MATHEMATICAL-PHYSICAL MODELING OF DYNAMICAL PROCEsS OF PLANT'S GROWTH，DEVELOPMENT AND EVOLUTION*

Since the middle of the 20-th century, a new interdisciplinary subject isgradually formed at the edge of fields of biology and physics, mechanics andmathematics, the so-called mathematical biology. It treats the biological,living system as a complex dynamics system and aims at a thoroughresearch from the angle of applied mathematics. The topics currentlyinvestigated in mathematical biology are far beyond the area ofbio-mechanics that people are familiar with. The rapid growth of this subjectprofoundly changed the feature of the ancient, traditional that ismainly dealing biologywith the observations, classifications and experiments as itscharacteristics.The aim of this article attempts to introduce and discuss a research direction, in mathematics biology\linebreak------ mathematical physical modeling studies of  growth, development andevolution of the plant system. It is evident that such a researchdirection is vital both theoretically and practically. In doing so, thearticle briefly reviews the research activities alongthis direction in China and in other countries during therecent years, elucidates the essential differences between the dynamicalmathematical modeling, statistical modeling and computer simulation,which have been applied in the investigations of this subject.The present article further selects the topic of growth of the plant root systemas the break-through point of the investigation. It demonstrates that bytreating the system of root growth as a thermo-dynamical open system,based on the principles of irreversible thermo-dynamics, plant cytology andphysiology, combining the microstructure of the plant internal organization, onemay establish a system of governing differential equations, that properlydescribes the macroscopic transport processes of the  internalmaterials, energy and signals in the system. Through solving these equations with thepowerful methods of nonlinear science and applied mathematics, and comparingthe theoretical results obtained with the experimental observations, onemay moredeeply explore and better understand the mechanisms of up-taking process ofwater and nutrients from the environment throught the root system, as well as the variousinstability and bifurcation phenomena of biological interface during the rootgrowth.