5,958 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
Noise measurements for a twin-engine commercial jet aircraft during 3 deg approaches and level flyovers
Noise measurements have been made with a twin-engine commercial jet aircraft making 3 deg approaches and level flyovers. The flight-test data showed that, in the standard 3 deg approach configuration with 40 deg flaps, effective perceived noise level (EPNL) had a value of 109.5 effective perceived noise decibels (EPNdB). This result was in agreement with unpublished data obtained with the same type of aircraft during noise certification tests; the 3 deg approaches made with 30 deg flaps and slightly reduced thrust reduced the EPNL value by 1 EPNdB. Extended center-line noise determined during the 3 deg approaches with 40 deg flaps showed that the maximum reference A-weighted sound pressure level (LA,max)ref varied from 100.0 A-weighted decibels 2.01 km (108 n. mi.) from the threshold to 87.4 db(A) at 6.12 km (3.30 n. mi.) from the threshold. These test values were about 3 db(A) higher than estimates used for comparison. The test data along the extended center line during approaches with 30 deg flaps were 1 db(A) lower than those for approaches with 40 deg flaps. Flight-test data correlating (LA,max)ref with thrust at altitudes of 122 m (400 ft) and 610 m (2000 ft) were in agreement with reference data used for comparison
Multiscaling at Point J: Jamming is a Critical Phenomenon
We analyze the jamming transition that occurs as a function of increasing
packing density in a disordered two-dimensional assembly of disks at zero
temperature for ``Point J'' of the recently proposed jamming phase diagram. We
measure the total number of moving disks and the transverse length of the
moving region, and find a power law divergence as the packing density increases
toward a critical jamming density. This provides evidence that the T = 0
jamming transition as a function of packing density is a {\it second order}
phase transition. Additionally we find evidence for multiscaling, indicating
the importance of long tails in the velocity fluctuations.Comment: 4 pages, 5 figures; extensive new numerical data; final version in
press at PR
Noise data for a twin-engine commercial jet aircraft flying conventional, steep, and two-segment approaches
Center-line noise measurements of a twin-engine commercial jet aircraft were made during steep landing approach profiles, and during two-segment approach profiles for comparison with similar measurements made during conventional approaches. The steep and two-segment approaches showed significant noise reductions when compared with the -3 deg base line. The measured noise data were also used to develop a method for estimating the noise under the test aircraft at thrust and altitude conditions typical of current landing procedures and of landing procedures under development for the Advanced Air Traffic Control System
Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model
We show that the fractal growth described by the dielectric breakdown model
exhibits a phase transition in the multifractal spectrum of the growth measure.
The transition takes place because the tip-splitting of branches forms a fixed
angle. This angle is eta dependent but it can be rescaled onto an
``effectively'' universal angle of the DLA branching process. We derive an
analytic rescaling relation which is in agreement with numerical simulations.
The dimension of the clusters decreases linearly with the angle and the growth
becomes non-fractal at an angle close to 74 degrees (which corresponds to eta=
4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure
Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation
We consider the polynomials orthonormal with respect to the weight on the unit circle in the complex plane. The leading coefficient
is found to satisfy a difference-differential (spatially discrete)
equation which is further proved to approach a third order differential
equation by double scaling. The third order differential equation is equivalent
to the Painlev\'e II equation. The leading coefficient and second leading
coefficient of can be expressed asymptotically in terms of the
Painlev\'e II function.Comment: 16 page
Developing the evidence base for adult social care practice: The NIHR School for Social Care Research
In a foreword to 'Shaping the Future of Care Together', Prime Minister Gordon Brown says that a care and support system reflecting the needs of our times and meeting our rising aspirations is achievable, but 'only if we are prepared to rise to the challenge of radical reform'. A number of initiatives will be needed to meet the challenge of improving social care for the growing older population. Before the unveiling of the green paper, The National Institute for Health Research (NIHR) announced that it has provided 15m pounds over a five-year period to establish the NIHR School for Social Care Research. The School's primary aim is to conduct or commission research that will help to improve adult social care practice in England. The School is seeking ideas for research topics, outline proposals for new studies and expert advice in developing research methods
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
Exact Multifractal Spectra for Arbitrary Laplacian Random Walks
Iterated conformal mappings are used to obtain exact multifractal spectra of
the harmonic measure for arbitrary Laplacian random walks in two dimensions.
Separate spectra are found to describe scaling of the growth measure in time,
of the measure near the growth tip, and of the measure away from the growth
tip. The spectra away from the tip coincide with those of conformally invariant
equilibrium systems with arbitrary central charge , with related
to the particular walk chosen, while the scaling in time and near the tip
cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction
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