A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

The role of hydrological transience in peatland pattern formation

The sloping flanks of peatlands are commonly patterned with non-random, contour-parallel stripes of distinct microhabitats such as hummocks, lawns and hollows. Patterning seems to be governed by feedbacks among peatland hydrological processes, plant micro-succession, plant litter production and peat decomposition. An improved understanding of peatland patterning may provide important insights into broader aspects of the long-term development of peatlands and their likely response to future climate change.

Towards a unifying framework for pattern transformation in swarm systems

This paper identifies the major challenges in the area of pattern formation. The work is also motivated by the need for development of a single framework to surmount these challenges. A framework based on the control of macroscopic parameters is proposed. The issue of transformation of patterns is specifically considered. A definition for transformation and four special cases, namely elementary and geometrical transformations by repositioning all or some robots in the pattern are provided. Two feasible tools for pattern transformation namely, a macroscopic parameter method and a mathematical tool - Moebius transformation also known as the linear fractional transformation are introduced. The realization of the unifying framework considering planning and communication is reported.

A swarm pattern transformation method based on macroscopic parameter operations

The work reported in this paper is motivated by biomimetic inspiration - the transformation of patterns. The major issue addressed is the development of feasible methods for transformation based on a macroscopic tool. The general requirement for the feasibility of the transformation method is determined by classifying pattern formation approaches an their characteristics. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some robotic agents are introduced. A feasible method for transforming patterns geometrically, based on the macroscopic parameter operation of a swarm is considered. The transformation method is applied to a swarm model which lends itself to the transformation technique. Simulation studies are developed to validate the feasibility of the approach, and do indeed confirm the approach.

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

The dependence of contrail formation on the weather pattern and altitude in the North Atlantic

Aircraft flying through cold ice-supersaturated air produce persistent contrails which contribute to the climate impact of aviation. Here, we demonstrate the importance of the weather situation, together with the route and altitude of the aircraft through this, on estimating contrail coverage. The results have implications for determining the climate impact of contrails as well as potential mitigation strategies. Twenty-one years of re-analysis data are used to produce a climatological assessment of conditions favorable for persistent contrail formation between 200 and 300 hPa over the north Atlantic in winter. The seasonal-mean frequency of cold ice-supersaturated regions is highest near 300 hPa, and decreases with altitude. The frequency of occurrence of ice-supersaturated regions varies with large-scale weather pattern; the most common locations are over Greenland, on the southern side of the jet stream and around the northern edge of high pressure ridges. Assuming aircraft take a great circle route, as opposed to a more realistic time-optimal route, is likely to lead to an error in the estimated contrail coverage, which can exceed 50% for westbound north Atlantic flights. The probability of contrail formation can increase or decrease with height, depending on the weather pattern, indicating that the generic suggestion that flying higher leads to fewer contrails is not robust.

Revisiting Asian monsoon formation and change associated with Tibetan Plateau forcing: II. Change

Data analysis based on station observations reveals that many meteorological variables averaged over the Tibetan Plateau (TP) are closely correlated, and their trends during the past decades are well correlated with the rainfall trend of the Asian summer monsoon. However, such correlation does not necessarily imply causality. Further diagnosis confirms the existence of a weakening trend in TP thermal forcing, characterized by weakened surface sensible heat flux in spring and summer during the past decades. This weakening trend is associated with decreasing summer precipitation over northern South Asia and North China and increasing precipitation over northwestern China, South China, and Korea. An atmospheric general circulation model, the HadAM3, is employed to elucidate the causality between the weakening TP forcing and the change in the Asian summer monsoon rainfall. Results demonstrate that a weakening in surface sensible heating over the TP results in reduced summer precipitation in the plateau region and a reduction in the associated latent heat release in summer. These changes in turn result in the weakening of the near-surface cyclonic circulation surrounding the plateau and the subtropical anticyclone over the subtropical western North Pacific, similar to the results obtained from the idealized TP experiment in Part I of this study. The southerly that normally dominates East Asia, ranging from the South China Sea to North China, weakens, resulting in a weaker equilibrated Sverdrup balance between positive vorticity generation and latent heat release. Consequently, the convergence of water vapor transport is confined to South China, forming a unique anomaly pattern in monsoon rainfall, the so-called “south wet and north dry.” Because the weakening trend in TP thermal forcing is associated with global warming, the present results provide an effective means for assessing projections of regional climate over Asia in the context of global warming.

Influence of time on the plant availability of Cd, Ni and Zn after sewage sludge has been applied to soils

A pot experiment was conducted to test the hypothesis that decomposition of organic matter in sewage sludge and the consequent formation of dissolved organic compounds (DOC) would lead to an increase in the bioavailability of the heavy metals. Two Brown Earth soils, one with clayey loam texture (CL) and the other a loamy sand (LS) were mixed with sewage sludge at rates equivalent to 0, 10 and 50 1 dry sludge ha(-1) and the pots were sown with ryegrass (Lolium perenne L.). The organic matter content and heavy metal availability assessed with soil extractions with 0.05 M CaCl2 were monitored over a residual time of two years, while plant uptake over one year, after addition of the sludge. It was found that the concentrations of Cd and Ni in both the ryegrass and the soil extracts increased slightly but significantly during the first year. In most cases, this increase was most evident especially at the higher sludge application rate (50 t ha(-1)). However, in the second year metal availability reached a plateau. Zinc concentrations in the ryegrass did not show an increase but the CaCl2 extracts increased during the first year. In contrast, organic matter content decreased rapidly in the first months of the first year and much more slowly in the second (total decrease of 16%). The concentrations of DOC increased significantly in the more organic rich CL soil in the course of two years. The pattern followed by the decomposition of organic matter with time and the production of DOC may provide at least a partial explanation for trend towards increased metal availability.

Formation and circulation of the cold intermediate layer in the Gulf of Saint Lawrence

[ 1] The local heat content and formation rate of the cold intermediate layer (CIL) in the Gulf of Saint Lawrence are examined using a combination of new in situ wintertime observations and a three-dimensional numerical model. The field observations consist of five moorings located throughout the gulf over the period of November 2002 to June 2003. The observations demonstrate a substantially deeper surface mixed layer in the central and northeast gulf than in regions downstream of the buoyant surface outflow from the Saint Lawrence Estuary. The mixed-layer depth in the estuary remains shallow (< 60 m) throughout winter, with the arrival of a layer of near-freezing waters between 40 and 100 m depth in April. An eddy-permitting ice-ocean model with realistic forcing is used to hindcast the period of observation. The model simulates well the seasonal evolution of mixed-layer depth and CIL heat content. Although the greatest heat losses occur in the northeast, the most significant change in CIL heat content over winter occurs in the Anticosti Trough. The observed renewal of CIL in the estuary in spring is captured by the model. The simulation highlights the role of the northwest gulf, and in particular, the separation of the Gaspe Current, in controlling the exchange of CIL between the estuary and the gulf. In order to isolate the effects of inflow through the Strait of Belle Isle on the CIL heat content, we examine a sensitivity experiment in which the strait is closed. This simulation shows that the inflow has a less important effect on the CIL than was suggested by previous studies.