226 research outputs found
Well-posedness of Hydrodynamics on the Moving Elastic Surface
The dynamics of a membrane is a coupled system comprising a moving elastic
surface and an incompressible membrane fluid. We will consider a reduced
elastic surface model, which involves the evolution equations of the moving
surface, the dynamic equations of the two-dimensional fluid, and the
incompressible equation, all of which operate within a curved geometry. In this
paper, we prove the local existence and uniqueness of the solution to the
reduced elastic surface model by reformulating the model into a new system in
the isothermal coordinates. One major difficulty is that of constructing an
appropriate iterative scheme such that the limit system is consistent with the
original system.Comment: The introduction is rewritte
Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
As two-dimensional fluid shells, lipid bilayer membranes resist bending and
stretching but are unable to sustain shear stresses. This property gives
membranes the ability to adopt dramatic shape changes. In this paper, a finite
element model is developed to study static equilibrium mechanics of membranes.
In particular, a viscous regularization method is proposed to stabilize
tangential mesh deformations and improve the convergence rate of nonlinear
solvers. The Augmented Lagrangian method is used to enforce global constraints
on area and volume during membrane deformations. As a validation of the method,
equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are
calculated. These numerical techniques are also shown to be useful for
simulations of three-dimensional large-deformation problems: the formation of
tethers (long tube-like exetensions); and Ginzburg-Landau phase separation of a
two-lipid-component vesicle. To deal with the large mesh distortions of the
two-phase model, modification of vicous regularization is explored to achieve
r-adaptive mesh optimization
Polarization Studies of Comet C/2000 WM1 (LINEAR)
Linear polarization observations were carried out on comet C/2000 WM1 with
the 1.2m telescope at Mt. Abu Observatory during November 2001 and March 2002.
The observations in November were at low phase angle (<~22\degr) when the
polarization is negative and where the data for most of the comets are rather
meager. The observations during March were made when the phase angle was
47\degr. Observations were conducted through the IHW narrow band and BVR broad
band filters. Based on these polarization observations we infer that the comet
C/2000 WM1 belongs to high polarization class i.e. the dusty comet family.Comment: 7 pages, 3 figures, accepted for publication in Astron. & Astrop
The fundamental constants and their variation: observational status and theoretical motivations
This article describes the various experimental bounds on the variation of
the fundamental constants of nature. After a discussion on the role of
fundamental constants, of their definition and link with metrology, the various
constraints on the variation of the fine structure constant, the gravitational,
weak and strong interactions couplings and the electron to proton mass ratio
are reviewed. This review aims (1) to provide the basics of each measurement,
(2) to show as clearly as possible why it constrains a given constant and (3)
to point out the underlying hypotheses. Such an investigation is of importance
to compare the different results, particularly in view of understanding the
recent claims of the detections of a variation of the fine structure constant
and of the electron to proton mass ratio in quasar absorption spectra. The
theoretical models leading to the prediction of such variation are also
reviewed, including Kaluza-Klein theories, string theories and other
alternative theories and cosmological implications of these results are
discussed. The links with the tests of general relativity are emphasized.Comment: 56 pages, l7 figures, submitted to Rev. Mod. Phy
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