44,264 research outputs found
Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?
Recent findings suggest that wall-bounded turbulent flow can take different
statistically stationary turbulent states, with different transport properties,
even for the very same values of the control parameters. What state the system
takes depends on the initial conditions. Here we analyze the multiple states in
large-aspect ratio () two-dimensional turbulent Rayleigh--B\'enard flow
with no-slip plates and horizontally periodic boundary conditions as model
system. We determine the number of convection rolls, their mean aspect
ratios , and the corresponding transport properties of
the flow (i.e., the Nusselt number ), as function of the control parameters
Rayleigh () and Prandtl number. The effective scaling exponent in
is found to depend on the realized state and thus
, with a larger value for the smaller . By making use of a
generalized Friedrichs inequality, we show that the elliptical instability and
viscous damping determine the -window for the realizable turbulent
states. The theoretical results are in excellent agreement with our numerical
finding , where the lower threshold is approached for
the larger . Finally, we show that the theoretical approach to frame
also works for free-slip boundary conditions.Comment: 6 pages, 5 figure
Uncertainty in Economic Growth and Inequality
A step to consilience, starting with a deconstruction of the causality of
uncertainty that is embedded in the fundamentals of growth and inequality,
following a construction of aggregation laws that disclose the invariance
principle across heterogeneous individuals, ending with a reconstruction of
metric models that yields deeper structural connections via U.S. GDP and income
data
Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion
The Negative Binomial distribution becomes highly skewed under extreme
dispersion. Even at moderately large sample sizes, the sample mean exhibits a
heavy right tail. The standard Normal approximation often does not provide
adequate inferences about the data's mean in this setting. In previous work, we
have examined alternative methods of generating confidence intervals for the
expected value. These methods were based upon Gamma and Chi Square
approximations or tail probability bounds such as Bernstein's Inequality. We
now propose growth estimators of the Negative Binomial mean. Under high
dispersion, zero values are likely to be overrepresented in the data. A growth
estimator constructs a Normal-style confidence interval by effectively removing
a small, pre--determined number of zeros from the data. We propose growth
estimators based upon multiplicative adjustments of the sample mean and direct
removal of zeros from the sample. These methods do not require estimating the
nuisance dispersion parameter. We will demonstrate that the growth estimators'
confidence intervals provide improved coverage over a wide range of parameter
values and asymptotically converge to the sample mean. Interestingly, the
proposed methods succeed despite adding both bias and variance to the Normal
approximation
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Implementing the multimodel generalized beta estimator in stata and its application
The multimodel generalized beta estimator (MGBE) described by von Hippel, Scarpino and Hola (2014) provides researchers with an improved way to estimate inequality from binned incomes. To extend the application of MGBE, the mgbe command is developed in Stata. In this report, the implementation and performance of mgbe are discussed.Statistic
Functional inequalities for modified Bessel functions
In this paper our aim is to show some mean value inequalities for the
modified Bessel functions of the first and second kinds. Our proofs are based
on some bounds for the logarithmic derivatives of these functions, which are in
fact equivalent to the corresponding Tur\'an type inequalities for these
functions. As an application of the results concerning the modified Bessel
function of the second kind we prove that the cumulative distribution function
of the gamma-gamma distribution is log-concave. At the end of this paper
several open problems are posed, which may be of interest for further research.Comment: 14 page
Some completely monotonic functions involving the -gamma function
We present some completely monotonic functions involving the -gamma
function that are inspired by their analogues involving the gamma function.Comment: 8 page
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