Ocean acidification impacts on nitrogen fixation in the coastal western Mediterranean Sea

The effects of ocean acidification on nitrogen (N2) fixation rates and on the community composition of N2-fixing microbes (diazotrophs) were examined in coastal waters of the North-Western Mediterranean Sea. Nine experimental mesocosm enclosures of ∼50 m3 each were deployed for 20 days during June-July 2012 in the Bay of Calvi, Corsica, France. Three control mesocosms were maintained under ambient conditions of carbonate chemistry. The remainder were manipulated with CO2 saturated seawater to attain target amendments of pCO2 of 550, 650, 750, 850, 1000 and 1250 μatm. Rates of N2 fixation were elevated up to 10 times relative to control rates (2.00 ± 1.21 nmol L-1d-1) when pCO2 concentrations were >1000 μatm and pHT (total scale) < 7.74. Diazotrophic phylotypes commonly found in oligotrophic marine waters, including the Mediterranean, were not present at the onset of the experiment and therefore, the diazotroph community composition was characterised by amplifying partial nifH genes from the mesocosms. The diazotroph community was comprised primarily of cluster III nifH sequences (which include possible anaerobes), and proteobacterial (α and γ) sequences, in addition to small numbers of filamentous (or pseudo-filamentous) cyanobacterial phylotypes. The implication from this study is that there is some potential for elevated N2 fixation rates in the coastal western Mediterranean before the end of this century as a result of increasing ocean acidification. Observations made of variability in the diazotroph community composition could not be correlated with changes in carbon chemistry, which highlights the complexity of the relationship between ocean acidification and these keystone organisms.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.