Spatial patterns of competing random walkers

We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals perform random walks of different types (Gaussian diffusion and L\'{e}vy flights). We focus on how competition and random motions affect each other, from which spatial instabilities and extinctions arise. Under suitable conditions, competitive interactions lead to clustering of individuals and periodic pattern formation. Random motion has a homogenizing effect and then delays this clustering instability. When individuals from species differing in their random walk characteristics are allowed to compete together, the ones with a tendency to form narrower clusters get a competitive advantage over the others. Mean-field deterministic equations are analyzed and compared with the outcome of the individual-based simulations.Comment: 38 pages, including 6 figure

Spatial patterns in intermunicipal Danish commuting

Intermunicipal variations in in-commuting are mainly explained by variations in number of workplaces, urbanization degree and wealth, whereas variations in out- commuting are mainly determined by variations in workforce size, number of workplaces, living patterns and unemployment. This is quite satisfactory according to existing theory. However, of these explanatory factors only the number of workplaces influences the net in-commuting. But by using spatial lag structures it is shown that unemployment in neighbourhood municipalities influences net in-commuting. Finally, evidence of impact of local spatial industrial patterns on the commuting behaviour is provided, and the nature and reasons for these spatial patterns are discussed.

Complex Networks Unveiling Spatial Patterns in Turbulence

Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on the complex network theory, offering a powerful framework to explore complex systems with a huge number of interacting elements. Although interest on complex networks has been increasing in the last years, few recent studies have been applied to turbulence. We propose an investigation starting from a two-point correlation for the kinetic energy of a forced isotropic field numerically solved. Among all the metrics analyzed, the degree centrality is the most significant, suggesting the formation of spatial patterns which coherently move with similar vorticity over the large eddy turnover time scale. Pattern size can be quantified through a newly-introduced parameter (i.e., average physical distance) and varies from small to intermediate scales. The network analysis allows a systematic identification of different spatial regions, providing new insights into the spatial characterization of turbulent flows. Based on present findings, the application to highly inhomogeneous flows seems promising and deserves additional future investigation.Comment: 12 pages, 7 figures, 3 table

Nonlinear diffusion effects on biological population spatial patterns

Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The standard model includes growth and competition in a logistic expression, and spreading is modeled through normal diffusion. Moreover, the competition term is nonlocal, which has been shown to give rise to spatial patterns. We generalize the diffusion term through the nonlinear form $\partial_t u(x,t) = D \partial_{xx} u(x,t)^\nu$ (with $D, \nu>0$), encompassing the cases where the state-dependent diffusion coefficient either increases ($\nu>1$) or decreases ($\nu<1$) with the density, yielding subdiffusion or superdiffusion, respectively. By means of numerical simulations and analytical considerations, we display how that nonlinearity alters the phase diagram. The type of diffusion imposes critical values of the model parameters for the onset of patterns and strongly influences their shape, inducing fragmentation in the subdiffusive case. The detection of the main persistent mode allows analytical prediction of the critical thresholds

Spatial Patterns in Chemically and Biologically Reacting Flows

We present here a number of processes, inspired by concepts in Nonlinear Dynamics such as chaotic advection and excitability, that can be useful to understand generic behaviors in chemical or biological systems in fluid flows. Emphasis is put on the description of observed plankton patchiness in the sea. The linearly decaying tracer, and excitable kinetics in a chaotic flow are mainly the models described. Finally, some warnings are given about the difficulties in modeling discrete individuals (such as planktonic organisms) in terms of continuous concentration fields.Comment: 41 pages, 10 figures; To appear in the Proceedings of the 2001 ISSAOS School on 'Chaos in Geophysical Flows

Emergence and Evolution of Heterogeneous Spatial Patterns

We live in a quite heterogeneous space. There are cities and rural areas, and population density varies a lot across space. People migrate and commute to the places of their work. The goal of this article is to clarify the mechanism of commuting as an equilibrium in heterogeneous space with different technologies. It is well known that agricultural production requires substantial amount of land per unit of labour, while most industrial production and services require much lower land input. We assume that all industrial production and service sector is located in urban areas, while all agriculture is in rural area. Historically, the share of labour in agriculture was declining due to more rapid growth of productivity there in comparison to service sector. At the same time, people change the location of their residence much slower. That is why at some point in time we face the situation, when rural area has excessive labour (not enough work for all in agriculture), while urban areas create an increasing number of jobs. A relatively simple mathematical model is proposed to explain the emergence of spatial pattern with heterogeneous density and phase transition between urban and rural areas. There are three types of agents: workers who live in a city, farmers who live in a rural area and workers-commuters from rural area to a city. In an equilibrium they are indifferent between occupation and residence. An indifference across locations for a priori identical agents implies the shape of land rent. If some parameters of the model change, they imply the change of the whole spatial pattern. In particular, split of rural residents into commuters and farmers depends on road infrastructure development through transport cost. Two types of shocks (decline in commuting transport cost by construction of fast roads and the relative decline in agricultural price) can perturb agricultural zone. Some former farmers start commuting to city while keeping residence in rural area. This is how a functional area of a city with integrated labour market emerges.

Spatial Patterns of Headquarters

This study of the spatial concentration of the headquarters of exchange-listed companies suggests that the relevancy of the "efficiency parameter" of agglomeration theory still holds in explaining the location of headquarters, especially when the production function is reinterpreted as a productivity function. The sample of 5189 headquarters exceeds previous studies of Fortune 500 firms. Across industries, a high degree of clustering is found: 40% of the nation's headquarters were found in twenty counties. Cluster analysis suggests grouping patterns for headquarters; discriminant analysis confirms the uniqueness of these spatial clustering patterns across 229 urban counties. For certain industries, the clustering occurs within small areas. The headquarters of these spatially-correlated groups of firms money and media, gas and electric, business services, and machining technology were mapped at the county and zipcode level for counties within major metropolitan areas. The spatial density patterns take on traditional urban forms: core, ring and wedge.

Spatial patterns of innovation and trade competitiveness

A renewed concern has been growing recently for the role that the spatial organisation of innovation and production plays in determining trade performances. Purely technological externalities can be seen as a core component of this process, and their degree of influence can be investigated in terms of how factors that shape the structure of the innovative activity are definite in space. In the present paper we explore the relationship between technological and trade performances by focusing on the spatial configuration of different structures of the innovative activity in high technology industries in Italy. The data used in the analysis are based on the European Patent Office data base and on trade statistics from the five digit S.I.T.C. classification, and are spatially referenced to the Italy NUT 3 regional partition. Technological and knowledge externalities are modelled through the use of information associated to the connectivity structure of the geographical system under study. The analysis is ultimately aimed at investigating how technology factors evolve with respect to specific and space related carachteristics of the industrial context giving rise to cumulativeness of technology advantages, and to what extent these factors appear to affect trade competitiveness in specific industries. Keywords: spatial externalities. spatial innovation systems. trade competitiveness