Multiple SLE and the complex Burgers equation

2016 ◽  
Vol 289 (16) ◽  
pp. 2007-2018 ◽  
Author(s):  
Andrea del Monaco ◽  
Sebastian Schleißinger
Keyword(s):  
Burgers Equation ◽  
Complex Burgers Equation ◽  
Multiple Sle

Direct perturbation method for perturbed complex Burgers equation

2009 ◽  
Vol 18 (2) ◽  
pp. 391-394 ◽  
Author(s):  
Cheng Xue-Ping ◽  
Lin Ji ◽  
Yao Jian-Ming
Keyword(s):  
Perturbation Method ◽  
Burgers Equation ◽  
Complex Burgers Equation ◽  
Direct Perturbation

scholarly journals Exact solutions for the formation of stagnant caps of insoluble surfactant on a planar free surface

2021 ◽  
Vol 131 (1) ◽  
Author(s):  
Darren G. Crowdy
Keyword(s):  
Exact Solutions ◽  
Peclet Number ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Implicit Representation ◽  
Péclet Number ◽  
New Exact Solutions ◽  
Kinetics Modelling ◽  
Complex Burgers Equation ◽  
Insoluble Surfactant

AbstractA class of exact solutions is presented describing the time evolution of insoluble surfactant to a stagnant cap equilibrium on the surface of deep water in the Stokes flow regime at zero capillary number and infinite surface Péclet number. This is done by demonstrating, in a two-dimensional model setting, the relevance of the forced complex Burgers equation to this problem when a linear equation of state relates the surface tension to the surfactant concentration. A complex-variable version of the method of characteristics can then be deployed to find an implicit representation of the general solution. A special class of initial conditions is considered for which the associated solutions can be given explicitly. The new exact solutions, which include both spreading and compactifying scenarios, provide analytical insight into the unsteady formation of stagnant caps of insoluble surfactant. It is also shown that first-order reaction kinetics modelling sublimation or evaporation of the insoluble surfactant to the upper gas phase can be incorporated into the framework; this leads to a forced complex Burgers equation with linear damping. Generalized exact solutions to the latter equation at infinite surface Péclet number are also found and used to study how reaction effects destroy the surfactant cap equilibrium.

scholarly journals Limit shapes and the complex Burgers equation

2007 ◽  
Vol 199 (2) ◽  
pp. 263-302 ◽  
Author(s):  
Richard Kenyon ◽  
Andrei Okounkov
Keyword(s):  
Burgers Equation ◽  
Complex Burgers Equation ◽  
Limit Shapes
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