Modelling trends in OH radical concentrations using generalized additive models

During the TORCH campaign a zero dimensional box model based on the Master Chemical Mechanism was used to model concentrations of OH radicals. The model provided a close overall fit to measured concentrations but with some significant deviations. In this research, an approach was established for applying Generalized Additive Models (GAM) to atmospheric concentration data. Two GAM models were fitted to OH radical concentrations using TORCH data, the first using measured OH data and the second using MCM model results. GAM models with five smooth functions provided a close fit to the data with 78% of the deviance explained for measured OH and 83% for modelled OH. The GAM model for measured OH produced substantially better predictions of OH concentrations than the original MCM model results. The diurnal profile of OH concentration was reproduced and the predicted mean diurnal OH concentration was only 0.2% less than the measured concentration compared to 16.3% over-estimation by the MCM model. Photolysis reactions were identified as most important in explaining concentrations of OH. The GAM models combined both primary and secondary pollutants and also anthropogenic and biogenic species to explain changes in OH concentrations. Differences identified in the dependencies of modelled and measured OH concentrations, particularly for aromatic and biogenic species, may help to understand why the MCM model predictions sometimes disagree with measurements of atmospheric species

Universality of Quantum Entropy for Extreme Black Holes

We consider the extremal limit of a black hole geometry of the Reissner-Nordstrom type and compute the quantum corrections to its entropy. Universally, the limiting geometry is the direct product of two 2-dimensional spaces and is characterized by just a few parameters. We argue that the quantum corrections to the entropy of such extremal black holes due to a massless scalar field have a universal behavior. We obtain explicitly the form of the quantum entropy in this extremal limit as function of the parameters of the limiting geometry. We generalize these results to black holes with toroidal or higher genus horizon topologies. In general, the extreme quantum entropy is completely determined by the spectral geometry of the horizon and in the ultra-extreme case it is just a determinant of the 2-dimensional Laplacian. As a byproduct of our considerations we obtain expressions for the quantum entropy of black holes which are not of the Reissner-Nordstrom type: the extreme dilaton and extreme Kerr-Newman black holes. In both cases the classical Bekenstein-Hawking entropy is modified by logarithmic corrections.Comment: 18 pages, latex, no figures, minor changes, to appear in Nucl. Phys.

Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains

We analyze the 1D focusing nonlinear Schr\"{o}dinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally these equations elucidate the unique role of the zero mode for the Neumann boundary conditions

Diffusion of a granular pulse in a rotating drum

The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to elucidate the effect of the confining end-plate of the drum. We then show that the diffusion is neither subdiffusive nor superdiffusive but normal. This is demonstrated by rescaling the concentration profiles obtained at various stages and by studying the time evolution of the mean squared deviation. Finally we study the self-diffusion of both large and small grains and we show that it is normal and that the diffusion coefficient is independent of the grain size

Constraining uncertainty in aerosol direct forcing

The uncertainty in present-day anthropogenic forcing is dominated by uncertainty in the strength of the contribution from aerosol. Much of the uncertainty in the direct aerosol forcing can be attributed to uncertainty in the anthropogenic fraction of aerosol in the present-day atmosphere, due to a lack of historical observations. Here we present a robust relationship between total present-day aerosol optical depth and the anthropogenic contribution across three multi-model ensembles and a large single-model perturbed parameter ensemble. Using observations of aerosol optical depth, we determine a reduced likely range of the anthropogenic component and hence a reduced uncertainty in the direct forcing of aerosol

Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?

We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions that all start at the same position L to the right of the lamb and a haven at x=0. If the lamb reaches this haven before meeting any lion, the lamb survives. We investigate the survival probability of the lamb, S_N(x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We determine S_N(x,L) analytically for the special cases of N=1 and N--->oo. For large but finite N, we determine the unusual asymptotic form whose leading behavior is S_N(z)\simN^{-z^2}, with z=x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10^{500}.Comment: 13 pages, 6 figures, IOP format; v2: small changes in response to referee and editor comment

2D pattern evolution constrained by complex network dynamics

Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, lesser attention has been focused on hybrid systems, \textit{i.e.} involving more than one type of network and/or dynamics. Because several real systems present such an organization (\textit{e.g.} the dynamics of a disease coexisting with the dynamics of the immune system), it becomes important to address such hybrid systems. The current paper investigates a specific system involving a diffusive (linear and non-linear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models, whose nodes can be displaced spatially. More specifically, the complex network is expected to control, and if possible to extinguish, the diffusion of some given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray-Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the spreading. The main findings include the identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome

Quantum scalar field on three-dimensional (BTZ) black hole instanton: heat kernel, effective action and thermodynamics

We consider the behaviour of a quantum scalar field on three-dimensional Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole instanton and the BTZ instanton with a conical singularity at the horizon. The corresponding heat kernel and effective action are calculated explicitly for both rotating and non-rotating holes. The quantum entropy of the BTZ black hole is calculated by differentiating the effective action with respect to the angular deficit at the conical singularity. The renormalization of the UV-divergent terms in the action and entropy is considered. The structure of the UV-finite term in the quantum entropy is of particular interest. Being negligible for large outer horizon area $A_+$ it behaves logarithmically for small $A_+$. Such behaviour might be important at late stages of black hole evaporation.Comment: 28 pages, latex, 2 figures now include

Observations and impacts of bleach washing on indoor chlorine chemistry

Ambient levels of chlorinated gases and aerosol components were measured by on-line chemical ionization and aerosol mass spectrometers after an indoor floor was repeatedly washed with a commercial bleach solution. Gaseous chlorine (Cl_2, 10′s of ppbv) and hypochlorous acid (HOCl, 100′s of ppbv) arise after floor washing, along with nitryl chloride (ClNO_2), dichlorine monoxide (Cl2O) and chloramines (NHCl_2, NCl_3). Much higher mixing ratios would prevail in a room with lower and more commonly encountered air exchange rates than that observed in the study (12.7 h^(−1)). Coincident with the formation of gas-phase species, particulate chlorine levels also rise. Cl_2, ClNO_2, NHCl_2 and NCl_3 exist in the headspace of the bleach solution whereas HOCl was only observed after floor washing. HOCl decays away 1.4 times faster than the air exchange rate, indicative of uptake onto room surfaces and consistent with the well-known chlorinating ability of HOCl. Photochemical box modeling captures the temporal profiles of Cl_2 and HOCl very well, and indicates that the OH, Cl and ClO gas-phase radical concentrations in the indoor environment could be greatly enhanced (> 10^6 and 10^5 cm^(−3) for OH and Cl, respectively) in such washing conditions, dependent on the amount of indoor illumination

First passages in bounded domains: When is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(\omega) distribution of the random variable \omega=\tau_1/(\tau_1+\tau_2), which is a measure for how similar the first passage times \tau_1 and \tau_2 are of two independent realisations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(\omega) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behaviour. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behaviour, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(\omega), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behaviour even in bounded domains, in which all moments of the first passage distribution exist.Comment: 9 pages, 6 figure