Tracking bifurcating solutions of a model biological pattern generator

We study heterogeneous steady-state solutions of a cell-chemotaxis model for generating biological spatial patterns in two-dimensional domains with zero flux boundary conditions. We use the finite-element package ENTWIFE to investigate bifurcation from the uniform solution as the chemotactic parameter varies and as the domain scale and geometry change. We show that this simple cell-chemotaxis model can produce a remarkably wide and surprising range of complex spatial patterns

Competition of spatial and temporal instabilities under time delay near codimension-two Turing-Hopf bifurcations

Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes. The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realize the control of the transformation between the Turing and Hopf patterns. Two dimensional numerical simulations validate the analytical results.Comment: 13 pages, 6 figure

Boundary-driven instability

We analyse a reaction-diffusion system and show that complex spatial patterns can be generated by imposing Dirichlet boundary conditions on one or more of the reactant concentrations. This pattern persists even when the homogeneous steady state with Neumann conditions is stable

Scoping the impact of tidal and wave energy extraction on suspended sediment concentrations and underwater light climate

The depth to which sunlight penetrates below the sea surface is one of the key factors determining the species composition and productivity of marine ecosystems. The effects range from the rate and fate of primary production, through the performance of visual predators such as fish, the potential for refuge from predators by migrating to depth, to the scope for seabed stabilisation by algal mats. Light penetration depends partly on spectral absorption by seawater and dissolved substances, but mainly on the scattering caused by suspended particulate material (SPM). Some of this SPM may be of biological origin, but in coastal waters the majority is mineral material originating ultimately from seabed disturbance and land erosion, the latter being deposited in the sea by rivers and aerial processes. SPM is maintained in the water column or deposited on the seabed depending on combinations of hydrodynamic processes including baroclinic (density-driven) or barotropic (mainly tidal and wind driven) currents, and wave action (Ward et al. 1984; Huettel et al. 1996). Since tidal and wave energy extraction must alter these hydrodynamic properties at some scales depending on the nature of the extraction process, we can expect some kind of impact on the concentration of the SPM. If these are large enough, we may have to consider the extent to which these may impact the underwater light environment and the local or regional ecology. Whilst several coupled hydrodynamic-sediment models exist to predict SPM distributions in aquatic systems, their skill level in open coastal and offshore marine waters is acknowledged to be relatively low. This is largely because the processes are not well understood and the formulations are largely based on empirical relationships rather than fundamental physical principles. The models are also highly demanding in terms of calibration data and computational resources. Hence their utility for predicting relatively subtle effects arising from changes in flow or wave environments due to energy extraction devices seems rather low. Here, we summarise the key mathematical functions describing the processes involved in sediment suspension, and propose a lightweight one-dimensional (vertical) model which can be used to scope the effects of changes in flow and wave energy on SPM

The quantum information manifold for epsilon-bounded forms

Let H be a self-adjoint operator bounded below by 1, and let V be a small form perturbation such that RVS has finite norm, where R is the resolvent at zero to the power 1/2 +epsilon, and S is the resolvent to the power 1/2-epsilon. Here, epsilon lies between 0 and 1/2. If the Gibbs state defined by H is sufficiently regular, we show that the free energy is an analytic function of V in the sense of Frechet, and that the family of density operators defined in this way is an analytic manifold modelled on a Banach space.Comment: 12 pages, report to Torun Conference, 199

Spatio-temporal patterns generated by Salmonella typhimurium

We present experimental results on the bacterium Salmonella typhimurium which show that cells of chemotactic strains aggregate in response to gradients of amino acids, attractants that they themselves excrete. Depending on the conditions under which cells are cultured, they form periodic arrays of continuous or perforated rings, which arise sequentially within a spreading bacterial lawn. Based on these experiments, we develop a biologically realistic cell-chemotaxis model to describe the self-organization of bacteria. Numerical and analytical investigations of the model mechanism show how the two types of observed geometric patterns can be generated by the interaction of the cells with chemoattractant they produce

Single-grain and multi-grain OSL dating of river terrace sediments in the Tabernas Basin, SE Spain

River terraces represent important records of landscape response to e.g. base-level change and tectonic movement. Both these driving forces are important in the southern Iberian Peninsula. In this study, Optically Stimulated Luminescence (OSL) dating was used to date two principal river terraces in the Tabernas Basin, SE Spain. A total of 23 samples was collected from the fluvial terraces for dating using quartz OSL. Sixteen of the samples could not be dated because of low saturation levels (e.g. typical 2xD0 < 50 Gy). The remaining seven samples (5 fossil and 2 modern analogues) were investigated using both multi-grain and single-grain analysis. Single grain results show that: (i) measurements from multi-grain aliquots overestimate ages by up to ∼ 4 ka for modern analogues and young samples (<5 ka), presumably because (ii) the presence of many saturated grains has biased the multi-grain results to older ages. Despite the unfavourable luminescence characteristics we are able to present the first numerical ages for two terrace aggradation stages in the Tabernas Basin, one at ∼16 ka and the other within the last 2 ka

A Novel Adaptation of a Parent-Child Observational Assessment Tool for Appraisals and Coping in Children Exposed to Acute Trauma

Background: Millions of children worldwide are exposed to acute potentially traumatic events (PTEs) annually. Many children and their families experience significant emotional distress and/or functional impairment following PTEs. While current research has begun to highlight a role for early appraisals and coping in promoting or preventing full recovery from PTEs, the exact nature of the relationships among appraisals, coping, and traumatic stress reactions as well as how appraisals and coping behaviors are influenced by the child\u27s environment (e.g., parents) remains unclear; assessment tools that reach beyond self-report are needed to improve this understanding. Objective: The objective of the current study is to describe the newly created Trauma Ambiguous Situations Tool (TAST; i.e., an observational child–parent interview and discussion task that allows assessment of appraisals, coping, and parent–child processes) and to report on initial feasibility and validation of TAST implemented with child–parent dyads in which children were exposed to a PTE. Method: As part of a larger study on the role of biopsychosocial factors in posttraumatic stress reactions, children (aged 8–13) and parents (n=25 child–parent dyads) completed the TAST during the child\u27s hospitalization for injury. Results: Children and parents engaged well with the TAST. The time to administer the TAST was feasible, even in a peri-trauma context. The TAST solicited a wide array of appraisals (threat and neutral) and coping solutions (proactive and avoidant). Forced-choice and open-ended appraisal assessments provided unique information. The parent–child discussion portion of the TAST allowed for direct observation of parent–child processes and demonstrated parental influence on children\u27s appraisals and coping solutions. Conclusions: The TAST is a promising new research tool, which may help to explicate how parents influence their child\u27s developing appraisals and coping solutions following a PTE. More research should examine the relationships of appraisals, coping, and parent–child processes assessed by the TAST with traumatic stress outcomes

The Christiansen Effect in Saturn's narrow dusty rings and the spectral identification of clumps in the F ring

Stellar occultations by Saturn's rings observed with the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveal that dusty features such as the F ring and the ringlets in the Encke and the Laplace Gaps have distinctive infrared transmission spectra. These spectra show a narrow optical depth minimum at wavelengths around 2.87 microns. This minimum is likely due to the Christiansen Effect, a reduction in the extinction of small particles when their (complex) refractive index is close to that of the surrounding medium. Simple Mie-scattering models demonstrate that the strength of this opacity dip is sensitive to the size distribution of particles between 1 and 100 microns across. Furthermore, the spatial resolution of the occultation data is sufficient to reveal variations in the transmission spectra within and among these rings. For example, in both the Encke Gap ringlets and F ring, the opacity dip weakens with increasing local optical depth, which is consistent with the larger particles being concentrated near the cores of these rings. The strength of the opacity dip varies most dramatically within the F ring; certain compact regions of enhanced optical depth lack an opacity dip and therefore appear to have a greatly reduced fraction of grains in the few-micron size range.Such spectrally-identifiable structures probably represent a subset of the compact optically-thick clumps observed by other Cassini instruments. These variations in the ring's particle size distribution can provide new insights into the processes of grain aggregation, disruption and transport within dusty rings. For example, the unusual spectral properties of the F-ring clumps could perhaps be ascribed to small grains adhering onto the surface of larger particles in regions of anomalously low velocity dispersion.Comment: 42 pages, 15 figures, accepted for publication in Icarus. A few small typographical errors fixed to match correction in proof

Higher-Dimensional Twistor Transforms using Pure Spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (Euclidean) dimension d=2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on R^{2n}. For d=4 and d=6, these spaces are CP^1 and CP^3, and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d>6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations.Comment: 17 pages harvmac tex. Modified title, abstract, introduction and references to acknowledge earlier papers by Hughston and other