34,944 research outputs found
Understanding the Protected Nodes and Collapse of the Fermi Arcs in Underdoped Cuprate Superconductors
We show how recent angle resolved photoemission measurements addressing the
Fermi arcs in the cuprates reveal a very natural phenomenological description
of the complex superfluid phase. Importantly, this phenomenology is consistent
with a previously presented microscopic theory. By distinguishing the order
parameter and the excitation gap, we are able to demonstrate how the collapse
of the arcs below into well defined nodes is associated with the
\emph{smooth} emergence of superconducting coherence. Comparison of this theory
with experiment shows good semi-quantitative agreement.Comment: 4 pages, 4 figures, replaced with updated versio
Hurewicz Theorem for Assouad-Nagata dimension
Given a function of metric spaces, its {\it asymptotic
dimension} \asdim(f) is the supremum of \asdim(A) such that
and \asdim(f(A))=0. Our main result is \begin{Thm} \label{ThmAInAbstract}
\asdim(X)\leq \asdim(f)+\asdim(Y) for any large scale uniform function
. \end{Thm}
\ref{ThmAInAbstract} generalizes a result of Bell and Dranishnikov in which
is Lipschitz and is geodesic. We provide analogs of
\ref{ThmAInAbstract} for Assouad-Nagata dimension and asymptotic
Assouad-Nagata dimension \ANasdim. In case of linearly controlled asymptotic
dimension \Lasdim we provide counterexamples to three questions in a list of
problems of Dranishnikov.
As an application of analogs of \ref{ThmAInAbstract} we prove \begin{Thm}
\label{ThmBInAbstract} If is an exact sequence of
groups and is finitely generated, then \ANasdim (G,d_G)\leq \ANasdim
(K,d_G|K)+\ANasdim (H,d_H) for any word metrics metrics on and
on . \end{Thm}
\ref{ThmBInAbstract} extends a result of Bell and Dranishnikov for asymptotic
dimension
Kosterlitz-Thouless and Potts transitions in a generalized XY model
We present extensive numerical simulations of a generalized XY model with
nematic-like terms recently proposed by Poderoso {\it et al} [PRL
106(2011)067202]. Using finite size scaling and focusing on the case, we
locate the transitions between the paramagnetic (P), the nematic-like (N) and
the ferromagnetic (F) phases. The results are compared with the recently
derived lower bounds for the P-N and P-F transitions. While the P-N transition
is found to be very close to the lower bound, the P-F transition occurs
significantly above the bound. Finally, the transition between the nematic-like
and the ferromagnetic phases is found to belong to the 3-states Potts
universality class.Comment: Extended and updated version of arXiv:1207.3447v
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Education as a Complex System: Conceptual and Methodological Implications
Education is a complex system, which has conceptual and methodological implications for education research and policy. In this article, an overview is first provided of the Complex Systems Conceptual Framework for Learning (CSCFL), which consists of a set of conceptual perspectives that are generally shared by educational complex systems, organized into two focus areas: collective behaviors of a system, and behaviors of individual agents in a system. Complexity and research methodologies for education are then considered, and it is observed that commonly used quantitative and qualitative techniques are generally appropriate for studying linear dynamics of educational systems. However, it is proposed that computational modeling approaches, being extensively used for studying nonlinear characteristics of complex systems in other fields, can provide a methodological complement to quantitative and qualitative education research approaches. Two research case studies of this approach are discussed. We conclude with a consideration of how viewing education as a complex system using complex systems’ conceptual and methodological tools can help advance education research and also inform policy
Competing nematic interactions in a generalized XY model in two and three dimensions
We study a generalization of the XY model with an additional nematic-like
term through extensive numerical simulations and finite-size techniques, both
in two and three dimensions. While the original model favors local alignment,
the extra term induces angles of between neighboring spins. We focus
here on the case (while presenting new results for other values of as
well) whose phase diagram is much richer than the well known case. In
particular, the model presents not only continuous, standard transitions
between Berezinskii-Kosterlitz-Thouless (BKT) phases as in , but also
infinite order transitions involving intermediate, competition driven phases
absent for and 3. Besides presenting multiple transitions, our results
show that having vortices decoupling at a transition is not a suficient
condition for it to be of BKT type.Comment: 13 pages, 16 figure
On dynamical bit sequences
Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random
variables, each taking the values 1 or 0 with respective probabilities p and
1-p. As a process indexed by non-negative t, is
constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that
it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We
derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for
some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in
two very different settings:
(i) Where \ell is a constant; and
(ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is
described by the Kolmogorov capacitance of F for case (i) and Howroyd's
1/2-dimensional box-dimension profiles for case (ii). We also present
sample-path consequences, and a connection to capacities that answers a
question of Benjamini et. al. (2003)Comment: 25 pages. This a substantial revision of an earlier paper. The
material has been reorganized, and Theorem 1.3 is ne
Signature for the Shape of the Universe
If the universe has a nontrivial shape (topology) the sky may show multiple
correlated images of cosmic objects. These correlations can be couched in terms
of distance correlations. We propose a statistical quantity which can be used
to reveal the topological signature of any Robertson-Walker (RW) spacetime with
nontrivial topology. We also show through computer-aided simulations how one
can extract the topological signatures of flat, elliptic, and hyperbolic RW
universes with nontrivial topology.Comment: 11 pages, 3 figures, LaTeX2e. This paper is a direct ancestor of
gr-qc/9911049, put in gr-qc archive to make it more accessibl
Normal zone in -coated conductors
We consider the distribution of an electric field in YBCO-coated conductors
for a situation in which the DC transport current is forced into the copper
stabilizer due to a weak link -- a section of the superconducting film with a
critical current less than the transport current. The electric field in the
metal substrate is also discussed. The results are compared with recent
experiments on normal zone propagation in coated conductors for which the
substrate and stabilizer are insulated from each other. The potential
difference between the substrate and stabilizer, and the electric field in the
substrate outside the normal zone can be accounted for by a large screening
length in the substrate, comparable to the length of the sample. During a
quench, the electric field inside the interface between YBCO and stabilizer, as
well as in the buffer layer, can be several orders of magnitude greater than
the longitudinal macroscopic electric field inside the normal zone. We
speculate on the possibility of using possible microscopic electric discharges
caused by this large (kV/cm) electric field as a means to detect a
quench.Comment: 8 pages, 4 figure
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