5,944 research outputs found
Critical random graphs: limiting constructions and distributional properties
We consider the Erdos-Renyi random graph G(n,p) inside the critical window,
where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous
paper (arXiv:0903.4730) that considering the connected components of G(n,p) as
a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and
letting n go to infinity yields a non-trivial sequence of limit metric spaces C
= (C_1, C_2, ...). These limit metric spaces can be constructed from certain
random real trees with vertex-identifications. For a single such metric space,
we give here two equivalent constructions, both of which are in terms of more
standard probabilistic objects. The first is a global construction using
Dirichlet random variables and Aldous' Brownian continuum random tree. The
second is a recursive construction from an inhomogeneous Poisson point process
on R_+. These constructions allow us to characterize the distributions of the
masses and lengths in the constituent parts of a limit component when it is
decomposed according to its cycle structure. In particular, this strengthens
results of Luczak, Pittel and Wierman by providing precise distributional
convergence for the lengths of paths between kernel vertices and the length of
a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure
Critical random graphs : limiting constructions and distributional properties
We consider the Erdos-Renyi random graph G(n, p) inside the critical window, where p = 1/n + lambda n(-4/3) for some lambda is an element of R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n(-1/3) and letting n -> infinity yields a non-trivial sequence of limit metric spaces C = (C-1, C-2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak et al. [1994] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component
Large time dynamics and aging of a polymer chain in a random potential
We study the out-of-equilibrium large time dynamics of a gaussian polymer
chain in a quenched random potential. The dynamics studied is a simple Langevin
dynamics commonly referred to as the Rouse model. The equations for the
two-time correlation and response function are derived within the gaussian
variational approximation. In order to implement this approximation faithfully,
we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical
action. For a short ranged correlated random potential the equations are solved
analytically in the limit of large times using certain assumptions concerning
the asymptotic behavior. Two possible dynamical behaviors are identified
depending upon the time separation- a stationary regime and an aging regime. In
the stationary regime time translation invariance holds and so is the
fluctuation dissipation theorem. The aging regime which occurs for large time
separations of the two-time correlation functions is characterized by history
dependence and the breakdown of certain equilibrium relations. The large time
limit of the equations yields equations among the order parameters that are
similar to the equations obtained in the statics using replicas. In particular
the aging solution corresponds to the broken replica solution. But there is a
difference in one equation that leads to important consequences for the
solution. The stationary regime corresponds to the motion of the polymer inside
a local minimum of the random potential, whereas in the aging regime the
polymer hops between different minima. As a byproduct we also solve exactly the
dynamics of a chain in a random potential with quadratic correlations.Comment: 21 pages, RevTeX
Disorder effects in the quantum Heisenberg model: An Extended Dynamical mean-field theory analysis
We investigate a quantum Heisenberg model with both antiferromagnetic and
disordered nearest-neighbor couplings. We use an extended dynamical mean-field
approach, which reduces the lattice problem to a self-consistent local impurity
problem that we solve by using a quantum Monte Carlo algorithm. We consider
both two- and three-dimensional antiferromagnetic spin fluctuations and
systematically analyze the effect of disorder. We find that in three dimensions
for any small amount of disorder a spin-glass phase is realized. In two
dimensions, while clean systems display the properties of a highly correlated
spin-liquid (where the local spin susceptibility has a non-integer power-low
frequency and/or temperature dependence), in the present case this behavior is
more elusive unless disorder is very small. This is because the spin-glass
transition temperature leaves only an intermediate temperature regime where the
system can display the spin-liquid behavior, which turns out to be more
apparent in the static than in the dynamical susceptibility.Comment: 15 pages, 7 figure
The Response of a Hot-Wire Anemometer to a Bubble of Air in Water
The sensitivity of peak voltage drop and duration of the change In sensor voltages due to the impaction of different size bubbles are confuted and measured. Excellent agreement between these is found for bubbles somewhat larger than the sensor diameter and smaller than Its effective length in water streams in a range of 1.5 to 9 feet per second. The method suggests a reliable method for sizing bubbles in a water stream. The effects due to nondirect hits are not treated
Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class
The probability P(alpha, N) that search algorithms for random Satisfiability
problems successfully find a solution is studied as a function of the ratio
alpha of constraints per variable and the number N of variables. P is shown to
be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and
exponentially small in N above. The critical behaviour is universal for all
algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon)
alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to
the critical behaviour of random graphs, and the scaling function Phi is
exactly calculated through a mapping onto a diffusion-and-death problem.Comment: 7 pages; 3 figure
Analysis of Gamma Rays and Cosmic Muons with a Single Detector
In this paper, we report on the construction and upgrade of a 2002 Lawrence Berkeley National Laboratory (LBNL) Quanknet Cosmic Muons Detector. By adapting this model, we modify the electronics and mechanics to achieve a highly efficient gamma-ray and cosmic-ray detector. Each detector module uses a one-inch-thick scintillator, attached to a photomultiplier tube (PMT) and mounted on a solid aluminum frame. A mechanical support was designed to allow flexible positioning between the two modules. The detector uses scintillation to transform passing radiation into detectable photons that are guided toward a photocathode surface of the PMT, triggering the release of photoelectrons that are then amplified to yield measurable electronic signals. The modules were connected to an electronics section that compared the signals from the two PMTs and logically determined if they were coincidence events. A data-collection device was added for faster count rates and to enable counts for extended times ranging from a few hours to days as needed. Count rates were taken at a variety of distances from the radioactive source, 60Co (cobalt), which produced two gamma rays and a beta particle. To investigate the isotropic behavior of radiation, two detection modules were adjusted to different angles of rotation with respect to each other, and the coincidence counts were measured. The coincidence counts from the modules set at various angles were consistent throughout the angular spectrum, and only lead shielding visibly reduced the number of counts from the radioactive source. The inverse-square-law behavior of radiation has also been considered. The results were such that the number of counts decreased as a function of increasing distance from the source. Furthermore, positioning the detector to point toward the sky in different orientations, we measured cosmic ray muon flux as the angle from the vertical was decreased. In doing so, we scanned different patches of the atmosphere. For the optimum operation during the detection phase, we plateaued both PMTs to single out their best operating gain voltage while eliminating false background noise signals. The detector is more efficient and adaptable in collecting both gamma rays and cosmic-ray muon-flux information
The Stellar Populations and Evolution of Lyman Break Galaxies
Using deep near-IR and optical observations of the HDF-N from the HST NICMOS
and WFPC2 and from the ground, we examine the spectral energy distributions
(SEDs) of Lyman break galaxies (LBGs) at 2.0 < z < 3.5. The UV-to-optical
rest-frame SEDs of the galaxies are much bluer than those of present-day spiral
and elliptical galaxies, and are generally similar to those of local starburst
galaxies with modest amounts of reddening. We use stellar population synthesis
models to study the properties of the stars that dominate the light from LBGs.
Under the assumption that the star-formation rate is continuous or decreasing
with time, the best-fitting models provide a lower bound on the LBG mass
estimates. LBGs with ``L*'' UV luminosities are estimated to have minimum
stellar masses ~ 10^10 solar masses, or roughly 1/10th that of a present-day L*
galaxy. By considering the effects of a second component of maximally-old
stars, we set an upper bound on the stellar masses that is ~ 3-8 times the
minimum estimate. We find only loose constraints on the individual galaxy ages,
extinction, metallicities, initial mass functions, and prior star-formation
histories. We find no galaxies whose SEDs are consistent with young (< 10^8
yr), dust-free objects, which suggests that LBGs are not dominated by ``first
generation'' stars, and that such objects are rare at these redshifts. We also
find that the typical ages for the observed star-formation events are
significantly younger than the time interval covered by this redshift range (~
1.5 Gyr). From this, and from the relative absence of candidates for quiescent,
non-star-forming galaxies at these redshifts in the NICMOS data, we suggest
that star formation in LBGs may be recurrent, with short duty cycles and a
timescale between star-formation events of < 1 Gyr. [Abridged]Comment: LaTeX, 37 pages, 21 figures. Accepted for publication in the
Astrophysical Journa
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