Relevant Qualitative and Quantitative choices for building an efficient dynamic plant growth model : Greenlab Case

A systematic study of plant growth modeling is a real challenge for researchers and scientists because multidisciplinary aspects have to be integrated. Through a mathematical formalism, a plant functional-structural model needs to be developed based on knowledge from botany, agronomy, forestry, eco-physiology and computer sciences. Specialists in each discipline have proposed variety models, but most of these models are limited within their own field. It is well recognized that the malfunctioning and the limitations of these models are due to their mono-disciplinary aspects applied. A dialog between the various scientific domains involved in plant modeling is not obvious. It needs to choose, simplify and adapt the relevant knowledge from each other that is necessary and sufficient to build a plant functional-structural model. This needs also to define a right level of observations. Each notion is simplify, but the interactions between them give new theoretical results and applications. Several questions are discussed in this work. How botany gives keys to organize the multi-level information inside the plant topological structure and eventually speed up the growth computing? What kind of mathematical formalism is needed to introduce powerful tools of automatic control into plant modelling? The goal of this paper is to propose simple choices, from both biological and mathematical viewpoints, and adapt them to build an efficient dynamical model. With this model, it is possible to insure optimisation and control that are needed in agronomy

A comparison study of geostatistical simulation for predicting soil texture

Non-Peer Reviewe

Structural Factorization of Plants to Compute their Functional and Architectural Growth

Numerical simulation of plant growth has been facing a bottleneck due to the cumbersome computation implied by the complex plant topological structure. In this article, the authors present a new mathematical model for plant growth, GreenLab, overcoming these difficulties. GreenLab is based on a powerful factorization of the plant structure. Fast simulation algorithms are derived for deterministic and stochastic trees. The computation time no longer depends on the number of organs and grows at most quadratically with the age of the plant. This factorization finds applications to build trees very efficiently, in the context of geometric models, and to compute biomass production and distribution, in the context of functional structural models

Lax pairs, Painlev\'e properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation

We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV equation are integrable in the sense that they possess the Painlev\'e property. Some exact solutions are also constructed

Fitting a Functional-Structural growth model with plant architectural data

GreenLab is a recurrent discrete-time functional-structural model of plant growth and architecture. A method is presented estimating its parameters: the model is fitted to plant morphological and architectural data observed at one point of time. Since GreenLab output variables (number, size and fresh mass of organs) implicitly and nonlinearly depend on the model parameters, the fitting problem is solved by minimizing a generalized least-squares criterion and by implementing an iterative procedure. Fitting is satisfactorily performed on unbranched plants (cotton, maize, sunflower) using real data. The method is extended to more complex plants (i.e. with branches): a preliminary test on a virtual tree shows that the fitting algorithm also applies to such structured plants

GreenLab: A New Methodology Towards Plant Functional-Structural Model -- Structural Part

GreenLab model is an on-going research program conducted jointly by researchers from France and China since 1998. It is oriented to be a functional-structural model for agronomy/forestry applications. Therefore, while keeping a property of being faithful to botanical knowledge, a new methodology is developed within GreenLab by stressing on simplicity of the model. This paper presents briefly our understanding towards plant functional-structural model, but only a model related to plant structures is given to show some progresses of the GreenLab. For a single stand of plant, GreenLab applies its newly developed "dual-scale automaton" approach to generate stochastic structures of plants. Using graph-based interface, this approach provides users with straightforward means of integrating botanical knowledge, i.e., metamers and growth unit, in construction of topological and morphological structures of plants. On the other hand, for a complex tree or a plantation application, a strategy of substructures is employ d in GreenLab model for fast construction of plants and calculation of yields in terms of organs. Simulation results indicate promising benefits in using the new methodology to develop a generic plant model in regard to the structural part. (Résumé d'auteur

Stochastic 3D Tree Simulation Using Substructure Instancing

Tree growth is simulated using a stochastic model of organogenesis that is faithful to botanical knowledge. This model is based on the concept of bud "physiological age", on the statistical description of the transition from one physiological age to another as well as of bud death, bud growth and branching processes. In order to enhance simulation efficiency, a recurrent algorithm based on stochastic substructure instancing is proposed. The tree is hierarchically decomposed into substructures that are classified according to their physiological age, and a library of random substructure instances is constructed: the recurrent simulation starts with the simplest peripheral substructures, which are also the physiologically oldest; these substructures are then progressively assembled into more complex substructures, until the tree is completely simulated. When the size of the library of substructure instances is small, the time needed to build a single stochastic tree is much shorter than for a usual tree simul tion that operates on a bud-by-bud basis. in computing a group of trees, the speed gain is even much greater, because the library of substructure instances is built for the first tree, and then is reused for computing subsequent trees. A preliminary sensitivity analysis is carried out according to the size of the library: when the library is large, the simulated distribution of the number of organs fits well with the theoretical mean and variance; the algorithm can thus be tuned in order to obtain accurate predictions. On the other hand, a small library (e.g., with only 2 or 3 instances for each substructure class) is sufficient for generating visually realistic trees. A few examples illustrate the high performance of this algorithm which paves the way for the fast simulation of large forest scenes

Use of the Generalized Gradient Approximation in Pseudopotential Calculations of Solids

We present a study of the equilibrium properties of $sp$-bonded solids within the pseudopotential approach, employing recently proposed generalized gradient approximation (GGA) exchange correlation functionals. We analyze the effects of the gradient corrections on the behavior of the pseudopotentials and discuss possible approaches for constructing pseudopotentials self-consistently in the context of gradient corrected functionals. The calculated equilibrium properties of solids using the GGA functionals are compared to the ones obtained through the local density approximation (LDA) and to experimental data. A significant improvement over the LDA results is achieved with the use of the GGA functionals for cohesive energies. For the lattice constant, the same accuracy as in LDA can be obtained when the nonlinear coupling between core and valence electrons introduced by the exchange correlation functionals is properly taken into account. However, GGA functionals give bulk moduli that are too small compared to experiment.Comment: 15 pages, latex, no figure

Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network models. In formulating the Artificial Neural Network based predictive model, three layered networks have been constructed with sigmoid non-linearity. The models under study are different in the number of hidden neurons. After a thorough training and test procedure, neural net with three nodes in the hidden layer is found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure