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Cardone G.,University of Sannio | Nazarov S.A.,Institute of Mechanical Engineering Problems | Piatnitski A.L.,Narvik University College | Piatnitski A.L.,RAS Lebedev Physical Institute
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2011

The aim of the paper is to compare the asymptotic behavior of solutions of two boundary value problems for an elliptic equation posed in a thin periodically perforated plate. In the first problem, we impose homogeneous Dirichlet boundary condition only at the exterior lateral boundary of the plate, while at the remaining part of the boundary Neumann condition is assigned. In the second problem, Dirichlet condition is also imposed at the surface of one of the holes. Although in these two cases, the homogenized problem is the same, the asymptotic behavior of solutions is rather different. In particular, the presence of perturbation in the boundary condition in the second problem results in logarithmic rate of convergence, while for non-perturbed problem the rate of convergence is of power-law type. © 2010 Springer Basel AG. Source

Fischer S.,INSA Lyon | Kurbatova P.,Camille Jordan Institute | Kurbatova P.,French Institute for Research in Computer Science and Automation | Bessonov N.,Institute of Mechanical Engineering Problems | And 6 more authors.
Journal of Theoretical Biology | Year: 2012

The production and regulation of red blood cells, erythropoiesis, occurs in the bone marrow where erythroid cells proliferate and differentiate within particular structures, called erythroblastic islands. A typical structure of these islands consists of a macrophage (white cell) surrounded by immature erythroid cells (progenitors), with more mature cells on the periphery of the island, ready to leave the bone marrow and enter the bloodstream. A hybrid model, coupling a continuous model (ordinary differential equations) describing intracellular regulation through competition of two key proteins, to a discrete spatial model describing cell-cell interactions, with growth factor diffusion in the medium described by a continuous model (partial differential equations), is proposed to investigate the role of the central macrophage in normal erythropoiesis. Intracellular competition of the two proteins leads the erythroid cell to either proliferation, differentiation, or death by apoptosis. This approach allows considering spatial aspects of erythropoiesis, involved for instance in the occurrence of cellular interactions or the access to external factors, as well as dynamics of intracellular and extracellular scales of this complex cellular process, accounting for stochasticity in cell cycle durations and orientation of the mitotic spindle. The analysis of the model shows a strong effect of the central macrophage on the stability of an erythroblastic island, when assuming the macrophage releases pro-survival cytokines. Even though it is not clear whether or not erythroblastic island stability must be required, investigation of the model concludes that stability improves responsiveness of the model, hence stressing out the potential relevance of the central macrophage in normal erythropoiesis. © 2012 Elsevier Ltd. Source

Cardone G.,University of Sannio | Durante T.,University of Salerno | Nazarov S.A.,Institute of Mechanical Engineering Problems
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2010

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter ε > 0 while the distance of the body to the water surface is also of order ε. Under a certain symmetry assumption, the accumulation effect for trapped mode frequencies is established, namely it is proved that, for any given d > 0 and integer N > 0, there exists a number ε (d, N) > 0 such that the problem has at least N eigenvalues in the interval (0, d) of the continuous spectrum in the case ε ∈ (0, ε (d, N)). The corresponding eigenfunctions decay exponentially at infinity, have finite energy, and imply trapped modes. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source

Nazarov S.A.,Institute of Mechanical Engineering Problems | Sokolowski J.,University of Lorraine
Latin American Journal of Solids and Structures | Year: 2011

The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems. Source

Tosenberger A.,Camille Jordan Institute | Tosenberger A.,French Institute for Research in Computer Science and Automation | Ataullakhanov F.,Russian Academy of Sciences | Bessonov N.,Institute of Mechanical Engineering Problems | And 5 more authors.
Journal of Theoretical Biology | Year: 2013

Hemostatic plug covering the injury site (or a thrombus in the pathological case) is formed due to the complex interaction of aggregating platelets with biochemical reactions in plasma that participate in blood coagulation. The mechanisms that control clot growth and which lead to growth arrest are not yet completely understood. We model them with numerical simulations based on a hybrid DPD-PDE model. Dissipative particle dynamics (DPD) is used to model plasma flow with platelets while fibrin concentration is described by a simplified reaction-diffusion-advection equation.The model takes into account consecutive stages of clot growth. First, a platelet is weakly connected to the clot and after some time this connection becomes stronger due to other surface receptors involved in platelet adhesion. At the same time, the fibrin mesh is formed inside the clot. This becomes possible because flow does not penetrate the clot and cannot wash out the reactants participating in blood coagulation. Platelets covered by the fibrin mesh cannot attach new platelets. Modelling shows that the growth of a hemostatic plug can stop as a result of its exterior part being removed by the flow thus exposing its non-adhesive core to the flow. © 2013 Elsevier Ltd. Source

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