4,061 research outputs found
Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model
A fast method is presented for simulating the dielectric-breakdown model
using iterated conformal mappings. Numerical results for the dimension and for
corrections to scaling are in good agreement with the recent RG prediction of
an upper critical , at which a transition occurs between branching
fractal clusters and one-dimensional nonfractal clusters.Comment: 5 pages, 7 figures; corrections to scaling include
EAGLE ISS - A modular twin-channel integral-field near-IR spectrograph
The ISS (Integral-field Spectrograph System) has been designed as part of the
EAGLE Phase A Instrument Study for the E-ELT. It consists of two input channels
of 1.65x1.65 arcsec field-of-view, each reconfigured spatially by an
image-slicing integral-field unit to feed a single near-IR spectrograph using
cryogenic volume-phase-holographic (VPH) gratings to disperse the image
spectrally. A 4k x 4k array detector array records the dispersed images. The
optical design employs anamorphic magnification, image slicing, VPH gratings
scanned with a novel cryo-mechanism and a three-lens camera. The mechanical
implementation features IFU optics in Zerodur, a modular bench structure and a
number of high-precision cryo-mechanisms.Comment: 12 pages, to be published in Proc SPIE 7735: Ground-based & Airborne
Instrumentation for Astronomy II
Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
We compute the bipartite entanglement properties of the spin-half
square-lattice Heisenberg model by a variety of numerical techniques that
include valence bond quantum Monte Carlo (QMC), stochastic series expansion
QMC, high temperature series expansions and zero temperature coupling constant
expansions around the Ising limit. We find that the area law is always
satisfied, but in addition to the entanglement entropy per unit boundary
length, there are other terms that depend logarithmically on the subregion
size, arising from broken symmetry in the bulk and from the existence of
corners at the boundary. We find that the numerical results are anomalous in
several ways. First, the bulk term arising from broken symmetry deviates from
an exact calculation that can be done for a mean-field Neel state. Second, the
corner logs do not agree with the known results for non-interacting Boson
modes. And, third, even the finite temperature mutual information shows an
anomalous behavior as T goes to zero, suggesting that T->0 and L->infinity
limits do not commute. These calculations show that entanglement entropy
demonstrates a very rich behavior in d>1, which deserves further attention.Comment: 12 pages, 7 figures, 2 tables. Numerical values in Table I correcte
Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives
We investigate the dynamical motion of particles on a two-dimensional
symmetric periodic substrate in the presence of both a dc drive along a
symmetry direction of the periodic substrate and an additional circular ac
drive. For large enough ac drives, the particle orbit encircles one or more
potential maxima of the periodic substrate. In this case, when an additional
increasing dc drive is applied in the longitudinal direction, the longitudinal
velocity increases in a series of discrete steps that are integer multiples of
the lattice constant of the substrate times the frequency. Fractional steps can
also occur. These integer and fractional steps correspond to distinct stable
dynamical orbits. A number of these phases also show a rectification in the
positive or negative transverse direction where a non-zero transverse velocity
occurs in the absence of a dc transverse drive. We map out the phase diagrams
of the regions of rectification as a function of ac amplitude, and find a
series of tongues. Most of the features, including the steps in the
longitudinal velocity and the transverse rectification, can be captured with a
simple toy model and by arguments from nonlinear maps. We have also
investigated the effects of thermal disorder and incommensuration on the
rectification phenomena, and find that for increasing disorder, the
rectification regions are gradually smeared and the longitudinal velocity steps
are no longer flat but show a linearly increasing velocity.Comment: 14 pages, 17 postscript figure
The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
We study families H_n of 1D quantum spin systems, where n is the number of
spins, which have a spectral gap \Delta E between the ground-state and
first-excited state energy that scales, asymptotically, as a constant in n. We
show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins,
where m is an O(1) constant, is locally the same as the ground state
|\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to
the ground state of H_n can be stored efficiently for all n. We formulate a
conjecture that, if true, would imply our result applies to all noncritical 1D
spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change
Perceptions and discourses relating to genetic testing : interviews with people with Down syndrome
Background:
The perceptions of individuals with Down syndrome are conspicuously absent in discussions about the use of prenatal testing.
Method:
Eight individuals with Down syndrome were interviewed about their views and experience of the topic of prenatal testing.
Results:
Interpretative Phenomenological Analysis revealed two major themes with sub themes: 1) A devalued condition and a valued life and 2) A question of âwant?â Foucauldian Discourse Analysis highlighted two main discursive practices: 1) Social deviance and 2) Tragedy and catastrophe of the birth of a baby with Down syndrome.
Conclusions:
The findings suggest that individuals with intellectual disabilities can make a valuable contribution to discussions surrounding the use of prenatal testing. Implications for clinical practice include the use of information about Down syndrome given to prospective parents, and the possible psychological impact of prenatal testing practices on individuals with Down syndrome
Topology and Phases in Fermionic Systems
There can exist topological obstructions to continuously deforming a gapped
Hamiltonian for free fermions into a trivial form without closing the gap.
These topological obstructions are closely related to obstructions to the
existence of exponentially localized Wannier functions. We show that by taking
two copies of a gapped, free fermionic system with complex conjugate
Hamiltonians, it is always possible to overcome these obstructions. This allows
us to write the ground state in matrix product form using Grassman-valued bond
variables, and show insensitivity of the ground state density matrix to
boundary conditions.Comment: 4 pages, see also arxiv:0710.329
Community Detection as an Inference Problem
We express community detection as an inference problem of determining the
most likely arrangement of communities. We then apply belief propagation and
mean-field theory to this problem, and show that this leads to fast, accurate
algorithms for community detection.Comment: 4 pages, 2 figure
Statistics of Partial Minima
Motivated by multi-objective optimization, we study extrema of a set of N
points independently distributed inside the d-dimensional hypercube. A point in
this set is k-dominated by another point when at least k of its coordinates are
larger, and is a k-minimum if it is not k-dominated by any other point. We
obtain statistical properties of these partial minima using exact probabilistic
methods and heuristic scaling techniques. The average number of partial minima,
A, decays algebraically with the total number of points, A ~ N^{-(d-k)/k}, when
1<=k<d. Interestingly, there are k-1 distinct scaling laws characterizing the
largest coordinates as the distribution P(y_j) of the jth largest coordinate,
y_j, decays algebraically, P(y_j) ~ (y_j)^{-alpha_j-1}, with
alpha_j=j(d-k)/(k-j) for 1<=j<=k-1. The average number of partial minima grows
logarithmically, A ~ [1/(d-1)!](ln N)^{d-1}, when k=d. The full distribution of
the number of minima is obtained in closed form in two-dimensions.Comment: 6 pages, 1 figur
Diffusion limited aggregation as a Markovian process: site-sticking conditions
Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width
N, is solved for site-sticking conditions using a Markovian matrix method
(which was previously developed for the bond-sticking case). This matrix
contains the probabilities that the front moves from one configuration to
another at each growth step, calculated exactly by solving the Laplace equation
and using the proper normalization. The method is applied for a series of
approximations, which include only a finite number of rows near the front. The
fractal dimensionality of the aggregate is extrapolated to a value near 1.68.Comment: 27 Revtex pages, 16 figure
- âŠ