Active biopolymer networks generate scale-free but euclidean clusters

We report analytical and numerical modelling of active elastic networks, motivated by experiments on crosslinked actin networks contracted by myosin motors. Within a broad range of parameters, the motor-driven collapse of active elastic networks leads to a critical state. We show that this state is qualitatively different from that of the random percolation model. Intriguingly, it possesses both euclidean and scale-free structure with Fisher exponent smaller than $2$. Remarkably, an indistinguishable Fisher exponent and the same euclidean structure is obtained at the critical point of the random percolation model after absorbing all enclaves into their surrounding clusters. We propose that in the experiment the enclaves are absorbed due to steric interactions of network elements. We model the network collapse, taking into account the steric interactions. The model shows how the system robustly drives itself towards the critical point of the random percolation model with absorbed enclaves, in agreement with the experiment.Comment: 6 pages, 7 figure

Normal stresses in semiflexible polymer hydrogels

Biopolymer gels such as fibrin and collagen networks are known to develop tensile axial stress when subject to torsion. This negative normal stress is opposite to the classical Poynting effect observed for most elastic solids including synthetic polymer gels, where torsion provokes a positive normal stress. As recently shown, this anomalous behavior in fibrin gels depends on the open, porous network structure of biopolymer gels, which facilitates interstitial fluid flow during shear and can be described by a phenomenological two-fluid model with viscous coupling between network and solvent. Here we extend this model and develop a microscopic model for the individual diagonal components of the stress tensor that determine the axial response of semi-flexible polymer hydrogels. This microscopic model predicts that the magnitude of these stress components depends inversely on the characteristic strain for the onset of nonlinear shear stress, which we confirm experimentally by shear rheometry on fibrin gels. Moreover, our model predicts a transient behavior of the normal stress, which is in excellent agreement with the full time-dependent normal stress we measure.Comment: 12 pages, 8 figure

Multi-scale strain-stiffening of semiflexible bundle networks

Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial for normal blood clotting, protofibrils self-assemble and bundle to form networks of semiflexible fibers. Here we show that the extraordinary strain-stiffening response of fibrin networks is a direct reflection of the hierarchical architecture of the fibrin fibers. We measure the rheology of networks of unbundled protofibrils and find excellent agreement with an affine model of extensible wormlike polymers. By direct comparison with these data, we show that physiological fibrin networks composed of thick fibers can be modeled as networks of tight protofibril bundles. We demonstrate that the tightness of coupling between protofibrils in the fibers can be tuned by the degree of enzymatic intermolecular crosslinking by the coagulation Factor XIII. Furthermore, at high stress, the protofibrils contribute independently to the network elasticity, which may reflect a decoupling of the tight bundle structure. The hierarchical architecture of fibrin fibers can thus account for the nonlinearity and enormous elastic resilience characteristic of blood clots.Comment: 27 pages including 8 figures and Supplementary Dat

Development of a comprehensive monitoring and auditing tool for oxidation ponds systems in the Middle Vaal and Upper Orange catchment areas

An investigation of the current status of municipal sewage pond systems in the Free State region was undertaken to provide the Department of Water Affairs and Forestry (DWAF) Free State Regional Office with a strategic decision support tool to evaluate the current status of sewage pond systems in order to provide base-line information required by the Department. This will also contribute to a healthy environment by ensuring that strategic environmental issues associated with sewage systems are identified and that potential strategies for impact minimisation and prevention are implemented. This paper provides feedback on the background to the study, literature review conducted, the tool developed that can be utilised to assess pond systems and its outputs. This tool must be seen as a positive evaluation tool to ensure good management of pond systems to promote a healthy environment

One- and two-particle microrheology

We study the dynamics of rigid spheres embedded in viscoelastic media and address two questions of importance to microrheology. First we calculate the complete response to an external force of a single bead in a homogeneous elastic network viscously coupled to an incompressible fluid. From this response function we find the frequency range where the standard assumptions of microrheology are valid. Second we study fluctuations when embedded spheres perturb the media around them and show that mutual fluctuations of two separated spheres provide a more accurate determination of the complex shear modulus than do the fluctuations of a single sphere.Comment: 4 pages, 1 figur

Anomalous Discontinuity at the Percolation Critical Point of Active Gels

We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a cluster distribution inconsistent with RP. Our model not only can account for these experiments, but also exhibits an unusual type of mixed phase transition: We find that the transition is characterized by signatures of criticality, but with a discontinuity in the order parameter.Netherlands Organization for Scientific Research. Foundation for Fundamental Research on Matter (Netherlands

Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution $\eta$ and $q=N_H/N_C$, the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of $q$, for $q \gg 1$ and $q \lesssim 1$ respectively.Comment: 5 figure

Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering

We investigate the properties of the optical model wave function for light heavy-ion systems where absorption is incomplete, such as $\alpha + ^{40}$Ca and $\alpha + ^{16}$O around 30 MeV incident energy. Strong focusing effects are predicted to occur well inside the nucleus, where the probability density can reach values much higher than that of the incident wave. This focusing is shown to be correlated with the presence at back angles of a strong enhancement in the elastic cross section, the so-called ALAS (anomalous large angle scattering) phenomenon; this is substantiated by calculations of the quantum probability flux and of classical trajectories. To clarify this mechanism, we decompose the scattering wave function and the associated probability flux into their barrier and internal wave contributions within a fully quantal calculation. Finally, a calculation of the divergence of the quantum flux shows that when absorption is incomplete, the focal region gives a sizeable contribution to nonelastic processes.Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The figures are only available via anonynous FTP on ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat