1,016 research outputs found
Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results
We formulate dynamical rate equations for physical processes driven by a
combination of diffusive growth, size fragmentation and fragment coagulation.
Initially, we consider processes where coagulation is absent. In this case we
solve the rate equation exactly leading to size distributions of Bessel type
which fall off as for large -values. Moreover, we provide
explicit formulas for the expansion coefficients in terms of Airy functions.
Introducing the coagulation term, the full non-linear model is mapped exactly
onto a Riccati equation that enables us to derive various asymptotic solutions
for the distribution function. In particular, we find a standard exponential
decay, , for large , and observe a crossover from the Bessel
function for intermediate values of . These findings are checked by
numerical simulations and we find perfect agreement between the theoretical
predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections
Pitch Dynamics of Unmanned Aerial Vehicles
Dynamic stability requirements for manned aircraft have been in place for many years. However, we cannot expect stability constraints for UAVs to match those for manned aircraft; and dynamic stability requirements specific to UAVs have not been developed. The boundaries of controllability for both remotely-piloted and auto-piloted aircraft must be established before UAV technology can reach its full potential. The development of dynamic stability requirements specific to UAVs could improve flying qualities and facilitate more efficient UAV designs to meet specific mission requirements. As a first step to developing UAV stability requirements in general, test techniques must be established that will allow the stability characteristics of current UAVs to be quantified. This paper consolidates analytical details associated with procedures that could be used to experimentally determine the pitch stability boundaries for good UAV flying qualities. The procedures require determining only the maneuver margin and pitch radius of gyration and are simple enough to be used in an educational setting where resources are limited. The premise is that these procedures could be applied to UAVs now in use, in order to characterize the longitudinal flying qualities of current aircraft. This is but a stepping stone to the evaluation of candidate metrics for establishing flying-quality constraints for unmanned aircraft
Fossil shark teeth from upland Fleurieu Peninsula, South Australia: evidence for previously unknown Tertiary marine sediments
Neville S Pledge, Anthony R Milnes, Robert P Bourman, and Neville F Alle
Short-wavelength collective modes in a binary hard-sphere mixture
We use hard-sphere generalized hydrodynamic equations to discuss the extended
hydrodynamic modes of a binary mixture. The theory presented here is analytic
and it provides us with a simple description of the collective excitations of a
dense binary mixture at molecular length scales. The behavior we predict is in
qualitative agreement with molecular-dynamics results for soft-sphere mixtures.
This study provides some insight into the role of compositional disorder in
forming glassy configurations.Comment: Published; withdrawn since already published. Ordering in the archive
gives misleading impression of new publicatio
Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime
The Landau-Lifshitz fluctuating hydrodynamics is used to study the
statistical properties of the linearized Kolmogorov flow. The relative
simplicity of this flow allows a detailed analysis of the fluctuation spectrum
from near equilibrium regime up to the vicinity of the first convective
instability threshold. It is shown that in the long time limit the flow behaves
as an incompressible fluid, regardless of the value of the Reynolds number.
This is not the case for the short time behavior where the incompressibility
assumption leads in general to a wrong form of the static correlation
functions, except near the instability threshold. The theoretical predictions
are confirmed by numerical simulations of the full nonlinear fluctuating
hydrodynamic equations.Comment: 20 pages, 4 figure
A Delayed Choice Quantum Eraser
This paper reports a "delayed choice quantum eraser" experiment proposed by
Scully and Dr\"{u}hl in 1982. The experimental results demonstrated the
possibility of simultaneously observing both particle-like and wave-like
behavior of a quantum via quantum entanglement. The which-path or both-path
information of a quantum can be erased or marked by its entangled twin even
after the registration of the quantum.Comment: twocolumn, 4pages, submitted to PR
Realistic Calculation of the hep Astrophysical Factor
The astrophysical factor for the proton weak capture on 3He is calculated
with correlated-hyperspherical-harmonics bound and continuum wave functions
corresponding to a realistic Hamiltonian consisting of the Argonne v18
two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak charge
and current operators have vector and axial-vector components, that include
one- and many-body terms. All possible multipole transitions connecting any of
the p-3He S- and P-wave channels to the 4He bound state are considered. The
S-factor at a p-3He center-of-mass energy of 10 keV, close to the Gamow-peak
energy, is predicted to be 10.1 10^{-20} keV b, a factor of five larger than
the standard-solar-model value. The P-wave transitions are found to be
important, contributing about 40 % of the calculated S-factor.Comment: 8 pages RevTex file, submitted to Phys. Rev. Let
Is subarctic forest advance able to keep pace with climate change?
Recent climate warming and scenarios for further warming have led to expectations of rapid movement of ecological boundaries. Here we focus on the circumarctic forest-tundra ecotone (FTE), which represents an important bioclimatic zone with feedbacks from forest advance and corresponding tundra disappearance (up to 50% loss predicted this century) driving widespread ecological and climatic changes. We address FTE advance and climate history relations over the 20th century, using FTE response data from 151 sites across the circumarctic area and site-specific climate data. Specifically, we investigate spatial uniformity of FTE advance, statistical associations with 20th century climate trends, and whether advance rates match climate change velocities (CCVs). Study sites diverged into four regions (Eastern Canada; Central and Western Canada and Alaska; Siberia; and Western Eurasia) based on their climate history, although all were characterized by similar qualitative patterns of behaviour (with about half of the sites showing advancing behaviour). The main associations between climate trend variables and behaviour indicate the importance of precipitation rather than temperature for both qualitative and quantitative behaviours, and the importance of non-growing season as well as growing season months. Poleward latitudinal advance rates differed significantly among regions, being smallest in Eastern Canada (~10Â m/year) and largest in Western Eurasia (~100Â m/year). These rates were 1-2 orders of magnitude smaller than expected if vegetation distribution remained in equilibrium with climate. The many biotic and abiotic factors influencing FTE behaviour make poleward advance rates matching predicted 21st century CCVs (~103 -104 Â m/year) unlikely. The lack of empirical evidence for swift forest relocation and the discrepancy between CCV and FTE response contradict equilibrium model-based assumptions and warrant caution when assessing global-change-related biotic and abiotic implications, including land-atmosphere feedbacks and carbon sequestration.Funding was provided by the Norwegian Research Council (grants 176065/S30, 185023/S50, 160022/F40 and 244557/RI), the Government of Canada Program for International Polar Year, the US National Science Foundation, and the University of Cambridge
A mathematical framework for critical transitions: normal forms, variance and applications
Critical transitions occur in a wide variety of applications including
mathematical biology, climate change, human physiology and economics. Therefore
it is highly desirable to find early-warning signs. We show that it is possible
to classify critical transitions by using bifurcation theory and normal forms
in the singular limit. Based on this elementary classification, we analyze
stochastic fluctuations and calculate scaling laws of the variance of
stochastic sample paths near critical transitions for fast subsystem
bifurcations up to codimension two. The theory is applied to several models:
the Stommel-Cessi box model for the thermohaline circulation from geoscience,
an epidemic-spreading model on an adaptive network, an activator-inhibitor
switch from systems biology, a predator-prey system from ecology and to the
Euler buckling problem from classical mechanics. For the Stommel-Cessi model we
compare different detrending techniques to calculate early-warning signs. In
the epidemics model we show that link densities could be better variables for
prediction than population densities. The activator-inhibitor switch
demonstrates effects in three time-scale systems and points out that excitable
cells and molecular units have information for subthreshold prediction. In the
predator-prey model explosive population growth near a codimension two
bifurcation is investigated and we show that early-warnings from normal forms
can be misleading in this context. In the biomechanical model we demonstrate
that early-warning signs for buckling depend crucially on the control strategy
near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio
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