Investigating tree and fruit growth through functional–structural modelling: implications of carbon autonomy at different scales

Background and Aims Many experimental studies assume that some topological units are autonomous with regard to carbon because it is convenient. Some plant models simulate carbon allocation, employing complex approaches that require calibration and fitted parameters. For whole-tree canopy simulations, simpler carbon allocation models can provide useful insights. Methods We propose a new method for simulating carbon allocation in the whole tree canopy considering various scales of carbon autonomy, i.e. branchlets, branches, limbs, and no autonomy. This method was implemented in a functional–structural plant model of growth of individual organs for studying macadamia tree growth during one growing season. Key Results This model allows the simulation of various scales of carbon autonomy in a simple tree canopy, showing organ within-tree variability according to the scale of autonomy. Using a real tree canopy, we observed differences in growth variability within the tree and in tree growth, with several scales of carbon autonomy. The simulations that assumed autonomy at branch scale, i.e. 2-year-old wood, showed the most realistic results. Conclusions Simulations using this model were employed to investigate and explain aspects of differences in carbon autonomy between trees, organ growth variability, competition between shoot and fruit growth, and time of autonomy.

Effect of Street Canyon Shape and Tree Layout on Pollutant Diffusion under Real Tree Model

Trees have a significant impact on the airflow and pollutant diffusion in the street canyon and are directly related to the comfort and health of residents. In this paper, OpenFOAM is used for simulating the airflow and pollutant diffusion in the street canyon at different height–width ratios and tree layouts. Different from the drag source model in the previous numerical simulation, this study focuses on the characterization of the blocking effect of tree branches on airflow by using more precise and real tree models. It is found that the airflow is blocked by the tree branches in the canopy, resulting in slower airflow and varying velocity direction; the air flows in the pore area between trees more easily, and the vortex centers are different in cases where the street canyon shape and tree layout are different. Low-velocity airflow distributes around and between two tree canopies, especially under the influence of two trees with different spacing. At the height of the pedestrian, the tree branches change the vortex structure of airflow, and thereby high pollutant concentration distribution on both sides of the bottom of the leeward side of the street canyon changes constantly. In the street canyon, the small change in tree spacing has a very limited influence on the pollutant concentration. The street canyon has the lowest average pollutant concentration at the largest y-axis direction spacing between two trees.

Generating sets consisting of pairwise conjugate elements

We consider groups [Formula: see text] which have generating sets consisting of pairwise conjugate elements. We introduce a natural condition on such sets, namely path-connectedness, which has strong consequences when [Formula: see text] acts on a real tree. The main result of the paper states that the group of type-preserving automorphisms of a regular simplicial tree has a generating set with this property.

An Automatic Tree Skeleton Extracting Method Based on Point Cloud of Terrestrial Laser Scanner

Tree skeleton could describe the shape and topological structure of a tree, which are useful to forest researchers. Terrestrial laser scanner (TLS) can scan trees with high accuracy and speed to acquire the point cloud data, which could be used to extract tree skeletons. An adaptive extracting method of tree skeleton based on the point cloud data of TLS was proposed in this paper. The point cloud data were segmented by artificial filtration and k-means clustering, and the point cloud data of trunk and branches remained to extract skeleton. Then the skeleton nodes were calculated by using breadth first search (BFS) method, quantifying method, and clustering method. Based on their connectivity, the skeleton nodes were connected to generate the tree skeleton, which would be smoothed by using Laplace smoothing method. In this paper, the point cloud data of a toona tree and peach tree were used to test the proposed method and for comparing the proposed method with the shortest path method to illustrate the robustness and superiority of the method. The experimental results showed that the shape of tree skeleton extracted was consistent with the real tree, which showed the method proposed in the paper is effective and feasible.

Ergodic currents dual to a real tree

Let $T$ be an $\mathbb{R}$-tree with dense orbits in the boundary of outer space. When the free group $\mathbb{F}_{N}$ acts freely on $T$, we prove that the number of projective classes of ergodic currents dual to $T$ is bounded above by $3N-5$. We combine Rips induction and splitting induction to define unfolding induction for such an $\mathbb{R}$-tree $T$. Given a current ${\it\mu}$ dual to $T$, the unfolding induction produces a sequence of approximations converging towards ${\it\mu}$. We also give a unique ergodicity criterion.