19,796 research outputs found
Forward-backward eccentricity and participant-plane angle fluctuations and their influences on longitudinal dynamics of collective flow
We argue that the transverse shape of the fireball created in heavy ion
collision is controlled by event-by-event fluctuations of the eccentricity
vectors for the forward-going and backward-going wounded nucleons:
and . Due to the asymmetric
energy deposition of each wounded nucleon along its direction of motion, the
eccentricity vector of the produced fireball is expected to interpolate between
and along the
pseudorapidity, and hence exhibits sizable forward-backward(FB) asymmetry
() and/or FB-twist
(). A transport model calculation
shows that these initial state longitudinal fluctuations for and 3
survive the collective expansion, and result in similar FB asymmetry and/or a
twist in the final state event-plane angles. These novel EbyE longitudinal flow
fluctuations should be accessible at RHIC and the LHC using the event-shape
selection technique proposed in earlier papers. If these effects are observed
experimentally, it could improve our understanding of the initial state
fluctuations, particle production and collective expansion dynamics of the
heavy ion collision.Comment: 13 pages, 16 figure
Optimal Time Decay Rate for the Compressible Viscoelastic Equations in Critical Spaces
In this paper, we are concerned with the convergence rates of the global
strong solution to constant equilibrium state for the compressible viscoelastic
fluids in the whole space. We combine both analysis about Green's matrix method
and energy estimate method to get optimal time decay rate in critical Besov
space framework. Our result imply the optimal -time decay rate and only
need the initial data to be small in critical Besov space which have very low
regularity compared with traditional Sobolev space.Comment: 20 page
Optimal Time Decay of Navier-Stokes Equations With Low Regularity Initial Data
In this paper, we study the optimal time decay rate of isentropic
Navier-Stokes equations under the low regularity assumptions about initial
data. In the previous works about optimal time decay rate, the initial data
need to be small in . Our work combined negative
Besov space estimates and the conventional energy estimates in Besov space
framework which is developed by R. Danchin. Though our methods, we can get
optimal time decay rate with initial data just small in and belong to some negative Besov space(need not to
be small). Finally, combining the recent results in \cite{zhang2014} with our
methods, we can only need the initial data to be small in homogeneous Besov
space to get the optimal time decay
rate in space .Comment: arXiv admin note: text overlap with arXiv:1410.794
A note on characterizations of G-normal distribution
In this paper, we show that the G-normality of X and Y can be characterized
according to the form of f such that the distribution of
{\lambda}+f({\lambda})Y does not depend on {\lambda}, where Y is an independent
copy of X and {\lambda} is in the domain of f. Without the condition that Y is
identically distributed with X, we still have a similar argument
On -Liouville property for smooth metric measure spaces
In this short paper we study -Liouville property with for
nonnegative -subharmonic functions on a complete noncompact smooth metric
measure space with bounded below for
. We prove a sharp -Liouville theorem when .
We also prove an -Liouville theorem when and
.Comment: Preliminary version, all comments are welcome
Heat Kernel on Smooth Metric Measure Spaces with Nonnegative Curvature
We derive a local Gaussian upper bound for the -heat kernel on complete
smooth metric measure space with nonnegative Bakry-\'{E}mery
Ricci curvature, which generalizes the classic Li-Yau estimate. As
applications, we obtain a sharp -Liouville theorem for -subharmonic
functions and an -uniqueness property for nonnegative solutions of the
-heat equation, assuming is of at most quadratic growth. In particular,
any -integrable -subharmonic function on gradient shrinking or steady
Ricci solitons must be constant. We also provide explicit -heat kernel for
Gaussian solitons.Comment: Revised version. Math. Annalen, to appea
Heat kernel on smooth metric measure spaces and applications
We derive a Harnack inequality for positive solutions of the -heat
equation and Gaussian upper and lower bounds for the -heat kernel on
complete smooth metric measure spaces with Bakry-\'Emery
Ricci curvature bounded below. The lower bound is sharp. The main argument is
the De Giorgi-Nash-Moser theory. As applications, we prove an -Liouville
theorem for -subharmonic functions and an -uniqueness theorem for
-heat equations when has at most linear growth. We also obtain
eigenvalues estimates and -Green's function estimates for the -Laplace
operator.Comment: 30 page
Elucidating the event-by-event flow fluctuations in heavy-ion collisions via the event shape selection technique
The presence of large event-by-event flow fluctuations in heavy ion
collisions at RHIC and the LHC provides an opportunity to study a broad class
of flow observables. This paper explores the correlations among harmonic flow
coefficients and their phases , and the rapidity fluctuation of
. The study is carried out usin Pb+Pb events generated by the AMPT model
with fixed impact parameter. The overall ellipticity/triangularity of events is
varied by selecting on the eccentricities or the magnitudes of the
flow vector for n=2 and 3, respectively. The responses of the , the
event-plane correlations, and the rapidity fluctuations, to the change in
and are then systematized. Strong positive correlations are
observed among all even harmonics , and (all increase with
), between and (both increase with ) and between
and (both increase with ), consistent with the effects of nonlinear
collective response. In contrast, an anti-correlation is observed between
and similar to that seen between and . These
correlation patterns are found to be independent of whether selecting on
or , validating the ability of in selecting the initial
geometry. A forward/backward asymmetry of is observed for events
selected on but not on , reflecting dynamical fluctuations
exposed by the selection. Many event-plane correlators show good
agreement between and selections, suggesting that their
variations with are controlled by the change of in the
initial geometry. Hence these correlators may serve as promising observables
for disentangling the fluctuations generated in various stages of the evolution
of the matter created in heavy ion collisions.Comment: 14 pages, 20 figure
Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle
In this paper, we focus on a space-time fractional diffusion equation with
the generalized Caputo's fractional derivative operator and a general space
nonlocal operator (with the fractional Laplace operator as a special case). A
weak Harnack's inequality has been established by using a special test function
and some properties of the space nonlocal operator. Based on the weak Harnack's
inequality, a strong maximum principle has been obtained which is an important
characterization of fractional parabolic equations. With these tools, we
establish a uniqueness result for an inverse source problem on the
determination of the temporal component of the inhomogeneous term.Comment: 30 pages. arXiv admin note: text overlap with arXiv:1009.4852 by
other author
Bayesian approach to inverse problems for functions with variable index Besov prior
We adopt Bayesian approach to consider the inverse problem of estimate a
function from noisy observations. One important component of this approach is
the prior measure. Total variation prior has been proved with no discretization
invariant property, so Besov prior has been proposed recently. Different prior
measures usually connect to different regularization terms. Variable index TV,
variable index Besov regularization terms have been proposed in image analysis,
however, there are no such prior measure in Bayesian theory. So in this paper,
we propose a variable index Besov prior measure which is a Non-Guassian
measure. Based on the variable index Besov prior measure, we build the Bayesian
inverse theory. Then applying our theory to integer and fractional order
backward diffusion problems. Although there are many researches about
fractional order backward diffusion problems, we firstly apply Bayesian inverse
theory to this problem which provide an opportunity to quantify the
uncertainties for this problem.Comment: 31 pages. arXiv admin note: text overlap with arXiv:1302.6989 by
other author
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