Biomedical subjects

MirFaez Miri

Publications and source records attributed to MirFaez Miri.

4 recordsLinked to original sources

PubMed2006

Persistent random walk on a site-disordered one-dimensional lattice: photon subdiffusion.

We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density f(t). Depending on the behavior of f(t) near t=0, diffusive and subdiffusive transports are predicted by the disorder expansion of the mean square-displacement and the effective medium approximation. Monte Carlo simulations confirm the anomalous diffusion of photons. To observe photon subdiffusion experimentally, we suggest a dielectric film stack for realization of a distribution f(t).

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PubMed2006

Universality in two-dimensional cellular structures evolving by cell division and disappearance.

The dynamics of two-dimensional cellular networks is written in terms of coupled population equations, which describe how the population of s-sided cells is affected by cell division and disappearance. In these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field. Under not too restrictive conditions, the equilibrium distribution P(s) of cells satisfies a linear difference equation of order two or higher. The population equations are asymptotically integrable. The asymptotic integrability implies a "universal" distribution P(s) approximately Cs-kZs for large values of s, which is also the Boltzmann distribution associated with the maximum entropy inference. Asymptotic integrability of the population equations is absent in a global mean-field approximation. The importance of short-range topological information to control the evolution of foams is thus confirmed.

Apoptosis↗

PubMed2005

Diffusive transport of light in a Kelvin foam.

Although diffusing-wave spectroscopy has already been successfully applied to study dynamic properties of foams, we still lack a clear understanding of the diffusive transport of photons in foams. In this paper, we present a thorough study of photon diffusion in the Kelvin structure as an example for a three-dimensional model foam. We consider the photons' random walk as they are reflected or transmitted by the liquid films according to the rules of ray optics. For constant reflectance and special one- and two-dimensional photon paths, we are able to calculate diffusion constants analytically. Extensive numerical simulations reveal a remarkable similarity with our previous two-dimensional investigations. To implement a more realistic model, we use thin-film reflectances. The simulated diffusion constants exhibit oscillations for varying film thickness d which vanish when disorder is introduced in d. Absolute values and the behavior at small d agree with measurements in very dry foams providing a strong argument for the importance of liquid films in the diffusive photon transport. An analytical theory with a minimum of input parameters reproduces the numerical results.

Journal Article↗

PubMed2003

Persistent random walk in a honeycomb structure: light transport in foams.

We study light transport in a honeycomb structure as the simplest two-dimensional model foam. We apply geometrical optics to set up a persistent random walk for the photons. For three special injection angles of 30 degrees, 60 degrees, and 90 degrees relative to a hexagon's edge, we are able to demonstrate by analytical means the diffusive behavior of the photons and to derive their diffusion constants in terms of intensity reflectance, edge length, and velocity of light. Numerical simulations reveal an interesting dependence of the diffusion constant on the injection angle in contrast to the usual assumption that in the diffusive limit the photon has no memory for its initial conditions. Furthermore, for injection angles close to 30 degrees, the diffusion constant does not converge to the value at 30 degrees. We explain this observation in terms of a two-state model.

Journal Article↗