We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

Whole-grain cereal breakfast consumption has been associated with beneficial effects on glucose and insulin metabolism as well as satiety. Pearl millet is a popular ancient grain variety that can be grown in hot, dry regions. However, little is known about its health effects. The present study investigated the effect of a pearl millet porridge (PMP) compared with a well-known Scottish oats porridge (SOP) on glycaemic, gastrointestinal, hormonal and appetitive responses. In a randomised, two-way crossover trial, twenty-six healthy participants consumed two isoenergetic/isovolumetric PMP or SOP breakfast meals, served with a drink of water. Blood samples for glucose, insulin, glucagon-like peptide 1, glucose-dependent insulinotropic polypeptide (GIP), peptide YY, gastric volumes and appetite ratings were collected 2 h postprandially, followed by an ad libitum meal and food intake records for the remainder of the day. The incremental AUC (iAUC2h) for blood glucose was not significantly different between the porridges (P > 0·05). The iAUC2h for gastric volume was larger for PMP compared with SOP (P = 0·045). The iAUC2h for GIP concentration was significantly lower for PMP compared with SOP (P = 0·001). Other hormones and appetite responses were similar between meals. In conclusion, the present study reports, for the first time, data on glycaemic and physiological responses to a pearl millet breakfast, showing that this ancient grain could represent a sustainable alternative with health-promoting characteristics comparable with oats. GIP is an incretin hormone linked to TAG absorption in adipose tissue; therefore, the lower GIP response for PMP may be an added health benefit.

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) in a wall-bounded shear flow. The flow is assumed as almost inertialess. The suspension of RBCs, modelled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma, $\unicode[STIX]{x1D706}=0.1$ –10, for volume fractions up to $\unicode[STIX]{x1D719}=0.41$ and for different capillary numbers ( $Ca$ ). Our numerical results show that an RBC at low $Ca$ tends to orient to the shear plane and exhibits so-called rolling motion, a stable mode with higher intrinsic viscosity than the so-called tumbling motion. As $Ca$ increases, the mode shifts from the rolling to the swinging motion. Hydrodynamic interactions (higher volume fraction) also allow RBCs to exhibit tumbling or swinging motions resulting in a drop of the intrinsic viscosity for dilute and semi-dilute suspensions. Because of this mode change, conventional ways of modelling the relative viscosity as a polynomial function of $\unicode[STIX]{x1D719}$ cannot be simply applied in suspensions of RBCs at low volume fractions. The relative viscosity for high volume fractions, however, can be well described as a function of an effective volume fraction, defined by the volume of spheres of radius equal to the semi-middle axis of a deformed RBC. We find that the relative viscosity successfully collapses on a single nonlinear curve independently of $\unicode[STIX]{x1D706}$ except for the case with $Ca\geqslant 0.4$ , where the fit works only in the case of low/moderate volume fraction, and fails in the case of a fully dense suspension.

We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree 2q, where q is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units and allows one to recover similar formulas which have appeared in the literature. As a corollary of our main result, we obtain explicit bounds on the (finitely many) possible values which can occur as ratio of class numbers in dihedral extensions. Such bounds are obtained by arithmetic means, without resorting to deep integral representation theory.

There is an unprecedented demand for bushmeat in large cities in sub-Saharan Africa, and this is a major threat to many species. We conducted 2,040 interviews in six cities in four West African countries, in forest and savannah settings. We analysed age- and sex-related differences in the frequency of bushmeat consumption. Overall, we found similar patterns in all cities: 62.2% of men and 72.1% of women said they would never eat bushmeat, whereas 12.8% of men and 8.8% of women said they liked bushmeat and ate it regularly. Younger generations of both sexes tended not to eat bushmeat, regardless of their city of origin. This study of the effects of age, gender and geographical location on bushmeat consumption in African cities provides insights regarding which population groups to target in campaigns to change behaviours.

We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl’s secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity.

The silver fly Leucopis glyphinivora Tanasijtshuk (Diptera: Chamaemyiidae) is an aphidophagous predator during its larval stage. Our study describes the life cycle of L. glyphinivora and evaluates its potential as a biocontrol agent. The development, survival and longevity of L. glyphinivora were observed and compared with those of the aphid gall midge Aphidoletes aphidimyza Rondani (Diptera: Cecidomyiidae). Tests were conducted under laboratory conditions in Petri dishes with the green peach aphid Myzus persicae Sulzer (Hemiptera: Aphididae) on potato leaves. Leucopis glyphinivora has a 42% longer life cycle than A. aphidimyza. Larval development was 27% longer in L. glyphinivora than in A. aphidimyza. Egg hatch rate and pupal emergence rate were similar in both species, but larval survival was 20% lower for L. glyphinivora than for A. aphidimyza. Sex ratio was approximately 50% in both species. A longer development time for L. glyphinivora in the larval stage could be an advantage for biocontrol by providing more time to exert predation pressure against aphids. However, this may be offset by the lower survival rate found in the silver fly larvae.

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier–Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.

The commentaries on our target article are insightful and constructive. There were some critical notes, but many commentaries agreed with, or even amplified our message. The first section of our response addresses comments pertaining to specific parts of the target article. The second section provides a response to the commentaries' suggestions to make replication mainstream. The final section contains concluding remarks.

An ostracode fauna is described from lacustrine sediments of the Hettangian, Lower Jurassic, Whitmore Point Member of the Moenave Formation. The Moenave is well known for its rich, Late Triassic?–Early Jurassic fossil record, which includes fossil fishes, stromatolites, ostracodes, spinicaudatans, and a diverse ichnofauna of invertebrates and vertebrates. Four ostracode species, all belonging to the suborder Darwinulocopina, were recovered from these sediments: Suchonellina globosa, S. stricta, Whipplella? sp. 1, and W.? sp. 2. The diversity and composition of the Whitmore Point Member ostracode fauna agree with previous interpretations about Lake Dixie and nearby paleoenvironments as shallow lakes inhabited by darwinulocopine species that survived the effects of the Central Atlantic Magmatic Province and the subsequent end-Triassic extinction and quickly recolonized these areas, thanks to asexual reproduction by parthenogenesis. The Lake Dixie region, in its geographical isolation, could represent the last episode of darwinulocopine dominance in nonmarine environments before the Late Jurassic diversification of the cypridocopine/cytherocopine modern ostracodes.

We obtain a nontrivial upper bound for almost all elements of the sequences of real numbers which are multiplicative and at the prime indices are distributed according to the Sato–Tate density. Examples of such sequences come from coefficients of several L-functions of elliptic curves and modular forms. In particular, we show that |τ(n)| ⩽ n11/2(logn)−1/2+o(1) for a set of n of asymptotic density 1, where τ(n) is the Ramanujan τ function while the standard argument yields log 2 instead of −1/2 in the power of the logarithm. Another consequence of our result is that in the number of representations of n by a binary quadratic form one has slightly more than square-root cancellations for almost all integers n.

In addition, we obtain a central limit theorem for such sequences, assuming a weak hypothesis on the rate of convergence to the Sato–Tate law. For Fourier coefficients of primitive holomorphic cusp forms such a hypothesis is known conditionally and might be within reach unconditionally using the currently established potential automorphy.

For a positive integer $n$ let

$$\begin{eqnarray}\mathfrak{P}_{n}=\mathop{\prod }_{\substack{ p \\ s_{p}(n)\geqslant p}}p,\end{eqnarray}$$

$p$

$s_{p}(n)$

$p$

$n$

$n$

$\mathfrak{P}_{n}$

$\mathfrak{P}_{n}$

$\sqrt{n}$

$n^{20/37}$

$\sqrt{n}$

$\unicode[STIX]{x1D705}\sqrt{n}/\text{log}\,n$

$\unicode[STIX]{x1D705}$

$\unicode[STIX]{x1D705}=2$

$\mathfrak{P}_{n}$

$\mathfrak{P}_{n+1}$

$\mathfrak{P}_{n}$

$n$

$\mathfrak{P}_{n}>\mathfrak{P}_{n+1}$

The effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than 20 % by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall-normal velocity at the interface while promoting an increase of the tangential slip velocity leading to an almost ‘one-component’ turbulence where the low- and high-speed streak coherence is strongly enhanced. On the other hand, strong drag increase is found when high wall-normal and low wall-parallel permeabilities are prescribed. In this condition, the enhancement of the wall-normal fluctuations due to the reduced wall-blocking effect triggers the onset of structures which are strongly correlated in the spanwise direction, a phenomenon observed by other authors in flows over isotropic porous layers or over ribletted walls with large protrusion heights. The use of anisotropic porous walls for drag reduction is particularly attractive since equal gains can be achieved at different Reynolds numbers by rescaling the magnitude of the permeability only.

Nine species of the gall-associated doryctine genus Allorhogas Gahan (Hymenoptera: Braconidae) are described from Brazil (A. clidemiae Martínez and Zaldívar-Riverón new species, A. granivorus Zaldívar-Riverón and Martínez new species, A. mineiro Zaldívar-Riverón and Martínez new species, and A. vulgaris Zaldívar-Riverón and Martínez new species) and Costa Rica (A. brevithorax Zaldívar-Riverón and Martínez new species, A. pallidus Martínez and Zaldívar-Riverón new species, A. psychotria Zaldívar-Riverón and Martínez new species, A. punctatus Martínez and Zaldívar-Riverón new species, and A. tico Martínez and Zaldívar-Riverón new species). We provide host plant records for the described species, including information that reveals that at least three of them feed on seeds. Allorhogas granivorus had previously been confirmed to represent a natural enemy of the invasive weed Miconia calvescens de Candolle (Melastomataceae). Updated keys to the species of Allorhogas from Brazil and Costa Rica are provided.

In the current work, we evaluate the influence of the processing parameters on the electrical properties of aluminium zinc oxide (AZO) thin films produced by airbrush spray-pyrolysis deposition technique. Spray-deposited AZO thin-films were produced with Al:Zn molar ratios varying from 0 % (pure ZnO) up to 30 %, using aluminium acetate and zinc acetate as organic precursors and water as solvent. Thermogravimetric analysis (TGA) and infrared spectroscopy (FTIR-ATR) were used to monitor the metal-oxide formation from the organic precursors as a function of the temperature. The results show that a temperature of 400 °C is necessary to completely degrade the organic phase and to obtain the desired inorganic metal-oxides films. The electrical properties of the TMOs were evaluated by d.c. current-voltage (I-V) analysis using planar thermally evaporated Al electrodes on top of the TMO layer, with different aspect ratios (1/18, 2/9, 5/13, 5/9 and 8/9). The lowest sheet resistance was obtained for AZO films at a molar Al concentration of 5 %. We also observed that, after carrying out a post-annealing treatment (30 mbar, 150 °C) the samples presented a decrease on the sheet resistance superior to 60 %, in comparison to the samples before the treatment.