The Regularity Problem for Uniformly Elliptic Operators in Weighted Spaces

This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the Muckenhoupt classes. Our results generalize those of S. Mayboroda (and those of P. Auscher and S. Stahlhut employing the first order method) who considered the unweighted case. To obtain our main results we use the weighted Hardy space theory associated with elliptic operators recently developed by the last two named authors. One of the novel contributions of this paper is the use of an “inhomogeneous” vertical square function which is shown to be controlled by the gradient of the function to which is applied in weighted Lebesgue spaces.

Reduction of tris(2,2’-bipyridine)cobalt(III) complex by thiosulphate ion in an aqueous acidic medium

The reduction of tris(2,2-bipyridine)cobalt(III) complex by thiosulphate ion in an aqueous acidic medium gave a notable outcome. The stoichiometric evaluation indicates that one mole of the reducing agent has been consumed by one mole of the oxidant, and the reaction complies with an overall equation: 2[Co(bpy)3]3+ + 2S2O32− 2[Co(bpy)3]2+ + S4O62− The kinetics study conducted under a pseudo-first-order method shows that the rate of the reaction was acid-reliant and third-order overall; zero-order in the [oxidant], second-order in the [reductant], and first-order in the hydrogen ion concentration. The empirical rate expression complies with the equation:− [Co(bpy)33+] = a [H+][S2O32−]2‘a’ = 77.82 dm6 mol−2 s−1; at [H+] = 2.0 × 10−2 mol dm−3, µ = 0.4 mol dm−3 (NaCl), T = 28 ± 1˚C and λmax = 560 nm.With increased ionic strength and decreased medium dielectric constant, the reaction rate increased. The inclusion of cations and anions accelerate and constricted the reaction rates respectively. Spectroscopic examination and kinetic evidence indicate an outer sphere mechanism, and the mechanism was therefore proposed via an outer-sphere route.

Sparseness and Smoothness Regularized Imaging for improving the resolution of Cryo-EM single-particle reconstruction

In this paper, we present a refinement method for cryo-electron microscopy (cryo-EM) single-particle reconstruction, termed as OPUS-SSRI (Sparseness and Smoothness Regularized Imaging). In OPUS-SSRI, spatially varying sparseness and smoothness priors are incorporated to improve the regularity of electron density map, and a type of real space penalty function is designed. Moreover, we define the back-projection step as a local kernel regression and propose a first-order method to solve the resulting optimization problem. On the seven cryo-EM datasets that we tested, the average improvement in resolution by OPUS-SSRI over that from RELION 3.0, the commonly used image-processing software for single-particle cryo-EM, was 0.64 Å, with the largest improvement being 1.25 Å. We expect OPUS-SSRI to be an invaluable tool to the broad field of cryo-EM single-particle analysis. The implementation of OPUS-SSRI can be found at https://github.com/alncat/cryoem.

Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics

Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics (mean and variance) of the stochastic cost function are computed through either a gradient-enhanced kriging (GEK) surrogate or through the less expensive, lower fidelity, first-order method of moments (MoM). Both the continuous (non-intrusive) and discrete (intrusive) adjoint methods are evaluated for computing the gradients required for GEK and MoM. In all cases, the results are assessed against a reference kriging UQ surrogate not using gradient information. Subsequently, the GEK and MoM UQ solvers are fused together to build a multi-fidelity surrogate with adaptive infill enrichment for the SMOGA optimizer. The resulting hybrid multi-fidelity SMOGA RDO strategy ensures a good tradeoff between cost and accuracy, thus representing an efficient approach for complex RDO problems.

Optimization of ER8 and 42CrMo4 Steel Rail Wheel for Road–Rail Vehicles

Railway track maintenance services aim to shorten the time of removing failures on the railways. One of the most important element that shorten the repair time is the quick access to the failure site with an appropriate equipment. The use of road-rail vehicles is becoming increasingly important in this field. In this type of constructions, it is possible to use proven road vehicles such as self-propelled machines or trucks running on wheels with tires. Equipping these vehicles with a parallel rail drive system allows for quick access to the failure site using both roads and railways. Steel rail wheels of road-rail vehicles are designed for specific applications. Since the total weight of vehicle is a crucial parameter for roadworthiness, the effort is made to minimize the mass of rail wheels. The wheel under consideration is mounted directly on the hydraulic motor. This method of assembly is structurally convenient, as no shafts or intermediate couplings are required. On the other hand, it results in strict requirements for the wheel geometry and can cause significant stress concentration. Therefore, the problem of wheel geometry optimization is discussed. Consideration is given to the use of ER8 steel for railway application and 42CrMo4 high-strength steel. Finite element analysis within Ansys software and various optimization tools and methods, such as random tool, subproblem approximation method and first-order method are applied. The obtained results allow to minimize the rail wheel mass with respect to the used material. Moreover, computational demands and methods leading to the best results are compared.

D-SPIDER-SFO: A Decentralized Optimization Algorithm with Faster Convergence Rate for Nonconvex Problems

Decentralized optimization algorithms have attracted intensive interests recently, as it has a balanced communication pattern, especially when solving large-scale machine learning problems. Stochastic Path Integrated Differential Estimator Stochastic First-Order method (SPIDER-SFO) nearly achieves the algorithmic lower bound in certain regimes for nonconvex problems. However, whether we can find a decentralized algorithm which achieves a similar convergence rate to SPIDER-SFO is still unclear. To tackle this problem, we propose a decentralized variant of SPIDER-SFO, called decentralized SPIDER-SFO (D-SPIDER-SFO). We show that D-SPIDER-SFO achieves a similar gradient computation cost—that is, O(ε−3) for finding an ϵ-approximate first-order stationary point—to its centralized counterpart. To the best of our knowledge, D-SPIDER-SFO achieves the state-of-the-art performance for solving nonconvex optimization problems on decentralized networks in terms of the computational cost. Experiments on different network configurations demonstrate the efficiency of the proposed method.

Glacial Lake Changes and Identification of Potentially Dangerous Glacial Lakes in the Yi’ong Zangbo River Basin

The southeastern Tibetan Plateau, where monsoonal temperate glaciers are most developed, has a huge number of glacial lakes. Based on Landsat Operational Land Imager (OLI) images, 192 glacial lakes with a total area of 45.73 ± 6.18 km2 in 2016 were delineated in the Yi’ong Zangbo River Basin. Glacial lakes with areas of less than 0.1 km2 accounted for 81.77% of the total number, and glacial lakes located above 4500 m elevation comprised 83.33%. Dramatic glacier melting caused by climate warming has occurred, resulting in the formation and expansion of glacial lakes and the increase of potential glacial lake outburst floods (GLOFs) risk. From 1970 to 2016, the total area of glaciers in the basin has decreased by 35.39%, whereas the number and total area of glacial lakes have, respectively, increased by 86 and 1.59 km2. In that time, 110 new glacial lakes emerged, whereas 24 of the original lakes disappeared. The newly formed lakes have a smaller mean area but higher mean elevation than the lakes that disappeared. Based on five indicators, a first-order method was used to identify glacial lakes that pose potential threats. We identified 10 lakes with very high, 7 with high, 31 with medium, and 19 with low GLOF susceptibility, out of 67 moraine-dammed glacial lakes with areas larger than 0.02 km2. Understanding the behavior of glaciers and glacial lakes is a vital aspect of GLOFs disaster management, and the monitoring of glacial lakes should be strengthened.

Parametric Resonances of a Three-Blade-Rotor System With Reference to Wind Turbines

Coupled blade-hub dynamics of a coupled three-blade-rotor system with parametric stiffness, which is similar to a horizontal-axis wind turbine, is studied. Blade equations have parametric and direct excitation terms due to gravity and are coupled through the hub equation. For a single degree-of-freedom blade model with only in-plane transverse vibrations, the reduced-order model shows parametric resonances. A small parameter is established for large blades, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By expressing the system dynamics in the rotor angle domain and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The interdependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using a first-order method of multiple scales (MMS). The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude-frequency relations and stabilities of these resonances are studied. The MMS solutions are compared with numerical simulations for verification.