Singularity methods

Singularity of the Drug. The principle involved in the singularity method of linking a drug with an ADR is based on two assumptions Only one drug was administered, and there was no basic disease or co-morbid state that could be related to the ADR marker being used in the assessment. 

C. Pozrikidis. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University, 1992. 

Electrochemical oxidation of resonance stabilized aromatic molecules is a common and singular method used to prepare CPs. It involves the oxidative coupling of monomers and is an ideal method to prepare conductive films that show reversible redox reaction. The polymerization can be monitored by in situ combination of the electrolysis system and appropriate spectroscopic or electro-analytical techniques the electrochemistry of CPs is the subject of a recent review with 748 references. 

A. T. Chwang and T. Y. Wu, Hydromechanics of low-Reynolds number flow, Part 1, Rotation of axisymmetric prolate bodies, J. Fluid Mech. 63, 607-22 (1974) A. T. Chwang and T. Y. Wu, Hydromechanics of low-Reynolds number flow, Part 2, Singularity method for Stokes flows, J. Fluid Mech. 67, 787-815 (1975) A. T. Chwang, Hydromechanics of low-Reynolds number flow, Part 3, Motion of a spheroidal particle in quadratic flows, J. Fluid Mech. 72, 17-34 (1975) A. T. Chwang and T. Y. Wu, Hydromechanics of low-Reynolds number flow, Part 4, Translation of spheroids, J. Fluid Mech. 75, 677-89 (1975). 

Problem 8-3. Consider the flow that is due to a point source of fluid, such that the fluid emanates from the origin at a rate Q (vol/time - a scalar). We may assume that this flow is a creeping motion. Under what conditions will this be true What is the resulting pressure and velocity distribution There is obviously more than one way to solve this problem, but the objective here is to use the singularity methods of this chapter. 

Pozrikidis C (1992) Boundary-integral and singularity methods for linearized viscous flow. Cambridge University Press, Cambridge... 

ME, but of less mathematical rigour, is the singularity method (SM), which reconstructs the potential field by a superposition of singularity fields from point charges (Phillips 1995). Additionally, it is possible to approximate compact, isometric aggregates as porous spheres (PS), for which analytical expressions of the double layer structure are available (Ohshima 2008). Some of the mentioned methods assume a certain shape of the aggregates or primary particles, some of them are based on the Unearised PBE (BEM, ME, PS). Only a few have already been employed for particle clusters (CoeUio et al. 1996 Kwon et al. 1998 Schiefil et al. 2012). 

Calculation of Double Layer Interaction with the Singularity Method... 

The singularity method is based on the linearised PBE (Eq. (3.17)) and on the simple analytical expression of the radially-symmetric potential field y/ r) around a point charge ... 

SchieBl et al. (2012) discussed the performance of the singularity method with regard to numeric stability and agreement to other numerical methods. There are apparently two limits ... 

In Fig. 4.41, the results of the singularity method are compared with two approximate solutions—the APPI and pairwise summation approximation. For Ka = 5, there is obviously no deviation between the approximations and the numerical calculation—independent from the aggregate type. In the case of DLCA aggregates, both approximations perform weU even for xa = 1. However, both approaches fail as soon as the double layer thickness is large compared to the primary particle size Ka < 1). The APPI systematically underestimates the interaction energy, whereas the pairwise summation approximation overvalues it. Regarding the deviation from the numerical solution, none of the two approaches can be preferred. However, the APPI requires less computation steps than the pairwise summation approach. 

The Sect. 4.6.2 introduces a numerical scheme for calculating the potential distribution in the EDL of arbitrary clusters of spherical particles the singularity method (PhiUips 1995). This approach considers the total electric field in EDL as superposition of the electric fields of point charges, which are located inside the particles. Such a field is easily described by ... 

Moreover, for constant potential the interaction energy is defined by Eq. (3.32) instead of Eq. (3.31). That means for the singularity method that Eq. (4.127) has to be substituted by ... 

Supply chain project management (PM) No discernible PM Common language Common process Singular method -ology Bench- marking Continuous improve -ment... 

Zhou and Wipf [292] described a singular method for deposition of conducting P(ANi) patterns using the so-called "scanning electrochemical microscope" (SECM). Fig. 8-7 fal summarizes this method, while Fig. 8-7 tbl shows a typical result. Substrates used included Au, Pt and C. The mechanism of deposition was a local pH change caused by proton reduction at the electrode tip. A 3 /im resolution was claimed. Conductivity of the resulting patterns was verified by SECM imaging. 

Abstract A complete approach to modeling adhesives and sealants needs to include considerations for deformation theories and viscoelasticity with linearity and nonlinearity considerations, rubber elasticity, singularity methods, bulk adhesive as composite material, damage models, the effects of cure and processing conditions on the mechanical behavior, and the concept of the interphase. ... 

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