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We study passive scalar fluctuations convected by statistically stationary homogeneous isotropic turbulence under a uniform mean scalar gradient. In order to elucidate the parameter dependence of small-scale statistics of scalar fluctuations, we conduct direct numerical simulations of passive scalar turbulence with 59 different combinations of Reynolds number and Schmidt number. For all the cases, we compute time-average statistics of various quantities, which include the scalar derivative skewness and flatness, the ratio of parallel-to-perpendicular scalar-gradient variances, and the anisotropy parameter recently proposed (Hill, Phys. Rev. Fluids, vol. 2, 2017, 094601). Notably, the degree of small-scale anisotropy of passive scalar fluctuation is characterised by a universal function of the Péclet number
is the root mean square velocity,
the Taylor microscale of scalar fluctuation,
the mass diffusivity. In the definition of the Péclet number, the use of
, rather than the Taylor microscale of velocity fluctuation, is key to collapsing the data of different Reynolds and Schmidt numbers. When the Péclet number is low, large-scale anisotropic scalar structures emerge irrespective of the Reynolds number. These structures are elongated along the direction of the uniform mean scalar gradient, and their size is significantly larger than the integral length scale of velocity fluctuation.
Patients with schizophrenia show a significantly higher frequency of hyperbilirubinemia the patients suffering from other psychiatric disorders and the general healthy population. The objective of the current study was to determine whether patients with schizophrenia-associated idiopathic unconjugated hyperbilirubinemia (Gilbert's syndrome, GS) have specific changes in signal intensities on fluid-attenuated inversion-recovery (FLAIR) magnetic resonance (MR) images.
Axial 5-mm-thick FLAIR MR images from schizophrenia patients with GS (n = 18) and schizophrenia patients without GS (n = 18), all diagnosed according to DSM-IV criteria, were compared with age- and sex-matched non-psychiatric controls (n = 18). Signal intensities in the hippocampus, amygdala, caudate, putamen, thalamus, cingulate gyrus, and insula were graded relative to cortical signal intensity in the frontal lobe.
Compared to both schizophrenia patients without GS and normal controls, the schizophrenia patients with GS showed significantly increased signal intensities in almost all regions studied.
Patients with schizophrenia-associated GS have specific changes of signal intensities on FLAIR MR images, suggesting that schizophrenia with GS produces changes in the fronto-temporal cortex, limbic system, and basal ganglia.
We prove an analogue of Belyi’s theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called pseudo-tameness for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a ‘pseudo-tame’ rational function by showing the vanishing of an obstruction class. Finally, we construct a tamely ramified rational function from the ‘pseudo-tame’ rational function.
Turbulent vortex dynamics is investigated in triply periodic turbulent flow with Kida’s high symmetry (Kida, J. Phys. Soc. Japan, vol. 54, 1985, pp. 2132–2136) by means of unstable periodic motion representing both the statistical and dynamical properties of turbulence (van Veen et al., Fluid Dyn. Res., vol. 38, 2006, pp. 19–46). In the periodic motion, the large-scale columnar vortices, the smaller-scale vortices and the large-amplitude axial waves on the large-scale columnar vortices are detected. In terms of mutual dynamical interaction between the large-scale columnar vortices and smaller-scale vortices, we demonstrate a cyclic process of excitation of the axial waves, which leads to large-amplitude fluctuations of the total kinetic energy and enstrophy. This cyclic process is characterised by three distinct phases and is therefore reminiscent of the regeneration cycle of near-wall turbulence structures (Hamilton et al., J. Fluid Mech., vol. 287, 1995, pp. 317–348). Notably, such oscillatory behaviour is observed even in freely decaying turbulence as a consequence of the instantaneous energy transfer from smaller to larger scales.
Sexual differences in behaviours are often affected by the difference in individual interests between the sexes: growth in males and egg production in females. Some hermit crabs show sexual differences in shell use patterns during the reproductive season. In the non-reproductive season, however, when both sexes are focused on increasing growth, this sexual difference is expected to be reduced. In this study, we compared the pattern of shell use in the hermit crab Pagurus minutus between seasons, while focusing on the effects of shell shape on growth or egg production. As we predicted, sexual differences in shell use in P. minutus showed seasonal change. In the non-reproductive season, both sexes appeared to use shells well suited for growth. In the reproductive season, sexual differences became more evident, especially in larger solitary crabs and guarding pairs; males monopolized round-type shells such as those of Umbonium moniliferum, whereas more than 80% of females relied on high-spired Batillaria-type shells such as those of Batillaria zonalis. A lack of advantage for egg number in females using Batillaria-type shells suggests that female shell use is explained by factors other than maximizing clutch size. Both sexes can moult during the reproductive season, and larger body size is advantageous for reproduction. Given that Batillaria-type shells resulted in a lower growth increment and males have an advantage in shell fights in congeneric crabs, our findings suggest the importance of intersexual competition for shells and female compromise in determining the seasonal change of shell use patterns in P. minutus.
In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative term, the spatial turbulent transport of fluctuating energy and the pressure–velocity term. These fluctuations are correlated with each other and with the intense intermittent fluctuations of the interscale energy transfer rate. These correlations are caused by the sweeping effect, the link between nonlinearity and non-locality, and also relate to geometrical alignments between the two-point fluctuating pressure force difference and the two-point fluctuating velocity difference in the case of the correlation between the interscale transfer rate and the pressure–velocity term. All these processes are absent from the spatio-temporal-average picture of the turbulence cascade in statistically stationary and homogeneous turbulence.