Nineth Workshop on Mathematical Modelling of Environmental and Life Sciences Problems Constanta, November 1{4, 2012 ROMANIAN ACADEMY "Gheorghe Mihoc - Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics Department of Applied Mathematics Bucharest, Romania "OVIDIUS" UNIVERSITY Faculty of Mathematics and Informatics Research Center of Applied Mathematics Constanta, Romania sponsored by BITDEFENDER Bucharest Scientific Prof. Dr. Dorel Homentcovschi Committee Acad. Marius Iosifescu Prof. Dr. Alexandru Morega Prof. Dr. Ulrich R¨ude Prof. Dr. Christoph Schn¨orr Prof. Dr. Harry Vereeken Organizing Prof. Dr. Eduard Marius Craciun Committee Dr. Stelian Ion Dr. Gabriela Marinoschi Prof. Dr. Constantin Popa Conference Dr. Aurelian Nicola Secretariat Dr. Elena Pelican General Schedule Thursday, November 1st, 2012 16.00-18.00 Registration Friday, November 2nd, 2012 9.00-10.00 Opening Ceremony 10.00-12.30 Communications on Diffusion Processes and Material Sciences 12.30-14.30 Lunch 14.30-16.30 Communications on Mathematical Models in Biology (I) 16.30-17.00 Coffee break 17.00-18.30 Roundtable: Bio-geo-chemical processes 19.00-23.00 Banquet Saturday, November 3rd, 2012 9.20-10.30 Communications on Numerical Analysis 10.30-11.00 Coffee break 11.00-12.00 Communications on Image Recognition 12.00-14.00 Lunch 14.00-15.00 Communications on Mathematical Models in Biology (II) 3 Conference Lectures Friday November 2nd, 2012 10.00-12.30 Diffusion Processes and Material Sciences Chairpersons Adrian Carabineanu, Olivian Simionescu-Panait 1 Gheorghe Juncu, Aurelian Nicola, and Constantin Popa Splitting method for ternary mass transfer equations 2 Petru Jebelean and Constantin Popa Shooting method for numerical solution of singular φ-Laplacian equations ———————-Coffee break||||||| 3 Elena Stroil˘a Splitting method for multicomponent mass transfer equations 4 Eduard Marius Cr˘aciun Mathematical modeling of the multiple cracks interaction in pre-stressed elastic composites 5 Olivian Simionescu-Panait TH-wave propagation in a pre-stressed layered formation 14.30-16.30 Mathematical Models in Biology Chairpersons Alexadru Morega, Gheorghe Juncu 6 Alexei Leahu and Bogdan Munteanu Monte Carlo simulation for some reliability systems 7 Alexandru M. Morega, Alin A. Dobre and Mihaela Morega Hemodynamic - Electrical Field Interactions by Impedance Cardiography and Electro-Cardiometry 8 Anca Veronica Ion Study of behavior of density of proliferating cells in a delay differential equations model of leukemia ———————-Coffee break||||||| 9 Adrian Carabineanu Free-Surface Flow Past Submerged Hydrofoils 10 Stefan-Gicu Cruceanu and Dorin Marinescu Parameter Estimation for Survival Models 4 17.00-18.30 Roundtable: Bio-geo-chemical processes Moderator Stelian Ion 11 Virgil Iordache, Bodescu F., Ion S., Scradeanu D. Open problems in modeling biogeochemical processes 12 Stelian Ion PDE and CA models of soil erosion Saturday November 3rd, 2012 9.20-10.30 Numerical Analysis Chairpersons Doina Carp 13 Doina Carp and Constantin Popa On numerical solution of inconsistent systems of linear inequalities 14 Ioana Pomparau On an accelerated version of Kaczmarz algorithm with a priori clustering 15 Cristina S¸erban and Adam Dosa Iterative Solution of Augmented Systems for Structural Mechanics 11.00-12.00 Image Recognition Chairpersons Constantin Popa 16 L˘acr˘amioaraLit¸˘aand Elena Pelican Comparative Study of NN, PCA and COD algorithms for Pattern Recog- nition 17 Ljiljana Cvetkovi´c Nekrasov matrices - generalizations and benefits 18 Stefania Petra, Constantin Popa, Christoph Schn¨orr Multiplicative Updates for Box Constrained Linear Systems 14.00-15.00 Mathematical Models in Biology Chairpersons Eduard Marius Craciun 19 N. Ray, T. von Norden, F.A. Radu, P. Knabner, W. Friess Drug release from collagen matrices including an evolving microstructure 20 Tudor Udrescu On using adaptive wavelet compression to approximate committor probabilities in metastable biochemical systems 5 Abstracts 6 Free-Surface Flow Past Submerged Hydrofoils by Adrian Carabineanu We construct a Green function in order to obtain an integral representa- tion of the velocity field. We obtain an integral equation for the tangential velocity on the hydrofoil. The integral equation is solved numerically and the hydrodynamic coefficients are calculated. On numerical solution of inconsistent systems of linear inequalities by Doina Carp and Constantin Popa In the paper [1] the author described a finitely terminating algorithm for solving an inconsistent system Ax ≤ b of linear inequalities in a least squares sense. His algorithm uses a singular value decomposition of a submatrix of A om each iteration, making it impractical for all but only smaller problems. In this paper we show that a modification of Han's algorithm allows us to introduce a controlled (possible iterative) approximation to the original singular value solution. Ref. [1] s. -P. Han, Least squares solution of linear inequalities, tech. rep. TR-2141, Mathematics Research Center, University of Wisconsin - Madison, 1980. Mathematical modeling of the multiple cracks interaction in pre-stressed elastic composites by Eduard Marius Cr˘aciun We consider a composite containing three equal and collinear cracks in the same plane. The upper and lower faces of the cracks are acted by sym- metrically distributed normal stresses. Our aim is to determine the elastic states in the body, cracks interaction and the cracks propagation directions. The present paper represents analitical, numerical and experimental studies of the three equal and collinear cracks propagation and interaction. In or- der to assess the displacement and strain fields in the tested materials, the 7 3-D image correlation system ARAMIS has been used. The tests were per- formed at Lublin University of Technology from Poland on the orthotropic polymer matrix composite material used for helicopter parts manufacturing, prepared by Polish Aviation Works in Poland. Parameter Estimation for Survival Models by S¸tefan Gicu Cruceanu and Dorin Marinescu We consider some survival models derived from the classical Gompertz model. Using real data, our purpose is to determine a set of unknown pa- rameters associated to each of these models by efficiently solving either a Least Square or a Least Absolute Value minimization problem. In order to numerically evaluate the values of these parameters, we will adapt Cellu- lar Exclusion Methods for direct solving the previous global optimization problems. Nekrasov matrices - generalizations and benefits by Ljiljana Cvetkovi´c While the class of strictly diagonally dominant (SDD) matrices is closely related to the Jacobi iterative method, in a similar fashion, the class of Nekrasov matrices arises from the Gauss-Seidel method. There is a con- nection between these two classes, which enables several interesting appli- cations. On the other hand, some of generalization directions for the SDD class can be applied to Nekrasov class, and produce further benefits in sev- eral areas of matrix theory. Study of behavior of density of proliferating cells in a delay differential equations model of leukemia by Anca Veronica Ion We consider a model of leukemia (found in the literature), model consisting of two delay differential equations, one for the evolution of the density of 8 proliferating cells P and one for the density of so called "resting" cells N - cells that, for a certain period of time do not divide within the cancerous process. The equation for N is independent of P hence it can be studied separately. In previous works, we studied for this equation the stability of equilibrium points, the points of Hopf and Bautin bifurcation, and the stability of the periodic solutions emerged by these bifurcations. In the present work we study the equation for the proliferating cells, P . PDE and CA models of soil erosion by Stelian Ion The soil erosion is a very complex phenomenon that needs an interdisci- plinary treatment to quantify it or to make predictions about its evolution. In a rough classification the mathematical models cast in the regressive models and physically based models. Among the physically based models the distributed models gain attention of the modelers and practitioners due, mainly, to the progress in data acquisition technics and the development of mathematical tools and calculus power. In the paper we discuss two types of physically based and distributed model, the models that use the partial differential equations in their formulation and the cellular automata based models. We focus on their common points and what makes them different. Some numerical simulations illustrate our talk. Shooting method for numerical solution of singular φ-Laplacian equations by Petru Jebelean and Constantin Popa In this paper we are concerned with numerical solutions to Dirichlet problem [φ(u0)]0 = f(x) in [α; β]; u(α) = A; u(β) = B; where φ :(−η; η) ! R (η < +1) is an increasing diffeomorphism with φ0(y) ≥ d > 0 for all y 2 (−η; η). The obtained algorithm combines the shooting method with Euler's method and it is convergent whenever the problem is solvable. We provide numerical experiments confirming the the- oretical aspects. 9 Splitting method for ternary mass transfer equations by Gheorghe Juncu, Aurelian Nicola, and Constantin Popa In a multi-component system the diffusion of a certain species is dictated not only by its own concentration gradient but also by the concentration gradient of the other species. In this case, the mathematical model is a system of strongly coupled