Related papers: Physical Parameters for Biconcave Shape Vesicles
We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation…
We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1},…
Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length-scales are involved has not…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of…
Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for…
We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss…
We discuss the property of the number density of a fluid of particles living in a curved surface without boundaries to be constant in the thermodynamic limit. In particular we find a sufficient condition for the density to be constant along…
We describe a natural decomposition of a normal complex surface singularity $(X,0)$ into its "thick" and "thin" parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin.…
The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for…
The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the…
We consider rotating equilibrium states of fluid deformable surfaces. These states are characterized by a force balance between centrifugal and bending forces, involve surface Killing vector fields and are independent on the surface…
In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed of a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number…
The values of liquid odd-viscosity coefficients remain largely unknown, with only a single experimental measurement reported to date [Nature Physics 15, 1188 (2019)]. In this work, inspired by the well-known consequences of dispersion…
We give real Jacobian elliptic function parametrizations for a genuinely asymmetric biquadratic curve where the variables and parameters are real.
As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
A model of vesicle electrodeformation is described which obtains a parametrized vesicle shape by minimizing the sum of the membrane bending energy and the energy due to the electric field. Both the vesicle membrane and the aqueous media…