively
on the details of the electronic structure.Comment: 52 pages, 26 figures, plus supporting information of 24 page
More on the O(n) model on random maps via nested loops: loops with bending energy
We continue our investigation of the nested loop approach to the O(n) model
on random maps, by extending it to the case where loops may visit faces of
arbitrary degree. This allows to express the partition function of the O(n)
loop model as a specialization of the multivariate generating function of maps
with controlled face degrees, where the face weights are determined by a fixed
point condition. We deduce a functional equation for the resolvent of the
model, involving some ring generating function describing the immediate
vicinity of the loops. When the ring generating function has a single pole, the
model is amenable to a full solution. Physically, such situation is realized
upon considering loops visiting triangles only and further weighting these
loops by some local bending energy. Our model interpolates between the two
previously solved cases of triangulations without bending energy and
quadrangulations with rigid loops. We analyze the phase diagram of our model in
details and derive in particular the location of its non-generic critical
points, which are in the universality classes of the dense and dilute O(n)
model coupled to 2D quantum gravity. Similar techniques are also used to solve
a twisting loop model on quadrangulations where loops are forced to make turns
within each visited square. Along the way, we revisit the problem of maps with
controlled, possibly unbounded, face degrees and give combinatorial derivations
of the one-cut lemma and of the functional equation for the resolvent.Comment: 40 pages, 9 figures, final accepted versio
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