772 research outputs found
Shapes of implied volatility with positive mass at zero
We study the shapes of the implied volatility when the underlying distribution has an atom at zero and analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of the smile. We further show that the behaviour at small strikes is uniquely determined by the mass of the atom up to high asymptotic order, under mild assumptions on the remaining distribution on the positive real line. We investigate the structural di erence with the no-mass-at-zero case, showing how one can{ theoretically{distinguish between mass at the origin and a heavy-left-tailed distribution. We numerically test our model-free results in stochastic models with absorption at the boundary, such as the CEV process, and in jump-to-default models. Note that while Lee's moment formula [ 25 ] tells that implied variance is at most asymptotically linear in log-strike, other celebrated results for exact smile asymptotics such as [ 3 , 17 ] do not apply in this setting{essentially due to the breakdown of Put-Call duality
Existence of global strong solutions to a beam-fluid interaction system
We study an unsteady non linear fluid-structure interaction problem which is
a simplified model to describe blood flow through viscoleastic arteries. We
consider a Newtonian incompressible two-dimensional flow described by the
Navier-Stokes equations set in an unknown domain depending on the displacement
of a structure, which itself satisfies a linear viscoelastic beam equation. The
fluid and the structure are fully coupled via interface conditions prescribing
the continuity of the velocities at the fluid-structure interface and the
action-reaction principle. We prove that strong solutions to this problem are
global-in-time. We obtain in particular that contact between the viscoleastic
wall and the bottom of the fluid cavity does not occur in finite time. To our
knowledge, this is the first occurrence of a no-contact result, but also of
existence of strong solutions globally in time, in the frame of interactions
between a viscous fluid and a deformable structure
On discretization in time in simulations of particulate flows
We propose a time discretization scheme for a class of ordinary differential
equations arising in simulations of fluid/particle flows. The scheme is
intended to work robustly in the lubrication regime when the distance between
two particles immersed in the fluid or between a particle and the wall tends to
zero. The idea consists in introducing a small threshold for the particle-wall
distance below which the real trajectory of the particle is replaced by an
approximated one where the distance is kept equal to the threshold value. The
error of this approximation is estimated both theoretically and by numerical
experiments. Our time marching scheme can be easily incorporated into a full
simulation method where the velocity of the fluid is obtained by a numerical
solution to Stokes or Navier-Stokes equations. We also provide a derivation of
the asymptotic expansion for the lubrication force (used in our numerical
experiments) acting on a disk immersed in a Newtonian fluid and approaching the
wall. The method of this derivation is new and can be easily adapted to other
cases
Probabilistic analysis of the upwind scheme for transport
We provide a probabilistic analysis of the upwind scheme for
multi-dimensional transport equations. We associate a Markov chain with the
numerical scheme and then obtain a backward representation formula of
Kolmogorov type for the numerical solution. We then understand that the error
induced by the scheme is governed by the fluctuations of the Markov chain
around the characteristics of the flow. We show, in various situations, that
the fluctuations are of diffusive type. As a by-product, we prove that the
scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all
a>0, for a Lipschitz continuous initial datum. Our analysis provides a new
interpretation of the numerical diffusion phenomenon
A search for two body muon decay signals
Lepton family number violation is tested by searching for
decays among the 5.8 positive muon decay events analyzed by the
TWIST collaboration. Limits are set on the production of both massless and
massive bosons. The large angular acceptance of this experiment allows
limits to be placed on anisotropic decays, which can arise
from interactions violating both lepton flavor and parity conservation.
Branching ratio limits of order are obtained for bosons with masses
of 13 - 80 MeV/c and with different decay asymmetries. For bosons with
masses less than 13 MeV/c the asymmetry dependence is much stronger and
the 90% limit on the branching ratio varies up to . This is
the first study that explicitly evaluates the limits for anisotropic two body
muon decays.Comment: 7 pages, 5 figures, 2 tables, accepted by PR
TOPLHA: an accurate and efficient numerical tool for analysis and design of LH antennas
This paper presents a self-consistent, integral-equation approach for the analysis of plasma-facing lower hybrid (LH) launchers; the geometry of the waveguide grill structure can be completely arbitrary, including the non-planar mouth of the grill. This work is based on the theoretical approach and code implementation of the TOPICA code, of which it shares the modular structure and constitutes the extension into the LH range. Code results are validated against the literature results and simulations from similar code
- …