Homeostatic maintenance via degradation and repair of elastic fibers under tension.

Cellular maintenance of the extracellular matrix requires an effective regulation that balances enzymatic degradation with the repair of collagen fibrils and fibers. Here, we investigate the long-term maintenance of elastic fibers under tension combined with diffusion of general degradative and regenerative particles associated with digestion and repair processes. Computational results show that homeostatic fiber stiffness can be achieved by assuming that cells periodically probe fiber stiffness to adjust the production and release of degradative and regenerative particles.

Entropy Production and the Pressure-Volume Curve of the Lung.

We investigate analytically the production of entropy during a breathing cycle in healthy and diseased lungs. First, we calculate entropy production in healthy lungs by applying the laws of thermodynamics to the well-known transpulmonary pressure-volume (P-V) curves of the lung under the assumption that lung tissue behaves as an entropic spring similar to rubber. The bulk modulus, B, of the lung is also derived from these calculations.

A network model of correlated growth of tissue stiffening in pulmonary fibrosis.

During the progression of pulmonary fibrosis, initially isolated regions of high stiffness form and grow in the lung tissue due to collagen deposition by fibroblast cells. We have previously shown that ongoing collagen deposition may not lead to significant increases in the bulk modulus of the lung until these local remodeled regions have become sufficiently numerous and extensive to percolate in a continuous path across the entire tissue [Bates . 2007 .

Explosive electric breakdown due to conducting-particle deposition on an insulating substrate.

We introduce a theoretical model to investigate the electric breakdown of a substrate on which highly conducting particles are adsorbed and desorbed with a probability that depends on the local electric field. We find that, by tuning the relative strength q of this dependence, the breakdown can change from continuous to explosive. Precisely, in the limit in which the adsorption probability is the same for any finite voltage drop, we can map our model exactly onto the q-state Potts model and thus the transition to a jump occurs at q = 4.

Enhanced flow in small-world networks.

The proper addition of shortcuts to a regular substrate can lead to the formation of a complex network with a highly efficient structure for navigation [J. M. Kleinberg, Nature 406, 845 (2000)].

Oil displacement through a porous medium with a temperature gradient.

We investigate the effect of a temperature gradient on oil recovery in a two-dimensional pore-network model. The oil viscosity depends on temperature as μ(o) [Please see text] e(B/T), where B is a physicochemical parameter, depending on the type of oil, and T is the temperature. A temperature gradient is applied across the medium in the flow direction.

Transport on exploding percolation clusters.

We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is randomly chosen.