Temperature scaling, glassiness and stationarity in the Bak-Sneppen model

We show that the emergence of criticality in the locally-defined Bak-Sneppen model corresponds to separation over a hierarchy of timescales. Near to the critical point the model obeys scaling relations, with exponents which we derive numerically for a one-dimensional system. We further describe how the model can be related to the glass model of Bouchaud [{\em J. Phys. I France {\bf 2}, 1705 (1992)}], and we use this insight to comment on the usual assumption of stationarity in the Bak-Sneppen model. Finally, we propose a general definition of self-organised criticality which is in partial agreement with other recent definitions.Comment: 5 pages, 4 figures; differences to previous work clarified. To appear in EPJ

Rheological instability in a simple shear thickening model

We study the strain response to steady imposed stress in a spatially homogeneous, scalar model for shear thickening, in which the local rate of yielding \Gamma(l) of mesoscopic `elastic elements' is not monotonic in the local strain l. Despite this, the macroscopic, steady-state flow curve (stress vs. strain rate) is monotonic. However, for a broad class of \Gamma(l), the response to steady stress is not in fact steady flow, but spontaneous oscillation. We discuss this finding in relation to other theoretical and experimental flow instabilities. Within the parameter ranges we studied, the model does not exhibit rheo-chaos.Comment: 8 pages, 3 figs. Minor corrections made. To appear in Euro. Phys. Let

Robust propagation direction of stresses in a minimal granular packing

By employing the adaptive network simulation method, we demonstrate that the ensemble-averaged stress caused by a local force for packings of frictionless rigid beads is concentrated along rays whose slope is consistent with unity: forces propagate along lines at 45 degrees to the horizontal or vertical. This slope is shown to be independent of polydispersity or the degree to which the system is sheared. Further confirmation of this result comes from fitting the components of the stress tensor to the null stress constitutive equation. The magnitude of the response is also shown to fall off with the -1/2 power of distance. We argue that our findings are a natural consequence of a system that preserves its volume under small perturbations.Comment: 8 pages, 6 figures. Some extra clarification and minor improvements. To appear in EPJ-

Geology of the Venus equatorial region from Pioneer Venus radar imaging

The surface characteristics and morphology of the equatorial region of Venus were first described by Masursky et al. who showed this part of the planet to be characterized by two topographic provinces, rolling plains and highlands, and more recently by Schaber who described and interpreted tectonic zones in the highlands. Using Pioneer Venus (PV) radar image data (15 deg S to 45 deg N), Senske and Head examined the distribution, characteristics, and deposits of individual volcanic features in the equatorial region, and in addition classified major equatorial physiographic and tectonic units on the basis of morphology, topographic signature, and radar properties derived from the PV data. Included in this classification are: plains (undivided), inter-highland tectonic zones, tectonically segmented linear highlands, upland rises, tectonic junctions, dark halo plains, and upland plateaus. In addition to the physiographic units, features interpreted as coronae and volcanic mountains have also been mapped. The latter four of the physiographic units along with features interpreted to be coronae

Deformation of crosslinked semiflexible polymer networks

Networks of filamentous proteins play a crucial role in cell mechanics. These cytoskeletal networks, together with various crosslinking and other associated proteins largely determine the (visco)elastic response of cells. In this letter we study a model system of crosslinked, stiff filaments in order to explore the connection between the microstructure under strain and the macroscopic response of cytoskeletal networks. We find two distinct regimes as a function primarily of crosslink density and filament rigidity: one characterized by affine deformation and one by non-affine deformation. We characterize the crossover between these two.Comment: Typos fixed and some technical details clarified. To appear in Phys. Rev. Let

Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.Comment: 7 pages in J. Phys. Cond. Mat. spec; 4 figs (2 low-quality to reach LANL's over-restrictive size limits; ask for high-detailed versions if required

Non-local fluctuation correlations in active gels

Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations is essential for understanding the properties and behaviors of such systems. Here we present a mathematical procedure to estimate the local action of force-generating agents from the observed fluctuating displacement fields. The active agents are modeled as oriented force dipoles or isotropic compression foci, and the matrix on which they act is assumed to be either a compressible elastic continuum or a coupled network-solvent system. Correlations at a single point and between points separated by an arbitrary distance are obtained, giving a total of three independent fluctuation modes that can be tested with microrheology experiments. Since oriented dipoles and isotropic compression foci give different contributions to these fluctuation modes, ratiometric analysis allows us characterize the force generators. We also predict and experimentally find a high-frequency ballistic regime, arising from individual force generating events in the form of the slow build-up of stress followed by rapid but finite decay. Finally, we provide a quantitative statistical model to estimate the mean filament tension from these athermal fluctuations, which leads to stiffening of active networks.Comment: 12 pages, 7 figures; some clarifications and ammended figure notation

Energy Distribution in disordered elastic Networks

Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed

Extremal driving as a mechanism for generating long-term memory

It is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit long-term memory. This is verified for the minimal extremally driven model, which is first defined and then solved for all system sizes N\geq2 and times t\geq0, yielding exact expressions for the persistence R(t)=[1+t/(N-1)]^{-1} and the two-time correlation function C(t_{\rm w}+t,t_{\rm w})=(1-1/N)(N+t_{\rm w})/(N+t_{\rm w}+t-1). The existence of long-term memory is inferred from the scaling of C(t_{\rm w}+t,t_{\rm w})\sim f(t/t_{\rm w}), denoting {\em aging}. Finally, we suggest ways of investigating the robustness of this mechanism when competing processes are present.Comment: 5 pages, no figures; requires IOP style files. To appear as a J. Phys. A. lette

The mechanical response of semiflexible networks to localized perturbations

Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or non-uniform (non-affine) under external stress. Associated with these regimes, it has been further suggested that a new fundamental length scale emerges, which characterizes the scale for the crossover from non-affine to affine deformations. Here, we extend these studies by probing the response to localized forces and force dipoles. We show that the previously identified nonaffinity length [D.A. Head et al. PRE 68, 061907 (2003).] controls the mesoscopic response to point forces and the crossover to continuum elastic behavior at large distances.Comment: 16 pages, 18 figures; substantial changes to text and figures to clarify the crossover to continuum elasticity and the role of finite-size effect