A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger

We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen-Lo\`eve expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

The potential of metering roundabouts: influence in transportation externalities

Roundabouts are increasingly being used on busy arterial streets for traffic calming purposes. However, if one roundabout leg is near a distribution hub, e.g. parking areas of shopping centers, the entry traffic volumes will be particularly high in peak hours. This paper investigated a partial-metering based strategy to reduce traffic-related costs in a corridor. Specifically, the resulting traffic performance, energy, environmental and exposure impacts associated with access roundabouts were studied in an urban commercial area, namely: a) to characterize corridor operations in terms of link-specific travel time, fuel consumption, carbon dioxide and nitrogen oxides emissions, and noise costs; b) to propose an optimization model to minimize above outputs; and c) to demonstrate the model applicability under different traffic demand and directional splits combinations. Traffic, noise and vehicle dynamics data were collected from a corridor with roundabouts and signalized intersections near a commercial area of Guimarães, Portugal. Microscopic traffic and emission modeling platforms were used to model traffic operations and estimate pollutant emissions, respectively. Traffic noise was estimated with a semi-dynamical model. Link-based cost functions were developed based on the integrated modeling structure. Lastly, a Sequential quadratic programming type approach was applied to find optimal timing settings. The benefit of the partial-metering system, in terms of costs, could be up to 13% with observed traffic volumes. The efficiency of the proposed system increased as entering traffic at the metered approaches increased (~7% less costs). The findings let one to quantify metering benefits near shopping areas

Coupling of ORL1 (NOP) receptor to G proteins differs in the nucleus accumbens of anxious and non anxious mice.

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