Molecular Dynamics Simulation of Vascular Network Formation

Endothelial cells are responsible for the formation of the capillary blood vessel network. We describe a system of endothelial cells by means of two-dimensional molecular dynamics simulations of point-like particles. Cells' motion is governed by the gradient of the concentration of a chemical substance that they produce (chemotaxis). The typical time of degradation of the chemical substance introduces a characteristic length in the system. We show that point-like model cells form network resembling structures tuned by this characteristic length, before collapsing altogether. Successively, we improve the non-realistic point-like model cells by introducing an isotropic strong repulsive force between them and a velocity dependent force mimicking the observed peculiarity of endothelial cells to preserve the direction of their motion (persistence). This more realistic model does not show a clear network formation. We ascribe this partial fault in reproducing the experiments to the static geometry of our model cells that, in reality, change their shapes by elongating toward neighboring cells.Comment: 10 pages, 3 figures, 2 of which composite with 8 pictures each. Accepted on J.Stat.Mech. (2009). Appeared at the poster session of StatPhys23, Genoa, Italy, July 13 (2007

Quenched large deviations for Glauber evolution with Kac interaction and Random Field

We study a spin-flip model with Kac type interaction, in the presence of a random field given by i.i.d. bounded random variables. The system, spatially inhomogeneous, evolves according to a non conservative (Glauber) dynamics. We show an almost sure (with respect to the random field) large deviations principle for the empirical magnetizations of this process. The rate functional depends on the statistical properties of the external random field, it is lower semicontinuous with compact level sets.Comment: 40 page

A genralization of the H-Theorem to steady nonequilibrium states. 1 . A basic decomposition and the linear case

A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in 'bulk' and in 'boundary' terms is given; for the linear case both have a definite sign. The relation with the strong L(1) stability is pointed out

A genralization of the H-Theorem to steady nonequilibrium states. 1 . A basic decomposition and the linear case

A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in 'bulk' and in 'boundary' terms is given; for the linear case both have a definite sign. The relation with the strong L(1) stability is pointed out

The continuum reaction-diffusion limit of a stochastic cellular growth model

A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit.The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered. The asymptotic behavior of the system can be partially described through the analysis of the stationary wave which connects different equilibria

Travelling fronts in nonlocal models for phase separation in an external field

We consider the one-dimensional, nonlocal, evolution equation derived by De Masi et al. (1995) for Ising systems with Glauber dynamics, Kac potentials and magnetic field. We prove the existence of travelling fronts, their uniqueness module translations among the monotone profiles and their linear stability for all the admissible values of the magnetic field for which the underlying spin system exhibits a stable and metastable phase

Use of the Ising model for doubly ordered macromolecules

We developed a statistical model, based on a one-dimensional Ising model, for a recently studied polypeptide which displays an endothermic helix-to-coil transition with an “anomalous” behavior in the heat of solution. The model supports the assumption of an ordering of the chains due to a specific hydrogen bond interaction among them, beside the helical ordering of the backbone; this double ordering of the macromolecule produces the “anomalous” experimental behavior. With the hypothesis of a highly coopertive interaction among amide groups and side chains, we find that the backbone cooperation increases the chains cooperation, but not vice versa; this influence when the cooperation in the backbone increases

The Competition-Diffusion limit of a stochastic growth model

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