Maximum solutions of normalized Ricci flows on 4-manifolds

We consider maximum solution $g(t)$, $t\in [0, +\infty)$, to the normalized Ricci flow. Among other things, we prove that, if $(M, \omega)$ is a smooth compact symplectic 4-manifold such that $b_2^+(M)>1$ and let $g(t),t\in[0,\infty)$, be a solution to (1.3) on $M$ whose Ricci curvature satisfies that $|\text{Ric}(g(t))|\leq 3$ and additionally $\chi(M)=3 \tau (M)>0$, then there exists an $m\in \mathbb{N}$, and a sequence of points $\{x_{j,k}\in M\}$, $j=1, ..., m$, satisfying that, by passing to a subsequence, $$(M, g(t_{k}+t), x_{1,k},..., x_{m,k}) \stackrel{d_{GH}}\longrightarrow (\coprod_{j=1}^m N_j, g_{\infty}, x_{1,\infty}, ...,, x_{m,\infty}),$$ $t\in [0, \infty)$, in the $m$-pointed Gromov-Hausdorff sense for any sequence $t_{k}\longrightarrow \infty$, where $(N_{j}, g_{\infty})$, $j=1,..., m$, are complete complex hyperbolic orbifolds of complex dimension 2 with at most finitely many isolated orbifold points. Moreover, the convergence is $C^{\infty}$ in the non-singular part of $\coprod_1^m N_{j}$ and $\text{Vol}_{g_{0}}(M)=\sum_{j=1}^{m}\text{Vol}_{g_{\infty}}(N_{j})$, where $\chi(M)$ (resp. $\tau(M)$) is the Euler characteristic (resp. signature) of $M$.Comment: 23 page

UK Geoenergy Observatories, Glasgow environmental baseline soil chemistry dataset

This report describes the environmental baseline topsoil chemistry dataset collected in February-March 2018 (03-18) as part of the United Kingdom Geoenergy Observatories (UKGEOS) project. Ninety, samples were collected from the shallow coal-mine Glasgow Geothermal Energy Research Field Site (GGERFS). The report accompanies the GGERFS Soil Chemistry03-18 dataset. It provides valuable information on soil chemistry prior to installation of the GGERFS-facility boreholes, against which any future change during the development/ running of the facility can be assessed. This information is necessary to help understand and de-risk similar shallow geothermal schemes in the future, provide public reassurance, and inform sustainable energy policy

Entanglement preparation using symmetric multiports

We investigate the entanglement produced by a multi-path interferometer that is composed of two symmetric multiports, with phase shifts applied to the output of the first multiport. Particular attention is paid to the case when we have a single photon entering the interferometer. For this situation we derive a simple condition that characterize the types of entanglement that one can generate. We then show how one can use the results from the single photon case to determine what kinds of multi-photon entangled states one can prepare using the interferometer.Comment: 6 pages, 2 figures, accepted for publication in European Journal of Physics

Entanglement preparation using symmetric multiports

We investigate the entanglement produced by a multi-path interferometer that is composed of two symmetric multiports, with phase shifts applied to the output of the first multiport. Particular attention is paid to the case when we have a single photon entering the interferometer. For this situation we derive a simple condition that characterize the types of entanglement that one can generate. We then show how one can use the results from the single photon case to determine what kinds of multi-photon entangled states one can prepare using the interferometer.Comment: 6 pages, 2 figures, accepted for publication in European Journal of Physics

Natural and anthropogenic lead in sediments of the Rotorua lakes, New Zealand

Global atmospheric sources of lead have increased more than 100-fold over the past century as a result of deforestation, coal combustion, ore smelting and leaded petroleum. Lead compounds generally accumulate in depositional areas across the globe where, due to low solubility and relative freedom from microbial degradation, the history of their inputs is preserved. In lakes there is rapid deposition and often little bioturbation of lead, resulting in an excellent depositional history of changes in both natural and anthropogenic sources. The objective of this study was to use sediments from a regionally bounded set of lakes to provide an indication of the rates of environmental inputs of lead whilst taking into account differences of trophic state and lead exposure between lakes. Intact sediment gravity cores were collected from 13 Rotorua lakes in North Island of New Zealand between March 2006 and January 2007. Cores penetrated sediments to a depth of 16–30 cm and contained volcanic tephra from the 1886 AD Tarawera eruption. The upper depth of the Tarawera tephra enabled prescription of a date for the associated depth in the core (120 years). Each core showed a sub-surface peak in lead concentration above the Tarawera tephra which was contemporaneous with the peak use of lead alkyl as a petroleum additive in New Zealand. An 8 m piston core was taken in the largest of the lakes, Lake Rotorua, in March 2007. The lake is antipodal to the pre-industrial sources of atmospheric lead but still shows increasing lead concentrations from <2 up to 3.5 μg g−1 between the Whakatane eruption (5530 ± 60 cal. yr BP) and the Tarawera eruption. Peaks in lead concentration in Lake Rotorua are associated with volcanic tephras, but are small compared with those arising from recent anthropogenic-derived lead deposition. Our results show that diagenetic processes associated with iron, manganese and sulfate oxidation-reduction, and sulfide precipitation, act to smooth distributions of lead from anthropogenic sources in the lake sediments. The extent of this smoothing can be related to changes in sulfate availability and reduction in sulfide driven by differences in trophic status amongst the lakes. Greatest lead mobilisation occurs in mesotrophic lakes during seasonal anoxia as iron and manganese are released to the porewater, allowing upward migration of lead towards the sediment–water interface. This lead mobilisation can only occur if sulfides are not present. The sub-surface peak in lead concentrations in lake sediments ascribed to lead alkyl in petroleum persists despite the diagenetic processes acting to disperse lead within the sediments and into the overlying water

Exotic smooth structures on 4-manifolds with zero signature

For every integer $k\geq 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and (2k-1)(\CP#\CPb), the connected sums of $2k-1$ copies of $S^2\times S^2$ and \CP#\CPb.Comment: 6 page

Coherent information analysis of quantum channels in simple quantum systems

The coherent information concept is used to analyze a variety of simple quantum systems. Coherent information was calculated for the information decay in a two-level atom in the presence of an external resonant field, for the information exchange between two coupled two-level atoms, and for the information transfer from a two-level atom to another atom and to a photon field. The coherent information is shown to be equal to zero for all full-measurement procedures, but it completely retains its original value for quantum duplication. Transmission of information from one open subsystem to another one in the entire closed system is analyzed to learn quantum information about the forbidden atomic transition via a dipole active transition of the same atom. It is argued that coherent information can be used effectively to quantify the information channels in physical systems where quantum coherence plays an important role.Comment: 24 pages, 7 figs; Final versiob after minor changes, title changed; to be published in Phys. Rev. A, September 200

A straw drift chamber spectrometer for studies of rare kaon decays

We describe the design, construction, readout, tests, and performance of planar drift chambers, based on 5 mm diameter copperized Mylar and Kapton straws, used in an experimental search for rare kaon decays. The experiment took place in the high-intensity neutral beam at the Alternating Gradient Synchrotron of Brookhaven National Laboratory, using a neutral beam stop, two analyzing dipoles, and redundant particle identification to remove backgrounds

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm