291 research outputs found
Ion-beam mixing induced by atomic and cluster bombardment in the electronic stopping-power regime
Single crystals of magnesium oxide containing nanoprecipitates of sodium were bombarded with swift ions (∼GeV-Pb, U) or cluster beams (∼20 MeV-C60) to study the phase change induced by electronic processes at high stopping power (≳10 keV/nm). The sodium precipitates and the defect creation were characterized by optical absorption and transmission electron microscopy. The ion or cluster bombardment leads to an evolution of the Na precipitate concentration but the size distribution remains unchanged. The decrease in Na metallic concentration is attributed to mixing effects at the interfaces between Na clusters and MgO. In addition, optical-absorption measurements show a broadening of the absorption band associated with electron plasma oscillations in Na clusters. This effect is due to a decrease of the electron mean free path, which could be induced by defect creation in the metal. All these results show an influence of high electronic stopping power in materials known to be very resistant to irradiation with weak ionizing projectiles. The dependence of these effects on electronic stopping power and on various solid-state parameters is discussed
Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations
We establish a connection between Optimal Transport Theory and classical
Convection Theory for geophysical flows. Our starting point is the model
designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal
Transport problems. This model can be seen as a generalization of the
Darcy-Boussinesq equations, which is a degenerate version of the
Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate
different variants of the NSB equations (in particular what we call the
generalized Hydrostatic-Boussinesq equations) to various models involving
Optimal Transport (and the related Monge-Ampere equation. This includes the 2D
semi-geostrophic equations and some fully non-linear versions of the so-called
high-field limit of the Vlasov-Poisson system and of the Keller-Segel for
Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model
can be related to the magnetic relaxation model studied by Arnold and Moffatt
to obtain stationary solutions of the Euler equations with prescribed topology
Remarks on the KLS conjecture and Hardy-type inequalities
We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary
functions on a convex body , not necessarily
vanishing on the boundary . This reduces the study of the
Neumann Poincar\'e constant on to that of the cone and Lebesgue
measures on ; these may be bounded via the curvature of
. A second reduction is obtained to the class of harmonic
functions on . We also study the relation between the Poincar\'e
constant of a log-concave measure and its associated K. Ball body
. In particular, we obtain a simple proof of a conjecture of
Kannan--Lov\'asz--Simonovits for unit-balls of , originally due to
Sodin and Lata{\l}a--Wojtaszczyk.Comment: 18 pages. Numbering of propositions, theorems, etc.. as appeared in
final form in GAFA seminar note
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB)
model of plasma physics. This model consists of the pressureless gas dynamics
equations coupled with the Poisson equation and where the Boltzmann relation
relates the potential to the electron density. If the quasi-neutral assumption
is made, the Poisson equation is replaced by the constraint of zero local
charge and the model reduces to the Isothermal Compressible Euler (ICE) model.
We compare a numerical strategy based on the EPB model to a strategy using a
reformulation (called REPB formulation). The REPB scheme captures the
quasi-neutral limit more accurately
Observational biases in Lagrangian reconstructions of cosmic velocity fields
Lagrangian reconstruction of large-scale peculiar velocity fields can be
strongly affected by observational biases. We develop a thorough analysis of
these systematic effects by relying on specially selected mock catalogues. For
the purpose of this paper, we use the MAK reconstruction method, although any
other Lagrangian reconstruction method should be sensitive to the same
problems. We extensively study the uncertainty in the mass-to-light assignment
due to luminosity incompleteness, and the poorly-determined relation between
mass and luminosity. The impact of redshift distortion corrections is analyzed
in the context of MAK and we check the importance of edge and finite-volume
effects on the reconstructed velocities. Using three mock catalogues with
different average densities, we also study the effect of cosmic variance. In
particular, one of them presents the same global features as found in
observational catalogues that extend to 80 Mpc/h scales. We give recipes,
checked using the aforementioned mock catalogues, to handle these particular
observational effects, after having introduced them into the mock catalogues so
as to quantitatively mimic the most densely sampled currently available galaxy
catalogue of the nearby universe. Once biases have been taken care of, the
typical resulting error in reconstructed velocities is typically about a
quarter of the overall velocity dispersion, and without significant bias. We
finally model our reconstruction errors to propose an improved Bayesian
approach to measure Omega_m in an unbiased way by comparing the reconstructed
velocities to the measured ones in distance space, even though they may be
plagued by large errors. We show that, in the context of observational data, a
nearly unbiased estimator of Omega_m may be built using MAK reconstruction.Comment: 29 pages, 21 figures, 6 tables, Accepted by MNRAS on 2007 October 2.
Received 2007 September 30; in original form 2007 July 2
Mass Transportation on Sub-Riemannian Manifolds
We study the optimal transport problem in sub-Riemannian manifolds where the
cost function is given by the square of the sub-Riemannian distance. Under
appropriate assumptions, we generalize Brenier-McCann's Theorem proving
existence and uniqueness of the optimal transport map. We show the absolute
continuity property of Wassertein geodesics, and we address the regularity
issue of the optimal map. In particular, we are able to show its approximate
differentiability a.e. in the Heisenberg group (and under some weak assumptions
on the measures the differentiability a.e.), which allows to write a weak form
of the Monge-Amp\`ere equation
On the upstream mobility scheme for two-phase flow in porous media
When neglecting capillarity, two-phase incompressible flow in porous media is
modelled as a scalar nonlinear hyperbolic conservation law. A change in the
rock type results in a change of the flux function. Discretizing in
one-dimensional with a finite volume method, we investigate two numerical
fluxes, an extension of the Godunov flux and the upstream mobility flux, the
latter being widely used in hydrogeology and petroleum engineering. Then, in
the case of a changing rock type, one can give examples when the upstream
mobility flux does not give the right answer.Comment: A preprint to be published in Computational Geoscience
A Wasserstein approach to the one-dimensional sticky particle system
We present a simple approach to study the one-dimensional pressureless Euler
system via adhesion dynamics in the Wasserstein space of probability measures
with finite quadratic moments.
Starting from a discrete system of a finite number of "sticky" particles, we
obtain new explicit estimates of the solution in terms of the initial mass and
momentum and we are able to construct an evolution semigroup in a
measure-theoretic phase space, allowing mass distributions with finite
quadratic moment and corresponding L^2-velocity fields. We investigate various
interesting properties of this semigroup, in particular its link with the
gradient flow of the (opposite) squared Wasserstein distance.
Our arguments rely on an equivalent formulation of the evolution as a
gradient flow in the convex cone of nondecreasing functions in the Hilbert
space L^2(0,1), which corresponds to the Lagrangian system of coordinates given
by the canonical monotone rearrangement of the measures.Comment: Added reference
A glimpse into the differential topology and geometry of optimal transport
This note exposes the differential topology and geometry underlying some of
the basic phenomena of optimal transportation. It surveys basic questions
concerning Monge maps and Kantorovich measures: existence and regularity of the
former, uniqueness of the latter, and estimates for the dimension of its
support, as well as the associated linear programming duality. It shows the
answers to these questions concern the differential geometry and topology of
the chosen transportation cost. It also establishes new connections --- some
heuristic and others rigorous --- based on the properties of the
cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page
Reconstruction of the early Universe as a convex optimization problem
We show that the deterministic past history of the Universe can be uniquely
reconstructed from the knowledge of the present mass density field, the latter
being inferred from the 3D distribution of luminous matter, assumed to be
tracing the distribution of dark matter up to a known bias. Reconstruction
ceases to be unique below those scales -- a few Mpc -- where multi-streaming
becomes significant. Above 6 Mpc/h we propose and implement an effective
Monge-Ampere-Kantorovich method of unique reconstruction. At such scales the
Zel'dovich approximation is well satisfied and reconstruction becomes an
instance of optimal mass transportation, a problem which goes back to Monge
(1781). After discretization into N point masses one obtains an assignment
problem that can be handled by effective algorithms with not more than cubic
time complexity in N and reasonable CPU time requirements. Testing against
N-body cosmological simulations gives over 60% of exactly reconstructed points.
We apply several interrelated tools from optimization theory that were not
used in cosmological reconstruction before, such as the Monge-Ampere equation,
its relation to the mass transportation problem, the Kantorovich duality and
the auction algorithm for optimal assignment. Self-contained discussion of
relevant notions and techniques is provided.Comment: 26 pages, 14 figures; accepted to MNRAS. Version 2: numerous minour
clarifications in the text, additional material on the history of the
Monge-Ampere equation, improved description of the auction algorithm, updated
bibliography. Version 3: several misprints correcte
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