4,129 research outputs found
Minimal mass blow up solutions for a double power nonlinear Schr\"odinger equation
We consider a nonlinear Schr\"odinger equation with double power
nonlinearity, where one power is focusing and mass critical and the other mass
sub-critical. Classical variational arguments ensure that initial data with
mass less than the mass of the ground state of the mass critical problem lead
to global in time solutions. We are interested by the threshold dynamic and in
particular by the existence of finite time blow up minimal solutions. For the
mass critical problem, such an object exists thanks to the explicit conformal
symmetry, and is in fact unique. For the focusing double power nonlinearity, we
exhibit a new class of minimal blow up solutions with blow up rates deeply
affected by the double power nonlinearity. The analysis adapts the recent
approach developed by Rapha\"el and Szeftel for the construction of minimal
blow up elements
Dewetting of thin polymer films: Influence of interface evolution
The dewetting dynamics of ultrathin polymer films, e.g. in the model system
of polystyrene on a polydimethylsiloxane-covered substrate, exhibits
interesting behavior like a fast decay of the dewetting velocity and a maximum
in the width of the built-up rim in the course of time. These features have
been recently ascribed to the relaxation of residual stresses in the film that
stem from the nonequilibrium preparation of the samples. Recent experiments by
Coppee et al. on PS with low molecular weight, where such stresses could not be
evidenced, showed however similar behavior. By scaling arguments and numerical
solution of a thin film viscoelastic model we show that the maximum in the
width of the rim can be caused by a temporal evolution of the friction
coefficient (or equivalently of the slip length), for which we discuss two
possible mechanisms. In addition, the maximum in the width is affected by the
sample age. As a consequence, knowing the temporal behavior of friction (or
slip length) in principle allows to measure the aging dynamics of a
polymer-polymer interface by simple dewetting experiments.Comment: 6 pages, 2 figure
On the successful culture of Gracilaria edulis from spores
Gradlaria is a commercially valauble agarophyte. Culture of Gracilaria edulis from spores on an experimental scale liberating the spores on different substrata like coir rope, circular cement blocks,nylon- ropes, coral stones and nylon raphae has been studied
Finite-Dimensional Bicomplex Hilbert Spaces
This paper is a detailed study of finite-dimensional modules defined on
bicomplex numbers. A number of results are proved on bicomplex square matrices,
linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces,
including the spectral decomposition theorem. Applications to concepts relevant
to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page
q-Schur algebras and complex reflection groups, I
We show that the category O for a rational Cherednik algebra of type A is
equivalent to modules over a q-Schur algebra (parameter not a half integer),
providing thus character formulas for simple modules. We give some
generalization to B_n(d). We prove an ``abstract'' translation principle. These
results follow from the unicity of certain highest categories covering Hecke
algebras. We also provide a semi-simplicity criterion for Hecke algebras of
complex reflection groups.Comment: Corrected version, 5.2.3 and 5.2.4 are ne
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