The Relation between Drift, Entropy Distribution and Kirkendall Plane Position during Diffusion

2014 ◽  
Vol 354 ◽  
pp. 67-71
Author(s):  
Bartek Wierzba ◽  
Wojciech Skibiński ◽  
Marek Danielewski
Keyword(s):  
Numerical Methods ◽  
Diffusion Couple ◽  
Density Distribution ◽  
Kirkendall Effect ◽  
Entropy Density ◽  
Conservation Of Mass ◽  
Vacancy Flux ◽  
First Time

The Kirkendall effect appears due to the unbalanced diffusion fluxes causing the vacancy flux. There are several numerical methods that allow to predict the position of Kirkendall plane after the diffusion couple annealing. In this work for the first time the entropy density distribution is used to estimate the trajectory of the Kirkendall plane. The entropy density distribution is calculated with use of the bi-velocity method, which combines: (1) the volume continuity, (2) the conservation of mass, (3) momentum and (4) entropy-density. The method is applied to simulate the diffusion in Ni-Pd diffusion couple.

Senile Coconut Palm Hierarchical Structure as Foundation for Biomimetic Applications

2014 ◽  
Vol 553 ◽  
pp. 344-349 ◽  
Author(s):  
O.M. Gonzalez ◽  
Benoit P. Gilbert ◽  
H. Bailleres ◽  
Hong Guan
Keyword(s):  
Density Distribution ◽  
Hierarchical Structure ◽  
Triple Helix ◽  
Mechanical Characteristics ◽  
Weather Conditions ◽  
Scientific Basis ◽  
Coconut Palm ◽  
Characteristic Radius ◽  
First Time ◽  
Stem Structure

Superior to hardwood and softwood trees, coconut palms are able to withstand extreme weather conditions without failure. Previous studies have shown that the internal structure of coconut palm stems significantly differs from hardwood, softwood and even other palm stems, in terms of fibre orientation and density distribution, likely influencing the mechanical characteristics of the tree. This paper aims at quantifying the cocowood hierarchical structure at an integral level (stem structure). To achieved this, quantitative analysis of more than 40 senile coconut palms from Fiji and Samoa has been carried out. This paper defines and analyses the typical cocowood morphology (form-structure) in terms of such factors as characteristic radius, fibrovascular bundles orientation and density distribution. For the first time, the characteristic triple helix configuration traced out by the fibrovascular bundles within the cocowood structure is modelled for the whole coconut stem. Specific equations are proposed to determine these factors at any given position in the tree. Knowledge advanced from this study will provide a scientific basis for future cocowood biomechanics research, including finite element modelling and analysis for biomimetic engineering applications.

scholarly journals Comparative Study of Some Numerical Methods for the Burgers–Huxley Equation

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1333 ◽  
Author(s):  
Appanah Appadu ◽  
Bilge İnan ◽  
Yusuf Tijani
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Fully Implicit ◽  
Huxley Equation ◽  
Relative Errors ◽  
First Time

In this paper, we construct four numerical methods to solve the Burgers–Huxley equation with specified initial and boundary conditions. The four methods are two novel versions of nonstandard finite difference schemes (NSFD1 and NSFD2), explicit exponential finite difference method (EEFDM) and fully implicit exponential finite difference method (FIEFDM). These two classes of numerical methods are popular in the mathematical biology community and it is the first time that such a comparison is made between nonstandard and exponential finite difference schemes. Moreover, the use of both nonstandard and exponential finite difference schemes are very new for the Burgers–Huxley equations. We considered eleven different combination for the parameters controlling diffusion, advection and reaction, which give rise to four different regimes. We obtained stability region or condition for positivity. The performances of the four methods are analysed by computing absolute errors, relative errors, L 1 and L ∞ errors and CPU time.

scholarly journals Benchmarking Current Capabilities for the Generation of Excitation and Photoionisation Atomic Data

Galaxies ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 90 ◽  
Author(s):  
Catherine Ramsbottom ◽  
Connor Ballance ◽  
Ryan Smyth ◽  
Andrew Conroy ◽  
Luis Fernández-Menchero ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Cross Sections ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Radiative Transition ◽  
Atomic Data ◽  
High Quality ◽  
Astronomical Instruments ◽  
First Time ◽  
Line Strengths

The spectra currently emerging from modern ground- and space-based astronomical instruments are of exceptionally high quality and resolution. To meaningfully analyse these spectra, researchers utilise complex modelling codes to replicate the observations. The main inputs to these codes are atomic data such as excitation and photoionisation cross sections, as well as radiative transition probabilities, energy levels, and line strengths. In this publication, the current capabilities of the numerical methods and computer packages used in the generation of these data are discussed. Particular emphasis is given to Fe-peak species and the heavy systems of tungsten and molybdenum. Some of the results presented to highlight certain issues and/or advances have already been published in the literature, while other sections present new recently evaluated atomic data for the first time.

Computer Assisted Design of Rubber Mounting Springs

1992 ◽  
Author(s):  
T. E. Shoup ◽  
L. A. Sanchez
Keyword(s):  
Numerical Methods ◽  
Numerical Procedure ◽  
Design Procedure ◽  
Computer Assisted ◽  
Numerical Techniques ◽  
Numerical Approximations ◽  
Design Procedures ◽  
Computer Assisted Design ◽  
First Time ◽  
Digital Computers

Abstract While analysis procedures for the design of rubber mountings have existed for a number of years, the nonlinearity of these useful devices has limited the number of design procedures that are available. This paper presents a design procedure for the static deflections of rubber mountings. It is believed that this is the first time that such numerical procedures have been described in the design literature. The procedures are made possible by a combination of numerical approximations of data in the engineering literature and numerical methods for handling transcendental relationships. Such design procedures would clearly not be possible without the use of the digital computers and the numerical techniques that it facilitates. Design examples are presented to illustrate the use of the numerical procedure.

Computer Assisted Design of Rubber Shear Springs

1993 ◽  
Author(s):  
T. E. Shoup ◽  
G. R. Fegan
Keyword(s):  
Numerical Methods ◽  
Numerical Optimization ◽  
Numerical Procedure ◽  
Design Procedure ◽  
Nonlinear Behavior ◽  
Optimization Techniques ◽  
Computer Assisted ◽  
Design Procedures ◽  
Computer Assisted Design ◽  
First Time

Abstract While analysis procedures for the design of rubber mountings have existed for a number of years, the nonlinearity of these useful devices has limited the number of robust design procedures that are available. This paper presents a design procedure for the static deflections of rubber shear springs that accommodates the nonlinear behavior of these devices. It is believed that this is the first time such numerical procedures have been described in the design literature. The procedures are made possible by a combination of numerical approximations of nonlinear data in the engineering literature and numerical methods for handling transcendental relationships. Such design procedures would clearly not be possible without the use of digital computers and numerical optimization techniques. Design examples are presented to illustrate the use of the numerical procedure.

scholarly journals Optical Feedback Interferometry Based Microfluidic Sensing: Impact of Multi-Parameters on Doppler Spectral Properties

2019 ◽  
Vol 9 (18) ◽  
pp. 3903 ◽  
Author(s):  
Yu Zhao ◽  
Thierry Camps ◽  
Véronique Bardinal ◽  
Julien Perchoux
Keyword(s):  
Numerical Methods ◽  
Experimental Validation ◽  
Optical Feedback ◽  
Scattered Light ◽  
Doppler Frequency ◽  
Angle Distribution ◽  
Sensor Performance ◽  
Microscale Flow ◽  
First Time ◽  
System Characteristics

As a compact and simple sensing technique, optical feedback interferometry (OFI) can be a promising flowmetry method in various microfluidic applications. In this paper, OFI-based flowmetry sensor performance in a microscale flow scheme is studied theoretically and experimentally. An innovating model and different numerical methods are investigated, where the scattering light angle distribution is involved to predict the Doppler frequency distribution. For the first time, our model describes the influences of multiple OFI sensor system characteristics, such as flowing particle size, concentration, channel interface reflectivity and channel dimension, on the OFI signal spectral performances. In particular, a significant OFI signal level enhancement was achieved by deposing a high reflectivity gold layer on the rear channel interface due to the increased forward scattered light reflection. The consistent experimental validation associated with the simulations verifies this numerical simulation method’s reliability. The numerical methods presented here provide a new tool to design novel microfluidic reactors and sensors.

Exact Vibration Solution for Exponentially Tapered Cantilever With Tip Mass

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
C.Y. Wang ◽  
C. M. Wang
Keyword(s):  
Numerical Methods ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Technical Note ◽  
Mode Shapes ◽  
Constant Thickness ◽  
Vibration Frequencies ◽  
Tapered Cantilever Beam ◽  
Tip Mass ◽  
First Time

This technical note is concerned with the free vibration problem of a cantilever beam with constant thickness and exponentially decaying width. Existing analytical results for such a vibration beam problem are found to be incomplete because lower frequencies could not be obtained. Presented herein is the exact characteristic equation for generating the complete vibration frequencies for the considered vibrating beam problem. Also the note treated for the first time such a tapered cantilever beam with a tip mass. The exact solutions (frequencies and mode shapes) are important to engineers designing such tapered beams and the results serve as benchmarks for assessing the validity, convergence and accuracy of numerical methods and solutions.

scholarly journals Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Marek Danielewski ◽  
Henryk Leszczyński
Keyword(s):  
Diffusion Couple ◽  
Three Dimensional ◽  
Transformation Method ◽  
Kirkendall Effect ◽  
Initial Distribution ◽  
Displacement Fields ◽  
Ternary Diffusion ◽  
Transform Method ◽  
Ternary Diffusion Couple ◽  
Diagonalization Method

The problem of Kirkendall’s trajectories in finite, three- and one-dimensional ternary diffusion couples is studied. By means of the parabolic transformation method, we calculate the solute field, the Kirkendall marker velocity, and displacement fields. The velocity field is generally continuous and can be integrated to obtain a displacement field that is continuous everywhere. Special features observed experimentally and reported in the literature are also studied: (i) multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple evolve into two locations as a result of the initial distribution, (ii) multiple Kirkendall’s planes where markers placed on an initial compositional discontinuity of the diffusion couple move into two locations due to composition dependent mobilities, and (iii) a Kirkendall plane that coincides with the interphase interface. The details of the deformation (material trajectories) in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect. Our nonlinear transform generalizes the diagonalization method by Krishtal, Mokrov, Akimov, and Zakharov, whose transform of diffusivities was linear.

Formation of a Hollow Binary Alloy Nanosphere: A Kinetic Monte Carlo Study

2009 ◽  
Vol 7 ◽  
pp. 11-17 ◽  
Author(s):  
Alexander V. Evteev ◽  
Elena V. Levchenko ◽  
Irina V. Belova ◽  
Graeme E. Murch
Keyword(s):  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
Void Formation ◽  
Monte Carlo Study ◽  
Kirkendall Effect ◽  
Hollow Nanosphere ◽  
The Core ◽  
Sphere Formation ◽  
First Time ◽  
Kirkendall Porosity

Results of kinetic Monte Carlo simulation of the formation of a hollow nanosphere by interdiffusion from a core-shell binary system are presented for the first time. The faster diffusing species is located in the core whilst the slower diffusing species form the shell. With its self-generated vacancy composition all stages of the hollow sphere formation process are observed in our model: interdiffusion, the supersaturation of the core of the nanosphere by vacancies, precipitation of pores and eventual void formation. Results of this simulation confirm the experimental conclusions that interdiffusion accompanied by the Kirkendall effect and Kirkendall porosity is one of the mechanisms responsible for the formation of hollow nano-objects.

scholarly journals Compression of a mixed antiproton and electron non-neutral plasma to high densities

2018 ◽  
Vol 72 (4) ◽  
Author(s):  
Stefano Aghion ◽  
Claude Amsler ◽  
Germano Bonomi ◽  
Roberto S. Brusa ◽  
Massimo Caccia ◽  
...  
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Plasma ◽  
Single Shot ◽  
Compression Method ◽  
Experimental Conditions ◽  
Rotating Wall ◽  
Antihydrogen Production ◽  
Neutral Plasma ◽  
First Time

Abstract We describe a multi-step “rotating wall” compression of a mixed cold antiproton–electron non-neutral plasma in a 4.46 T Penning–Malmberg trap developed in the context of the AEḡIS experiment at CERN. Such traps are routinely used for the preparation of cold antiprotons suitable for antihydrogen production. A tenfold antiproton radius compression has been achieved, with a minimum antiproton radius of only 0.17 mm. We describe the experimental conditions necessary to perform such a compression: minimizing the tails of the electron density distribution is paramount to ensure that the antiproton density distribution follows that of the electrons. Such electron density tails are remnants of rotating wall compression and in many cases can remain unnoticed. We observe that the compression dynamics for a pure electron plasma behaves the same way as that of a mixed antiproton and electron plasma. Thanks to this optimized compression method and the high single shot antiproton catching efficiency, we observe for the first time cold and dense non-neutral antiproton plasmas with particle densities n ≥ 1013 m−3, which pave the way for an efficient pulsed antihydrogen production in AEḡIS. Graphical abstract

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