66,139 research outputs found
Replica-symmetry breaking in dynamical glasses
Systems of globally coupled logistic maps (GCLM) can display complex
collective behaviour characterized by the formation of synchronous clusters. In
the dynamical clustering regime, such systems possess a large number of
coexisting attractors and might be viewed as dynamical glasses. Glass
properties of GCLM in the thermodynamical limit of large system sizes are
investigated. Replicas, representing orbits that start from various initial
conditions, are introduced and distributions of their overlaps are numerically
determined. We show that for fixed-field ensembles of initial conditions, as
used in previous numerical studies, all attractors of the system become
identical in the thermodynamical limit up to variations of order
because the initial value of the coupling field is characterized by vanishing
fluctuations, and thus replica symmetry is recovered for . In
contrast to this, when random-field ensembles of initial conditions are chosen,
replica symmetry remains broken in the thermodynamical limit.Comment: 19 pages, 18 figure
Non-principal ultrafilters, program extraction and higher order reverse mathematics
We investigate the strength of the existence of a non-principal ultrafilter
over fragments of higher order arithmetic.
Let U be the statement that a non-principal ultrafilter exists and let
ACA_0^{\omega} be the higher order extension of ACA_0. We show that
ACA_0^{\omega}+U is \Pi^1_2-conservative over ACA_0^{\omega} and thus that
ACA_0^{\omega}+\U is conservative over PA.
Moreover, we provide a program extraction method and show that from a proof
of a strictly \Pi^1_2 statement \forall f \exists g A(f,g) in ACA_0^{\omega}+U
a realizing term in G\"odel's system T can be extracted. This means that one
can extract a term t, such that A(f,t(f))
Large N lattice QCD and its extended strong-weak connection to the hypersphere
We calculate an effective Polyakov line action of QCD at large Nc and large
Nf from a combined lattice strong coupling and hopping expansion working to
second order in both, where the order is defined by the number of windings in
the Polyakov line. We compare with the action, truncated at the same order, of
continuum QCD on S^1 x S^d at weak coupling from one loop perturbation theory,
and find that a large Nc correspondence of equations of motion found in
\cite{Hollowood:2012nr} at leading order, can be extended to the next order.
Throughout the paper, we review the background necessary for computing higher
order corrections to the lattice effective action, in order to make higher
order comparisons more straightforward.Comment: 33 pages, 7 figure
Random Walk with Shrinking Steps: First Passage Characteristics
We study the mean first passage time of a one-dimensional random walker with
step sizes decaying exponentially in discrete time. That is step sizes go like
with . We also present, for pedagogical purposes,
a continuum system with a diffusion constant decaying exponentially in
continuous time. Qualitatively both systems are alike in their global
properties. However, the discrete case shows very rich mathematical structure,
depending on the value of the shrinking parameter, such as self-repetitive and
fractal-like structure for the first passage characteristics. The results we
present show that the most important quantitative behavior of the discrete case
is that the support of the distribution function evolves in time in a rather
complicated way in contrast to the time independent lattice structure of the
ordinary random walker. We also show that there are critical values of
defined by the equation with
where the mean first passage time undergo transitions.Comment: Major Re-Editing of the article. Conclusions unaltere
The Internet's unexploited path diversity
The connectivity of the Internet at the Autonomous System level is influenced
by the network operator policies implemented. These in turn impose a direction
to the announcement of address advertisements and, consequently, to the paths
that can be used to reach back such destinations. We propose to use directed
graphs to properly represent how destinations propagate through the Internet
and the number of arc-disjoint paths to quantify this network's path diversity.
Moreover, in order to understand the effects that policies have on the
connectivity of the Internet, numerical analyses of the resulting directed
graphs were conducted. Results demonstrate that, even after policies have been
applied, there is still path diversity which the Border Gateway Protocol cannot
currently exploit.Comment: Submitted to IEEE Communications Letter
Resonant relaxation near a massive black hole: the stellar distribution and gravitational wave sources
Resonant relaxation (RR) of orbital angular momenta occurs near massive black
holes (MBHs) where the stellar orbits are nearly Keplerian and so do not
precess significantly. The resulting coherent torques efficiently change the
magnitude of the angular momenta and rotate the orbital inclination in all
directions. As a result, many of the tightly bound stars very near the MBH are
rapidly destroyed by falling into the MBH on low-angular momentum orbits, while
the orbits of the remaining stars are efficiently randomized. We solve
numerically the Fokker-Planck equation in energy for the steady state
distribution of a single mass population with a RR sink term. We find that the
steady state current of stars, which sustains the accelerated drainage close to
the MBH, can be up to ~10 times larger than that due to non-coherent 2-body
relaxation alone. RR mostly affects tightly bound stars, and so it increases
only moderately the total tidal disruption rate, which is dominated by stars
originating from less bound orbits farther away. We show that the event rate of
gravitational wave (GW) emission from inspiraling stars, originating much
closer to the MBH, is dominated by RR dynamics. The GW event rate depends on
the uncertain efficiency of RR. The efficiency indicated by the few available
simulations implies rates ~10 times higher than those predicted by 2-body
relaxation, which would improve the prospects of detecting such events by
future GW detectors, such as LISA. However, a higher, but still plausible RR
efficiency can lead to the drainage of all tightly bound stars and strong
suppression of GW events from inspiraling stars. We apply our results to the
Galactic MBH, and show that the observed dynamical properties of stars there
are consistent with RR.Comment: Accepted to ApJ; Minor revision
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