A macroscopic multifractal analysis of parabolic stochastic PDEs

It is generally argued that the solution to a stochastic PDE with multiplicative noise---such as $\dot{u}=\frac12 u"+u\xi$, where $\xi$ denotes space-time white noise---routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (2005), Gibbon and Titi (2005), and Zimmermann et al (2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (1989; 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.Comment: 41 page

Missing sea level rise in southeastern Greenland during and since the Little Ice Age

The Greenland Ice Sheet has been losing mass at an accelerating rate over the past 2 decades. Understanding ice mass and glacier changes during the preceding several hundred years prior to geodetic measurements is more difficult because evidence of past ice extent in many places was later overridden. Salt marshes provide the only continuous records of relative sea level (RSL) from close to the Greenland Ice Sheet that span the period of time during and since the Little Ice Age (LIA) and can be used to reconstruct ice mass gain and loss over recent centuries. Salt marsh sediments collected at the mouth of Dronning Marie Dal, close to the Greenland Ice Sheet margin in southeastern Greenland, record RSL changes over the past ca. 300 years through changing sediment and diatom stratigraphy. These RSL changes record a combination of processes that are dominated by local and regional changes in Greenland Ice Sheet mass balance during this critical period that spans the maximum of the LIA and 20th-century warming. In the early part of the record (1725–1762 CE) the rate of RSL rise is higher than reconstructed from the closest isolation basin at Timmiarmiut, but between 1762 and 1880 CE the RSL rate is within the error range of the rate of RSL change recorded in the isolation basin. RSL begins to slowly fall around 1880 CE, with a total amount of RSL fall of 0.09±0.1 m in the last 140 years. Modelled RSL, which takes into account contributions from post-LIA Greenland Ice Sheet glacio-isostatic adjustment (GIA), ongoing deglacial GIA, the global non-ice sheet glacial melt fingerprint, contributions from thermosteric effects, the Antarctic mass loss sea level fingerprint and terrestrial water storage, overpredicts the amount of RSL fall since the end of the LIA by at least 0.5 m. The GIA signal caused by post-LIA Greenland Ice Sheet mass loss is by far the largest contributor to this modelled RSL, and error in its calculation has a large impact on RSL predictions at Dronning Marie Dal. We cannot reconcile the modelled RSL and the salt marsh observations, even when moving the termination of the LIA to 1700 CE and reducing the post-LIA Greenland mass loss signal by 30 %, and a “budget residual” of + ~ 3 mm yr−1 since the end of the LIA remains unexplained. This new RSL record backs up other studies that suggest that there are significant regional differences in the timing and magnitude of the response of the Greenland Ice Sheet to the climate shift from the LIA into the 20th century

On the origin of M81 group extended dust emission

Galactic cirrus emission at far-infrared wavelengths affects many extragalactic observations. Separating this emission from that associated with extragalactic objects is both important and difficult. In this paper we discuss a particular case, the M81 group, and the identification of diffuse structures prominent in the infrared, but also detected at optical wavelengths. The origin of these structures has previously been controversial, ranging from them being the result of a past interaction between M81 and M82 or due to more local Galactic emission. We show that over an order of a few arcmin scales, the far-infrared (Herschel 250 mu m) emission correlates spatially very well with a particular narrow-velocity (2-3 km s(-1)) component of the Galactic HI. We find no evidence that any of the far-infrared emission associated with these features actually originates in the M81 group. Thus we infer that the associated diffuse optical emission must be due to galactic light-back scattered off dust in our galaxy. Ultraviolet observations pick out young stellar associations around M81, but no detectable far-infrared emission. We consider in detail one of the Galactic cirrus features, finding that the far-infrared HI relation breaks down below arcmin scales and that at smaller scales there can be quite large dust-temperature variation

Numerical properties of isotrivial fibrations

In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations \varphi \colon X \lr C, where $X$ is a smooth, projective surface and $C$ is a curve. In particular we prove that, if $g(C) \geq 1$ and $X$ is neither ruled nor isomorphic to a quasi-bundle, then K_X^2 \leq 8 \chi(\mO_X)-2; this inequality is sharp and if equality holds then $X$ is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that $K_X$ is ample, we obtain K_X^2 \leq 8 \chi(\mO_X)-5 and the inequality is also sharp. This improves previous results of Serrano and Tan.Comment: 30 pages. Final version, to appear in Geometriae Dedicat

Measurement of K^0_e3 form factors

The semileptonic decay of the neutral K meson, KL -> pi e nu (Ke3), was used to study the strangeness-changing weak interaction of hadrons. A sample of 5.6 million reconstructed events recorded by the NA48 experiment was used to measure the Dalitz plot density. Admitting all possible Lorentz-covariant couplings, the form factors for vector (f_+(q^2)), scalar (f_S) and tensor (f_T) interactions were measured. The linear slope of the vector form factor lambda_+ = 0.0284+-0.0007+-0.0013 and values for the ratios |f_S/f_+(0)| = 0.015^{+0.007}_{-0.010}+-0.012 and |f_T/f_+(0)| = 0.05^{+0.03}_{-0.04}+-0.03 were obtained. The values for f_S and f_T are consistent with zero. Assuming only Vector-Axial vector couplings, lambda_+ = 0.0288+-0.0004+-0.0011 and a good fit consistent with pure V-A couplings were obtained. Alternatively, a fit to a dipole form factor yields a pole mass of M = 859+-18 MeV, consistent with the K^*(892) mass.Comment: 16 pages, 7 figures. submitted to Phys. Lett.

A measurement of the tau mass and the first CPT test with tau leptons

We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV using tau pairs from Z0 decays. To test CPT invariance we compare the masses of the positively and negatively charged tau leptons. The relative mass difference is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.

First Measurement of Z/gamma* Production in Compton Scattering of Quasi-real Photons

We report the first observation of Z/gamma* production in Compton scattering of quasi-real photons. This is a subprocess of the reaction e+e- to e+e-Z/gamma*, where one of the final state electrons is undetected. Approximately 55 pb-1 of data collected in the year 1997 at an e+e- centre-of-mass energy of 183 GeV with the OPAL detector at LEP have been analysed. The Z/gamma* from Compton scattering has been detected in the hadronic decay channel. Within well defined kinematic bounds, we measure the product of cross-section and Z/gamma* branching ratio to hadrons to be (0.9+-0.3+-0.1) pb for events with a hadronic mass larger than 60 GeV, dominated by (e)eZ production. In the hadronic mass region between 5 GeV and 60 GeV, dominated by (e)egamma* production, this product is found to be (4.1+-1.6+-0.6) pb. Our results agree with the predictions of two Monte Carlo event generators, grc4f and PYTHIA.Comment: 18 pages, LaTeX, 5 eps figures included, submitted to Physics Letters

Search for Higgs Bosons in e+e- Collisions at 183 GeV

The data collected by the OPAL experiment at sqrts=183 GeV were used to search for Higgs bosons which are predicted by the Standard Model and various extensions, such as general models with two Higgs field doublets and the Minimal Supersymmetric Standard Model (MSSM). The data correspond to an integrated luminosity of approximately 54pb-1. None of the searches for neutral and charged Higgs bosons have revealed an excess of events beyond the expected background. This negative outcome, in combination with similar results from searches at lower energies, leads to new limits for the Higgs boson masses and other model parameters. In particular, the 95% confidence level lower limit for the mass of the Standard Model Higgs boson is 88.3 GeV. Charged Higgs bosons can be excluded for masses up to 59.5 GeV. In the MSSM, mh > 70.5 GeV and mA > 72.0 GeV are obtained for tan{beta}>1, no and maximal scalar top mixing and soft SUSY-breaking masses of 1 TeV. The range 0.8 < tanb < 1.9 is excluded for minimal scalar top mixing and m{top} < 175 GeV. More general scans of the MSSM parameter space are also considered.Comment: 49 pages. LaTeX, including 33 eps figures, submitted to European Physical Journal

A Measurement of the Product Branching Ratio f(b->Lambda_b).BR(Lambda_b->Lambda X) in Z0 Decays

The product branching ratio, f(b->Lambda_b).BR(Lambda_b->Lambda X), where Lambda_b denotes any weakly-decaying b-baryon, has been measured using the OPAL detector at LEP. Lambda_b are selected by the presence of energetic Lambda particles in bottom events tagged by the presence of displaced secondary vertices. A fit to the momenta of the Lambda particles separates signal from B meson and fragmentation backgrounds. The measured product branching ratio is f(b->Lambda_b).BR(Lambda_b->Lambda X) = (2.67+-0.38(stat)+0.67-0.60(sys))% Combined with a previous OPAL measurement, one obtains f(b->Lambda_b).BR(Lambda_b->Lambda X) = (3.50+-0.32(stat)+-0.35(sys))%.Comment: 16 pages, LaTeX, 3 eps figs included, submitted to the European Physical Journal