862 research outputs found
Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments
We consider a population living in a patchy environment that varies
stochastically in space and time. The population is composed of two morphs
(that is, individuals of the same species with different genotypes). In terms
of survival and reproductive success, the associated phenotypes differ only in
their habitat selection strategies. We compute invasion rates corresponding to
the rates at which the abundance of an initially rare morph increases in the
presence of the other morph established at equilibrium. If both morphs have
positive invasion rates when rare, then there is an equilibrium distribution
such that the two morphs coexist; that is, there is a protected polymorphism
for habitat selection. Alternatively, if one morph has a negative invasion rate
when rare, then it is asymptotically displaced by the other morph under all
initial conditions where both morphs are present. We refine the
characterization of an evolutionary stable strategy for habitat selection from
[Schreiber, 2012] in a mathematically rigorous manner. We provide a necessary
and sufficient condition for the existence of an ESS that uses all patches and
determine when using a single patch is an ESS. We also provide an explicit
formula for the ESS when there are two habitat types. We show that adding
environmental stochasticity results in an ESS that, when compared to the ESS
for the corresponding model without stochasticity, spends less time in patches
with larger carrying capacities and possibly makes use of sink patches, thereby
practicing a spatial form of bet hedging.Comment: Revised in light of referees' comments, Published on-line Journal of
Mathematical Biology 2014
http://link.springer.com/article/10.1007/s00285-014-0824-
The statistics of the trajectory in a certain billiard in a flat two-torus
We consider a billiard in the punctured torus obtained by removing a small
disk from the two-dimensional flat torus, with trajectory starting from the
center of the puncture. In this case the phase space is given by the range of
the velocity only. We prove that the probability measures on
associated with the first exit time are weakly convergent when the size of the
puncture tends to zero and explicitly compute the density of the limit.Comment: 21 pages, 6 figure
Simulink modeling and design of an efficient hardware-constrained FPGA-based PMSM speed controller
The aim of this paper is to present a holistic approach to modeling and FPGA implementation of a permanent magnet synchronous motor (PMSM) speed controller. The whole system is modeled in the Matlab Simulink environment. The controller is then translated to discrete time and remodeled using System Generator blocks, directly synthesizable into FPGA hardware. The algorithm is further refined and factorized to take into account hardware constraints, so as to fit into a low cost FPGA, without significantly increasing the execution time. The resulting controller is then integrated together with sensor interfaces and analysis tools and implemented into an FPGA device. Experimental results validate the controller and verify the design
Killed Brownian motion with a prescribed lifetime distribution and models of default
The inverse first passage time problem asks whether, for a Brownian motion
and a nonnegative random variable , there exists a time-varying
barrier such that . We study a "smoothed" version of this problem and
ask whether there is a "barrier" such that ,
where is a killing rate parameter, and is a
nonincreasing function. We prove that if is suitably smooth, the
function is twice continuously differentiable,
and the condition 0t\}}{dt}<\lambda holds for
the hazard rate of , then there exists a unique continuously
differentiable function solving the smoothed problem. We show how this
result leads to flexible models of default for which it is possible to compute
expected values of contingent claims.Comment: Published in at http://dx.doi.org/10.1214/12-AAP902 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On Quasi-Periodicity in Proth-Gilbreath Triangles
Let PG be the Proth-Gilbreath operator that transforms a sequence of integers
into the sequence of the absolute values of the differences between all pairs
of neighbor terms. Consider the infinite tables obtained by successive
iterations of PG applied to different initial sequences of integers. We study
these tables of higher order differences and characterize those that have
near-periodic features. As a biproduct, we also obtain two results on a class
of formal power series over the field with two elements F2 that can be
expressed as rational functions in several ways
Faraday waves in binary non-miscible Bose-Einstein condensates
We show by extensive numerical simulations and analytical variational
calculations that elongated binary non-miscible Bose-Einstein condensates
subject to periodic modulations of the radial confinement exhibit a Faraday
instability similar to that seen in one-component condensates. Considering the
hyperfine states of Rb condensates, we show that there are two
experimentally relevant stationary state configurations: the one in which the
components form a dark-bright symbiotic pair (the ground state of the system),
and the one in which the components are segregated (first excited state). For
each of these two configurations, we show numerically that far from resonances
the Faraday waves excited in the two components are of similar periods, emerge
simultaneously, and do not impact the dynamics of the bulk of the condensate.
We derive analytically the period of the Faraday waves using a variational
treatment of the coupled Gross-Pitaevskii equations combined with a
Mathieu-type analysis for the selection mechanism of the excited waves.
Finally, we show that for a modulation frequency close to twice that of the
radial trapping, the emergent surface waves fade out in favor of a forceful
collective mode that turns the two condensate components miscible.Comment: 13 pages, 10 figure
Graphene-coated holey metal films: tunable molecular sensing by surface plasmon resonance
We report on the enhancement of surface plasmon resonances in a holey
bidimensional grating of subwavelength size, drilled in a gold thin film coated
by a graphene sheet. The enhancement originates from the coupling between
charge carriers in graphene and gold surface plasmons. The main plasmon
resonance peak is located around 1.5 microns. A lower constraint on the
gold-induced doping concentration of graphene is specified and the interest of
this architecture for molecular sensing is also highlighted.Comment: 5 pages, 4 figures, Final version. Published in Applied Physics
Letter
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