1,612 research outputs found
Renormalizing Partial Differential Equations
In this review paper, we explain how to apply Renormalization Group ideas to
the analysis of the long-time asymptotics of solutions of partial differential
equations. We illustrate the method on several examples of nonlinear parabolic
equations. We discuss many applications, including the stability of profiles
and fronts in the Ginzburg-Landau equation, anomalous scaling laws in
reaction-diffusion equations, and the shape of a solution near a blow-up point.Comment: 34 pages, Latex; [email protected]; [email protected]
Construction and Expected Performance of the Hadron Blind Detector for the PHENIX Experiment at RHIC
A new Hadron Blind Detector (HBD) for electron identification in high density
hadron environment has been installed in the PHENIX detector at RHIC in the
fall of 2006. The HBD will identify low momentum electron-positron pairs to
reduce the combinatorial background in the mass spectrum, mainly
in the low-mass region below 1 GeV/c. The HBD is a windowless
proximity-focusing Cherenkov detector with a radiator length of 50 cm, a CsI
photocathode and three layers of Gas Electron Multipliers (GEM). The HBD uses
pure CF as a radiator and a detector gas. Construction details and the
expected performance of the detector are described.Comment: QM2006 proceedings, 4 pages 3 figure
Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations
Let be a solution of the Cauchy problem for the nonlinear parabolic
equation and
assume that the solution behaves like the Gauss kernel as . In
this paper, under suitable assumptions of the reaction term and the initial
function , we establish the method of obtaining higher order
asymptotic expansions of the solution as . This paper is a
generalization of our previous paper, and our arguments are applicable to the
large class of nonlinear parabolic equations
Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source
This paper deals with the long-time behavior of solutions of nonlinear
reaction-diffusion equations describing formation of morphogen gradients, the
concentration fields of molecules acting as spatial regulators of cell
differentiation in developing tissues. For the considered class of models, we
establish existence of a new type of ultra-singular self-similar solutions.
These solutions arise as limits of the solutions of the initial value problem
with zero initial data and infinitely strong source at the boundary. We prove
existence and uniqueness of such solutions in the suitable weighted energy
spaces. Moreover, we prove that the obtained self-similar solutions are the
long-time limits of the solutions of the initial value problem with zero
initial data and a time-independent boundary source
Ultrastructural and functional fate of recycled vesicles in hippocampal synapses
Efficient recycling of synaptic vesicles is thought to be critical for sustained information transfer at central terminals. However, the specific contribution that retrieved vesicles make to future transmission events remains unclear. Here we exploit fluorescence and time-stamped electron microscopy to track the functional and positional fate of vesicles endocytosed after readily releasable pool (RRP) stimulation in rat hippocampal synapses. We show that most vesicles are recovered near the active zone but subsequently take up random positions in the cluster, without preferential bias for future use. These vesicles non-selectively queue, advancing towards the release site with further stimulation in an actin-dependent manner. Nonetheless, the small subset of vesicles retrieved recently in the stimulus train persist nearer the active zone and exhibit more privileged use in the next RRP. Our findings reveal heterogeneity in vesicle fate based on nanoscale position and timing rules, providing new insights into the origins of future pool constitution
Double Spin Asymmetry of Electrons from Heavy Flavor Decays in p+p Collisions at sqrt(s)=200 GeV
We report on the first measurement of double-spin asymmetry, A_LL, of
electrons from the decays of hadrons containing heavy flavor in longitudinally
polarized p+p collisions at sqrt(s)=200 GeV for p_T= 0.5 to 3.0 GeV/c. The
asymmetry was measured at mid-rapidity (|eta|<0.35) with the PHENIX detector at
the Relativistic Heavy Ion Collider. The measured asymmetries are consistent
with zero within the statistical errors. We obtained a constraint for the
polarized gluon distribution in the proton of |Delta g/g(log{_10}x=
-1.6^+0.5_-0.4, {mu}=m_T^c)|^2 < 0.033 (1 sigma), based on a leading-order
perturbative-quantum-chromodynamics model, using the measured asymmetry.Comment: 385 authors, 17 pages, 15 figures, 5 tables. Submitted to Phys. Rev.
D. Plain text data tables for the points plotted in figures for this and
previous PHENIX publications are (or will be) publicly available at
http://www.phenix.bnl.gov/papers.htm
J/psi suppression at forward rapidity in Au+Au collisions at sqrt(s_NN)=39 and 62.4 GeV
We present measurements of the J/psi invariant yields in sqrt(s_NN)=39 and
62.4 GeV Au+Au collisions at forward rapidity (1.2<|y|<2.2). Invariant yields
are presented as a function of both collision centrality and transverse
momentum. Nuclear modifications are obtained for central relative to peripheral
Au+Au collisions (R_CP) and for various centrality selections in Au+Au relative
to scaled p+p cross sections obtained from other measurements (R_AA). The
observed suppression patterns at 39 and 62.4 GeV are quite similar to those
previously measured at 200 GeV. This similar suppression presents a challenge
to theoretical models that contain various competing mechanisms with different
energy dependencies, some of which cause suppression and others enhancement.Comment: 365 authors, 10 pages, 11 figures, 4 tables. Submitted to Phys. Rev.
C. Plain text data tables for the points plotted in figures for this and
previous PHENIX publications are (or will be) publicly available at
http://www.phenix.bnl.gov/papers.htm
L\'evy-stable two-pion Bose-Einstein correlations in GeV AuAu collisions
We present a detailed measurement of charged two-pion correlation functions
in 0%-30% centrality GeV AuAu collisions by the
PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well
described by Bose-Einstein correlation functions stemming from L\'evy-stable
source distributions. Using a fine transverse momentum binning, we extract the
correlation strength parameter , the L\'evy index of stability
and the L\'evy length scale parameter as a function of average
transverse mass of the pair . We find that the positively and the
negatively charged pion pairs yield consistent results, and their correlation
functions are represented, within uncertainties, by the same L\'evy-stable
source functions. The measurements indicate a decrease of the
strength of the correlations at low . The L\'evy length scale parameter
decreases with increasing , following a hydrodynamically
predicted type of scaling behavior. The values of the L\'evy index of stability
are found to be significantly lower than the Gaussian case of
, but also significantly larger than the conjectured value that may
characterize the critical point of a second-order quark-hadron phase
transition.Comment: 448 authors, 25 pages, 11 figures, 4 tables, 2010 data. v2 is version
accepted for publication in Phys. Rev. C. Plain text data tables for the
points plotted in figures for this and previous PHENIX publications are (or
will be) publicly available at http://www.phenix.bnl.gov/papers.htm
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