Abstract. Linear scaling methods, or O(N ) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N , in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.

[1] Peatlands are widely regarded as a significant source of atmospheric CH 4 , a potent greenhouse gas. At present, most of the information on environmental emissions of CH 4 comes from infrequent, temporally discontinuous ground-based flux measurements. Enormous efforts have been made to extrapolate measured emission rates to establish seasonal or annual averages using relevant biogeochemical factors, such as water table positions or peat temperatures, by assuming that the flux was stationary during a substantial nonsampling period. However, this assumption has not been explicitly verified, and little is known about the continuous variation of the CH 4 flux in a timescale of individual flux measurement. In this study, we show an abrupt change in the CH 4 emission rate associated with falling atmospheric pressure. We found that the CH 4 flux can change by 2 orders of magnitude within a matter of tens of minutes owing to the release of free-phase CH 4 triggered by a drop in air pressure. The contribution of the ebullition to the total CH 4 flux during the measurements was significant (50-64%). These results clearly indicated that field campaigns must be designed to cover this rapid temporal variability caused by ebullition, which may be especially important in intemperate weather. Process-based CH 4 emission models should also be modified to include air pressure as a key factor for the control of ebullient CH 4 release from peatland.

An overview of the CONQUEST linear scaling density functional theory (DFT) code is given, focusing particularly on the scaling behaviour on modern high-performance computing platforms. We demonstrate that essentially perfect linear scaling and weak parallel scaling (with fixed number of atoms per processor core) can be achieved, and that DFT calculations on millions of atoms are now possible.

Within the framework of the density functional theory, we calculate the electronic structure of α-(BEDT-TTF)2I3 at 8 K and room temperature at ambient pressure and with uniaxial strain along the a-and b-axes. We confirm the existence of anisotropic Dirac cone dispersion near the chemical potential. We also extract the orthogonal tight-binding parameters to analyze physical properties. An investigation of the electronic structure near the chemical potential clarifies that effects of uniaxial strain along the a-axis is different from that along the b-axis. The carrier densities show T 2 dependence at low temperatures, which may explain the experimental findings not only qualitatively but also quantitatively.

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We describe recent progress in developing linear scaling ab initio electronic structure methods, referring in particular to our highly parallel code CONQUEST. After reviewing the state of the field, we present the basic ideas underlying almost all linear scaling methods, and discuss specific practical details of the implementation. We also note the connection between linear scaling methods and embedding techniques.

PACS 31.15. Ew, 71.15.Mb While the success of density functional theory (DFT) has led to its use in a wide variety of fields such as physics, chemistry, materials science and biochemistry, it has long been recognised that conventional methods are very inefficient for large complex systems, because the memory requirements scale as N 2 and the cpu requirements as N 3 (where N is the number of atoms). The principles necessary to develop methods with linear scaling of the cpu and memory requirements with system size (O(N) methods) have been established for more than ten years, but only recently have practical codes showing this scaling for DFT started to appear. We report recent progress in the development of the CONQUEST code, which performs O(N) DFT calculations on parallel computers, and has a demonstrated ability to handle systems of over 10 000 atoms. The code can be run at different levels of precision, ranging from empirical tight-binding, through ab initio tight-binding, to full ab initio, and techniques for calculating ionic forces in a consistent way at all levels of precision will be presented. Illustrations are given of practical CONQUEST calculations in the strained Ge/Si(001) system.

[1] Recent works on CH 4 emissions from peatlands have demonstrated that ebullition can be a more important emission pathway than it has been thought. However, knowledge of its features and associated environmental factors is still very limited. In this study, we investigated the quantitative relationship between the amount of CH 4 emitted via ebullition and changes in the atmospheric pressure through a laboratory experiment. During the flux measurement period, ebullition was recorded almost exclusively in air-pressure-declining phases. The increased volume of the gas bubbles due to reduction in atmospheric pressure and the amount of released gas bubbles revealed a strong linear relation, suggesting that in situ CH 4 emissions via ebullition can be estimated using this correlation. Our results clearly showed that atmospheric pressure can be one of the most important factors to control CH 4 emissions from peatlands and that ebullition can be the main transport mechanism during the pressure-falling phase.Citation: Tokida, T., T. Miyazaki, and M. Mizoguchi (2005), Ebullition of methane from peat with falling atmospheric pressure, Geophys. Res. Lett., 32, L13823,