Convergence of an Anisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems

2016 ◽  
Vol 9 (3) ◽  
pp. 358-382 ◽  
Author(s):  
Chao Liang ◽  
Xueshuang Xiang
Keyword(s):  
Vector Field ◽  
Numerical Experiments ◽  
Perfectly Matched Layer ◽  
Scattering Problems ◽  
New Approach ◽  
Layer Method ◽  
Continuous Vector Field ◽  
Shortest Distance ◽  
The Stability ◽  
Anisotropic Perfectly Matched Layer

AbstractThe anisotropic perfectly matched layer (APML) defines a continuous vector field outside a rectangle domain and performs the complex coordinate stretching along the vector field. Inspired by [Z. Chen et al., Inverse Probl. Imag., 7, (2013):663–678] and based on the idea of the shortest distance, we propose a new approach to construct the vector field which still allows us to prove the exponential decay of the stretched Green function without the constraint on the thickness of the PML layer. Moreover, by using the reflection argument, we prove the stability of the PML problem in the PML layer and the convergence of the PML method. Numerical experiments are also included.

Host-Guest Interactions on Electrode Surfaces for Immobilization of Molecular Catalysts

2020 ◽  
Author(s):  
Laurent Sévery ◽  
Jacek Szczerbiński ◽  
Mert Taskin ◽  
Isik Tuncay ◽  
Fernanda Brandalise Nunes ◽  
...  
Keyword(s):  
Aqueous Media ◽  
Heterogeneous Systems ◽  
Catalytic Systems ◽  
New Approach ◽  
Molecular Systems ◽  
Electrode Surfaces ◽  
Catalytic Surfaces ◽  
Oxide Electrodes ◽  
The Stability ◽  
Molecular Catalysts

The strategy of anchoring molecular catalysts on electrode surfaces combines the high selectivity and activity of molecular systems with the practicality of heterogeneous systems. The stability of molecular catalysts is, however, far less than that of traditional heterogeneous electrocatalysts, and therefore a method to easily replace anchored molecular catalysts that have degraded could make such electrosynthetic systems more attractive. Here, we apply a non-covalent “click” chemistry approach to reversibly bind molecular electrocatalysts to electrode surfaces via host-guest complexation with surface-anchored cyclodextrins. The host-guest interaction is remarkably strong and allows the flow of electrons between the electrode and the guest catalyst. Electrosynthesis in both organic and aqueous media was demonstrated on metal oxide electrodes, with stability on the order of hours. The catalytic surfaces can be recycled by controlled release of the guest from the host cavities and readsorption of fresh guest. This strategy represents a new approach to practical molecular-based catalytic systems.

A Stability Analysis of the Perfectly Matched Layer Method

1999 ◽  
Author(s):  
S. J. Yakura ◽  
David Dietz ◽  
Andy Greenwood ◽  
Ernest Baca
Keyword(s):  
Stability Analysis ◽  
Perfectly Matched Layer ◽  
Layer Method

scholarly journals Methodology and Models for Individuals’ Creditworthiness Management Using Digital Footprint Data and Machine Learning Methods

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1820
Author(s):  
Ekaterina V. Orlova
Keyword(s):  
Interest Rates ◽  
Additional Data ◽  
Risk Level ◽  
Gradient Boosting ◽  
Cluster Number ◽  
New Approach ◽  
Credit Risks ◽  
Stochastic Gradient Boosting ◽  
The Stability ◽  
Digital Footprints

This research deals with the challenge of reducing banks’ credit risks associated with the insolvency of borrowing individuals. To solve this challenge, we propose a new approach, methodology and models for assessing individual creditworthiness, with additional data about borrowers’ digital footprints to implement comprehensive analysis and prediction of a borrower’s credit profile. We suggest a model for borrowers’ clustering based on the method of hierarchical clustering and the k-means method, which groups actual borrowers having similar creditworthiness and similar credit risks into homogeneous clusters. We also design the model for borrowers’ classification based on the stochastic gradient boosting (SGB) method, which reliably determines the cluster number and therefore the risk level for a new borrower. The developed models are the basis for decision making regarding the decision about lending value, interest rates and lending terms for each risk-homogeneous borrower’s group. The modified version of the methodology for assessing individual creditworthiness is presented, which is to reduce the credit risks and to increase the stability and profitability of financial organizations.

A new approach to the stability analysis of thawing slopes

1980 ◽  
Vol 17 (4) ◽  
pp. 607-612 ◽  
Author(s):  
Luis E. Vallejo
Keyword(s):  
Stability Analysis ◽  
Water Content ◽  
Pore Water ◽  
Active Layer ◽  
Necessary Conditions ◽  
Mass Movements ◽  
New Approach ◽  
Pore Water Pressures ◽  
The Stability ◽  
Excess Pore

A new approach to the stability analysis of thawing slopes at shallow depths, taking into consideration their structure (this being a mixture of hard crumbs of soil and a fluid matrix), is presented. The new approach explains shallow mass movements such as skin flows and tongues of bimodal flows, which usually take place on very low slope inclinations independently of excess pore water pressures or increased water content in the active layer, which are necessary conditions in the methods available to date to explain these movements.

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