When does cyclic dominance lead to stable spiral waves?

Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion

Downward pumping of magnetic flux as the cause of filamentary structures in sunspot penumbrae

The structure of a sunspot is determined by the local interaction between magnetic fields and convection near the Sun's surface. The dark central umbra is surrounded by a filamentary penumbra, whose complicated fine structure has only recently been revealed by high-resolution observations. The penumbral magnetic field has an intricate and unexpected interlocking-comb structure and some field lines, with associated outflows of gas, dive back down below the solar surface at the outer edge of the spot. These field lines might be expected to float quickly back to the surface because of magnetic buoyancy, but they remain submerged. Here we show that the field lines are kept submerged outside the spot by turbulent, compressible convection, which is dominated by strong, coherent, descending plumes. Moreover, this downward pumping of magnetic flux explains the origin of the interlocking-comb structure of the penumbral magnetic field, and the behaviour of other magnetic features near the sunspot

Characterization of spiraling patterns in spatial rock-paper-scissors games

The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising “rock-paper-scissors” interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allow us to clarify when spatial “rock-paper-scissors” competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility

Chaos in magnetoconvection

The partial differential equations (PDEs) for two-dimensional incompressible convection in a strong vertical magnetic field have a codimension-three bifurcation when the parameters are chosen so that the bifurcations to steady and oscillatory convection coincide and the limit of narrow rolls is taken. The third-order set of ordinary differential equations (ODEs) that govern the behaviour of the PDEs near this bifurcation are derived using perturbation theory. These ODEs are the normal form of the codimension-three bifurcation; as such, they prove to be an excellent predictor of the behaviour of the PDEs. This is the first time that a detailed comparison has been made between the chaotic behaviour of a set of PDEs and that of the corresponding set of model ODEs, in a parameter regime where the ODEs are expected to provide accurate approximations to solutions of the PDEs. Most significantly, the transition from periodic orbits to a chaotic Lorenz attractor predicted by the ODEs is recovered in the PDEs, making this one of the few situations in which the nature of chaotic oscillations observed numerically in PDEs can be established firmly. Including correction terms obtained from the perturbation calculation enables the ODEs to track accurately the bifurcations in the PDEs over an appreciable range of parameter values. Numerical calculations suggest that the T-point (where there are heteroclinic connections between a saddle point and a pair of saddle-foci), which is associated with the transition from a Lorenz attractor to a quasi-attractor in the normal form, is also found in the PDEs. Further numerical simulations of the PDEs with square rolls confirm the existence of chaotic oscillations associated with a heteroclinic connection between a pair of saddle-foci

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic

Nearly inviscid Faraday waves

Many powerful techniques from Hamiltonian mechanics are available for the study of ideal hydrodynamics. This article explores some of the consequences of including small viscosity in a study of surface gravity-capillary waves excited by the vertical vibration of a container. It is shown that in this system, as in others, the addition of small viscosity provides a singular perturbation of the ideal fluid system, and that as a result its effects are nontrivial. The relevance of existing studies of ideal fluid problems is discussed from this point of view

Autism Symptoms and Internalizing Psychopathology in Girls and Boys with Autism Spectrum Disorders

Findings regarding phenotypic differences between boys and girls with ASD are mixed. We compared autism and internalizing symptoms in a sample of 8-18 year-old girls (n = 20) and boys (n = 20) with ASD and typically developing (TYP) girls (n = 19) and boys (n = 17). Girls with ASD were more impaired than TYP girls but did not differ from boys with ASD in autism symptoms. In adolescence, girls with ASD had higher internalizing symptoms than boys with ASD and TYP girls, and higher symptoms of depression than TYP girls. Girls ages 8-18 with ASD resemble boys with ASD and not TYP girls, and appear to be at increased risk for affective symptoms in the teen years

Diversidade de resultados no estudo do transtorno de déficit de atenção e hiperatividade

Com este artigo pretende-se abordar a problemática da diversidade de dados na investigação do Transtorno de Déficit de Atenção e Hiperatividade (TDAH). Apresenta-se uma revisão da literatura centrada na heterogeneidade de conclusões relativas à caracterização do transtorno, à distinção dos subtipos, aos contextos de informação, às diferenças de gênero e à comorbidade. Na tentativa de compreender a disparidade de conclusões, salientam-se potenciais fatores explicativos, nomeadamente a heterogeneidade das amostras, a diversidade de metodologias e de procedimentos de investigação, entre outros.With this paper we aimed at addressing the problem of data diversity in Attention-Deficit Hyperactivity Disorder (ADHD) research. We present a literature review based on the heterogeneity of findings about the characterization of the disorder, subtypes differentiation, sources of information, sex differences and comorbidities. In an effort to understand the variety of findings, we underline potential explanations, such as the sample’s heterogeneity or the multiplicity of methods and procedures, among others.(undefined

Are motor inhibition and cognitive flexibility dead ends in ADHD?

Contains fulltext : 53518.pdf (publisher's version ) (Closed access)Executive dysfunction has been postulated as the core deficit in ADHD, although many deficits in lower order cognitive processes have also been identified. By obtaining an appropriate baseline of lower order cognitive functioning light may be shed on as to whether executive deficits result from problems in lower order and/or higher order cognitive processes. We examined motor inhibition and cognitive flexibility in relation to a baseline measure in 816 children from ADHD and control families. Multiple children in a family were tested in order to examine the familiality of the measures. No evidence was found for deficits in motor inhibition or cognitive flexibility in children with ADHD or their nonaffected siblings: Compared to their baseline speed and accuracy of responding, children with ADHD and their (non)affected siblings were not disproportionally slower or inaccurate when demands for motor inhibition or cognitive flexibility were added to the task. However, children with ADHD and their (non)affected siblings were overall less accurate than controls, which could not be attributed to differences in response speed. This suggests that inaccuracy of responding is characteristic of children having (a familial risk for) ADHD. Motor inhibition and cognitive flexibility as operationalized with mean reaction time were found to be familial. It is concluded that poorer performance on executive tasks in children with ADHD and their (non)affected siblings may result from deficiencies in lower order cognitive processes and not (only) from higher order cognitive processes/executive functions