Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of deformable vesicle
s or soft tissue like cell walls, chorions, and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements - perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.
Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address these ques
tions is the percolation model, where the resilience of the system is quantified by the dependence of the size of the largest cluster on the number of failures. Numerically, the major challenge is the identification of this cluster and the calculation of its size. Here, we propose an efficient algorithm to tackle this problem. We show that the algorithm scales as O(N log N), where N is the number of nodes in the network, a significant improvement compared to O(N^2) for a greedy algorithm, what permits studying much larger networks. Our new strategy can be applied to any network topology and distribution of interdependencies, as well as any sequence of failures.
We performed numerical simulations of the $q$-state Potts model to compute the reduced conductivity exponent $t/ u$ for the critical Coniglio-Klein clusters in two dimensions, for values of $q$ in the range $[1;4]$. At criticality, at least for $q<4
$, the conductivity scales as $C(L) sim L^{-frac{t}{ u}}$, where $t$ and $ u$ are, respectively, the conductivity and correlation length exponents. For q=1, 2, 3, and 4, we followed two independent procedures to estimate $t / u$. First, we computed directly the conductivity at criticality and obtained $t / u$ from the size dependence. Second, using the relation between conductivity and transport properties, we obtained $t / u$ from the diffusion of a random walk on the backbone of the cluster. From both methods, we estimated $t / u$ to be $0.986 pm 0.012$, $0.877 pm 0.014$, $0.785 pm 0.015$, and $0.658 pm 0.030$, for q=1, 2, 3, and 4, respectively. We also evaluated $t / u$ for non integer values of $q$ and propose the following conjecture $40gt/ u=72+20g-3g^2$ for the dependence of the reduced conductivity exponent on $q$, in the range $ 0 leq q leq 4$, where $g$ is the Coulomb gas coupling.
106 -
Christian M. Schneider
, Tobias A. Kesselring
, Jose S. Andrade Jr. andn Hans J. Herrmann
2012
The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperform
s previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.
The recent work by Achlioptas, DSouza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several ques
tions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one. As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. The surface of the clusters is fractal, with the same fractal dimension of the watershed line.
The discrete element method constitutes a general class of modeling techniques to simulate the microscopic behavior (i.e. at the particle scale) of granular/soil materials. We present a contact dynamics method, accounting for the cohesive nature of f
ine powders and soils. A modification of the model adjusted to capture the essential physical processes underlying the dynamics of generation and collapse of loose systems is able to simulate quicksand behavior of a collapsing soil material, in particular of a specific type, which we call living quicksand. We investigate the penetration behavior of an object for varying density of the material. We also investigate the dynamics of the penetration process, by measuring the relation between the driving force and the resulting velocity of the intruder, leading to a power law behavior with exponent 1/2, i.e. a quadratic velocity dependence of the drag force on the intruder.
Loose granular structures stabilized against gravity by an effective cohesive force are investigated on a microscopic basis using contact dynamics. We study the influence of the granular Bond number on the density profiles and the generation process
of packings, generated by ballistic deposition under gravity. The internal compaction occurs discontinuously in small avalanches and we study their size distribution. We also develop a model explaining the final density profiles based on insight about the collapse of a packing under changes of the Bond number.
We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a Maxwell-Bolt
zmann distribution. The PDFs are symmetric around zero velocity and show a Gaussian core and exponential tails over more than six orders of magnitude of probability. Following the excellent agreement of our theory and simulation data, we demonstrate that the distribution functions scale with the shear rate, the particle volume concentration, as well as the fluid viscosity.
We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves
efficiency and accuracy of the Discrete Element Method (DEM) when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.
We generalize the recent study of random space-filling bearings to a more realistic situation, where the spacing offset varies randomly during the space-filling procedure, and show that it reproduces well the size-distributions observed in recent stu
dies of real fault gouges. In particular, we show that the fractal dimensions of random polydisperse bearings sweep predominantly the low range of values in the spectrum of fractal dimensions observed along real faults, which strengthen the evidence that polydisperse bearings may explain the occurrence of seismic gaps in nature. In addition, the influence of different distributions for the offset is studied and we find that the uniform distribution is the best choice for reproducing the size-distribution of fault gouges.
