Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport

We formulate a model for the mass exchange between oil at and below the sea surface. This is a particularly important aspect of modeling oil spills. Surface and subsurface oil have different chemical and transport characteristics and lumping them together would compromise the accuracy of the resulting model. Without observational or computational constraints, it is thus not possible to quantitatively predict oil spills based upon partial field observations of surface and/or sub-surface oil. The primary challenge in capturing the mass exchange is that the principal mechanisms are on the microscale. This is a serious barrier to developing practical models for oil spills that are capable of addressing questions regarding the fate of oil at the large spatio-temporal scales, as demanded by environmental questions. We use upscaling to propose an environmental-scale model which incorporates the mass exchange between surface and subsurface oil due to oil droplet dynamics, buoyancy effects, and sea surface and subsurface mechanics. While the mass exchange mechanism detailed here is generally applicable to oil transport models, it addresses the modeling needs of a particular to an oil spill model [1]. This transport model is designed to capture oil spills at very large spatio-temporal scales. It accomplishes this goal by specializing to shallow-water environments, in which depth averaging is a perfectly good approximation for the flow, while at the same time retaining mass conservation of oil over the whole oceanic domain.Comment: 18 pages, 6 figure

Phase Transition for Glauber Dynamics for Independent Sets on Regular Trees

We study the effect of boundary conditions on the relaxation time of the Glauber dynamics for the hard-core model on the tree. The hard-core model is defined on the set of independent sets weighted by a parameter $\lambda$, called the activity. The Glauber dynamics is the Markov chain that updates a randomly chosen vertex in each step. On the infinite tree with branching factor $b$, the hard-core model can be equivalently defined as a broadcasting process with a parameter $\omega$ which is the positive solution to $\lambda=\omega(1+\omega)^b$, and vertices are occupied with probability $\omega/(1+\omega)$ when their parent is unoccupied. This broadcasting process undergoes a phase transition between the so-called reconstruction and non-reconstruction regions at $\omega_r\approx \ln{b}/b$. Reconstruction has been of considerable interest recently since it appears to be intimately connected to the efficiency of local algorithms on locally tree-like graphs, such as sparse random graphs. In this paper we show that the relaxation time of the Glauber dynamics on regular $b$-ary trees $T_h$ of height $h$ and $n$ vertices, undergoes a phase transition around the reconstruction threshold. In particular, we construct a boundary condition for which the relaxation time slows down at the reconstruction threshold. More precisely, for any $\omega \le \ln{b}/b$, for $T_h$ with any boundary condition, the relaxation time is $\Omega(n)$ and $O(n^{1+o_b(1)})$. In contrast, above the reconstruction threshold we show that for every $\delta>0$, for $\omega=(1+\delta)\ln{b}/b$, the relaxation time on $T_h$ with any boundary condition is $O(n^{1+\delta + o_b(1)})$, and we construct a boundary condition where the relaxation time is $\Omega(n^{1+\delta/2 - o_b(1)})$

Displacement Data Assimilation

We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information important. While the displacement transformation is not tied to any particular assimilation scheme, here we implement it within an ensemble Kalman Filter and demonstrate its effectiveness in tracking stochastically perturbed vortices.Comment: 26 Pages, 9 figures, 5 table

Valoración de la garantía de pensión en las cuentas de ahorro individual en Colombia

El comportamiento del individuo como persona que aporta, y futuro beneficiario de una pensión, es determinante para cuantificar los efectos que su densidad de aportes tiene sobre el sistema de ahorro individual y la exigibilidad de las diferentes garantías. Por esta razón, en el presente trabajo se intenta buscar desde las finanzas personales una visión alterna a lo expuesto en diferentes estudios que sobre la materia se han realizado, no solo en Colombia sino a nivel internacional, y brindar una aproximación a la solución del problema de sostenibilidad en el retiro. Para calcular la magnitud de las garantías, se desarrolló un procedimiento que combina metodologías de modelos estocásticos con modelos de lógica difusa y con el cálculo actuarial. De esta forma, y soportado en resultados de otros estudios, se logró determinar el ahorro individual potencial alcanzable por cada individuo en función de su género y su cohorte salarial, y el posible déficit existente para conseguir una pensión mínima de retiro. Los resultados encontrados indican que en las condiciones de baja densidad de aportes es muy difícil para las cohortes de bajo y medio ingreso asegurar una pensión mínima sin el agotamiento de las garantías existentes y la participación del gobierno

The effects of geomorphic controls on sediment yield in the andean rivers of Colombia

This paper examines sediment yield rates and its response to control variables in the principal rivers of Colombian draining into the Caribbean and Pacific coasts. Based on a multi-year dataset of sediment load from six rivers, including Mira, Patía, and San Juan on the Pacific margin, and Magdalena, Atrato, and Sinú, on the Caribbean basin, various morphometric, hydrologic, and climatic variables were estimated in order to understand and predict the variation in sediment yield. A multiple regression model, including two control variables, runoff and relief ratio (the ratio of the maximum height of the drainage basin and the basin length), explains 83% of the variance in sediment yield. This model is efficient (ME = 0.93) and is a valuable tool for predicting total sediment yield from Colombian rivers. These two selected estimators refer to the relative importance of the fluvial transport component in the sediment routing system. Thus, regional-scale variance of sediment yield in the Andean basins of Colombia seems to be explained by the combined influence of tectonics (relief) and surface runoff available for weathering and transport processes. In general, high sediment yielded rivers are high runoff systems with narrow alluvial plains (i.e. Pacific rivers), while low sediment yielded rivers like the Caribbean systems, contain large sections with not significant gradient in their longitudinal profiles. These sections coincide with large floodplains, which all provide sediment storage capacity within the catchments. When considering the three gauged Pacific rivers at their furthest downstream stations, the combined annual sediment load from these rivers into the Pacific Ocean is ~40 Mt yr–1. In contrast, the Magdalena, Atrato and Sinu rivers deliver ~173 Mt yr-1 into the Caribbean. Overall, Andean rivers of Colombia exhibit the highest sediment yields of all medium-large sized rivers of South America due to the interplay of (1) high rates of runoff (1,750-7,300 mm yr-1), (2) steep relief within catchments, (3) low values of discharge variability (Qmax-Qmin), and (4) episodic sediment delivery due to either geologic events or climatic anomalies

Field observations of wave and current characteristics on a microtidal reflective beach

At Costa Verde beach, Colombia, an intermediate reflective beach, the contributions of gravity (G) and infragravity (IG) waves to the evolution of the free surface and the cross-shore and alongshore velocities during two climatic periods were determined by applying the continuous wavelet transformation to sensor data recorded in field campaigns. In the dry season, the highest values of IG energy were found in the vicinity of the coastline, due to reflection processes in the área near the foreshore. Additionally, the cross-wavelet and coherence spectra between the free surface and the cross-shore and alongshore velocities allowed the identification of cross-shore and alongshore standing ‘‘leaky’’ waves and standing ‘‘edge’’ waves. In the rainy (wet) season, cross-shore and alongshore progressive leaky waves predominated in the área farthest from the shoreline. Close to the shore, mostly cross-shore standing leaky waves predominated because of reflection dynamics. On Costa Verde beach, the wave breaking is usually of the plunging type, which is characteristic of an intermediate reflective beach. The dimensionless fall velocity parameter (X) indicated that Costa Verde assumes the form of an intermediate ridge-runnel beach in the rainy (wet) season (low swell energy) and an intermediate transverse bar and rip beach in the dry season (high swell energy). This means that the Costa Verde beach tends to have small rip currents and pronounced ‘‘cusps.’’ Despite the lack of conclusive evidence to suggest that the appearance of cusps and rip currents is due to the presence of standing edge waves during the dry season, the data show that during the period of high energy swell, IG waves exist simultaneously with the cusps as small rhythmic systems of rip currents

Session-based concurrency in Maude:Executable semantics and type checking

Session types are a well-established approach to communication correctness in message-passing processes. Widely studied from a process calculi perspective, here we pursue an unexplored strand and investigate the use of the Maude system for implementing session-typed process languages and reasoning about session-typed process specifications. We present four technical contributions. First, we develop and implement in Maude an executable specification of the operational semantics of a session-typed π-calculus by Vasconcelos. Second, we also develop an executable specification of its associated algorithmic type checking, and describe how both specifications can be integrated. Third, we show that our executable specification can be coupled with reachability and model checking tools in Maude to detect well-typed but deadlocked processes. Finally, we demonstrate the robustness of our approach by adapting it to a higher-order session π-calculus, in which exchanged values include names but also abstractions (functions from names to processes). All in all, our contributions define a promising new approach to the (semi)automated analysis of communication correctness in message-passing concurrency

Discriminating Between Different Streamflow Regimes by Using the Fisher-Shan Method: An Application to the Colombia Rivers

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