Morphological Transition between Patterns Formed by Threads of Magnetic Beads.

Magnetic beads attract each other, forming chains. We push such chains into an inclined Hele-Shaw cell and discover that they spontaneously form self-similar patterns. Depending on the angle of inclination of the cell, two completely different situations emerge; namely, above the static friction angle the patterns resemble the stacking of a rope and below they look similar to a fortress from above. Moreover, locally the first pattern forms a square lattice, while the second pattern exhibits triangular symmetry. For both patterns, the size distributions of enclosed areas follow power laws. We characterize the morphological transition between the two patterns experimentally and numerically and explain the change in polarization as a competition between friction-induced buckling and gravity.

Optimal array of sand fences.

Sand fences are widely applied to prevent soil erosion by wind in areas affected by desertification. Sand fences also provide a way to reduce the emission rate of dust particles, which is triggered mainly by the impacts of wind-blown sand grains onto the soil and affects the Earth's climate. Many different types of fence have been designed and their effects on the sediment transport dynamics studied since many years. However, the search for the optimal array of fences has remained largely an empirical task. In order to achieve maximal soil protection using the minimal amount of fence material, a quantitative understanding of the flow profile over the relief encompassing the area to be protected including all employed fences is required. Here we use Computational Fluid Dynamics to calculate the average turbulent airflow through an array of fences as a function of the porosity, spacing and height of the fences. Specifically, we investigate the factors controlling the fraction of soil area over which the basal average wind shear velocity drops below the threshold for sand transport when the fences are applied. We introduce a cost function, given by the amount of material necessary to construct the fences. We find that, for typical sand-moving wind velocities, the optimal fence height (which minimizes this cost function) is around 50 cm, while using fences of height around 1.25 m leads to maximal cost.

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. However, this mechanism is unable to maintain a homogeneous fiber. To account for axial homogeneity, we introduce a robust control mechanism that is locally governed by how the binding affinity of particles is modulated by mechanical forces applied to the ends of the fiber. This model predicts diameter variations along the fiber that are in agreement with the axial distribution of collagen fibril diameters obtained from scanning electron microscopic images of normal rat thoracic aorta. The model predictions match the experiments only when the applied force on the fiber is in the range where the variance of local stiffness along the fiber takes a minimum value. Our model thus predicts that the biophysical properties of the fibers play an important role in the long-term regulatory maintenance of these fibers.

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. Second, we extend this approach to elastic recoil disorders of the lung such as occur in pulmonary fibrosis and emphysema. These diseases are characterized by particular alterations in the P-V relationship. For example, in fibrotic lungs B increases monotonically with disease progression, while in emphysema the opposite occurs. These diseases can thus be mimicked simply by making appropriate adjustments to the parameters of the P-V curve. Using Clausius's formalism, we show that entropy production, ΔS, is related to the hysteresis area, ΔA, enclosed by the P-V curve during a breathing cycle, namely, ΔS=ΔA∕T, where T is the body temperature. Although ΔA is highly dependent on the disease, such formula applies to healthy as well as diseased lungs, regardless of the disease stage. Finally, we use an ansatz to predict analytically the entropy produced by the fibrotic and emphysematous lungs.

Numerical modeling of the wind flow over a transverse dune.

Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. Here we perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. We find that the length of the zone of recirculating flow at the dune lee - the separation bubble - displays a surprisingly strong dependence on the wind shear velocity, u: it is nearly independent of u for shear velocities within the range between 0.2 m/s and 0.8 m/s but increases linearly with u for larger shear velocities. Our calculations show that transport in the direction opposite to dune migration within the separation bubble can be sustained if u is larger than approximately 0.39 m/s, whereas a larger value of u (about 0.49 m/s) is required to initiate this reverse transport.

Nonequilibrium model on Apollonian networks.

We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, ß/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.

Mechanical failure, stress redistribution, elastase activity and binding site availability on elastin during the progression of emphysema.

Emphysema is a disease of the lung parenchyma with progressive alveolar tissue destruction that leads to peripheral airspace enlargement. In this review, we discuss how mechanical forces can contribute to disease progression at various length scales. Airspace enlargement requires mechanical failure of alveolar walls. Because the lung tissue is under a pre-existing tensile stress, called prestress, the failure of a single wall results in a redistribution of the local prestress. During this process, the prestress increases on neighboring alveolar walls which in turn increases the probability that these walls also undergo mechanical failure. There are several mechanisms that can contribute to this increased probability: exceeding the failure threshold of the ECM, triggering local mechanotransduction to release enzymes, altering enzymatic reactions on ECM molecules. Next, we specifically discuss recent findings that stretching of elastin induces an increase in the binding off rate of elastase to elastin as well as unfolds hidden binding sites along the fiber. We argue that these events can initiate a positive feedback loop which generates slow avalanches of breakdown that eventually give rise to the relentless progression of emphysema. We propose that combining modeling at various length scales with corresponding biological assays, imaging and mechanics data will provide new insight into the progressive nature of emphysema. Such approaches will have the potential to contribute to resolving many of the outstanding issues which in turn may lead to the amelioration or perhaps the treatment of emphysema in the future.

Dynamics of enzymatic digestion of elastic fibers and networks under tension.

We study the enzymatic degradation of an elastic fiber under tension using an anisotropic random-walk model coupled with binding-unbinding reactions that weaken the fiber. The fiber is represented by a chain of elastic springs in series along which enzyme molecules can diffuse. Numerical simulations show that the fiber stiffness decreases exponentially with two distinct regimes. The time constant of the first regime decreases with increasing tension. Using a mean field calculation, we partition the time constant into geometrical, chemical and externally controllable factors, which is corroborated by the simulations. We incorporate the fiber model into a multiscale network model of the extracellular matrix and find that network effects do not mask the exponential decay of stiffness at the fiber level. To test these predictions, we measure the force relaxation of elastin sheets stretched to 20% uniaxial strain in the presence of elastase. The decay of force is exponential and the time constant is proportional to the inverse of enzyme concentration in agreement with model predictions. Furthermore, the fragment mass released into the bath during digestion is linearly related to enzyme concentration that is also borne out in the model. We conclude that in the complex extracellular matrix, feedback between the local rate of fiber digestion and the force the fiber carries acts to attenuate any spatial heterogeneity of digestion such that molecular processes manifest directly at the macroscale. Our findings can help better understand remodeling processes during development or in disease in which enzyme concentrations and/or mechanical forces become abnormal.

Mechanical forces regulate elastase activity and binding site availability in lung elastin.

Many fundamental cellular and extracellular processes in the body are mediated by enzymes. At the single molecule level, enzyme activity is influenced by mechanical forces. However, the effects of mechanical forces on the kinetics of enzymatic reactions in complex tissues with intact extracellular matrix (ECM) have not been identified. Here we report that physiologically relevant macroscopic mechanical forces modify enzyme activity at the molecular level in the ECM of the lung parenchyma. Porcine pancreatic elastase (PPE), which binds to and digests elastin, was fluorescently conjugated (f-PPE) and fluorescent recovery after photobleach was used to evaluate the binding kinetics of f-PPE in the alveolar walls of normal mouse lungs. Fluorescent recovery after photobleach indicated that the dissociation rate constant (k(off)) for f-PPE was significantly larger in stretched than in relaxed alveolar walls with a linear relation between k(off) and macroscopic strain. Using a network model of the parenchyma, a linear relation was also found between k(off) and microscopic strain on elastin fibers. Further, the binding pattern of f-PPE suggested that binding sites on elastin unfold with strain. The increased overall reaction rate also resulted in stronger structural breakdown at the level of alveolar walls, as well as accelerated decay of stiffness and decreased failure stress of the ECM at the macroscopic scale. These results suggest an important role for the coupling between mechanical forces and enzyme activity in ECM breakdown and remodeling in development, and during diseases such as pulmonary emphysema or vascular aneurysm. Our findings may also have broader implications because in vivo, enzyme activity in nearly all cellular and extracellular processes takes place in the presence of mechanical forces.

Distribution of local fluxes in diluted porous media.

We study the distributions of channel openings, local fluxes, and velocities in a two-dimensional random medium of nonoverlapping disks. We present theoretical arguments supported by numerical data of high precision and find scaling laws as functions of the porosity. For the channel openings we observe a crossover to a highly correlated regime at small porosities. The distribution of velocities through these channels scales with the square of the porosity. The fluxes turn out to be the convolution of velocity and channel width corrected by a geometrical factor. Furthermore, while the distribution of velocities follows a Gaussian form, the fluxes are distributed according to a stretched exponential with exponent 1/2. Finally, our scaling analysis allows us to express the tortuosity and pore shape factors from the Kozeny-Carman equation as direct average properties from microscopic quantities related to the geometry as well as the flow through the disordered porous medium.