1,842 research outputs found
On a computer-aided approach to the computation of Abelian integrals
An accurate method to compute enclosures of Abelian integrals is developed.
This allows for an accurate description of the phase portraits of planar
polynomial systems that are perturbations of Hamiltonian systems. As an
example, it is applied to the study of bifurcations of limit cycles arising
from a cubic perturbation of an elliptic Hamiltonian of degree four
On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in
In this paper we use the blow up method of Dumortier and Roussarie
\cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to
Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of
singularities of piecewise smooth dynamical systems
\cite{filippov1988differential} in . Using the regularization
method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the
power of our approach by considering the case of a fold line. We quickly
recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a
simple manner. Then, for the two-fold singularity, we show that the regularized
system only fully retains the features of the singular canards in the piecewise
smooth system in the cases when the sliding region does not include a full
sector of singular canards. In particular, we show that every locally unique
primary singular canard persists the regularizing perturbation. For the case of
a sector of primary singular canards, we show that the regularized system
contains a canard, provided a certain non-resonance condition holds. Finally,
we provide numerical evidence for the existence of secondary canards near
resonance.Comment: To appear in SIAM Journal of Applied Dynamical System
Mixed-mode oscillations in a multiple time scale phantom bursting system
In this work we study mixed mode oscillations in a model of secretion of GnRH
(Gonadotropin Releasing Hormone). The model is a phantom burster consisting of
two feedforward coupled FitzHugh-Nagumo systems, with three time scales. The
forcing system (Regulator) evolves on the slowest scale and acts by moving the
slow nullcline of the forced system (Secretor). There are three modes of
dynamics: pulsatility (transient relaxation oscillation), surge (quasi steady
state) and small oscillations related to the passage of the slow nullcline
through a fold point of the fast nullcline. We derive a variety of reductions,
taking advantage of the mentioned features of the system. We obtain two
results; one on the local dynamics near the fold in the parameter regime
corresponding to the presence of small oscillations and the other on the global
dynamics, more specifically on the existence of an attracting limit cycle. Our
local result is a rigorous characterization of small canards and sectors of
rotation in the case of folded node with an additional time scale, a feature
allowing for a clear geometric argument. The global result gives the existence
of an attracting unique limit cycle, which, in some parameter regimes, remains
attracting and unique even during passages through a canard explosion.Comment: 38 pages, 16 figure
Production and Spatial Distribution of Switchgrass and Miscanthus in the United States under Uncertainty and Sunk Cost
The U.S. cellulosic biofuel mandate has not been enforced in recent years. Uncertainty surrounding the enforcement of the mandate in addition to high production and harvest cost have contributed to a delay in the widespread planting of bioenergy crops such as switchgrass and miscanthus. Previous literature has shown that under uncertainty and sunk cost, an investment threshold is further increased due to the value associated from holding the investment option. In this paper, we extend the previous literature by applying a real option switching model to bioenergy crop production. First, we calculate the county-level break-even price which triggers a switching away from traditional field crops (corn, soybeans, and wheat) to bioenergy crops under various scenarios differing by commodity prices, production cost and biomass price expectations. We show that the resulting break-even prices at the county-level can be substantially higher than previously estimated due to the inclusion of the option value. In a second step, we identify counties that are most likely to grow switchgrass or miscanthus by simulating a stochastic biomass price over time. Our results highlight two issues: First, switchgrass or miscanthus are not grown in the Midwest under any scenario. Under low agricultural residue removal rates, biomass crops are mostly grown in the Southeast. Second, under the assumption of a high removal rates, bioenergy crops are not grown anywhere in the U.S. since the cellulosic biofuel mandate can be covered by agricultural residues
Comparative analysis of inhaled particles contained in human bronchoalveolar lavage fluids, lung parenchyma and lymph nodes.
Translocation of inhaled particles from the alveolar spaces to lung parenchyma and lymph nodes is one of the mechanisms that determine the biopersistence of particles. This study compares the nonfibrous particulate burden in bronchoalveolar lavage (BAL) fluids, lung parenchyma, and thoracic lymph nodes and attempts to detect the degree of differentiation, if any, based on particle size or type. This comparison can only be done on BAL, lung parenchyma, and lymph node samples collected from the same subject over a short time. Patients undergoing surgical lung resection are suitable for this purpose. Particles recovered by digestion-filtration were counted, sized, and analyzed by analytical transmission electron microscopy. Total particle load ranges grossly between 10(5) to 10(7) p/ml in BAL, 10(9) to 10(10) p/g dry tissue in parenchyma and 10(10) to 10(11) p/g dry tissue in lymph nodes. Diameters are log-normally distributed and mean diameters range between 0.5 to 0.9 micron. Nonlamellar silicate particles have a significantly larger diameter in lymph nodes. Differences in particle type between the three sampling sites are small and nonsystematic
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