Analytical solutions to validate 3D numerical methods for solving direct ultraviolet photoionization and charge recombination of aerosol nanoparticles with laminar flow in circular ducts

2020 ◽  
Vol 128 (8) ◽  
pp. 084904
Author(s):  
Julio M. Fernández-Díaz ◽  
Sergio L. Palacios ◽  
Alberto Menéndez-Blanco
Keyword(s):  
Numerical Methods ◽  
Laminar Flow ◽  
Analytical Solutions ◽  
Charge Recombination ◽  
Aerosol Nanoparticles

scholarly journals Proposed Framework for Comparison of Continuous Probabilistic Genotyping Systems amongst Different Laboratories

2021 ◽  
Vol 1 (1) ◽  
pp. 33-45
Author(s):  
Dennis McNevin ◽  
Kirsty Wright ◽  
Mark Barash ◽  
Sara Gomes ◽  
Allan Jamieson ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Analytical Solutions ◽  
Peak Height ◽  
Dna Profiling ◽  
Likelihood Ratios ◽  
Dna Mixtures ◽  
Individual Laboratory ◽  
Multiple Variables

Continuous probabilistic genotyping (PG) systems are becoming the default method for calculating likelihood ratios (LRs) for competing propositions about DNA mixtures. Calculation of the LR relies on numerical methods and simultaneous probabilistic simulations of multiple variables rather than on analytical solutions alone. Some also require modelling of individual laboratory processes that give rise to electropherogram artefacts and peak height variance. For these reasons, it has been argued that any LR produced by continuous PG is unique and cannot be compared with another. We challenge this assumption and demonstrate that there are a set of conditions defining specific DNA mixtures which can produce an aspirational LR and thereby provide a measure of reproducibility for DNA profiling systems incorporating PG. Such DNA mixtures could serve as the basis for inter-laboratory comparisons, even when different STR amplification kits are employed. We propose a procedure for an inter-laboratory comparison consistent with these conditions.

XVI.—Dual Series Relations. III. Dual Relations Involving Trigonometric Series

1963 ◽  
Vol 66 (3) ◽  
pp. 173-184 ◽  
Author(s):  
R. P. Srivastav
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Integral Equations ◽  
Trigonometric Series ◽  
Analytical Solutions ◽  
Fredholm Integral Equation ◽  
Auxiliary Function

SynopsisThe methods developed in I, II of this series of papers are applied to a solution of a variety of dual series relations involving trigonometric series. In general the problem is reduced to one of solving (usually by numerical methods) a Fredholm integral equation of the second kind for an auxiliary function g(t), but for certain values of the parameters it is possible to obtain analytical solutions of the integral equations and these cases are considered in detail.

Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
W. Wayne Chen ◽  
Shuangbiao Liu ◽  
Q. Jane Wang
Keyword(s):  
Fourier Transform ◽  
Numerical Methods ◽  
Fast Fourier Transform ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Response Functions ◽  
Strain Fields ◽  
Flat Surfaces

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally flat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces.

Customized Profiles — The Beginning of an Era: A Short History of Blade Design

2004 ◽  
Author(s):  
Hanns-Juergen Lichtfuss
Keyword(s):  
Numerical Methods ◽  
Laminar Flow ◽  
Wind Tunnels ◽  
Blade Design ◽  
Design Strategies ◽  
Short History ◽  
Compressor Blades ◽  
History Of ◽  
Electronic Computers ◽  
Made In

The paper presents the evolutionary progress made in the design process of turbo machines from using standardized profiles — for turbine and compressor blades — towards individual profile designs. The emerging new power of numerical methods on continuously faster running electronic computers has made this progress possible. In addition there were regularly experimental verifications in cascade wind tunnels and turbo machinery test beds as well as applications of new design strategies. These strategies, i.e. naturally laminar flow in turbines and supercritical flow in compressors, also made use of reinvented inverse methods, as one tool to optimise problematic areas.

A Numerical Study of the Laminar Flow of Non-Newtonian Fluids Along a Vertical Wall

1973 ◽  
Vol 40 (1) ◽  
pp. 290-292 ◽  
Author(s):  
T. M. T. Yang ◽  
D. W. Yarbrough
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Laminar Flow ◽  
Power Law ◽  
Analytical Solutions ◽  
Numerical Study ◽  
Vertical Wall ◽  
Newtonian Fluids ◽  
Momentum Integral ◽  
Accelerating Flow

The momentum integral technique is used to describe the steady-state, laminar, accelerating flow of a power-law liquid film along a vertical wall. Values for film thicknesses and boundary-layer thicknesses are obtained numerically and compared with existing analytical solutions for Newtonian fluids.

scholarly journals A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Linearization Method ◽  
Exact Analytical Solutions ◽  
Successive Linearization Method ◽  
Method Approach ◽  
Better Than

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and performs better than some numerical methods.

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