This Is How You Lose Me

I liked the intimate setting of the class at first. The silence before the professor walked in. The cramped room. It always smelled like citrus cleaning products. Some hair gel mixed in there, too. There was peanut butter stuck on the roof of my mouth — from my sandwich at lunch — when he walked in that day, throwing a stack of Junot Díaz’s short story, “Alma,” onto the center of the shared table. I liked Junot Díaz’s writing. Loved it, actually. The way he captures pain and molds stories by weaving together the language of diary entries and love letters and suicide notes. The way he uses magic and grit and blood. Darkness and love simultaneously. His work is tragically beautiful. At least, that’s what I think. [excerpt

Chaotic diffusion of orbits in systems with divided phase space

In this paper we discuss the relevance of diffusive processes in multidimensional Hamiltonian systems. By means of a rather simple model, we present evidence that for moderate-to-strong chaotic systems the stochastic motion remains confined to disjoint domains on the energy surface, at least for mild motion times. We show that only for extremely large timescales and for rather large perturbations, does the chaotic component appear almost fully connected through the relics of the resonance structure. The discussion whether diffusion over the energy surface could actually occur in asteroidal or galaxy dynamics is also included.Fil: Giordano, Claudia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Cincotta, Pablo Miguel. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Global Dynamics in Galactic Triaxial Systems I

In this paper we present a theoretical analysis of the global dynamics in a triaxial galactic system using a 3D integrable Hamiltonian as a simple representation. We include a thorough discussion on the effect of adding a generic non--integrable perturbation to the global dynamics of the system. We adopt the triaxial Stackel Hamiltonian as the integrable model and compute its resonance structure in order to understand its global dynamics when a perturbation is introduced. Also do we take profit of this example in order to provide a theoretical discussion about diffussive processes taking place in phase space.Comment: Accepted A&

Testing the accuracy of the overlap criterion

Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D version. To this end, we consider respectively, two and three quartic oscillators as the unperturbed system, and couple the degrees of freedom by a cubic, non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O(\epsilon^2), and model each resonance by means of the pendulum approximation in order to estimate the theoretical critical value of the perturbation parameter for a global transition to chaos. We perform several surface of sections for the bidimensional case to derive an empirical value to be compared to our theoretical estimation, being both in good agreement. Also for the 3D case a numerical estimate is attained that we observe matches the critical value resulting from theoretical means. This confirms once again that reckoning resonances up to O(\epsilon^2) suffices in order the overlap criterion to work out. Keywords: {Chaos -- Resonances -- Theoretical and Numerical Methods}Comment: 16 page

Chaotic Diffusion in the Gliese-876 Planetary System

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disk, and a natural consequence of irregular motion. In this paper we show that resonant multi-planetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over timescales comparable to their age.Using the GJ-876 system as an example, we analyze the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincar\'e maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behavior of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.Comment: 13 pages, 7 figures, 2 tables. Accepted for publication in MNRA

Soil Aggregates: The mechanistic link to increased dissolved organic carbon in surface waters?

Dissolved organic carbon (DOC) plays an important role in the global carbon (C) cycle because increases in aqueous C potentially contribute to rising atmospheric CO2 levels. Over the past few decades, headwater streams of the northern hemisphere have shown increased amounts of DOC coinciding with decreased acid deposition. Although the issue is widely discussed in the literature, a mechanistic link between precipitation composition and stream water DOC has not yet been proposed. In this study, the breakup of soil aggregates is hypothesized as the mechanistic link between reduced acid deposition and DOC increases in surface waters. Specific hypotheses state that soil aggregate dispersion (and the ensuing release of DOC from these aggregates) is driven by a decrease in soil solution ionic strength (IS, decreasing the tendency of flocculation) as well as a shift from divalent to monovalent cations (reducing the propensity for cation bridging) in soil solution. These hypotheses were tested on soil samples collected from several riparian zone and hillslope positions along three flagged transects in the acid-impacted Sleepers River Research Watershed in northeastern Vermont. To determine soil C content by landscape position, samples from transects spanning hilltop to hillslope and riparian area, as well as replicated hillslope and riparian samples (n=40) were analyzed. Aqueous soil extracts simulate the flushing of soils during hydrologic events (e.g. rain or snowmelt) and were used to test the effect of soil solution chemistry on DOC release. Extracts were prepared with solutions of varying IS (0-0.005M) and composition (CaCl2 and NaCl) on replicated soil samples (n=54) and changes in DOC release and aggregate size were monitored. As IS of the extraction solution increased, the amount of DOC in solution decreased, and aggregate size increased. This was presumably due to cations bridging and diffuse double layer effects. This effect was reversed in low ionic strength solutions where DOC release was significantly higher and average aggregate size was smaller. While extraction solution controlled the amount of C liberated, landscape position impacted the quality, but not quantity, of released DOC. This study is the first to propose a mechanistic link observed changes in DOC in surface waters and recovery from acidification and provides initial experimental evidence that soil aggregates indeed play a role in the generation of DOC