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On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

Luca Formaggia, Alexandra Moura, Fabio Nobile (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the...

On the theory of remediability

Hassan Emamirad (2003)

Banach Center Publications

Suppose G ₁ ( t ) t ≥ 0 and G ₂ ( t ) t ≥ 0 are two families of semigroups on a Banach space X (not necessarily of class C₀) such that for some initial datum u₀, G₁(t)u₀ tends towards an undesirable state u*. After remedying by means of an operator ρ we continue the evolution of the state by applying G₂(t) and after time 2t we retrieve a prosperous state u given by u = G₂(t)ρG₁(t)u₀. Here we are concerned with various properties of the semigroup (t): ρ → G₂(t)ρG₁(t). We define (X) to be the space of remedial operators for...

On the Use of the Hill Functions in Mathematical Models of Gene Regulatory Networks

M. Santillán (2008)

Mathematical Modelling of Natural Phenomena

Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneously bind a single receptor. This result if often employed to interpret the Hill coefficient as the number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibrium states of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively and in a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate, but only an upper...

On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles

R. Dilão, A. Lakmeche (2010)

Mathematical Modelling of Natural Phenomena

We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time,...

On two methods for the parameter estimation problem with spatio-temporal FRAP data

Papáček, Štěpán, Jablonský, Jiří, Matonoha, Ctirad (2015)

Programs and Algorithms of Numerical Mathematics

FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model...

On useful schema in survival analysis after heart attack

Czesław Stępniak (2014)

Discussiones Mathematicae Probability and Statistics

Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers

One-two descriptor of graphs

K. CH. Das, I. Gutman, D. Vukičević (2011)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Optimal chemical balance weighing designs for v + 1 objects

Bronisław Ceranka, Małgorzata Graczyk (2003)

Kybernetika

The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for p = v objects implies the existence of an optimum chemical balance weighing design for p = v + 1 objects are given. The existence of an optimum chemical balance weighing design for p = v + 1 objects implies the existence of an optimum chemical...

Optimal control for a class of compartmental models in cancer chemotherapy

Andrzej Świerniak, Urszula Ledzewicz, Heinz Schättler (2003)

International Journal of Applied Mathematics and Computer Science

We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are...

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