10,031 research outputs found
Stochastic analysis of different rough surfaces
This paper shows in detail the application of a new stochastic approach for
the characterization of surface height profiles, which is based on the theory
of Markov processes. With this analysis we achieve a characterization of the
scale dependent complexity of surface roughness by means of a Fokker-Planck or
Langevin equation, providing the complete stochastic information of multiscale
joint probabilities. The method is applied to several surfaces with different
properties, for the purpose of showing the utility of this method in more
details. In particular we show the evidence of Markov properties, and we
estimate the parameters of the Fokker-Planck equation by pure, parameter-free
data analysis. The resulting Fokker-Planck equations are verified by numerical
reconstruction of conditional probability density functions. The results are
compared with those from the analysis of multi-affine and extended multi-affine
scaling properties which is often used for surface topographies. The different
surface structures analysed here show in details advantages and disadvantages
of these methods.Comment: Minor text changes to be identical with the published versio
Regeneration of Stochastic Processes: An Inverse Method
We propose a novel inverse method that utilizes a set of data to construct a
simple equation that governs the stochastic process for which the data have
been measured, hence enabling us to reconstruct the stochastic process. As an
example, we analyze the stochasticity in the beat-to-beat fluctuations in the
heart rates of healthy subjects as well as those with congestive heart failure.
The inverse method provides a novel technique for distinguishing the two
classes of subjects in terms of a drift and a diffusion coefficients which
behave completely differently for the two classes of subjects, hence
potentially providing a novel diagnostic tool for distinguishing healthy
subjects from those with congestive heart failure, even at the early stages of
the disease development.Comment: 5 pages, two columns, 7 figs. to appear, The European Physical
Journal B (2006
Silicon Burning II: Quasi-Equilibrium and Explosive Burning
Having examined the application of quasi-equilibrium to hydrostatic silicon
burning in Paper I of this series, Hix & Thielemann (1996), we now turn our
attention to explosive silicon burning. Previous authors have shown that for
material which is heated to high temperature by a passing shock and then cooled
by adiabatic expansion, the results can be divided into three broad categories;
\emph{incomplete burning}, \emph{normal freezeout} and \emph{-rich
freezeout}, with the outcome depending on the temperature, density and cooling
timescale. In all three cases, we find that the important abundances obey
quasi-equilibrium for temperatures greater than approximately 3 GK, with
relatively little nucleosynthesis occurring following the breakdown of
quasi-equilibrium. We will show that quasi-equilibrium provides better
abundance estimates than global nuclear statistical equilibrium, even for
normal freezeout and particularly for -rich freezeout. We will also
examine the accuracy with which the final nuclear abundances can be estimated
from quasi-equilibrium.Comment: 27 pages, including 15 inline figures. LaTeX 2e with aaspp4 and
graphicx packages. Accepted to Ap
On the existence of Killing vector fields
In covariant metric theories of coupled gravity-matter systems the necessary
and sufficient conditions ensuring the existence of a Killing vector field are
investigated. It is shown that the symmetries of initial data sets are
preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra
Electroweak Baryogenesis with Vector-like Leptons and Scalar Singlets
We investigate the viability of electroweak baryogenesis in a model with a
first order electroweak phase transition induced by the addition of two gauge
singlet scalars. A vector-like lepton doublet is introduced in order to provide
CP violating interactions with the singlets and Standard Model leptons, and the
asymmetry generation dynamics are examined using the vacuum expectation value
insertion approximation. We find that such a model is readily capable of
generating sufficient baryon asymmetry while satisfying electron electric
dipole moment and collider phenomenology constraints.Comment: 38 pages, 8 figures. Citations added. Benchmarks, figures and tables
updated, error fixed in calculations. Matches version published in JHE
Fano Lineshapes Revisited: Symmetric Photoionization Peaks from Pure Continuum Excitation
In a photoionization spectrum in which there is no excitation of the discrete
states, but only the underlying continuum, we have observed resonances which
appear as symmetric peaks, not the commonly expected window resonances.
Furthermore, since the excitation to the unperturbed continuum vanishes, the
cross section expected from Fano's configuration interaction theory is
identically zero. This shortcoming is removed by the explicit introduction of
the phase shifted continuum, which demonstrates that the shape of a resonance,
by itself, provides no information about the relative excitation amplitudes to
the discrete state and the continuum.Comment: 4 pages, 3 figure
Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies
It is shown that during expanding phases of flat homogeneous cosmologies all
small enough non-linear perturbations decay exponentially. This result holds
for a large class of perfect fluid equations of state, but notably not for very
``stiff'' fluids as the pure radiation case
Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen
A systematic semiclassical expansion of the hydrogen problem about the
classical Kepler problem is shown to yield remarkably accurate results. Ad hoc
changes of the centrifugal term, such as the standard Langer modification where
the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical
energy levels are shown to be exact to first order in with all higher
order contributions vanishing. The wave functions and dipole matrix elements
are also discussed.Comment: 5 pages, to appear in Phys. Rev.
Metric-affine gauge theory of gravity II. Exact solutions
In continuing our series on metric-affine gravity (see Gronwald IJMP D6
(1997) 263 for Part I), we review the exact solutions in this theory.Comment: Revtex file, 25 pages, final version to appear in IJMP
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