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 R3\mathbb{R}^3

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 $\mathbb R^3$. 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