Gyro-average method for global gyrokinetic particle simulation in realistic tokamak geometry

Gyro-average is a crucial operation to capture the essential finite Larmor radius effect (FLR) in gyrokinetic simulation. In order to simulate strongly shaped plasmas, an innovative multi-point average method based on non-orthogonal coordinates has been developed to improve the accuracy of the original multi-point average method in gyrokinetic particle simulation. This new gyro-average method has been implemented in the gyrokinetic toroidal code (GTC). Benchmarks have been carried out to prove the accuracy of this new method. In the limit of concircular tokamak, ion temperature gradient (ITG) instability is accurately recovered for this new method and consistency is achieved. The new gyro-average method is also used to solve the gyrokinetic Poisson equation, and its correctness has been confirmed in the long wavelength limit for realistic shaped plasmas. The improved GTC code with the new gyro-average method has been used to investigate the ITG instability with EAST magnetic geometry. The simulation results show that the correction induced by this new method in the linear growth rate is more significant for short wavelength modes where the finite Larmor radius (FLR) effect becomes important. Due to its simplicity and accuracy, this new gyro-average method can find broader applications in simulating the shaped plasmas in realistic tokamaks.

The effects of magnetic island on toroidal ion temperature gradient mode instability

In this work, we have investigated the influences of magnetic island (MI) on electrostatic toroidal ion temperature gradient (ITG) mode, where the ions are described by gyro-kinetic equations including MI, and adiabatic approximation is used for electrons. The eigen-equation for short-wavelength toroidal ITG mode in Fourier-ballooning representation is derived, and the corresponding eigen-value as well as mode structure are solved. Both the flattening effects of MI on plasma pressure and MI-scale shear flow are considered. It is found that when only considering the flattening effects of MI, ITG mode can be stabilized as compared to the case without MI. While, the effective drive of toroidal ITG mode could be enhanced by including MI-scale flow, which indicates the dominant destabilizing by MI-scale flow over the stabilizing by flattening profile and results in higher growth rate than the case without MI. It is also found that the total flow shearing may prevent the ITG turbulence spreading from X-point of MI but not strong enough to prevent spreading from the seperatrix across O-point of larger MI via comparison between the flow shearing rate and the linear growth rate. Furthermore, the corresponding width of lowest-order mode structure in ballooning angle is slightly widened (narrowed) for the case without (with) MI-scale flow, as compared to the case without MI. Besides, the shifted even symmetry in ballooning angle is not qualitatively influenced by the presence of MI. The mode structure is radially asymmetric, but is symmetric with respect to the phase of MI at the O-point.

Asymmetrical cell division with exponential growth

An advanced pantograph-type partial differential equation, supplemented with initial and boundary conditions, arises in a model of asymmetric cell division. Methods for solving such problems are limited owing to functional (nonlocal) terms. The separation of variables entails an eigenvalue problem that involves a nonlocal ordinary differential equation. We discuss plausible eigenvalues that may yield nontrivial solutions to the problem for certain choices of growth and division rates of cells. We also consider the asymmetric division of cells with linear growth rate which corresponds to "exponential growth” and exponential rate of cell division, and show that the solution to the problem is a certain Dirichlet series. The distribution of the first moment of the biomass is shown to be unimodal. doi:10.1017/S1446181121000109

Bio-safety assessment of nanozeolites of varying size and doses on soil beneficial microorganisms

Aim: To evaluate the toxic effects of nano-zeolites on soil beneficial microorganisms. Methodology: This study involved dry milling of zeolites at varying parameters to obtain dry-milled zeolites of four size regimes such as 10-100 nm, 200-400 nm, 500-1000 nm and 1000-2000 nm that were tested at incremental concentrations such as 100 ppm, 1000 ppm and 2000 ppm along with control on various soil beneficial microorganisms. Three replications were done for each treatment with factorial completely randomized design. The poison food technique, growth curve assessment followed by cytotoxicity and genotoxicity studies on all four bacterial genera treated with zeolites of varying sizes and doses were undertaken. The effects of zeolite on average linear growth rate (ALGR) of biocontrol agent, Trichoderma viride were also studied. Results: The effect of zeolites tested on four bacterial genera viz. Azotobacter chroococcum, Rhizobium leguminosarum, Bacillus megaterium and Pseudomonas fluorescens using poison food technique and growth curve revealed that zeolites regardless of size or concentration had positively influenced the growth dynamics of all four bacteria tested. The effect of zeolite on average linear growth rate (ALGR) of Trichoderma viride also indicated that incremental dose of zeolite had a positive effect. Lactose dehydrogenase revealed that 2000 ppm nano-zeolite exhibited cytotoxic effects on soil beneficial micro-organisms tested. On the other hand, comet assay demonstrated no quantifiable DNA damage in nano-zeolite treated cells in comparison to control cultures. Interpretation: This study unequivocally demonstrated that zeolites of size greater than 200-400 nm, irrespective of doses even up to 2000 ppm are quite safe for soil beneficial microbes.

EVALUATION OF LINEAR GROWTH INDICATORS OF RIVER PERCH (PERCA FLUVIATILIS L.) IN THE KUIBYSHEV RESERVOIR

This article analyzes the rate of linear growth of river perch from different ples of the Kuibyshev reservoir, and considers the possibility of identifying ecological forms of this species based on data on the growth rate. The dependence between the growth rate of fish and the hydrological characteristics of the studied areas of the reservoir is revealed. The linear growth rate of male and female river perch was compared, and sexual differences in growth were found. The rate of linear growth of perch in modern conditions of the Kuibyshev reservoir is compared with the results of other researchers.

ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH

An advanced pantograph-type partial differential equation, supplemented with initial and boundary conditions, arises in a model of asymmetric cell division. Methods for solving such problems are limited owing to functional (nonlocal) terms. The separation of variables entails an eigenvalue problem that involves a nonlocal ordinary differential equation. We discuss plausible eigenvalues that may yield nontrivial solutions to the problem for certain choices of growth and division rates of cells. We also consider the asymmetric division of cells with linear growth rate which corresponds to “exponential growth” and exponential rate of cell division, and show that the solution to the problem is a certain Dirichlet series. The distribution of the first moment of the biomass is shown to be unimodal.

Growth of Magnetorotational Instability in Circumstellar Disks around Class 0 Protostars

We investigate the possibility of the growth of magnetorotational instability (MRI) in disks around Class 0 protostars. We construct a disk model and calculate the chemical reactions of neutral and charged atoms, molecules and dust grains to derive the abundance of each species and the ionization degree of the disk. Then, we estimate the diffusion coefficients of non-ideal magnetohydrodynamics effects such as ohmic dissipation, ambipolar diffusion and the Hall effect. Finally, we evaluate the linear growth rate of MRI in each area of the disk. We investigate the effect of changes in the strength and direction of the magnetic field in our disk model and we adopt four different dust models to investigate the effect of dust size distribution on the diffusion coefficients. Our results indicate that an MRI active region possibly exists with a weak magnetic field in a region far from the protostar where the Hall effect plays a role in the growth of MRI. On the other hand, in all models the disk is stable against MRI in the region within <20 au from the protostar on the equatorial plane. Since the size of the disks in the early stage of star formation is limited to ≲ 10–20 au, it is difficult to develop MRI-driven turbulence in such disks.

EFFECT OF LINEAR GROWTH RATE AND CHANGE IN BODY MASS INDEX IN CHILDHOOD AND ADOLESCENCE ON BLOOD PRESSURE IN AFRO-CARIBBEAN YOUTH: THE VULNERABLE WINDOWS COHORT STUDY

ABSTRACTBackgroundFaster growth velocity during childhood may increase blood pressure (BP) in adults, but there are little data from African-origin populations. We evaluated the effect of postnatal linear growth (increase in height) and change in body mass index (BMI) from birth to adolescence on systolic and diastolic blood pressure (SBP and DBP) in Afro-Caribbean youth.MethodsWe used data from the Vulnerable Windows Birth Cohort Study in Jamaica. Children were followed from birth, with periodic anthropometric measurements. BP measurements started at age 1-year and every six months thereafter. Analyses used BP measurements (mmHg) from age 15-21 years. Linear growth and change in BMI measurements were calculated for: early infancy (0-6 months), late infancy (6 months - 2 years), early childhood (2-8 years), and later childhood (8-15 years). Conditional analyses were used to compute growth rates (as z-scores). Linear mixed models were used to estimate the effect of growth rates on BP.ResultsAnalyses included 365 individuals (162 males, 203 females) with mean age 16.7 years. In multivariable models, after adjustment for age, sex, birth length, gestational age and BMI at age 15 years, faster linear growth for early infancy (β=1.06, p=0.010) was significantly associated with higher SBP. For change in BMI, after adjustment for age, sex, gestational age, height and SES at birth, significant associations of higher SBP were seen for greater increase in BMI in late infancy (β=1.41, p=0.001), early childhood (β=1.22, p=0.001) and later childhood (β=0.74, p=0.035). Faster post-natal linear growth had no significant associations with DBP, but greater increase in BMI for each of the late infancy to late childhood periods was significantly associated with higher DBP. When both growth rates were modeled together, rate of change of BMI and faster linear growth in early infancy retained significance for SBP, but only change in BMI retained significance for DBP.ConclusionFaster linear growth and greater rate of increase in BMI were associated with higher SBP and DBP in Afro-Caribbean youth, but the BMI effect was stronger.

Nonlinear wave growth theory of whistler-mode chorus and hiss emissions in the magnetosphere

Nonlinear processes associated with the generation process of whistler-mode chorus emissions are summarized. The nonlinear dynamics of energetic electrons interacting with a coherent whistler-mode wave and the formation of electromagnetic electron holes or hills in the velocity phase space are described. The condition for resonant electrons to be free from the anomalous trapping at low pitch angles is obtained. In the presence of the inhomogeneity due to the frequency variation and the gradient of the magnetic field, the electron holes or hills result in resonant currents generating rising-tone emissions or falling-tone emissions, respectively. After formation of a coherent wave at a frequency of the maximum linear growth rate, triggering of the nonlinear wave growth takes place when the wave amplitude is above the threshold amplitude. The wave grows to a level close to the optimum wave amplitude as an absolute instability near the magnetic equator. The nonlinear growth rate at a position away from the equator is derived for a subtracted Maxwellian momentum distribution function with correction to the formulas in the past publications. The triggering process is repeated sequentially at progressively higher frequencies in the case of a rising-tone emission, generating subpackets forming a chorus element. With a higher plasma density as in the plasmasphere, the triggering of subpackets takes place concurrently over a wide range of frequency forming discrete hiss elements with varying frequencies. The mechanism of nonlinear wave damping due to quasi-parallel propagation from the equator is presented, which results in the formation of a gap at half the electron cyclotron frequency, separating a long rising-tone chorus emission into the upper-band and lower-band chorus emissions. The theoretical formulation of an oblique whistler mode wave and its interaction with energetic electrons at the n-th resonance is also presented along with derivation of the inhomogeneity factor.

Kinetics and mechanism of linear crystal growth in As2Se3 glass

Ранее исследовано влияние малых добавок олова и свинца на кинетические параметры изотермической объемной кристаллизации стекол на основе As2Se3. Кинетика преимущественно поверхностной кристаллизация стекла As2Se3, используемого в электронной технике и волоконной ИК оптике, изучалась методами дифференциальной сканирующей калориметрии и микроскопии. Влияние величины переохлаждения ΔТ на механизм и кинетические параметры кристаллизации стекла As2Se3 изучено недостаточно. Автором статьи выполнен теоретический анализ экспериментальных зависимостей скорости линейного роста кристаллов As2Se3 от температуры и вязкости стекла As2Se3. На основе анализа существующих данных и приводимой работы показано, что в стекле As2Se3 при переохлаждениях ΔT = 30–135 вероятен дислокационный рост кристаллов в форме сферолитов. Для индивидуальных пластинчатых кристаллов As2Se3 с бездислокационными гранями внутри сферолитов при ΔT = 75–135° вероятен механизм роста с поверхностной двумерной нуклеацией, или 2Dsg–model. Скорость линейного роста кристаллов в стекле As2Se3 при 240−345 °C теоретически рассчитывается, если в формулу Тернбала–Коэна ввести вероятностный фактор f (ТΔT) роста на ступенях винтовых дислокаций, а свободную энергию активации роста кристаллов ΔGa'' (T) принять равной кинетическому барьеру при вязком течении стекла ΔGη # (T) в уравнении Эйринга. The influence of small additions of tin and lead on the kinetic parameters of isothermal bulk crystallization of glasses based on As2Se3. The kinetics of mainly surface crystallization of As2Se3 glass used in electronic engineering and fiber IR optics has been studied by differential scanning calorimetry and microscopy. The influence of the supercooling value ΔT on the mechanism and kinetic parameters of crystallization of As2Se3 glass is not sufficiently studied, The theoretical analysis of the experimental dependences of the linear growth rate of As2Se3 crystals on the temperature and viscosity of the As2Se3 glass has been performed. In the temperature range 240–345 °С (overcooling 135°–30°), a dislocation mechanism has appeared to be probable for the linear growth of spherulites and the surface crystallized layer in the bulk As2Se3 glass. For individual crystals with dislocation-free faces in As2Se3 spherulites, the lamellar (plate-like) growth mechanism with surface two dimensional nucleation (2Dsg model) appeared to be probable. The linear growth rate in glass As2Se3 at 240–345°C can be theoretically calculated, if we introduce the probability factor f (ТΔT) to the Turnball–Cohen formula of the growth on the steps of screw dislocations and assume the free activation energy for the crystal growth ΔGa'' (T) to be equal to the kinetic barrier at the viscous flow of the glass ΔGη # (T) in the Heiring equation.