On elasticity of spring network models used in blood flow simulations in espresso∗

For the proper simulation of processes inside microfluidic devices, proper model for blood flow must be used. We use the lattice-Boltzmann method for the blood plasma flow and the immersed boundary method for the description of red blood cells and other components of blood. One of the four key mechanisms governing the elastic behaviour of a red blood cell is the in-plane shear modulus of elasticity. The membrane of red blood cell is modeled with a triangular network of springs with stretching coefficient k. Physical properties of the membrane is given by the in-plane shear modulus of elasticity µ. We study the dependence of the stretching coefficients of the springs on the in-plane shear modulus. First we derive analytical results for regular two dimensional networks. For networks, or meshes, covering the surface of three dimensional objects we first define the mesh density. Then we state the hypothesis deriving the relation between µ and k and finally we verify the hypothesis by numerous simulations

Determination of precession and dissipation parameters in micromagnetism

AbstractThe precession β and the dissipation parameter α of a ferromagnetic material can be considered microscopically space dependent. Their space distribution is difficult to obtain by direct measurements. In this article we consider an inverse problem, where we aim at recovering α and β from space measurements of the magnetization. The evolution of the magnetization in micromagnetism is governed by the Landau–Lifshitz (LL) equation. We first study the sensitivity of the LL equation. We derive the existence, uniqueness and stability results for the LL equation and the corresponding sensitivity equations. On the basis of the results we analyze the inverse problem. We employ the energy method and we minimize the underlying cost functional by means of the steepest descent method. We derive a convergence result for the proposed algorithm. The presented numerical examples support the theoretical results

Modelling and simulation of processes in microfluidic devices for biomedical applications

AbstractWe investigate a mathematical model describing the flow of a liquid in a microchannel. The model incorporates immersed objects in the fluid as well as fixed obstacles and boundaries of the microchannel. Objects can have different elastic properties, including solid objects and deformable objects. The flow description accounts for all types of mechanical interactions: fluid–object, object–object, fluid–walls, and object–walls interactions

On elasticity of spring network models used in blood flow simulations in espresso∗

For the proper simulation of processes inside microfluidic devices, proper model for blood flow must be used. We use the lattice-Boltzmann method for the blood plasma flow and the immersed boundary method for the description of red blood cells and other components of blood. One of the four key mechanisms governing the elastic behaviour of a red blood cell is the in-plane shear modulus of elasticity. The membrane of red blood cell is modeled with a triangular network of springs with stretching coefficient k. Physical properties of the membrane is given by the in-plane shear modulus of elasticity µ. We study the dependence of the stretching coefficients of the springs on the in-plane shear modulus. First we derive analytical results for regular two dimensional networks. For networks, or meshes, covering the surface of three dimensional objects we first define the mesh density. Then we state the hypothesis deriving the relation between µ and k and finally we verify the hypothesis by numerous simulations