scholarly journals Asymmetric shape transitions of epitaxial quantum dots

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160262 ◽  
Author(s):  
Chaozhen Wei ◽  
Brian J. Spencer
Keyword(s):  
Quantum Dots ◽  
Elastic Energy ◽  
Order Approximation ◽  
Equilibrium Solutions ◽  
Third Order ◽  
Island Type ◽  
Asymmetric Shape ◽  
Metastable Transition ◽  
Third Order Approximation ◽  
Shape Transitions

We construct a two-dimensional continuum model to describe the energetics of shape transitions in fully faceted epitaxial quantum dots (strained islands) via minimization of elastic energy and surface energy at fixed volume. The elastic energy of the island is based on a third-order approximation, enabling us to consider shape transitions between pyramids, domes, multifaceted domes and asymmetric intermediate states. The energetics of the shape transitions are determined by numerically calculating the facet lengths that minimize the energy of a given island type of prescribed island volume. By comparing the energy of different island types with the same volume and analysing the energy surface as a function of the island shape parameters, we determine the bifurcation diagram of equilibrium solutions and their stability, as well as the lowest barrier transition pathway for the island shape as a function of increasing volume. The main result is that the shape transition from pyramid to dome to multifaceted dome occurs through sequential nucleation of facets and involves asymmetric metastable transition shapes. We also explicitly determine the effect of corner energy (facet edge energy) on shape transitions and interpret the results in terms of the relative stability of asymmetric island shapes as observed in experiment.

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

2016 ◽  
Vol 24 (01) ◽  
pp. 1550021 ◽  
Author(s):  
Heekyu Woo ◽  
Young S. Shin
Keyword(s):  
Order Approximation ◽  
Stable Model ◽  
Approximation Model ◽  
Third Order ◽  
Acoustic Structure ◽  
Structure Interaction ◽  
Proposed Model ◽  
The Stability ◽  
Third Order Approximation ◽  
Interaction Problem

In this paper, a new third-order approximation model for an acoustic-structure interaction problem is introduced. The new approximation model is designed to be an accurate and a stable model for predicting the response of a submerged structure. The proposed model is obtained by combining two lower order approximation models instead of using an operator matching method. The stability of this model is checked by a modal analysis. Finally, the approximation model is coupled to the spherical shell structure, and its performance is checked by a shock analysis.

scholarly journals Interval estimation of trigonometrical splines

2019 ◽  
Vol 292 ◽  
pp. 03001
Author(s):  
I.G. Burova ◽  
E.G. Ivanova ◽  
V.A. Kostin
Keyword(s):  
Function Approximation ◽  
Order Approximation ◽  
Spline Approximation ◽  
Approximation Error ◽  
Interval Estimation ◽  
Polynomial Splines ◽  
Third Order ◽  
Variation Range ◽  
Local Spline ◽  
Third Order Approximation

Quite often, it is necessary to quickly determine variation range of the function. If the function values are known at some points, then it is easy to construct the local spline approximation of this function and use the interval analysis rules. As a result, we get the area within which the approximation of this function changes. It is necessary to take into account the approximation error when studying the obtained area of change of function approximation. Thus, we get the range of changing the function with the approximation error. This paper discusses the features of using polynomial and trigonometrical splines of the third order approximation to determine the upper and lower boundaries of the area (domain) in which the values of the approximation are contained. Theorems of approximation by these local trigonometric and polynomial splines are formulated. The values of the constants in the estimates of the errors of approximation by the trigonometrical and polynomial splines are given. It is shown that these constants cannot be reduced. An algorithm for constructing the variation domain of the approximation of the function is described. The results of the numerical experiments are given.

Mutations, perturbations and evolutionarily stable strategies

1982 ◽  
Vol 19 (01) ◽  
pp. 204-209 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Population Model ◽  
Order Approximation ◽  
Population Diversity ◽  
Mixed Strategies ◽  
Competitive Strategies ◽  
Evolutionarily Stable Strategies ◽  
Third Order ◽  
Population Mean ◽  
Third Order Approximation ◽  
Evolutionarily Stable

The changes in diversity of competitive strategies in a Maynard Smith population model with mixed strategies are related to the changes in population mean strategy. The effects of slight mutations in strategy frequencies, and of slight perturbations of the contest payoff rules are then investigated, and found to increase and decrease diversity respectively (to a third-order approximation). A relation among mutational effects, payoff perturbation effects and stable population diversity is suggested.

scholarly journals Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Gianni Mattioli ◽  
Massimo Scalia ◽  
Carlo Cattani
Keyword(s):  
Dynamical System ◽  
Order Approximation ◽  
Nonlinear Dynamical System ◽  
High Amplitude ◽  
Time Dependent ◽  
Third Order ◽  
Time Intervals ◽  
Nonlinear Dynamical ◽  
Short Time ◽  
Third Order Approximation

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude (time-dependent) pulse. The corresponding numerical solution for some given values of parameters are analyzed through the wavelet coefficients, showing both the sensitivity to local jumps and some unexpected inertia of neuron's as response to the high-amplitude spike.

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