Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations

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]

Effects of Repeated Intrathecal Triamcinolone-Acetonide Application on Cerebrospinal Fluid Biomarkers of Axonal Damage and Glial Activity in Multiple Sclerosis Patients

Multiple sclerosis (MS) is the most common inflammatory disease of the central nervous system in young adults. Over time, the disease progresses and, with accumulating disability, symptoms such as spasticity may occur. Although several treatment options are available, some patients may not respond to first-line therapeutics. However, some of these patients may benefit from intrathecally administered triamcinolone-acetonide (TCA), a derivative of glucocorticosteroids (GCS).GCSmay have neurotoxic effects, and cell apoptosis may occur. The aim of this study was to investigate the effects of TCA on biomarkers in the cerebrospinal fluid (CSF) suggestive of neurodegeneration

Hydroxylated fluorescent dyes for live-cell labeling: Synthesis, spectra and super-resolution STED.

Hydroxylated rhodamines, carbopyronines, silico- and germanorhodamines with absorption maxima in the range of 530-640 nm were prepared and applied in specific labeling of living cells. The direct and high-yielding entry to germa- and silaxanthones tolerates the presence of protected heteroatoms and may be considered for the syntheses of various sila- and germafluoresceins, as well as -rhodols. Application in stimulated emission depletion (STED) fluorescence microscopy revealed a resolution of 50-75 nm in one- and two-color imaging of vimentin-HaloTag fused protein and native tubulin. The established structure-property relationships allow prediction of the spectral properties and the positions of spirolactone/zwitterion equilibria for the new analogs of rhodamines, carbo-, silico- and germanorhodamines using simple additive schemes

A Bio-Logical Theory of Animal Learning

This article provides the foundation for a new predictive theory of animal learning that is based upon a simple logical model. The knowledge of experimental subjects at a given time is described using logical equations. These logical equations are then used to predict a subject’s response when presented with a known or a previously unknown situation. This new theory suc- cessfully anticipates phenomena that existing theories predict, as well as phenomena that they cannot. It provides a theoretical account for phenomena that are beyond the domain of existing models, such as extinction and the detection of novelty, from which “external inhibition” can be explained. Examples of the methods applied to make predictions are given using previously published results. The present theory proposes a new way to envision the minimal functions of the nervous system, and provides possible new insights into the way that brains ultimately create and use knowledge about the world

Potential of a cyclone prototype spacer to improve in vitro dry powder delivery

Copyright The Author(s) 2013. This article is published with open access at Springerlink.com. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are creditedPurpose: Low inspiratory force in patients with lung disease is associated with poor deagglomeration and high throat deposition when using dry powder inhalers (DPIs). The potential of two reverse flow cyclone prototypes as spacers for commercial carrierbased DPIs was investigated. Methods: Cyclohaler®, Accuhaler® and Easyhaler® were tested with and without the spacers between 30-60 Lmin-1. Deposition of particles in the next generation impactor and within the devices was determined by high performance liquid chromatography. Results: Reduced induction port deposition of the emitted particles from the cyclones was observed due to the high retention of the drug within the spacers (e.g. salbutamol sulphate (SS): 67.89 ± 6.51 % at 30 Lmin-1 in Cheng 1). Fine particle fractions of aerosol as emitted from the cyclones were substantially higher than the DPIs alone. Moreover, the aerodynamic diameters of particles emitted from the cyclones were halved compared to the DPIs alone (e.g. SS from the Cyclohaler® at 4 kPa: 1.08 ± 0.05 μm vs. 3.00 ± 0.12 μm, with and without Cheng 2, respectively) and unaltered with increased flow rates. Conclusion: This work has shown the potential of employing a cyclone spacer for commercial carrier-based DPIs to improve inhaled drug delivery.Peer reviewe

Cross sections and double-helicity asymmetries of midrapidity inclusive charged hadrons in p+p collisions at sqrt(s)=62.4 GeV

Unpolarized cross sections and double-helicity asymmetries of single-inclusive positive and negative charged hadrons at midrapidity from p+p collisions at sqrt(s)=62.4 GeV are presented. The PHENIX measurements for 1.0 < p_T < 4.5 GeV/c are consistent with perturbative QCD calculations at next-to-leading order in the strong coupling constant, alpha_s. Resummed pQCD calculations including terms with next-to-leading-log accuracy, yielding reduced theoretical uncertainties, also agree with the data. The double-helicity asymmetry, sensitive at leading order to the gluon polarization in a momentum-fraction range of 0.05 ~< x_gluon ~< 0.2, is consistent with recent global parameterizations disfavoring large gluon polarization.Comment: PHENIX Collaboration. 447 authors, 12 pages, 5 figures, 5 tables. Submitted to Physical Review

Measurement of higher cumulants of net-charge multiplicity distributions in Au++Au collisions at sNN=7.7−200\sqrt{s_{_{NN}}}=7.7-200 GeV

We report the measurement of cumulants ($C_n, n=1\ldots4$) of the net-charge distributions measured within pseudorapidity ($|\eta|<0.35$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=7.7-200$ GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The ratios of cumulants (e.g. $C_1/C_2$, $C_3/C_1$) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of $C_1/C_2 = \mu/\sigma^2$ and $C_3/C_1 = S\sigma^3/\mu$ can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy.Comment: 512 authors, 8 pages, 4 figures, 1 table. v2 is version accepted for publication in Phys. Rev. C as a Rapid Communication. 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

Inclusive cross section and double helicity asymmetry for pi^0 production in p+p collisions at sqrt(s) = 62.4 GeV

The PHENIX experiment presents results from the RHIC 2006 run with polarized proton collisions at sqrt(s) = 62.4 GeV for inclusive pi^0 production at mid-rapidity. Unpolarized cross section results are measured for transverse momenta p_T = 0.5 to 7 GeV/c. Next-to-leading order perturbative quantum chromodynamics calculations are compared with the data, and while the calculations are consistent with the measurements, next-to-leading logarithmic corrections improve the agreement. Double helicity asymmetries A_LL are presented for p_T = 1 to 4 GeV/c and probe the higher range of Bjorken_x of the gluon (x_g) with better statistical precision than our previous measurements at sqrt(s)=200 GeV. These measurements are sensitive to the gluon polarization in the proton for 0.06 < x_g < 0.4.Comment: 387 authors from 63 institutions, 10 pages, 6 figures, 1 table. Submitted to Physical Review 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

Inclusive cross section and single-transverse-spin asymmetry for very forward neutron production in polarized p+p collisions at sqrt(s)=200 GeV

The energy dependence of the single-transverse-spin asymmetry, A_N, and the cross section for neutron production at very forward angles were measured in the PHENIX experiment at RHIC for polarized p+p collisions at sqrt(s)=200 GeV. The neutrons were observed in forward detectors covering an angular range of up to 2.2 mrad. We report results for neutrons with momentum fraction of x_F=0.45 to 1.0. The energy dependence of the measured cross sections were consistent with x_F scaling, compared to measurements by an ISR experiment which measured neutron production in unpolarized p+p collisions at sqrt(s)=30.6--62.7 GeV. The cross sections for large x_F neutron production for p+p collisions, as well as those in e+p collisions measured at HERA, are described by a pion exchange mechanism. The observed forward neutron asymmetries were large, reaching A_N=-0.08+/-0.02 for x_F=0.8; the measured backward asymmetries, for negative x_F, were consistent with zero. The observed asymmetry for forward neutron production is discussed within the pion exchange framework, with interference between the spin-flip amplitude due to the pion exchange and nonflip amplitudes from all Reggeon exchanges. Within the pion exchange description, the measured neutron asymmetry is sensitive to the contribution of other Reggeon exchanges even for small amplitudes.Comment: 383 authors, 16 pages, 18 figures, 6 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