Energy Characteristics of Acoustic Emission at the Volume-Expansion Point of a Rock Bridge: A New Insight into the Evolutionary Mechanism of Coastal Cliff Collapse

The recession of a coast can destabilize coastal cliffs. The stability of a cliff is controlled by a rock bridge. Identifying the volume-expansion point of rock bridges is crucial to assess cliff stability, but currently there are few identifying methods. Using a numerical analytical tool, we investigate the acoustic emission characteristics during shear tests on rock bridges. Acoustic emission events with a high energy level, i.e., characteristic events which occur at the volume-expansion point of rock bridges, can indicate this point. The characteristic events, the mainshock (the maximum event corresponding to rock-bridge rupture), and the smaller events between them constitute a special activity pattern, as the micro-seismicity during the evolutionary process of a coastal cliff collapse in Mesnil-Val, NW France showed. This pattern arises in rock bridges with different mechanical properties and geometry, or under different loading conditions. Although the energy level of characteristic events and mainshocks changes with the variation of the conditions, the difference of their energy level is approximately constant. The spatial distribution of characteristic events and mainshocks can indicate the location of rock bridges. These findings help to better understand the evolutionary mechanism of collapses and provide guidelines for monitoring the stability of coastal cliffs.

A Broadband Enhanced Structure-Preserving Reduced-Order Interconnect Macromodeling Method for Large-Scale Equation Sets of Transient Interconnect Circuit Problems

In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature. Compared to other MOR methods, the structure-preserving reduced-order interconnect macromodeling (SPRIM) based on Krylov subspaces will achieve a higher reduction radio and precision for large multi-port Resistor-Capacitor-Inductor (RCL) circuits. However, for very wide band frequency transients, the performance of a Krylov subspace-based MOR method is not satisfactory. Moreover, the selection of the expansion point in this method has not been comprehensively studied in the literature. From this point of view, a broadband enhanced structure-preserving reduced-order interconnect macromodeling (SPRIM) method is proposed to reduce the order of equation sets of a transient interconnect circuit model. In addition, a method is introduced to determine the optimal expansion point at each frequency in the proposed method. The proposed method is validated by the numerical results on a transient problem of an insulated-gate bipolar transistor (IGBT)-based inverter busbar under different exciting conditions.

Effect of Angle of Attack on Pressure and Lift Coefficient of ONERA OA206 Wing Model Using Computational Fluid Dynamics Method

In this study, we computed the lift force of the aircraft with ONERA OA206 airfoil type. It was positioned at 0%, 25%, 50%, 75%, and 100% of the wingspan for Angle of Attack (AoA) variations of 0o, 4o, 8o, 12o, and 16o. The research was to determine the effect of AoA on pressure, pressure coefficient (Cp), and lift coefficient (CL) on the ONERA OA206 aircraft wing. It shows that the greater AoA on the result of the pressure contour causes the increase in the difference of span at AoA 0o to 16o t these are 0.25%; 0.26%; 0.43%; 0.52%; and 0.53%. Through the graph of the pressure coefficient (Cp) against x/c, it can be seen that the greater AoA, the expansion point, and the stagnation point will shift to the right with the direction of x/c. In addition, the Cp at the lower is greater than the upper of the airfoil. Based on the research results, it was found that CL at the position of 0% to 50% increased when given AoA from 0o to 12o (CL max) and decreased at AoA = 16o (stall). Meanwhile, CL at 75% to 100% increased when given AoA from 0o to 8o (CL max) and decreased at AoA = 12o (stall). With these results, it can be concluded that the maximum AoA that can be applied to the wing of the ONERA OA206 aircraft is 8o. The closer to the end position of the airfoil, the higher the CL measured.

Application of Adomian Decomposition Method to Bounded and Unbounded Stokes’ Problems

The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.

An Iterative Dimension-Wise Approach to the Structural Analysis with Interval Uncertainties

The structural analysis is inevitably surrounded with uncertainties and the interval analysis is a favorable method if insufficient data is available on uncertainties. The accuracy of current interval analysis methods including the interval perturbation method (IPM), subinterval perturbation method (SIPM) and dimension-wise approach (DWA) depends on a reference point (RP), e.g., the expansion point in IPM, for some problems due to ignoring the co-operative effects of multiple interval inputs on the response. To this end, an iterative dimension-wise approach (IDWA) is proposed. Either the minimal or maximal input vector of the response is identified as an RP by a global update in which a novel RP is dimension-wisely assembled by the minimal or maximal points of all sectional curves of the response surface at a previous RP through a local update. The interval response is calculated by deterministic solvers at the minimal and maximal input vectors. An acoustic analysis problem is studied eventually to validate the effectiveness of the proposed method, from which conclusions are drawn.

A revised moment error expression for the AIRGA algorithm

The fully adaptive rational global Arnoldi method (AIRGA) for the modelorder reduction of second-order multi-input multi-output systems with proportional damping is revisited. The method automatically generates a reduced system approximating the transfer function. It is based on a moment-matching approach. The expansion points are determined iteratively. The reduced order and the number of moments matched per expansion point are determined adaptively using a heuristic based on an error estimation. A revised moment error expression is presented as well as some related findings.

The Fundamental Aspects of TEMOM Model for Particle Coagulation due to Brownian Motion—Part II: In the Continuum Regime

The fundamental aspects of the Taylor-series expansion method of moment (TEMOM) model proposed to model the aerosol population balance equation due to Brownian coagulation in the continuum regime is shown in this study, such as the choice of the expansion pointu, the relationship between asymptotic behavior and analytical solution, and the error of the high-order moment equations. All these analyses will contribute to the buildup of the theoretical system of the TEMOM model.