10,835 research outputs found
Topography influence on the Lake equations in bounded domains
We investigate the influence of the topography on the lake equations which
describe the two-dimensional horizontal velocity of a three-dimensional
incompressible flow. We show that the lake equations are structurally stable
under Hausdorff approximations of the fluid domain and perturbations of
the depth. As a byproduct, we obtain the existence of a weak solution to the
lake equations in the case of singular domains and rough bottoms. Our result
thus extends earlier works by Bresch and M\'etivier treating the lake equations
with a fixed topography and by G\'erard-Varet and Lacave treating the Euler
equations in singular domains
Canard-like phenomena in piecewise-smooth Van der Pol systems
We show that a nonlinear, piecewise-smooth, planar dynamical system can
exhibit canard phenomena. Canard solutions and explosion in nonlinear,
piecewise-smooth systems can be qualitatively more similar to the phenomena in
smooth systems than piecewise-linear systems, since the nonlinearity allows for
canards to transition from small cycles to canards ``with heads." The canards
are born of a bifurcation that occurs as the slow-nullcline coincides with the
splitting manifold. However, there are conditions under which this bifurcation
leads to a phenomenon called super-explosion, the instantaneous transition from
a globally attracting periodic orbit to relaxations oscillations. Also, we
demonstrate that the bifurcation---whether leading to canards or
super-explosion---can be subcritical.Comment: 17 pages, 11 figure
Cell division: a source of active stress in cellular monolayers
We introduce the notion of cell division-induced activity and show that the
cell division generates extensile forces and drives dynamical patterns in cell
assemblies. Extending the hydrodynamic models of lyotropic active nematics we
describe turbulent-like velocity fields that are generated by the cell division
in a confluent monolayer of cells. We show that the experimentally measured
flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by
our modeling approach. Division-induced activity acts together with intrinsic
activity of the cells in extensile and contractile cell assemblies to change
the flow and director patterns and the density of topological defects. Finally
we model the evolution of the boundary of a cellular colony and compare the
fingering instabilities induced by cell division to experimental observations
on the expansion of MDCK cell cultures.Comment: Accepted Manuscript for Celebrating Soft Matter's 10th Anniversar
Anharmonicity and asymmetry of Landau levels for a two-dimensional electron gas
We calculate the density of states of a two dimensional electron gas located
at the interface of a GaAlAs/GaAs heterojunction. The disorder potential which
is generally created by a single doping layer behind a spacer, is here enhanced
by the presence of a second delta doped layer of scatterers which can be
repulsive or attractive impurities. We have calculated the density of states by
means of the Klauder's approximation, in the presence of a magnetic field of
arbitrary strength. At low field either band tails or impurity bands are
observed for attractive potentials, depending on the impurity concentration. At
higher field, impurity bands are observed for both repulsive and attractive
potentials. We discuss the effect of such an asymmetrical density of states on
the transport properties in the quantum Hall effect regime.Comment: 22 pages, 12 figures. submitted to Phys. Rev.
Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals
The description of realistic strongly correlated systems has recently
advanced through the combination of density functional theory in the local
density approximation (LDA) and dynamical mean field theory (DMFT). This
LDA+DMFT method is able to treat both strongly correlated insulators and
metals. Several interfaces between LDA and DMFT have been used, such as (N-th
order) Linear Muffin Tin Orbitals or Maximally localized Wannier Functions.
Such schemes are however either complex in use or additional simplifications
are often performed (i.e., the atomic sphere approximation). We present an
alternative implementation of LDA+DMFT, which keeps the precision of the
Wannier implementation, but which is lighter. It relies on the projection of
localized orbitals onto a restricted set of Kohn-Sham states to define the
correlated subspace. The method is implemented within the Projector Augmented
Wave (PAW) and within the Mixed Basis Pseudopotential (MBPP) frameworks. This
opens the way to electronic structure calculations within LDA+DMFT for more
complex structures with the precision of an all-electron method. We present an
application to two correlated systems, namely SrVO3 and beta-NiS (a
charge-transfer material), including ligand states in the basis-set. The
results are compared to calculations done with Maximally Localized Wannier
functions, and the physical features appearing in the orbitally resolved
spectral functions are discussed.Comment: 15 pages, 17 figure
Enhancing the performance of a diazonium-modified carbon supercapacitor by controlling the grafting process
The activated Norit carbon was modified by grafting the 4-nitrobenzenediazonium salt in the presence or in the absence of a radical scavenger (DPPH: 2,2-diphenyl-1-picrylhydrazyl) to produce modified carbon powders having different surface organic layers going from monolayer to multilayer. The surface chemistry and pore texture of carbon products were studied by TGA, chemical elemental analysis and nitrogen gas adsorption measurements. The resulting powders were used as active components in supercapacitors working in alkaline media to investigate the impact of the grafting on the electrochemical performances. Cyclic voltammetry and electrochemical impedance spectroscopy were used to investigate the charge/discharge process in aqueous 1Â M KOH. The present work demonstrates that the high double-layer capacitance and the low ionic resistance of the pristine carbon can be preserved by limiting the growth of the grafted layer with DPPH
Optimization of Single-Sided Charge-Sharing Strip Detectors
Simulation of the charge sharing properties of single-sided CZT strip detectors with small anode pads are presented. The effect of initial event size, carrier repulsion, diffusion, drift, trapping and detrapping are considered. These simulations indicate that such a detector with a 150 µm pitch will provide good charge sharing between neighboring pads. This is supported by a comparison of simulations and measurements for a similar detector with a coarser pitch of 225 µm that could not provide sufficient sharing. The performance of such a detector used as a gamma-ray imager is discussed
Implicit Gradient Regularization
Gradient descent can be surprisingly good at optimizing deep neural networks
without overfitting and without explicit regularization. We find that the
discrete steps of gradient descent implicitly regularize models by penalizing
gradient descent trajectories that have large loss gradients. We call this
Implicit Gradient Regularization (IGR) and we use backward error analysis to
calculate the size of this regularization. We confirm empirically that implicit
gradient regularization biases gradient descent toward flat minima, where test
errors are small and solutions are robust to noisy parameter perturbations.
Furthermore, we demonstrate that the implicit gradient regularization term can
be used as an explicit regularizer, allowing us to control this gradient
regularization directly. More broadly, our work indicates that backward error
analysis is a useful theoretical approach to the perennial question of how
learning rate, model size, and parameter regularization interact to determine
the properties of overparameterized models optimized with gradient descent
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