Breeding vectors and predictability in the Oxford Mars GCM

A breeding vectors approach is used to study the intrinsic predictability of the Martian atmosphere using the Oxford Mars General Circulation Model (MGCM). The approach, described in detail below, is first tested using a terrestrial general circulation model, the United Kingdom Meteorological Office's Unified Model (UM), and results show growing modes of instability at mid to high latitudes on spatial scales of less than ~1,000km, in qualitative agreement with previous studies performed using terrestrial models. For the Martian atmosphere, and in the absence of radiatively active dust transport (so using a typical background dust distribution for each time of year), the technique reveals model states with approximately zero growth factors, and modes of instability on relatively large (up to ~5,000km) spatial scales. The implications of this for the predictability of the Martian atmosphere and for the usage of ensemble forecasting methods on Mars are also discussed

Dust cycles and storms in a Mars GCM

A number of different dust lifting parameterizations have been used to model the injection of dust from the Martian surface into the atmosphere, and the form of the resulting dust cycles and dust storms produced are found to be highly dependent on the precise form of the parameterization used, provided that it includes some threshold dependence, and particularly where radiatively active dust transport is employed. This talk will review the most interesting results from previous work. We have recently altered a key factor which particularly affects the dust lifting due to near-surface wind stress, however, so we will also present results using the new dust lifting formulation, and make some comparisons

Recent advances in the development of a European Mars climate model in Oxford

Since the early 1990s, efforts have been under way in Oxford to develop a range of numerical weather and climate prediction models for various studies of the Martian atmosphere and near-surface environment. Early versions of the Oxford model were more in the way of 'process models', aimed at relatively idealised studies e.g. of baroclinic instability[1] and low-level western boundary currents in the cross-equatorial solsticial Hadley circulation[2]. Since the mid-1990s, however, the group in Oxford have worked closely with the modelling group at LMD in Paris to develop a joint suite of more sophisticated and comprehensive numerical models of Mars' atmosphere. This collaboration, partly sponsored in recent years by the European Space Agency in connection with the associated development of a climate database for Mars[3], culminated in a suite of global circulation models[4], in which both groups share a library of parametrisation schemes, but in which the Oxford team use a spectral representation of horizontal fields (in the form of spherical harmonics) and the LMD group use a grid-point finite difference representation. These models were described in some detail by Forget et al.[4], and their preliminary validation and use in the construction of first versions of the European Mars Climate Database by Lewis et al.[3]. In the present report, we will review further developments which have taken place since the latter papers were published. Aspects of these developments which are common to both the LMD and Oxford groups will also be covered in the companion contribution by Forget et al. in this meeting, and so will only be touched on briefly here. Instead, we will concentrate on those advances which are more specific to the Oxford version of the model. In the following sections, we outline the main new developments to the model formulation since 1999. Subsequent sections then describe some recent examples where the new model is being utilised to advance a diverse range of studies of Mars atmospheric science

Scaling exponents and clustering coefficients of a growing random network

The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and multiple links of the same direction between any two nodes. Scaling exponents in the range of 1-2 are obtained through Monte Carlo simulations and various clustering coefficients are calculated, one of which, $C_{\rm out}$, is of order $10^{-1}$, indicating the network resembles a small-world. The out-degree distribution has an exponential cut-off for large out-degree.Comment: six pages, including 5 figures, RevTex 4 forma

Signatures of small-world and scale-free properties in large computer programs

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the ``information flow'' within the program. We show that, (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.Comment: 4 pages, 1 figure, to appear in Phys. Rev.

Live and Dead Nodes

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model incorporating this distinction and show that it can provide a quantitative description of the empirical network composed of citations and references (in- and out-links) between papers (nodes) in the SPIRES database of scientific papers in high energy physics. We also demonstrate that the death mechanism alone can result in power law degree distributions for the resulting network.Comment: 12 pages, 3 figures. To be published in Computational and Mathematical Organization Theor

Citation Networks in High Energy Physics

The citation network constituted by the SPIRES data base is investigated empirically. The probability that a given paper in the SPIRES data base has $k$ citations is well described by simple power laws, $P(k) \propto k^{-\alpha}$, with $\alpha \approx 1.2$ for $k$ less than 50 citations and $\alpha \approx 2.3$ for 50 or more citations. Two models are presented that both represent the data well, one which generates power laws and one which generates a stretched exponential. It is not possible to discriminate between these models on the present empirical basis. A consideration of citation distribution by subfield shows that the citation patterns of high energy physics form a remarkably homogeneous network. Further, we utilize the knowledge of the citation distributions to demonstrate the extreme improbability that the citation records of selected individuals and institutions have been obtained by a random draw on the resulting distribution.Comment: 9 pages, 6 figures, 2 table

World-Wide Web scaling exponent from Simon's 1955 model

Recently, statistical properties of the World-Wide Web have attracted considerable attention when self-similar regimes have been observed in the scaling of its link structure. Here we recall a classical model for general scaling phenomena and argue that it offers an explanation for the World-Wide Web's scaling exponent when combined with a recent measurement of internet growth.Comment: 1 page RevTeX, no figure

Solution of voter model dynamics on annealed small-world networks

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale $\tau$ separates a quasi-stationary disordered state with coexisting domains from a fully ordered frozen configuration. $\tau$ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.Comment: 11 pages, 4 figures, published version. Added section with extension to generic number of nearest neighbor

Coarsening in 2D slabs

We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs S_k = Z^2 x {0, ..., k-1} of all thicknesses k \geq 2 (with free and periodic boundary conditions in the third coordinate). We show that with free boundary conditions, for k \geq 3, some sites fixate for large times and some do not, whereas for k=2, all sites fixate. With periodic boundary conditions, for k \geq 4, some sites fixate and others do not, while for k=2 and 3, all sites fixate.Comment: 8 pages, 2 figure