216,238 research outputs found
Dynamical stabilization of matter-wave solitons revisited
We consider dynamical stabilization of Bose-Einstein condensates (BEC) by
time-dependent modulation of the scattering length. The problem has been
studied before by several methods: Gaussian variational approximation, the
method of moments, method of modulated Townes soliton, and the direct averaging
of the Gross-Pitaevskii (GP) equation. We summarize these methods and find that
the numerically obtained stabilized solution has different configuration than
that assumed by the theoretical methods (in particular a phase of the
wavefunction is not quadratic with ). We show that there is presently no
clear evidence for stabilization in a strict sense, because in the numerical
experiments only metastable (slowly decaying) solutions have been obtained. In
other words, neither numerical nor mathematical evidence for a new kind of
soliton solutions have been revealed so far. The existence of the metastable
solutions is nevertheless an interesting and complicated phenomenon on its own.
We try some non-Gaussian variational trial functions to obtain better
predictions for the critical nonlinearity for metastabilization but
other dynamical properties of the solutions remain difficult to predict
FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-006-0060-yWe present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.Peer ReviewedPostprint (author's final draft
Stability and Monotonicity for Some Discretizations of the Biot's Model
We consider finite element discretizations of the Biot's consolidation model
in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the
convergence of the fully discrete model based on spatial discretization with
these types of finite elements and implicit Euler method in time. We also
address the issue related to the presence of non-physical oscillations in the
pressure approximation for low permeabilities and/or small time steps. We show
that even in 1D a Stokes-stable finite element pair fails to provide a monotone
discretization for the pressure in such regimes. We then introduce a
stabilization term which removes the oscillations. We present numerical results
confirming the monotone behavior of the stabilized schemes
Energy scales in a stabilized brane world
Brane world gravity looks different for observers on positive and negative
tension branes. First we consider the well-known RS1 model with two branes
embedded into the AdS_5 space-time and recall the results on the relations
between the energy scales for an observer on the negative tension brane, which
is supposed to be "our" brane. Then from the point of view of this observer we
study energy scales and masses for the radion and graviton excitations in a
stabilized brane world model. We argue that there may be several possibilities
leading to scales of the order 1-10 TeV or even less for new physics effects on
our brane. In particular, an interesting scenario can arise in the case of a
"symmetric" brane world with a nontrivial warp factor in the bulk, which
however takes equal values on both branes.Comment: 15 pages, corrected typos, enlarged conten
Sterically stabilized lock and key colloids: A self-consistent field theory study
A self-consistent field theory study of lock and key type interactions
between sterically stabilized colloids in polymer solution is performed. Both
the key particle and the lock cavity are assumed to have cylindrical shape, and
their surfaces are uniformly grafted with polymer chains. The lock-key
potential of mean force is computed for various model parameters, such as
length of free and grafted chains, lock and key size matching, free chain
volume fraction, grafting density, and various enthalpic interactions present
in the system. The lock-key interaction is found to be highly tunable, which is
important in the rapidly developing field of particle self-assembly
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