1,584 research outputs found
Evolutionary dynamics of incubation periods
The incubation period of a disease is the time between an initiating
pathologic event and the onset of symptoms. For typhoid fever, polio, measles,
leukemia and many other diseases, the incubation period is highly variable.
Some affected people take much longer than average to show symptoms, leading to
a distribution of incubation periods that is right skewed and often
approximately lognormal. Although this statistical pattern was discovered more
than sixty years ago, it remains an open question to explain its ubiquity. Here
we propose an explanation based on evolutionary dynamics on graphs. For simple
models of a mutant or pathogen invading a network-structured population of
healthy cells, we show that skewed distributions of incubation periods emerge
for a wide range of assumptions about invader fitness, competition dynamics,
and network structure. The skewness stems from stochastic mechanisms associated
with two classic problems in probability theory: the coupon collector and the
random walk. Unlike previous explanations that rely crucially on heterogeneity,
our results hold even for homogeneous populations. Thus, we predict that two
equally healthy individuals subjected to equal doses of equally pathogenic
agents may, by chance alone, show remarkably different time courses of disease.Comment: 24 pages, 8 figures, 1 tabl
Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua
We compare and contrast two types of deformations inspired by mixing
applications -- one from the mixing of fluids (stretching and folding), the
other from the mixing of granular matter (cutting and shuffling). The
connection between mechanics and dynamical systems is discussed in the context
of the kinematics of deformation, emphasizing the equivalence between stretches
and Lyapunov exponents. The stretching and folding motion exemplified by the
baker's map is shown to give rise to a dynamical system with a positive
Lyapunov exponent, the hallmark of chaotic mixing. On the other hand, cutting
and shuffling does not stretch. When an interval exchange transformation is
used as the basis for cutting and shuffling, we establish that all of the map's
Lyapunov exponents are zero. Mixing, as quantified by the interfacial area per
unit volume, is shown to be exponentially fast when there is stretching and
folding, but linear when there is only cutting and shuffling. We also discuss
how a simple computational approach can discern stretching in discrete data.Comment: REVTeX 4.1, 9 pages, 3 figures; v2 corrects some misprints. The
following article appeared in the American Journal of Physics and may be
found at http://ajp.aapt.org/resource/1/ajpias/v79/i4/p359_s1 . Copyright
2011 American Association of Physics Teachers. This article may be downloaded
for personal use only. Any other use requires prior permission of the author
and the AAP
Experimental evidence of chaotic advection in a convective flow
Lagrangian chaos is experimentally investigated in a convective flow by means
of Particle Tracking Velocimetry. The Fnite Size Lyapunov Exponent analysis is
applied to quantify dispersion properties at different scales. In the range of
parameters of the experiment, Lagrangian motion is found to be chaotic.
Moreover, the Lyapunov depends on the Rayleigh number as . A
simple dimensional argument for explaining the observed power law scaling is
proposed.Comment: 7 pages, 3 figur
Optimization of 125-mu m Heterogeneous Multi-Core Fibre Design Using Artificial Intelligence
We propose an automated heterogeneous trench-assisted multi-core fibre (MCF) design method. This method uses neural networks to speed up coating loss estimation by ∼ 10^{6} times and using particle swarm optimization (PSO) algorithm to explore the optimal MCF design under various objectives and properties constraints. The latter reduces the permutation evaluations by ten orders of magnitude compared with the brute force method. The artificial intelligence (AI)-based method is used to design MCFs on two objectives: minimizing crosstalk (XT) and maximizing effective mode area ( A_{eff} ). By optimizing XT with different A_{eff} and cutoff wavelength constraints combinations for 6-core fibres, we achieved −92.1 dB/km ultra-low XT for C+L band fibre and −64 dB/km for E+S+C+L-band fibre. Meanwhile, we explored the upper limit of A_{eff} given different bandwidth constraints resulting in a 6.82 relative core multiplicity factor. We performed capacity analysis of fibres for two transmission lengths. It is shown that bandwidth is the dominant factor while the increase brought by A_{eff} and the penalty caused by XT are relevantly small. Our fibres exceed the cutoff-limited capacity of the 7-core fibre in literature by 35.1% and 84.8% for 1200 km and 6000 km transmission respectively
Design Optimization of Uncoupled Six-core Fibers in Standard Cladding Diameter Using Artificial Intelligence
We report on ultra-wide-band and long-haul compatible 125µm six-core trench-assisted fiber designs. The AI-optimization process considers crosstalk, effective area, and bandwidth. We show that homogeneous cores can lead to low complexity yet high capacity fiber
Transport and diffusion in the embedding map
We study the transport properties of passive inertial particles in a
incompressible flows. Here the particle dynamics is represented by the
dissipative embedding map of area-preserving standard map which models
the incompressible flow. The system is a model for impurity dynamics in a fluid
and is characterized by two parameters, the inertia parameter , and the
dissipation parameter . We obtain the statistical characterisers of
transport for this system in these dynamical regimes. These are, the recurrence
time statistics, the diffusion constant, and the distribution of jump lengths.
The recurrence time distribution shows a power law tail in the dynamical
regimes where there is preferential concentration of particles in sticky
regions of the phase space, and an exponential decay in mixing regimes. The
diffusion constant shows behaviour of three types - normal, subdiffusive and
superdiffusive, depending on the parameter regimes. Phase diagrams of the
system are constructed to differentiate different types of diffusion behaviour,
as well as the behaviour of the absolute drift. We correlate the dynamical
regimes seen for the system at different parameter values with the transport
properties observed at these regimes, and in the behaviour of the transients.
This system also shows the existence of a crisis and unstable dimension
variability at certain parameter values. The signature of the unstable
dimension variability is seen in the statistical characterisers of transport.
We discuss the implications of our results for realistic systems.Comment: 28 pages, 14 figures, To Appear in Phys. Rev. E; Vol. 79 (2009
Walls Inhibit Chaotic Mixing
We report on experiments of chaotic mixing in a closed vessel, in which a
highly viscous fluid is stirred by a moving rod. We analyze quantitatively how
the concentration field of a low-diffusivity dye relaxes towards homogeneity,
and we observe a slow algebraic decay of the inhomogeneity, at odds with the
exponential decay predicted by most previous studies. Visual observations
reveal the dominant role of the vessel wall, which strongly influences the
concentration field in the entire domain and causes the anomalous scaling. A
simplified 1D model supports our experimental results. Quantitative analysis of
the concentration pattern leads to scalings for the distributions and the
variance of the concentration field consistent with experimental and numerical
results.Comment: 4 pages, 3 figure
Targeted mixing in an array of alternating vortices
Transport and mixing properties of passive particles advected by an array of
vortices are investigated. Starting from the integrable case, it is shown that
a special class of perturbations allows one to preserve separatrices which act
as effective transport barriers, while triggering chaotic advection. In this
setting, mixing within the two dynamical barriers is enhanced while long range
transport is prevented. A numerical analysis of mixing properties depending on
parameter values is performed; regions for which optimal mixing is achieved are
proposed. Robustness of the targeted mixing properties regarding errors in the
applied perturbation are considered, as well as slip/no-slip boundary
conditions for the flow
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