818 research outputs found
On the distribution of exponential functionals for Levy processes with jumps of rational transform
We derive explicit formulas for the Mellin transform and the distribution of
the exponential functional for Levy processes with rational Laplace exponent.
This extends recent results by Cai and Kou on the processes with
hyper-exponential jumps [N. Cai and S. Kou "Prising Asian options under a
general jump diffusion model", (2010)].Comment: 11 page
Asymptotic optimality of the edge finite element approximation of the time-harmonic Maxwell's equations
We analyze the conforming approximation of the time-harmonic Maxwell's
equations using N\'ed\'elec (edge) finite elements. We prove that the
approximation is asymptotically optimal, i.e., the approximation error in the
energy norm is bounded by the best-approximation error times a constant that
tends to one as the mesh is refined and/or the polynomial degree is increased.
Moreover, under the same conditions on the mesh and/or the polynomial degree,
we establish discrete inf-sup stability with a constant that corresponds to the
continuous constant up to a factor of two at most. Our proofs apply under
minimal regularity assumptions on the exact solution, so that general domains,
material coefficients, and right-hand sides are allowed
Optical determination and identification of organic shells around nanoparticles: application to silver nanoparticles
We present a simple method to prove the presence of an organic shell around
silver nanoparticles. This method is based on the comparison between optical
extinction measurements of isolated nanoparticles and Mie calculations
predicting the expected wavelength of the Localized Surface Plasmon Resonance
of the nanoparticles with and without the presence of an organic layer. This
method was applied to silver nanoparticles which seemed to be well protected
from oxidation. Further experimental characterization via Surface Enhanced
Raman Spectroscopy (SERS) measurements allowed to identify this protective
shell as ethylene glycol. Combining LSPR and SERS measurements could thus give
proof of both presence and identification for other plasmonic nanoparticles
surrounded by organic shells
Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization
We consider the scalar Helmholtz equation with variable, discontinuous
coefficients, modelling transmission of acoustic waves through an anisotropic
penetrable obstacle. We first prove a well-posedness result and a
frequency-explicit bound on the solution operator, with both valid for
sufficiently-large frequency and for a class of coefficients that satisfy
certain monotonicity conditions in one spatial direction, and are only assumed
to be bounded (i.e., ) in the other spatial directions. This class of
coefficients therefore includes coefficients modelling transmission by
penetrable obstacles with a (potentially large) number of layers (in 2-d) or
fibres (in 3-d). Importantly, the frequency-explicit bound holds uniformly for
all coefficients in this class; this uniformity allows us to consider
highly-oscillatory coefficients and study the limiting behaviour when the
period of oscillations goes to zero. In particular, we bound the error
committed by the first-order bulk correction to the homogenized transmission
problem, with this bound explicit in both the period of oscillations of the
coefficients and the frequency of the Helmholtz equation; to our knowledge,
this is the first homogenization result for the Helmholtz equation that is
explicit in these two quantities and valid without the assumption that the
frequency is small
On a Fluctuation Identity for Random Walks and Lévy Processes
In this paper, some identities in laws involving ladder processes for random walks and Lévy processes are extended and unified. 2000 Mathematics Subject Classification 60G50, 60G51 (primary), 60G17 (secondary
Finite Element Simulations of Logging-While-Drilling and Extra-Deep Azimuthal Resistivity Measurements using Non-Fitting Grids
We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting grids when the geometry is complex. On the other side, fitting grids have been historically preferred because they offer additional accuracy for a fixed problem size in the general case. In this work, we analyse the use of non-fitting grids to simulate the response of logging instruments that are based on magnetic field resistivity measurements using 2.5D Maxwell’s equations. We provide various examples demonstrating that, for these applications, if the finite element matrix coefficients are properly integrated, the accuracy loss due to the use of non-fitting grids is negligible compared to the case where fitting grids are employed
Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media
We consider the time-harmonic Maxwell equations posed in . We
prove a priori bounds on the solution for coefficients
and satisfying certain monotonicity properties, with these bounds valid
for arbitrarily-large frequency, and explicit in the frequency and properties
of and . The class of coefficients covered includes (i) certain
and for which well-posedness of the time-harmonic Maxwell
equations had not previously been proved, and (ii) scattering by a penetrable
star-shaped obstacle where and are smaller inside the
obstacle than outside. In this latter setting, the bounds are uniform across
all such obstacles, and the first sharp frequency-explicit bounds for this
problem at high-frequency
AMORPHOUS PD-SI ALLOYS AND HYDRIDES PREPARED BY LOW-TEMPERATURE ION-IMPLANTATION
Ion implantation simultaneously produces compositional changes and radiation damage in the target. If the latter is not annealed, amorphization should ultimately result. Can implantation of a covalent solute into a transition metal host stabilize the damage and hence produce an amorphous alloy at lower concentrations than other techniques ? We have studied the composition-dependence of the resistivity and TCR of thin (600-800 Å) Pd films implanted at 6 K with Si ions : The results are compared to those obtained on the corresponding well-documented quench-condensed alloys, which are amorphous at Si concentrations ~.18. The resistivity of the implanted films saturates at about 90 µΩ·cm for Si concentrations above ~.18. Thus, the critical concentration for amorphization is presumably the same for the low-temperature implanted or quench-condensed Pd-Si alloy, confirming that local structure effects dominate amorphous alloy formation criteria. In a further experiment, hydrogen was implanted into the amorphous Pd-Si films (again at 6K). The resistivity increased sharply, doubling at H concentrations around 100 %. The resulting systems were superconducting ; their maximum critical temperature was 2.6 K
An ensemble approach to assess hydrological models’ contribution to uncertainties in the analysis of climate change impact on water resources
Over the recent years, several research efforts investigated the impact of climate
change on water resources for different regions of the world. The projection of future
river flows is affected by different sources of uncertainty in the hydro-climatic modelling chain. One of the aims of the QBic3 5 project (Que´bec-Bavarian International Collaboration on Climate Change) is to assess the contribution to uncertainty of hydrological models by using an ensemble of hydrological models presenting a diversity of structural complexity (i.e. lumped, semi distributed and distributed models). The study investigates two humid, mid-latitude catchments with natural flow conditions; one located in
10 Southern Que´bec (Canada) and one in Southern Bavaria (Germany). Daily flow is simulated with four different hydrological models, forced by outputs from regional climate
models driven by a given number of GCMs’ members over a reference (1971–2000)
and a future (2041–2070) periods. The results show that the choice of the hydrological model does strongly affect the climate change response of selected hydrological indicators, especially those related to low flows. Indicators related to high flows seem less sensitive on the choice of the hydrological model. Therefore, the computationally less demanding models (usually simple, lumped and conceptual) give a significant level of trust for high and overall mean flows
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