Successive Solution–Liquid–Solid (SLS) Growth of Heterogeneous Nanowires

2013 ◽  
Vol 25 (21) ◽  
pp. 4156-4164 ◽  
Author(s):  
Min-Seok Kim ◽  
Yun-Mo Sung
Keyword(s):  
Successive Solution

Morphological Evolution in Heteroepitaxial Thin Film Structures at the Nanoscale

2015 ◽  
Vol 364 ◽  
pp. 112-121 ◽  
Author(s):  
Mikhail A. Grekov ◽  
Sergey A. Kostyrko
Keyword(s):  
Thin Film ◽  
Elastic Stress ◽  
Morphological Evolution ◽  
Perturbation Technique ◽  
Film System ◽  
Boundary Perturbation ◽  
Surface And Interface ◽  
Thin Film System ◽  
Successive Solution ◽  
Surface Phases

The aim of this study is to resolve the phenomenon of formation of mesoscopic structures on the surface of heteroepitaxial thin film system due to surface diffusion by considering the effects of both surface and interface stresses. Elastic stress field caused by curved surface is solved by using the constitutive equations of linear elasticity for the bulk and surface phases. Based on the method of superposition, a boundary perturbation technique, Goursat-Kolosov complex potentials and Muskhelishvili representations, the boundary value problem is reduced to the successive solution of a system of singular and hypersingular integral equations for any order of approximation. This solution and thermodynamic approach allows us to derive a governing equation which gives the amplitude changing of a surface roughness with time.

Further Developments in the Aerodynamic Analysis of Unsteady Supersonic Cascades—Part 1: The Unsteady Pressure Field

1977 ◽  
Vol 99 (4) ◽  
pp. 509-516 ◽  
Author(s):  
J. M. Verdon
Keyword(s):  
Velocity Potential ◽  
Pressure Field ◽  
Supersonic Stream ◽  
Axial Velocity Component ◽  
Unsteady Pressure ◽  
Pressure Distributions ◽  
Successive Solution ◽  
Construction Procedure ◽  
Present Procedure ◽  
Dependent Variables

This paper presents, in two parts, a theoretical investigation of the aerodynamic response produced by an oscillating cascade placed in a supersonic stream with subsonic axial velocity component. Predictions are based on the successive solution of two linear boundary value problems which treat the velocity potential and the pressure, respectively, as basic dependent variables. A solution for the potential has been reported earlier and is used here to provide upper surface blade pressure distributions. This information serves as a boundary condition for the second problem. The solution for the unsteady pressure field, described in Part 1, is obtained by a construction procedure which parallels that used earlier to determine the potential. With the present procedure, blade pressure difference distributions and aerodynamic coefficients are accurately and efficiently determined for both subresonant and superresonant blade motions. Supersonic resonance phenomena and selected numerical results are discussed in Part 2 of the paper.

scholarly journals Trajectory analysis and extrapolation in barrier function methods

1978 ◽  
Vol 20 (3) ◽  
pp. 352-369 ◽  
Author(s):  
Krisorn Jittorntrum ◽  
M. R. Osborne
Keyword(s):  
Barrier Function ◽  
Trajectory Analysis ◽  
Degenerate Case ◽  
Extrapolation Methods ◽  
Extrapolation Procedure ◽  
Sensitivity Measure ◽  
Successive Solution ◽  
Degeneracy Condition ◽  
Special Case ◽  
Solution Estimates

AbstractIt has been known for some time that if a certain non-degeneracy condition is satisfied then the successive solution estimates x(r) produced by barrier function techniques lie on a smooth trajectory. Accordingly, extrapolation methods can be used to calculate x(0). In this paper we analyse the situation further treating the special case of the log barrier function. If the non-degeneracy assumption is not satisfied then the approach to x(0) is like r½ rather than like r which would be expected in the non-degenerate case. A measure of sensitivity is introduced which becomes large when the non- degeneracy assumption is close to violation, and it is shown that this sensitivity measure is related to the growth of dix/dri with respect to i for fixed r small enough on the solution trajectory. With this information it is possible to analyse the extrapolation procedure and to predict the number of stages of extrapolation which are useful.

scholarly journals A note on integral equations

1972 ◽  
Vol 13 (2) ◽  
pp. 119-121 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
General Class ◽  
Successive Solution ◽  
Dual Series Equations ◽  
Abel Integral Equations ◽  
Image Position

In a recent paper Cooke [1] obtained a solution of the integral equationby using the identityand the technique, first used by Copson, of interchanging the orders of integration and hence reducing the problem to that of the successive solution of two Abel integral equations. It is also shown in [1] that the above identity can also be used to solve the dual series equationsThe kernel in equation (1) is a particular member of a general class of kernels which the author [6] has shown to be such that the resulting integral equation is directly soluble by using Copson's technique. The particular example of equation (1) is given in [6] and the identity of equation (2) was used by the author [7] to obtain the solution of equation (3).

scholarly journals New Approach for Solving a Class of Doubly Singular Two-Point Boundary Value Problems Using Adomian Decomposition Method

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Randhir Singh ◽  
Jitendra Kumar ◽  
Gnaneshwar Nelakanti
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Multiple Roots ◽  
Point Boundary ◽  
New Approach ◽  
Successive Solution ◽  
Adomian Decomposition ◽  
Complete Calculation

We propose two new modified recursive schemes for solving a class of doubly singular two-point boundary value problems. These schemes are based on Adomian decomposition method (ADM) and new proposed integral operators. We use all the boundary conditions to derive an integral equation before establishing the recursive schemes for the solution components. Thus we develop recursive schemes without any undetermined coefficients while computing successive solution components, whereas several previous recursive schemes have done so. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients with multiple roots, which is required to complete calculation of the solution by several earlier modified recursion schemes using the ADM. The approximate solution is computed in the form of series with easily calculable components. The effectiveness of the proposed approach is tested by considering four examples and results are compared with previous known results.

scholarly journals Solving a Class of Singular Two-Point Boundary Value Problems Using New Modified Decomposition Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Randhir Singh ◽  
Jitendra Kumar
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Recursive Scheme ◽  
Successive Solution ◽  
Adomian Decomposition ◽  
Present Technique ◽  
Transcendental Equations

We introduce an effective methodology for solving a class of linear as well as nonlinear singular two-point boundary value problems. This methodology is based on a modification of Adomian decomposition method (ADM) and a new two fold integral operator. We use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components of solution. Thus, we develop modified recursive scheme without any undetermined coefficients while computing the successive solution components. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. However, most of earlier recursive schemes using ADM do require computation of undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the present technique. The results reveal that the method is very effective, straightforward, and simple.

Optimal Control: Successive Solution Methods

2021 ◽  
pp. 39-45
Author(s):  
Ido Halperin ◽  
Grigory Agranovich ◽  
Yuri Ribakov
Keyword(s):  
Optimal Control ◽  
Successive Solution ◽  
Solution Methods

The Synthesis of Pt/Ag Bimetallic Nanoparticles Using a Successive Solution Plasma Process

2014 ◽  
Vol 14 (12) ◽  
pp. 8925-8929 ◽  
Author(s):  
Sung Min Kim ◽  
Sang Yul Lee ◽  
Min Hyung Lee ◽  
Jung Wan Kim
Keyword(s):  
Bimetallic Nanoparticles ◽  
Plasma Process ◽  
Successive Solution
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