【正文】 ...................................................... 20 Key Findings ................................................................................................................ 21 Team 15263 Page 1 of 23 Ⅰ . Introduction As is known to all， there are not two leaves exactly alike. Plant leaves have diverse and elaborate shapes and venation patterns. The beauty of them has attracted curiosity of many people involving biologists, physicists, mathematician, artists, puter scientists, etc. for a long time. The leaf study of forests and of individual tree is important to understand resource allocation of trees, atmosphere—biosphere exchange processes, and the energy budget, it would also be valuable for individual tree growth. The aim of this article is to develop models for leaf shapes classification and to figure out the main factors which lead to the various leaf shapes. At the same time, we find out the interaction between tree (It?s profile/branching structure) and tree leaf. Though there are so many methods to estimate the leaf mass. We solve this problem through a correlation between the leaf mass and the size characteristics of the tree. Ⅱ . Some Definitions ? Leaf To a plant, leaves are food producing ans. Leaves absorb some of the energy in the sunlight that strikes their surfaces and also take in carbon dioxide from the surrounding air in order to run the metabolic process of photosynthesis. ? Phototropism[1] Phototropism is directional growth in which the direction of growth is determined by the direction of the light source. It causes the plant to have elongated cells on the farthest side from the light. Phototropism is one of the many plant tropisms or movements which respond to external stimuli. ? Polar Auxin Transport(PAT) [2] PAT is the regulated transport of the plant hormone auxin in plants. It is an active process, the hormone is transported in celltocell manner and one of the main features of the transport is its directionality (polarity). The polar auxin transport has coordinative function in plant development, the following spatial auxin distribution underpins most of plant growth responses to its environment and plant growth and developmental changes in general. ? Apical Dominance[3] It is the phenomenon whereby the main central stem of the plant is dominant over other side stems。 Internal factors: ? Deformation of cells, moisture loss of Mesophyll cells may cause volume decrease。 (c) and 。 Team 15263 Page 12 of 23 We introduce 2( , , ) * ( , , )F x y z k v x y z= (18) Then we can get: ( , , )( , , )( , , )s f N Fl g N Fb h N F=F=F=F (19) ( , , ) * ( , , ) * ( , , ) * ( , , )x y z v x y z x y z N x y zh a b g= + F + (20) where v is weed speed, F is Luminous flux, which used to quantify the influence of wind, ,abg is the corresponing weight coefficient. Whether tree branching influence leaves shape. Firstly, we believe that the main feature of tree profile would be tree shape. due to the subtle differences of light, temperature, humidity and velocity of wind among different tree shapes ,so that leaf shapes are various. In a word, leaf shapes are relative to tree shapes. There is a graph we can offer. Table : some explanation LAI : crown type parameter ELADP leaf area index MLA mean tilt angle ISF scattered light site figure DSF direct light site figure GSF general light site figure Table : The canopy characteristics indexes under different tree shape Tree shape LAI ELADP MLA ISF DSF CSF Open cebter shape * * *14a * * * Spindle shape 34b Disperse lamination shape *19a Note: Different letters in columns of the table show the significant differences( = ) Trees with open cebter shape ()OCS have the advantages of receiving more sunlight. It?s LAI lower than the other two, % lower than spindle shape ()SS , % lower than disperse lamination shape DLS . OCS has larger light site coefficient than the other two shapes. Its? ISF , DSF and GSF % 、 % 、 % larger than SS and is % 、 % 、% larger than DLS . Trees with Spindle shape have growing weakness, no apparent spacing between Team 15263 Page 13 of 23 layers and poor lighting. Its? LAI is the biggest among the three shapes. Its? increasing rang of ISF is 25% higher than DLS , its? DSF and GSF % , % lower than DLS . So it is obviously that leaf shape relates to tree shape. Electric tree branch angle’s impact analysis In addition to tree profile, tree branch angles also influence leaf shapes. Figure shows different tree branch angle effect on the tree area. When two new branch units (unit 3 and unit 5) arise from the distal end of a previous unit (mother unit) there is a regular asymmetry in the branch angles (θ1 and θ2, respectively) a previous theoretical model for treelike bodies to develop a reliable puter simulation of tree geometry for this species. The treelike bodies in the original, theoretical model were developed with only two parameters, the ratio of mother to daughter branch unit lengths and the asymmetry of forking. Figure : Tree branch angle?s impact on leaf area. Figure is variation of the effective leaf area of a branch tier depending on the branch angles, 1q and 2q . The titer of the five lateral branch plexes is simulated with three orders of bifurcation according to the rules of Terminaliabranching. The divergence angle of the first branch unit of each branch plex . The sign of the branch angles of the first branch unit in each successive branch plex alternate. The ratios of branch lengths of units 3 and 5 to that of their mother unit are and , respectively. The radius of the leaf disk approximation is where the length of the longest distal branch unit is unity. Simulations of the