Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page

СВОЙСТВА ДЕМИНЕРАЛИЗОВАННОГО КОСТНОГО МАТРИКСА ДЛЯ БИОИНЖЕНЕРИИ ТКАНЕЙ

The purpose. Determination of tissues of physico-mechanical properties of demineralized bone matrix of spongy and compact human bone important for bioengineering.Material and Methods.The methods for studying micromorphological, piezoelectric and transport properties, adapted for measuring the materials of potential scaffolds.Results. The results of studying the physico-mechanical properties of the demineralized bone matrix of spongy and compact human bones are presented. It is shown that the demineralized spongy bone possesses the best characteristics of the pore system for the colonization of matrix cells. The tensile strength and modulus of elasticity of samples from the demineralized heads of the femurs extracted during the initial hip arthroplasty vary widely. The modulus of elasticity varied from 50 to 250 MPa, and the ultimate strength was from 1.1 to 5.5 MPa.Conclusion. Methods for measuring micromorphological, piezoelectric and transport properties for materials of potential matrices were developed and / or adapted. It is shown that in the samples of materials from the human bone, these characteristics, as a rule, vary considerably. Proceeding from this, it becomes obvious that the development of protocols of measurement methods of the above listed properties is an important work for the creation of technology of bioengineering of tissue implants for reconstructive surgery. Цель. Определение значимых для биоинженерии тканей физико-механических свойств деминерализованного костного матрикса губчатой и компактной кости человека.Материалы и методы. Перечислены методы исследования микроморфологических, пьезоэлектрических и транспортных свойств, адаптированные для измерения у материалов потенциальных матриц.Результаты. Приведены результаты исследования физико-механических свойств деминерализованного костного матрикса губчатой и компактной кости человека. Показано, что деминерализованная губчатая кость обладает наилучшими характеристиками поровой системы для заселения матриксов клетками. Предел прочности и модуль упругости образцов из деминерализованных головок бедренных костей, извлеченных в ходе первичного эндопротезирования тазобедренного сустава, изменяются в широких пределах. Модуль упругости изменялся от 50 до 250 МПа, а предел прочности – от 1,1 до 5,5 МПа.Заключение. Были отработаны и/или адаптированы методы измерений микроморфологических, пьезоэлектрических и транспортных свойств у материалов потенциальных матриц. Показано, что у образцов материалов из кости человека данные характеристики, как правило, значительно варьируют. Исходя из этого, становится очевидным, что отработка протоколов методов измерения вышеперечисленных свойств является важной работой для создания технологии биоинженерии тканевых имплантатов для восстановительной хирургии.

MODELING OF PLANT TISSUE GROWTH AND DEVELOPMENT WITH L-SYSTEMS

An introduction to modeling of dynamical systems possessing dynamical structures with L-systems is given. Application of L systems is illustrated by models of plant tissue growth and control of state variable distribution in the growing tissue

AN L-SYSTEM FOR MODELING OF UNIDIMENSIONALLY GROWING FLAT PLANT TISSUES

In this work, a mathematical model and its implementation are proposed for computational simulation of one-dimensional symplastic growth of tissues. We modified the formal grammar of differential L-systems, and in this grammar, we described a dynamic model of symplastic growth with regard to its biomechanics. The results of the simulation of linear leaf blade growth are compared with those for a free-growing cell population. It is shown that in the model proposed symplastic growth causes a greater deviation of the actual cell length from its isosmotic length than in freely growing cells