1,000 research outputs found
Rigorous a-posteriori analysis using numerical eigenvalue bounds in a surface growth model
In order to prove numerically the global existence and uniqueness of smooth
solutions of a fourth order, nonlinear PDE, we derive rigorous a-posteriori
upper bounds on the supremum of the numerical range of the linearized operator.
These bounds also have to be easily computable in order to be applicable to our
rigorous a-posteriori methods, as we use them in each time-step of the
numerical discretization. The final goal is to establish global bounds on
smooth local solutions, which then establish global uniqueness.Comment: 19 pages, 9 figure
Matter inflation with A_4 flavour symmetry breaking
We discuss model building in tribrid inflation, which is a framework for
realising inflation in the matter sector of supersymmetric particle physics
models. The inflaton is a D-flat combination of matter fields, and inflation
ends by a phase transition in which some Higgs field obtains a vacuum
expectation value. We first describe the general procedure for implementing
tribrid inflation in realistic models of particle physics that can be applied
to a wide variety of BSM particle physics models around the GUT scale. We then
demonstrate how the procedure works for an explicit lepton flavour model based
on an A_4 family symmetry. The model is both predictive and phenomenologically
viable, and illustrates how tribrid inflation connects cosmological and
particle physics parameters. In particular, it predicts a relation between the
neutrino Yukawa coupling and the running of the spectral index alpha_s. We also
show how topological defects from the flavour symmetry breaking can be avoided
automatically.Comment: 26 pages, 4 figures, v2 matches publication in JCA
Asymptotic independence for unimodal densities
Asymptotic independence of the components of random vectors is a concept used
in many applications. The standard criteria for checking asymptotic
independence are given in terms of distribution functions (dfs). Dfs are rarely
available in an explicit form, especially in the multivariate case. Often we
are given the form of the density or, via the shape of the data clouds, one can
obtain a good geometric image of the asymptotic shape of the level sets of the
density. This paper establishes a simple sufficient condition for asymptotic
independence for light-tailed densities in terms of this asymptotic shape. This
condition extends Sibuya's classic result on asymptotic independence for
Gaussian densities.Comment: 33 pages, 4 figure
BICEP2 implications for single-field slow-roll inflation revisited
It is generally believed that in single-field slow-roll inflation, a large
tensor-to-scalar ratio requires inflaton field values close to or
above the Planck scale. Recently, it has been claimed that can be
achieved with much smaller inflaton field values . We
show that in single-field slow-roll inflation, it is impossible to reconcile with such small field values, independently of the form of the
potential, and that the recent claim to the contrary is based on an invalid
approximation. We conclude that the result of the BICEP2 measurement of , if confirmed, truly has the potential to rule out small-field models of
single-field slow-roll inflation.Comment: 9 pages, 2 figures, v3: references and note on arXiv:1404.3398v2
adde
Elicitability and backtesting: Perspectives for banking regulation
Conditional forecasts of risk measures play an important role in internal
risk management of financial institutions as well as in regulatory capital
calculations. In order to assess forecasting performance of a risk measurement
procedure, risk measure forecasts are compared to the realized financial losses
over a period of time and a statistical test of correctness of the procedure is
conducted. This process is known as backtesting. Such traditional backtests are
concerned with assessing some optimality property of a set of risk measure
estimates. However, they are not suited to compare different risk estimation
procedures. We investigate the proposal of comparative backtests, which are
better suited for method comparisons on the basis of forecasting accuracy, but
necessitate an elicitable risk measure. We argue that supplementing traditional
backtests with comparative backtests will enhance the existing trading book
regulatory framework for banks by providing the correct incentive for accuracy
of risk measure forecasts. In addition, the comparative backtesting framework
could be used by banks internally as well as by researchers to guide selection
of forecasting methods. The discussion focuses on three risk measures,
Value-at-Risk, expected shortfall and expectiles, and is supported by a
simulation study and data analysis
Hill crossing during preheating after hilltop inflation
In 'hilltop inflation', inflation takes place when the inflaton field slowly
rolls from close to a maximum of its potential (i.e. the 'hilltop') towards its
minimum. When the inflaton potential is associated with a phase transition,
possible topological defects produced during this phase transition, such as
domain walls, are efficiently diluted during inflation. It is typically assumed
that they also do not reform after inflation, i.e. that the inflaton field
stays on its side of the 'hill', finally performing damped oscillations around
the minimum of the potential. In this paper we study the linear and the
non-linear phases of preheating after hilltop inflation. We find that the
fluctuations of the inflaton field during the tachyonic oscillation phase grow
strong enough to allow the inflaton field to form regions in position space
where it crosses 'over the top of the hill' towards the 'wrong vacuum'. We
investigate the formation and behaviour of these overshooting regions using
lattice simulations: Rather than durable domain walls, these regions form
oscillon-like structures (i.e. localized bubbles that oscillate between the two
vacua) which should be included in a careful study of preheating in hilltop
inflation.Comment: 22 pages, 10 figures, v2 matches publication in JCAP. Animated movies
of our simulations are available online at
https://particlesandcosmology.unibas.ch/files/hilltop_preheating.htm
Hilltop inflation with preinflation from coupling to matter fields
We propose a class of models of supersymmetric hilltop inflation (also called
"new inflation") where the initial conditions of the inflaton close to the
hilltop are generated through "matter field preinflation". This is achieved via
a coupling term between the inflaton and matter fields (i.e. Standard Model
fields or a right-handed neutrino). The same coupling also opens up a decay
channel for the inflaton into Standard Model fields, which allows efficient
reheating of the universe. We discuss the multifield dynamics of the inflaton
and matter fields during inflation using the delta N formalism and show under
which conditions the model effectively reduces to single-field hilltop
inflation during the last 60 e-folds. We also study perturbative reheating
through the matter-inflaton coupling for a specific example where the matter
field is identified with a right-handed (s)neutrino, and demonstrate that in
this case the model can generate the observed baryon asymmetry through
nonthermal leptogenesis.Comment: 26 pages, 10 figures, v2: reference added to match publication in
JCA
Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions
A two parameter asymptotic analysis is employed to investigate some unusual long wave dispersion phenomena in respect of symmetric motion in a nearly incompressible elastic plate. The plate is not subject to the usual classical traction free boundary conditions, but rather has its faces fixed, precluding any displacement on the boundary. The abnormal long wave behaviour results in the derivation of non-local approximations for symmetric motion, giving frequency as a function of wave number. Motivated by these approximations, the asymptotic forms of displacement components established and long wave asymptotic integration is carried out
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