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

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

Sensitivity of Carbon Emission Estimates from Indirect Land-Use Change

We analyze the sensitivity of greenhouse gas (GHG) emissions from land-use change to modifications in assumptions concerning crop area, yield, and deforestation. For this purpose, we run a modified version of the Center for Agricultural and Rural Development (CARD) Agricultural Outlook Model, which was used previously to assess the impacts of energy price increases and biofuel policy changes on land conversion. To calculate the GHG implications of agricultural activity, we use GreenAgSiM, a model developed to evaluate emissions from land conversion and agricultural production. Both models are applied to scenarios that lead to higher US ethanol production. The results are contrasted with the findings of Searchinger et al., and we explain the role of model assumptions to elucidate the differences. We find that the payback period of corn ethanol’s carbon debt is sensitive to assumptions concerning land conversion and yield growth and can range from 31 to 180 years.biofuel, crop yield, greenhouse gas emissions, indirect land-use change.

Gravitomagnetic Jets

We present a family of dynamic rotating cylindrically symmetric Ricci-flat gravitational fields whose geodesic motions have the structure of gravitomagnetic jets. These correspond to helical motions of free test particles up and down parallel to the axis of cylindrical symmetry and are reminiscent of the motion of test charges in a magnetic field. The speed of a test particle in a gravitomagnetic jet asymptotically approaches the speed of light. Moreover, numerical evidence suggests that jets are attractors. The possible implications of our results for the role of gravitomagnetism in the formation of astrophysical jets are briefly discussed.Comment: 47 pages, 8 figures; v2: minor improvements; v3: paragraph added at the end of Sec. V and other minor improvements; v4: reference added, typos corrected, sentence added on p. 24; v5: a few minor improvement