A Closed-Form Solution for the Optimal Time Evolution of an Exponentially Decaying Signal with Thermal Noise

The signal-to-noise ratio of a monoexponentially decaying signal exhibits a maximum at an evolution time of approximately 1.26 T-2. It has previously been thought that there is no closed-form solution to express this maximum. We report in this note that this maximum can be represented in a specific, analytical closed form in terms of the negative real branch of an inverse function known as the Lambert W function. The Lambert function is finding increasing use in the solution of problems in a variety of areas in the physical sciences. (C) 2014 Wiley Periodicals, Inc.

Abandoned Coal Mine Drainage and Its Remediation: Impacts on Stream Ecosystem Structure and Function

The effects of abandoned mine drainage (AMD) on streams and responses to remediation efforts were studied using three streams (AMD-impacted, remediated, reference) in both the anthracite and the bituminous coal mining regions of Pennsylvania (USA). Response variables included ecosystem function as well as water chemistry and macroinvertebrate community composition. The bituminous AMD stream was extremely acidic with high dissolved metals concentrations, a prolific mid-summer growth of the filamentous alga, Mougeotia, and .10-fold more chlorophyll than the reference stream. The anthracite AMD stream had a higher pH, substrata coated with iron hydroxide(s), and negligible chlorophyll. Macroinvertebrate communities in the AMD streams were different from the reference streams, the remediated streams, and each other. Relative to the reference stream, the AMD stream(s) had (1) greater gross primary productivity (GPP) in the bituminous region and undetectable GPP in the anthracite region, (2) greater ecosystem respiration in both regions, (3) greatly reduced ammonium uptake and nitrification in both regions, (4) lower nitrate uptake in the bituminous (but not the anthracite) region, (5) more rapid phosphorus removal from the water column in both regions, (6) activities of phosphorus-acquiring, nitrogenacquiring, and hydrolytic-carbon-acquiring enzymes that indicated extreme phosphorus limitation in both regions, and (7) slower oak and maple leaf decomposition in the bituminous region and slower oak decomposition in the anthracite region. Remediation brought chlorophyll concentrations and GPP nearer to values for respective reference streams, depressed ecosystem respiration, restored ammonium uptake, and partially restored nitrification in the bituminous (but not the anthracite) region, reduced nitrate uptake to an undetectable level, restored phosphorus uptake to near normal rates, and brought enzyme activities more in line with the reference stream in the bituminous (but not the anthracite) region. Denitrification was not detected in any stream. Water chemistry and macroinvertebrate community structure analyses capture the impact of AMD at the local reach scale, but functional measures revealed that AMD has ramifications that can cascade to downstream reaches and perhaps to receiving estuaries.