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Odd-viscosity-induced instability of a falling thin film with an external electric field.
Phys Rev E
January 2021
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, People's Republic of China.
The influence of odd viscosity of Newtonian fluid on the instability of thin film flowing along an inclined plane under a normal electric field is studied. By odd viscosity, we mean apart from the well-known coefficient of shear viscosity, a classical liquid with broken time-reversal symmetry is endowed with a second viscosity coefficient in biological, colloidal, and granular systems. Under the long wave approximation, a nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion.
View Article and Find Full Text PDFQuantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation.
Phys Rev E Stat Nonlin Soft Matter Phys
May 2015
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom.
The Hasimoto transformation between the classical LIA (local induction approximation, a model approximating the motion of a thin vortex filament) and the nonlinear Schrödinger equation (NLS) has proven very useful in the past, since it allows one to construct new solutions to the LIA once a solution to the NLS is known. In the present paper, the quantum form of the LIA (which includes mutual friction effects) is put into correspondence with a type of complex nonlinear dispersive partial differential equation (PDE) with cubic nonlinearity (similar in form to a Ginsburg-Landau equation, with additional nonlinear terms). Transforming the quantum LIA in such a way enables one to obtain quantum vortex filament solutions once solutions to this dispersive PDE are known.
View Article and Find Full Text PDFComplexes of stationary domain walls in the resonantly forced Ginsburg-Landau equation.
Phys Rev E Stat Nonlin Soft Matter Phys
February 2005
Department of Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
The parametrically driven Ginsburg-Landau equation has well-known stationary solutions-the so-called Bloch and Ne el, or Ising, walls. In this paper, we construct an explicit stationary solution describing a bound state of two walls. We also demonstrate that stationary complexes of more than two walls do not exist.
View Article and Find Full Text PDFA dynamical model for phospholipid-calcium binding.
Biophys Chem
May 1991
Centro de Investigacion Sobre Fijacion de Nitrogeno, UNAM Apdo. Postal 565-A, Cuernavaca, Mor., Mexico.
A model for an isothermal gel-liquid crystalline transition induced by ionic binding is proposed. A Ginsburg-Landau functional was used to describe the long-range order that spontaneously arises during the transition. By calculation of the corresponding chemical potential we obtain the mass current of phospholipids in gel-phase described by an order parameter.
View Article and Find Full Text PDFGinsburg-Landau equation around the superconductor-insulator transition.
Phys Rev B Condens Matter
May 1991
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