Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known

Generalised dimensions of measures on almost self-affine sets

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees

Emergent behavior of soil fungal dynamics:influence of soil architecture and water distribution

Macroscopic measurements and observations in two-dimensional soil-thin sections indicate that fungal hyphae invade preferentially the larger, air-filled pores in soils. This suggests that the architecture of soils and the microscale distribution of water are likely to influence significantly the dynamics of fungal growth. Unfortunately, techniques are lacking at present to verify this hypothesis experimentally, and as a result, factors that control fungal growth in soils remain poorly understood. Nevertheless, to design appropriate experiments later on, it is useful to indirectly obtain estimates of the effects involved. Such estimates can be obtained via simulation, based on detailed micron-scale X-ray computed tomography information about the soil pore geometry. In this context, this article reports on a series of simulations resulting from the combination of an individual-based fungal growth model, describing in detail the physiological processes involved in fungal growth, and of a Lattice Boltzmann model used to predict the distribution of air-liquid interfaces in soils. Three soil samples with contrasting properties were used as test cases. Several quantitative parameters, including Minkowski functionals, were used to characterize the geometry of pores, air-water interfaces, and fungal hyphae. Simulation results show that the water distribution in the soils is affected more by the pore size distribution than by the porosity of the soils. The presence of water decreased the colonization efficiency of the fungi, as evinced by a decline in the magnitude of all fungal biomass functional measures, in all three samples. The architecture of the soils and water distribution had an effect on the general morphology of the hyphal network, with a "looped" configuration in one soil, due to growing around water droplets. These morphologic differences are satisfactorily discriminated by the Minkowski functionals, applied to the fungal biomass

Parametrization of global attractors experimental observations and turbulence

This paper is concerned with rigorous results in the theory of turbulence and fluid flow. While derived from the abstract theory of attractors in infinite-dimensional dynamical systems, they shed some light on the conventional heuristic theories of turbulence, and can be used to justify a well-known experimental method. Two results are discussed here in detail, both based on parametrization of the attractor. The first shows that any two fluid flows can be distinguished by a sufficient number of point observations of the velocity. This allows one to connect rigorously the dimension of the attractor with the Landau–Lifschitz ‘number of degrees of freedom’, and hence to obtain estimates on the ‘minimum length scale of the flow’ using bounds on this dimension. While for two-dimensional flows the rigorous estimate agrees with the heuristic approach, there is still a gap between rigorous results in the three-dimensional case and the Kolmogorov theory. Secondly, the problem of using experiments to reconstruct the dynamics of a flow is considered. The standard way of doing this is to take a number of repeated observations, and appeal to the Takens time-delay embedding theorem to guarantee that one can indeed follow the dynamics ‘faithfully’. However, this result relies on restrictive conditions that do not hold for spatially extended systems: an extension is given here that validates this important experimental technique for use in the study of turbulence. Although the abstract results underlying this paper have been presented elsewhere, making them specific to the Navier–Stokes equations provides answers to problems particular to fluid dynamics, and motivates further questions that would not arise from within the abstract theory itself

Being Moved by the Self and Others: Influence of Empathy on Self-Motion Perception

Background: The observation of conspecifics influences our bodily perceptions and actions: Contagious yawning, contagious itching, or empathy for pain, are all examples of mechanisms based on resonance between our own body and others. While there is evidence for the involvement of the mirror neuron system in the processing of motor, auditory and tactile information, it has not yet been associated with the perception of self-motion. Methodology/Principal Findings: We investigated whether viewing our own body, the body of another, and an object in motion influences self-motion perception. We found a visual-vestibular congruency effect for self-motion perception when observing self and object motion, and a reduction in this effect when observing someone else's body motion. The congruency effect was correlated with empathy scores, revealing the importance of empathy in mirroring mechanisms. Conclusions/Significance: The data show that vestibular perception is modulated by agent-specific mirroring mechanisms. The observation of conspecifics in motion is an essential component of social life, and self-motion perception is crucial for the distinction between the self and the other. Finally, our results hint at the presence of a “vestibular mirror neuron system”

Combination of techniques to quantify the distribution of bacteria in their soil microhabitats at different spatial scales

To address a number of issues of great societal concern at the moment, like the sequestration of carbon, information is direly needed about interactions between soil architecture and microbial dynamics. Unfortunately, soils are extremely complex, heterogeneous systems comprising highly variable and dynamic micro-habitats that have significant impacts on the growth and activity of inhabiting microbiota. Data remain scarce on the influence of soil physical parameters characterizing the pore space on the distribution and diversity of bacteria. In this context, the objective of the research described in this article was to develop a method where X-ray microtomography, to characterize the soil architecture, is combined with fluorescence microscopy to visualize and quantify bacterial distributions in resin-impregnated soil sections. The influence of pore geometry (at a resolution of 13.4 μm) on the distribution of Pseudomonas fluorescens was analysed at macro- (5.2 mm × 5.2 mm), meso- (1 mm × 1 mm) and microscales (0.2 mm × 0.2 mm) based on an experimental setup simulating different soil architectures. The cell density of P. fluorescens was 5.59 x 107(SE 2.6 x 106) cells g−1 soil in 1–2 mm and 5.84 x 107(SE 2.4 x 106) cells g−1 in 2–4 mm size aggregates soil. Solid-pore interfaces influenced bacterial distribution at micro- and macroscale, whereas the effect of soil porosity on bacterial distribution varied according to three observation scales in different soil architectures. The influence of soil porosity on the distribution of bacteria in different soil architectures was observed mainly at the macroscale, relative to micro- and mesoscales. Experimental data suggest that the effect of pore geometry on the distribution of bacteria varied with the spatial scale, thus highlighting the need to consider an “appropriate spatial scale” to understand the factors that regulate the distribution of microbial communities in soils. The results obtained to date also indicate that the proposed method is a significant step towards a full mechanistic understanding of microbial dynamics in structured soils

The effect of internal gravity waves on cloud evolution in sub-stellar atmospheres

Context. Sub-stellar objects exhibit photometric variability which is believed to be caused by a number of processes such as magnetically-driven spots or inhomogeneous cloud coverage. Recent sub-stellar models have shown that turbulent flows and waves, including internal gravity waves, may play an important role in cloud evolution.Aims. The aim of this paper is to investigate the effect of internal gravity waves on dust cloud nucleation and dust growth, and whether observations of the resulting cloud structures could be used to recover atmospheric density information.Methods. For a simplified atmosphere in two dimensions, we numerically solve the governing fluid equations to simulate the effect on dust nucleation and mantle growth as a result of the passage of an internal gravity wave. Furthermore, we derive an expression that relates the properties of the wave-induced cloud structures to observable parameters in order to deduce the atmospheric density.Results. Numerical simulations show that the density, pressure and temperature variations caused by gravity waves lead to an increase of dust nucleation by up to a factor 20, and dust mantle growth rate by up to a factor 1:6, compared to their equilibrium values. Through an exploration of the wider sub-stellar parameter space, we show that in absolute terms, the increase in dust nucleation due to internal gravity waves is stronger in cooler (T dwarfs) and TiO2-rich sub-stellar atmospheres. The relative increase however is greater in warm(L dwarf) and TiO2-poor atmospheres due to conditions less suited for efficient nucleation at equilibrium. These variations lead to banded areas in which dust formation is much more pronounced, and lead to banded cloud structures similar to those observed on Earth. Conclusions. Using the proposed method, potential observations of banded clouds could be used to estimate the atmospheric density of sub-stellar objects