Bayesian inference of earthquake rupture models using polynomial chaos expansion

In this paper, we employed polynomial chaos (PC) expansions to understand earthquake rupture model responses to random fault plane properties. A sensitivity analysis based on our PC surrogate model suggests that the hypocenter location plays a dominant role in peak ground velocity (PGV) responses, while elliptical patch properties only show secondary impact. In addition, the PC surrogate model is utilized for Bayesian inference of the most likely underlying fault plane configuration in light of a set of PGV observations from a ground-motion prediction equation (GMPE). A restricted sampling approach is also developed to incorporate additional physical constraints on the fault plane configuration and to increase the sampling efficiency.</p

Mixing and chemical reaction in an idealized swirl chamber

A vorticity-based, low-Mach-number model for simulating combustion in closed chambers is constructed. Numerical scheme is based on a mixed finite-difference pseudo-spectral discretization of the governing equations. Discrete evolution equations are integrated in time using a predictor-corrector scheme, while discrete elliptic systems are inverted with the help of fast-Poisson solver. Scheme is applied to analyze mixing and combustion in an idealized swirl cavity, which consists of the annular space between a spinning inner cylinder and a stationary reaction. To this end, we assume that the oxidizer and fuel are initially separated by a thin mixed region, and carefully control mixing levels by varying the duration of the swirl-driven mixing period. The mixture is then ignited along the boundary of the inner cylinder. When pre-mixing is complete, an axisymmetric flame front is established, and the reactants are consumed as the front propagates radially outwards. When the charge is partially mixed, combustion in the early stages predominantly occurs within a non-uniform premixed front. As this non-uniform front approaches the outer cylinder, a transition to a distributed combustion regime occurs. Following the transition, the remaining fuel burns at a slow rate within non-premixed flames which wrap around the inner cylinder. Results show that the mixing time has substantial effects on the pressure rise within the cavity and on the evolution of the burnt fraction, and that these effects become more pronounced as the Damkoehler number increases

Ecological Interactions of the Sexually Deceptive Orchid Orchis Galilaea

Plant species dependent on highly specific interactions with pollinators are vulnerable to environmental change. Conservation strategies therefore require a detailed understanding of pollination ecology. This two-year study examined the interactions between the sexually deceptive orchid, Orchis galilaea, and its pollinator Lasioglossum marginatum. Relationships were investigated across three different habitats known to support O. galilaea (garrigue, oak woodland, and mixed oak/pine woodland) in Lebanon. Visitation rates to flowers were extremely low and restricted to male bees. The reproductive success of O. galilaea under ambient conditions was 29.3% (±2.4), compared to 89.0% (±2.1) in plants receiving cross-pollination by hand. No difference in reproductive success was found between habitat types, but values of reproductive success were positively correlated to the abundance of male bees. Pollination limitation can have negative impacts on the population growth of orchids, and this study provides clear evidence for more holistic approaches to habitat conservation to support specific interactions

Towards an end-to-end analysis and prediction system for weather, climate, and Marine applications in the Red Sea

AbstractThe Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable energy applications, impact assessment, flood forecasting, and more.</jats:p

Sound generation by the interaction of a vortex ring with a rigid sphere

High-Reynolds-number interactions between a vortex ring and a stationary rigid sphere are computed using two Lagrangian particle models. The first is a 3D slender vortex filament scheme which tracks the motion of the filament centerline. The centerline velocity is expressed as the sum of a self-induced velocity and potential velocity added to satisfy potential boundary conditions on the surface of the sphere. The self-induced velocity is computed numerically from the line Biot-Savart integral, which is carefully desingularized so as to provide the correct behavior of the vorticity distribution in the asymptotic thin-core limit. The second model is a particle scheme for the simulation of axisymmetric viscous flow. The scheme is based on discretization of the vorticity field into desingularized vortex elements that are advected in a Lagrangian frame. The velocity of the particles is expressed as the sum of a vortex interaction velocity expressed in terms of a desingularized Biot-Savart law, a potential velocity expressed in terms of the image of vortex elements, and a diffusion velocity. The filament and the particle schemes are applied to compute the passage of axisymmetric vortex rings over a stationary rigid sphere in the high-Reynolds-number limit, and to analyze the far-field sound generated by this interaction. Both models show that as the ring passes over the sphere, its radius increases while its core shrinks due stretching. In the parameter regime considered, the two models yield very close predictions of vortex trajectories and speeds. The filament model indicates that the passage leads to the generation of a pressure spike in the acoustic far-field. Meanwhile, the particle computations reveal that in addition to a pressure spike the far-field sound can also exhibit a substantial high-frequency quadrupole emission. Analysis of the computations reveals that this high-frequency noise emission is due to filamentation within the vortex core. The results also show that the high-frequency quadrupole noise may be dominant, especially when the vortex core is thin and the Mach number is not very small

Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics

This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. A brief discussion is provided of only those theoretical aspects needed to set the stage for subsequent applications. These are demonstrated through detailed treatments of elementary problems, as well as in more elaborate examples involving vortex-dominated flows and compressible flows at low Mach numbers. Some recent developments are also outlined in the book, including iterative techniques (such as stochastic multigrids and Newton schemes), intrusive and non-intrusive formalisms, spectral representations using mixed and discontinuous bases, multi-resolution approximations, and adaptive techniques. Readers are assumed to be familiar with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral approximation is helpful but not essential