Collective motion of binary self-propelled particle mixtures

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations, linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both, spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripe-like flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripe-like flocks. The most interesting behavior is found for the case of preferred perpendicular alignment between different species. There, a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species.Comment: 16 pages, 10 figure

Shoot development, chlorophyll, gas exchange and carbohydrates in lychee seedlings (Litchi chinensis)

Shoot growth, chlorophyll concentrations, gas exchange and starch concentrations were studied in lychee (Litchi chinensis Sonn.) seedlings of cultivar “Wai Chee” grown in a heated greenhouse at Nambour in subtropical Australia (27° S). We also examined the effects of shoot defoliation and root pruning on leaf expansion. Shoot growth showed a rhythmic cycle under constant greenhouse conditions, with a mean duration of flushing of 20 days and an interval of 10 days over three cycles. Shoots and leaves expanded in a sigmoidal pattern to about 80 mm and 500 cm2, respectively, for each flush. Starch concentrations of the lower stem and roots decreased as the young red leaves expanded, and increased as the fully expanded leaves turned dark green. Chlorophyll concentrations and net CO2 assimilation rate were highest in the fully expanded dark green leaves.Removing 50% of the area of each fully expanded leaf had little effect on the expansion of younger leaves, but total biomass of defoliated plants was only 60% of that of controls. In contrast, removing half the roots just before bud swelling reduced final leaf area by 80%. We conclude that the young shoot has relatively low rates of photoassimilation until the leaves are fully expanded and dark green, and depends on assimilates from elsewhere in the plant. During leaf expansion, translocation of assimilates to the shoot occurred at the expense of the roots

Effects of leaf, shoot and fruit development on photosynthesis of lychee trees (Litchi chinensis)

Changes in gas exchange with leaf age and fruit growth were determined in lychee trees (Litchi chinensis Sonn.) growing in subtropical Queensland (27° S). Leaves expanded in a sigmoid pattern over 50 days during spring, with net CO2 assimilation (A) increasing from –4.1 ± 0.9 to 8.3 ± 0.5 μmol m−2 s−1 as the leaves changed from soft and red, to soft and light green, to hard and dark green. Over the same period, dark respiration (Rd) decreased from 5.0 ± 0.8 to 2.0 ± 0.1 μmol CO2 m−2 s−1. Net CO2 assimilation was above zero about 30 days after leaf emergence or when the leaves were half fully expanded. Chlorophyll concentrations increased from 0.7 ± 0.2 mg g−1 in young red leaves to 10.3 ± 0.7 mg g−1 in dark green leaves, along with stomatal conductance (gs, from 0.16 ± 0.09 to 0.47 ± 0.17 mol H2O m−2 s−1).Fruit growth was sigmoidal, with maximum values of fresh mass (29 g), dry mass (6 g) and fruit surface area (39 cm2) occurring 97 to 115 days after fruit set. Fruit CO2 exchange in the light (Rl) and dark (Rd) decreased from fruit set to fruit maturity, whether expressed on a surface area (10 to 3 μmol CO2 m−2 s−1 and 20 to 3 μmol CO2 m−2 s−1, respectively) or on a dry mass basis (24 to 2 nmol CO2 g−1 s−1 and 33 to 2 nmol CO2 g−1 s−1, respectively). Photosynthesis never exceeded respiration, however, the difference between Rl and Rd was greatest in young green fruit (4 to 8 μmol CO2 m−2 s−1). About 90% of the carbon required for fruit growth was accounted for in the dry matter of the fruit, with the remainder required for respiration. Fruit photosynthesis contributed about 3% of the total carbon requirement of the fruit over the season. Fruit growth was mainly dependent on CO2 assimilation in recently expanded dark green leaves

Effects of light availability on leaf gas exchange and expansion in lychee (Litchi chinensis)

Effects of photosynthetic photon flux density (PPFD) on leaf gas exchange of lychee (Litchi chinensis Sonn.) were studied in field-grown “Kwai May Pink” and “Salathiel” orchard trees and young potted “Kwai May Pink” plants during summer in subtropical Queensland (27° S). Variations in PPFD were achieved by shading the trees or plants 1 h before measurement at 0800 h. In a second experiment, potted seedlings of “Kwai May Pink” were grown in a heated greenhouse in 20% of full sun (equivalent to maximum noon PPFD of 200 μmol m−2 s−1) and their growth over three flush cycles was compared with seedlings grown in full sun (1080 μmol m−2 s−1). Young potted plants of “Kwai May Pink” were also grown outdoors in artificial shade that provided 20, 40, 70 or 100% of full sun (equivalent to maximum PPFDs of 500, 900, 1400 and 2000 μmol m−2 s−1) and measured for shoot extension and leaf area development over one flush cycle. Net CO2 assimilation increased asymptotically in response to increasing PPFD in both orchard trees and young potted plants. Maximum rates of CO2 assimilation (11.9 ± 0.5 versus 6.3 ± 0.2 μmol CO2 m−2 s−1), dark respiration (1.7 ± 0.3 versus 0.6 ± 0.2 μmol CO2 m−2 s−1), quantum yield (0.042 ± 0.005 versus 0.027 ± 0.003 mol CO2 mol−1) and light saturation point (1155 versus 959 μmol m−2 s−1) were higher in orchard trees than in young potted plants. In potted seedlings grown in a heated greenhouse, shoots and leaves exposed to full sun expanded in a sigmoidal pattern to 69 ± 12 mm and 497 ± 105 cm2 for each flush, compared with 27 ± 7 mm and 189 ± 88 cm2 in shaded seedlings. Shaded seedlings were smaller and had higher shoot:root ratios (3.7 versus 3.1) than seedlings grown in full sun. In the potted plants grown outdoors in 20, 40, 70 or 100% of full sun, final leaf area per shoot was 44 ± 1, 143 ± 3, 251 ± 7 and 362 ± 8 cm2, respectively. Shoots were also shorter in plants grown in shade than in plants grown in full sun (66 ± 5 mm versus 101 ± 2 mm). Photosynthesis in individual leaves of lychee appeared to be saturated at about half full sun, whereas maximum leaf expansion occurred at higher PPFDs. We conclude that lychee plants can persist as seedlings on the forest floor, but require high PPFDs for optimum growth

The effect of Coulombic friction on spatial displacement statistics

The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the corresponding Fokker-Planck equation including both velocity and spatial components, exhibiting a formal connection to a quantum mechanical harmonic oscillator in the presence of a delta potential. Numerical solutions for the resulting spatial displacement statistics show a crossover from exponential to Gaussian displacement statistics. We identify a transient intermediate regime that exhibits multiscaling properties arising from the contribution of Coulombic friction. The possible role of these effects during observations in diffusion experiments is shortly discussed.Comment: 11 pages, 9 figure

Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography

Quantum state reconstruction involves measurement devices that are usually described by idealized models, but not known in full detail in experiments. For weak propagating microwaves, the detection process requires linear amplifiers which obscure the signal with random noise. Here, we introduce a theory which nevertheless allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross-correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves.Comment: 11 pages, 3 figure