A Framework for Characterizing Structural Uncertainty in Large-Eddy Simulation Closures

Motivated by the sizable increase of available computing resources, large-eddy simulation of complex turbulent flow is becoming increasingly popular. The underlying filtering operation of this approach enables to represent only large-scale motions. However, the small-scale fluctuations and their effects on the resolved flow field require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of incertitude that can impact the quantities of interest. The objective of this work is to introduce a framework for the systematic estimation of structural uncertainty in large-eddy simulation closures. In particular, the methodology proposed is independent of the initial model form, computationally efficient, and suitable to general flow solvers. The approach is based on introducing controlled perturbations to the turbulent stress tensor in terms of magnitude, shape and orientation, such that propagation of their effects can be assessed. The framework is rigorously described, and physically plausible bounds for the perturbations are proposed. As a means to test its performance, a comprehensive set of numerical experiments are reported for which physical interpretation of the deviations in the quantities of interest are discussed.     

The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank-one tensor u ^⊗k ∈ (ℝⁿ)^⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ  _Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn^{(k − 2)/4} , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n^{(k − 2)/4} . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ^{−1/(k − 1)}) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ^{−1/(k − 2)}) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.     

Rapid Learning-Based and Geologically Consistent History Matching

Various types of data become available at different stages of a reservoir’s life. The production data are integrated into the flow simulation models through a process referred to as history matching. The history-matching process is iterative, and it usually involves a large number of simulation runs. Hence, this process requires significant computational time. In most history-matching methods, the initial geological assumptions in the reservoir model are destroyed or significantly altered in the process. Furthermore, they do not account for the information obtained during the previous trials, and lack learning from the previous failures. In this paper, we introduce a new methodology that maintains the geological realism. The candidate realizations are selected through a learning-based history-matching (LHM) algorithm by which all the previously successful patterns are preserved and used to assist the construction of the next realizations. The various pieces of matching regions are assembled together to make a pool of the successful candidates. Such regions are then utilized for making an auxiliary dataset in a multiscale framework by which the next model is generated. To prevent from trapping in local minima, ideas from the genetic algorithm is adapted. The LHM algorithm can be applied to both categorical and continuous distributions. The LHM provides a conditional map by which the new production data are immediately incorporated into the existing reservoir models. We apply the LHM algorithm to various 2D and 3D examples with very complex binary and continuous properties. The algorithm is shown to produce history-matched models with significantly smaller CPU times.     

The quartet theory of human emotions: An integrative and neurofunctional model

Despite an explosion of research in the affective sciences during the last few decades, interdisciplinary theories of human emotions are lacking. Here we present a neurobiological theory of emotions that includes emotions which are uniquely human (such as complex moral emotions), considers the role of language for emotions, advances the understanding of neural correlates of attachment-related emotions, and integrates emotion theories from different disciplines. We propose that four classes of emotions originate from four neuroanatomically distinct cerebral systems. These emotional core systems constitute a quartet of affect systems: the brainstem-, diencephalon-, hippocampus-, and orbitofrontal-centred affect systems. The affect systems were increasingly differentiated during the course of evolution, and each of these systems generates a specific class of affects (e.g., ascending activation, pain/pleasure, attachment-related affects, and moral affects). The affect systems interact with each other, and activity of the affect systems has effects on – and interacts with – biological systems denoted here as emotional effector systems. These effector systems include motor systems (which produce actions, action tendencies, and motoric expression of emotion), peripheral physiological arousal, as well as attentional and memory systems. Activity of affect systems and effector systems is synthesized into an emotion percept (pre-verbal subjective feeling), which can be transformed (or reconfigured) into a symbolic code such as language. Moreover, conscious cognitive appraisal (involving rational thought, logic, and usually language) can regulate, modulate, and partly initiate, activity of affect systems and effector systems. Our emotion theory integrates psychological, neurobiological, sociological, anthropological, and psycholinguistic perspectives on emotions in an interdisciplinary manner, aiming to advance the understanding of human emotions and their neural correlates.     

A Self‐Assembled Superhydrophobic Electrospun Carbon–Silica Nanofiber Sponge for Selective Removal and Recovery of Oils and Organic Solvents

An oil spill needs timely cleanup before it spreads and poses serious environmental threat to the polluted area. This always requires the cleanup techniques to be efficient and cost‐effective. In this work, a lightweight and compressible sponge made of carbon–silica nanofibers is derived from electrospinning nanotechnology that is low‐cost, versatile, and readily scalable. The fabricated sponge has high porosity (>99 %) and displays ultra‐hydrophobicity and superoleophilicity, thus making it a suitable material as an oil adsorbent. Owing to its high porosity and low density, the sponge is capable of adsorbing oil up to 140 times its own weight with its sorption rate showing solution viscosity dependence. Furthermore, sponge regeneration and oil recovery are feasible by using either cyclic distillation or mechanical squeezing.     

Maximum of the Characteristic Polynomial for a Random Permutation Matrix

Let P_N be a uniform random N × N permutation matrix and let χ_N(z) = det(zI_N − P_N) denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of χ_N on the unit circle, specifically, with probability tending to 1 as N → ∞ , for a numerical constant x₀ ≈ 0.652 . The main idea of the proof is to uncover a logarithmic correlation structure for the distribution of (the logarithm of) χ_N , viewed as a random field on the circle, and to adapt a well-known second-moment argument for the maximum of the branching random walk. Unlike the well-studied CUE field in which P_N is replaced with a Haar unitary, the distribution of χ_N(e^2πit) is sensitive to Diophantine properties of the point t . To deal with this we borrow tools from the Hardy-Littlewood circle method. © 2020 Wiley Periodicals LLC