1,384 research outputs found
Compressibility effects on the Rayleigh-Taylor instability growth between immiscible fluids
The linearized Navier-Stokes equations for a system of superposed immiscible
compressible ideal fluids are analyzed. The results of the analysis reconcile
the stabilizing and destabilizing effects of compressibility reported in the
literature. It is shown that the growth rate obtained for an inviscid,
compressible flow in an infinite domain is bounded by the growth rates obtained
for the corresponding incompressible flows with uniform and exponentially
varying density. As the equilibrium pressure at the interface
increases (less compressible flow), increases towards the uniform density
result, while as the ratio of specific heats increases (less
compressible fluid), decreases towards the exponentially varying density
incompressible flow result. This remains valid in the presence of surface
tension or for viscous fluids and the validity of the results is also discussed
for finite size domains. The critical wavenumber imposed by the presence of
surface tension is unaffected by compressibility. However, the results show
that the surface tension modifies the sensitivity of the growth rate to a
differential change in for the lower and upper fluids. For the viscous
case, the linearized equations are solved numerically for different values of
and . It is found that the largest differences compared with
the incompressible cases are obtained at small Atwood numbers. The most
unstable mode for the compressible case is also bounded by the most unstable
modes corresponding to the two limiting incompressible cases.Comment: To appear in Physics of Fluid
Extremes for the inradius in the Poisson line tessellation
A Poisson line tessellation is observed within a window. With each cell of
the tessellation, we associate the inradius, which is the radius of the largest
ball contained in the cell. Using Poisson approximation, we compute the limit
distributions of the largest and smallest order statistics for the inradii of
all cells whose nuclei are contained in the window in the limit as the window
is scaled to infinity. We additionally prove that the limit shape of the cells
minimising the inradius is a triangle
The Trace Problem for Toeplitz Matrices and Operators and its Impact in Probability
The trace approximation problem for Toeplitz matrices and its applications to
stationary processes dates back to the classic book by Grenander and Szeg\"o,
"Toeplitz forms and their applications". It has then been extensively studied
in the literature.
In this paper we provide a survey and unified treatment of the trace
approximation problem both for Toeplitz matrices and for operators and describe
applications to discrete- and continuous-time stationary processes.
The trace approximation problem serves indeed as a tool to study many
probabilistic and statistical topics for stationary models. These include
central and non-central limit theorems and large deviations of Toeplitz type
random quadratic functionals, parametric and nonparametric estimation,
prediction of the future value based on the observed past of the process, etc.
We review and summarize the known results concerning the trace approximation
problem, prove some new results, and provide a number of applications to
discrete- and continuous-time stationary time series models with various types
of memory structures, such as long memory, anti-persistent and short memory
Observation of the decay \psip\rar\kstark
Using 14 million events collected with the BESII detector,
branching fractions of \psip\rar\kstarkpm and \kstarknn are determined to
be: \calB(\psip\rar\kstarkpm)=(2.9^{+1.3}_{-1.7}\pm0.4)\times 10^{-5} and
\calB(\psip\rar\kstarknn)=(13.3^{+2.4}_{-2.7}\pm1.9)\times 10^{-5}. The
results confirm the violation of the "12%" rule for these two decay channels
with higher precision. A large isospin violation between the charged and
neutral modes is observed.Comment: 5 pages, 3 figure
A Microeconomic Explanation of the EPK Paradox
Supported by several recent investigations the empirical pricing kernel paradox might be considered as a stylized fact. In Chabi-Yo et al. (2008) simulation studies have been presented which suggest that this paradox might be caused by regime switching of stock prices in financial markets. Alternatively, we want to emphasize a microeconomic view. Based on an economic model with state dependent utilities for the financial investors we succeed in explaining the paradox by changes of the risk attitudes. Theoretically, the change behaviour is compressed by the pricing kernels. As a starting point for empirical insights we shall develop and investigate inverse problems in terms of data fits for estimated basic values of the pricing kernel.Pricing kernel, representative agent, empirical pricing kernel, epk paradox, state dependent utilities, switching points
Intergenerational justice when future worlds are uncertain
Let there be a positive (exogenous) probability that, at each date, the human species will disappear. We postulate an Ethical Observer (EO) who maximizes intertemporal welfare under this uncertainty, with expected-utility preferences. Various social welfare criteria entail alternative von Neumann- Morgenstern utility functions for the EO: utilitarian, Rawlsian, and an extension of the latter that corrects for the size of population. Our analysis covers, first, a cake-eating economy (without production), where the utilitarian and Rawlsian recommend the same allocation. Second, a productive economy with education and capital, where it turns out that the recommendations of the two EOs are in general different. But when the utilitarian program diverges, then we prove it is optimal for the extended Rawlsian to ignore the uncertainty concerning the possible disappearance of the human species in the future. We conclude by discussing the implications for intergenerational welfare maximization in the presence of global warming.Discounted utilitarianism, Rawlsian, sustainability, maximin, uncertainty, expected utility, von Neumann-Morgenstern, dynamic welfare maximization.
Functional Limit Theorems for Toeplitz Quadratic Functionals of Continuous time Gaussian Stationary Processes
\noindent The paper establishes weak convergence in of normalized
stochastic processes, generated by Toeplitz type quadratic functionals of a
continuous time Gaussian stationary process, exhibiting long-range dependence.
Both central and non-central functional limit theorems are obtained
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