Interpersonal coordination tendencies, decision-making and information governing dynamics in rugby union

In this chapter, ideas from ecological psychology and nonlinear dynamics are integrated to characterise decision-making as an emergent property of self-organisation processes in the interpersonal interactions that occur in sports teams. A conceptual model is proposed to capture constraints on dynamics of decisions and actions in dyadic systems, which has been empirically evaluated in simulations of interpersonal interactions in team sports. For this purpose, co-adaptive interpersonal dynamics in team sports such as rubgy union have been studied to reveal control parameter and collective variable relations in attacker-defender dyads. Although interpersonal dynamics of attackers and defenders in 1 vs 1 situations showed characteristics of chaotic attractors, the informational constraints of rugby union typically bounded dyadic systems into low dimensional attractors. Our work suggests that the dynamics of attacker-defender dyads can be characterised as an evolving sequence since players' positioning and movements are connected in diverse ways over time.

Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Patterns

In recent years there has been widespread interest in patterns, perhaps provoked by a realisation that they constitute a fundamental brain activity and underpin many artificial intelligence systems. Theorised concepts of spatial patterns including scale, proportion, and symmetry, as well as social and psychological understandings are being revived through digital/parametric means of visualisation and production. The effect of pattern as an ornamental device has also changed from applied styling to mediated dynamic effect. The interior has also seen patterned motifs applied to wall coverings, linen, furniture and artefacts with the effect of enhancing aesthetic appreciation, or in some cases causing psychological and/or perceptual distress (Rodemann 1999). ----- ----- While much of this work concerns a repeating array of surface treatment, Philip Ball’s The Self- Made Tapestry: Pattern Formation in Nature (1999) suggests a number of ways that patterns are present at the macro and micro level, both in their formation and disposition. Unlike the conventional notion of a pattern being the regular repetition of a motif (geometrical or pictorial) he suggests that in nature they are not necessarily restricted to a repeating array of identical units, but also include those that are similar rather than identical (Ball 1999, 9). From his observations Ball argues that they need not necessarily all be the same size, but do share similar features that we recognise as typical. Examples include self-organized patterns on a grand scale such as sand dunes, or fractal networks caused by rivers on hills and mountains, through to patterns of flow observed in both scientific experiments and the drawings of Leonardo da Vinci.

Front interactions in a three-component system

The three-component reaction-diffusion system introduced in [C. P. Schenk et al., Phys. Rev. Lett., 78 (1997), pp. 3781–3784] has become a paradigm model in pattern formation. It exhibits a rich variety of dynamics of fronts, pulses, and spots. The front and pulse interactions range in type from weak, in which the localized structures interact only through their exponentially small tails, to strong interactions, in which they annihilate or collide and in which all components are far from equilibrium in the domains between the localized structures. Intermediate to these two extremes sits the semistrong interaction regime, in which the activator component of the front is near equilibrium in the intervals between adjacent fronts but both inhibitor components are far from equilibrium there, and hence their concentration profiles drive the front evolution. In this paper, we focus on dynamically evolving N-front solutions in the semistrong regime. The primary result is use of a renormalization group method to rigorously derive the system of N coupled ODEs that governs the positions of the fronts. The operators associated with the linearization about the N-front solutions have N small eigenvalues, and the N-front solutions may be decomposed into a component in the space spanned by the associated eigenfunctions and a component projected onto the complement of this space. This decomposition is carried out iteratively at a sequence of times. The former projections yield the ODEs for the front positions, while the latter projections are associated with remainders that we show stay small in a suitable norm during each iteration of the renormalization group method. Our results also help extend the application of the renormalization group method from the weak interaction regime for which it was initially developed to the semistrong interaction regime. The second set of results that we present is a detailed analysis of this system of ODEs, providing a classification of the possible front interactions in the cases of $N=1,2,3,4$, as well as how front solutions interact with the stationary pulse solutions studied earlier in [A. Doelman, P. van Heijster, and T. J. Kaper, J. Dynam. Differential Equations, 21 (2009), pp. 73–115; P. van Heijster, A. Doelman, and T. J. Kaper, Phys. D, 237 (2008), pp. 3335–3368]. Moreover, we present some results on the general case of N-front interactions.

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

A description of the Mei2-like protein family; structure, phylogenetic distribution and biological context

The Schizosaccharomyces pombe Mei2 gene encodes an RNA recognition motif (RRM) protein that stimulates meiosis upon binding a specific non-coding RNA and subsequent accumulation in a “mei2-dot” in the nucleus. We present here the first systematic characterization of the family of proteins with characteristic Mei2-like amino acid sequences. Mei2-like proteins are an ancient eukaryotic protein family with three identifiable RRMs. The C-terminal RRM (RRM3) is unique to Mei2-like proteins and is the most highly conserved of the three RRMs. RRM3 also contains conserved sequence elements at its C-terminus not found in other RRM domains. Single copy Mei2-like genes are present in some fungi, in alveolates such as Paramecium and in the early branching eukaryote Entamoeba histolytica, while plants contain small families of Mei2-like genes. While the C-terminal RRM is highly conserved between plants and fungi, indicating conservation of molecular mechanisms, plant Mei2-like genes have changed biological context to regulate various aspects of developmental pattern formation.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Spatial variation of sequestered calcium in the multicellular stage of Dictyostelium discoideum as assayed by chlortetracycline fluorescence

Abstract. We have used chlortetracycline (CTC) as a fluorescent probe to detect the distribution of sequestered calcium in multicellular stages of Dictyostelium discoideum. Tips of late aggregates, slugs and early culminating masses fluoresce very strongly. Most of the fluorescence is intracellular in origin and emanates from a small number of intense punctate sources. The sources correspond in part to autophagic vacuoles viz. neutral-red staining, acidic digestive vesicles, and may also include intracellular organelles; cytoplasmic fluorescence is much weaker in comparison. The level of fluorescence drops in the middle portion of slugs and rises again in the posteriormost region, though not to as high a level as in the tip. This holds good irrespective of whether CTC is applied only in the neighbourhood of the aggregate centre, only in the aggregate periphery, or to the whole aggregate. We infer that there must be a good deal of mixing in the stages leading from aggregation to slug formation; thus the serial order in which cells enter an aggregate does not bear any relation to their ultimate fates. The other implication of our study is that calcium sequestration is much more extensive in prestalk and anterior-like cells than in prespore cells. These findings are discussed with regard to possible implications for pattern formation.

Sostdc1 Plays an Essential Role in Mammalian Tooth Patterning : Insight into the Rodent Dental Evolution

This thesis work focuses on the role of TGF-beta family antagonists during the development of mouse dentition. Tooth develops through an interaction between the dental epithelium and underlying neural crest derived mesenchyme. The reciprocal signaling between these tissues is mediated by soluble signaling molecules and the balance between activatory and inhibitory signals appears to be essential for the pattern formation. We showed the importance of Sostdc1 in the regulation of tooth shape and number. The absence of Sostdc1 altered the molar cusp patterning and led to supernumerary tooth formation both in the molar and incisor region. We showed that initially, Sostdc1 expression is in the mesenchyme, suggesting that dental mesenchyme may limit supernumerary tooth induction. We tested this in wild-type incisors by minimizing the amount of mesenchymal tissue surrounding the incisor tooth germs prior to culture in vitro. The cultured teeth phenocopied the extra incisor phenotype of the Sostdc1-deficient mice. Furthermore, we showed that minimizing the amount of dental mesenchyme in cultured Sostdc1-deficient incisors caused the formation of additional de novo incisors that resembled the successional incisor development resulting from activated Wnt signaling. Sostdc1 seemed to be able to inhibit both mesenchymal BMP4 and epithelial canonical Wnt signaling, which thus allows Sostdc1 to restrict the enamel knot size and regulate the tooth shape and number. Our work emphasizes the dual role for the tooth mesenchyme as a suppressor as well as an activator during tooth development. We found that the placode, forming the thick mouse incisor, is prone to disintegration during initiation of tooth development. The balance between two mesenchymal TGF-beta family signals, BMP4 and Activin is essential in this regulation. The inhibition of BMP4 or increase in Activin signaling led to the splitting of the large incisor placode into two smaller placodes resulting in thin incisors. These two signals appeared to have different effects on tooth epithelium and the analysis of the double null mutant mice lacking Sostdc1 and Follistatin indicated that these TGF-beta inhibitors regulate the mutual balance of BMP and Activin in vivo. In addition, this work provides an alternative explanation for the issue of incisor identity published in Science by Tucker et al. in 1998 and proposes that the molar like morphology that can be obtained by inhibiting BMP signaling is due to partial splitting of the incisor placodes and not due to change in tooth identity from the incisor to the molar. This thesis work presents possible molecular mechanisms that may have modified the mouse dental pattern during evolution leading to the typical rodent dentition of modern mouse. The rodent dentition is specialized for gnawing and consists of two large continuously growing incisors and toothless diastema region separating the molars and incisors. The ancestors of rodents had higher number of more slender incisors together with canines and premolars. Additionally, murine rodents, which include the mouse, have lost their ability for tooth replacement. This work has revealed that the inhibitory molecules appear to play a role in the tooth number suppression by delineating the spatial and temporal action of the inductive signals. The results suggest that Sostdc1 plays an essential role in several stages of tooth development through the regulation of both the BMP and Wnt pathway. The work shows a dormant sequential tooth forming potential present in wild type mouse incisor region and gives a new perspective on tooth suppression by dental mesenchyme. It reveals as well a novel mechanism to create a large mouse incisor through the regulation of mesenchymal balance between inductive and inhibitory signals.

Genetic regulation of flower development

Flower development provides a model system to study mechanisms that govern pattern formation in plants. Most flowers consist of four organ types that are present in a specific order from the periphery to the centre of the flower. Reviewed here are studies on flower development in two model species: Arabidopsis thaliana and Antirrhinum majus that focus on the molecular genetic analysis of homeotic mutations affecting pattern formation in the flower. Based on these studies a model was proposed that explains how three classes of regulatory genes can together control the development of the correct pattern of organs in the flower. The universality of the basic tenets of the model is apparent from the analysis of the homologues of the Arabidopsis genes from other plant species

Effect of Surface Energy Anisotropy on the Stability of Growth Fronts in Multiphase Alloys

Eutectic growth offers a variety of examples for pattern formation which are interesting both for theoreticians as well as experimentalists. One such example of patterns is ternary eutectic colonies which arise as a result of instabilities during growth of two solid phases. Here, in addition to the two major components being exchanged between the solid phases during eutectic growth, there is an impurity component which is rejected by both solid phases. During progress of solidification, there develops a boundary layer of the third impurity component ahead of the solidification front of the two solid phases. Similar to Mullins-Sekerka type instabilities, such a boundary layer tends to make the global solidification envelope unstable to morphological perturbations giving rise to two-phase cells. This phenomenon has been studied numerically in two dimensions for the conditions of directional solidification, by Plapp and Karma (Phys Rev E 66:061608, 2002) using phase-field simulations. While, in the work by Plapp and Karma (Phys Rev E 66:061608, 2002) all interfaces are isotropic, in our presentation, we extend the phase-field model by considering interfacial anisotropy in the solid-solid and solid-liquid interfaces and characterize the role of interfacial anisotropy on the stability of the growth front through phase-field simulations in two dimensions.

Rapid electrohydrodynamic lithography using low-viscosity polymers.

This study explores a number of low-viscosity glass-forming polymers for their suitability as high-speed materials in electrohydrodynamic (EHD) lithography. The use of low-viscosity polymer films significantly reduces the patterning time (to below 10 s) compared to earlier approaches, without compromising the high fidelity of the replicated structures. The rapid pace of this process requires a method to monitor the completion of EHD pattern formation. To this end, the leakage current across the device is monitored and the sigmoidal shape of the current curve is correlated with the various stages of EHD pattern formation.

Carbon nanotube alignment via electrohydrodynamic patterning of nanocomposites

Electrohydrodynamic (EHD) pattern formation in carbon nanotube-polymer composite films yields well-defined patterns on the micrometer scale along with the alignment of carbon nanotubes (CNTs) within these patterns. Conductive pathways in nanotube networks formed during EHD patterning of nanocomposite films results in a substantial increase in the composites' conductivity at loadings exceeding the percolation threshold. The degree of nanotube alignment can be tuned by adjusting the EHD parameters and the degree of alignment is mirrored by the conductivity across the film. Using etching techniques or by embedding relatively long nanotubes, patterned surfaces decorated by CNT brushes were generated. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On properties of hyperchaos: Case study

Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as. the origin of complexity of dynamical systems.