scholarly journals Behaviour of the Stokes operators under domain perturbation

2019 ◽  
Vol 62 (6) ◽  
pp. 1167-1174
Author(s):  
Sylvie Monniaux
Keyword(s):  
Domain Perturbation

scholarly journals Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

2021 ◽  
pp. 1-26
Author(s):  
Matteo Dalla Riva ◽  
Riccardo Molinarolo ◽  
Paolo Musolino
Keyword(s):  
Boundary Value Problem ◽  
Laplace Equation ◽  
Boundary Value ◽  
Perturbation Parameter ◽  
Existence Results ◽  
Transmission Problem ◽  
Perforated Domain ◽  
Analytic Dependence ◽  
Domain Perturbation ◽  
Fixed Domain

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$ . First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$ .

Review of the Secondary Flows of Complex Fluids

2003 ◽  
Author(s):  
Dennis A. Siginer
Keyword(s):  
Secondary Flow ◽  
Cross Sections ◽  
Secondary Flows ◽  
Laboratory Setting ◽  
Transfer Enhancement ◽  
Domain Perturbation ◽  
Novel Approach ◽  
Viscoelastic Liquids ◽  
First Time ◽  
Secondary Flow Field

A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively nonlinear simple fluid in straight tubes of arbitrary cross-sections is summarized. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

Switching Time of Electrowetting-Based Devices

2009 ◽  
Author(s):  
Jiwoo Hong ◽  
Jung Min Oh ◽  
Kwan Hyoung Kang
Keyword(s):  
Theoretical Analysis ◽  
Theoretical Prediction ◽  
Switching Time ◽  
Liquid Droplet ◽  
Volume Density ◽  
Drop Volume ◽  
Rf Switches ◽  
Domain Perturbation ◽  
Fast Spreading ◽  
Electronic Display

The switching time is important factor for enhancing performance of electrowetting-based devices, such as electronic display, liquid lens, and RF switches. These devices require fast spreading, receding time of droplet. In this work, we suggested an analytical method to predict the switching time. We considered the case of a liquid droplet on an insulator-coated electrode surrounded by air. The properties of droplet such as volume, density, viscosity, and interfacial tension affects the switching time. First we explored the influence of drop volume on switching time. To predict the switching time, the dynamics of a droplet are modeled by using the domain perturbation method. It is shown that the overall dynamics is governed by P2 shape mode. Based on theoretical analysis, we introduced a parameter which represents the switching time. We compared the theoretical prediction with experimental results, and then discussed the effect of contact-line hysteresis.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

Sign in / Sign up

Export Citation Format

Share Document