Effective rheology across the fragmentation transition for sea ice and ice shelves

Funding was provided by the NERC grant NE/P011365/1 Calving Laws for Ice Sheet Models CALISMO. Data files for the plots are found at: https://doi.org/10.5285/76D7D3CA-7B83-4BB0-AAE5-A8E92C7DA5B0Sea ice and ice shelves can be described by a viscoelastic rheology that is approximately linear elastic and brittle at high strain rates, and viscously shear‐thinning at low strain rates. Brittle ice easily fractures under compressive shear and forms shear bands as the material undergoes a transition to a fragmented, granular state. This transition plays a central role in the mechanical behaviour at large scales of sea‐ice in the Arctic Ocean or Antarctic ice shelves. Here we demonstrate that the fragmentation transition is characterized by an essentially discontinuous drop of 3‐5 orders of magnitude in effective viscosity and stress‐relaxation time. Beyond the fragmentation transition, grinding in shear zones further reduces both effective viscosity and shear stiffness, but with an essentially constant relaxation time of ∼10second. These results are relevant for ice‐rheology implementation in large‐scale climate‐related models of sea ice and thin ice shelves.Publisher PDFPeer reviewe

Scaling of impact fragmentation near the critical point

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition disagreed with that of percolation. However, the weighted mean mass of the fragments could be scaled using the pseudo-control parameter multiplicity. The data for highly fragmented samples included a cumulative fragment mass distribution that clearly obeyed a power-law. The exponent of this power-law was 0.5 and it was independent of sample size. The fragment mass distributions in this regime seemed to collapse into a unified scaling function using weighted mean fragment mass scaling. We also examined the behavior of higher order moments of the fragment mass distributions, and obtained multi-scaling exponents that agreed with those of the simple biased cascade model.Comment: 6 pages, 6 figure

Non-universality of elastic exponents in random bond-bending networks

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross-links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0\pm0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.Comment: 4 pages, 3 figures, minor clarifications and amendments. To appear in PRE Rap. Com

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

Development and Validation of a Tokamak Skin Effect Transformer model

A control oriented, lumped parameter model for the tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non linear interaction of the plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with Random Binary Signals (RBS) have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated in Ohmic conditions between 200kA and 300kA with 30ms rise time, several times faster than its time constant L/R\approx200ms. The model explains the most salient features of the plasma current transients without requiring detailed or explicit information about resistivity profiles. This proves that lumped parameter modeling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least in Ohmic conditions without external heating and current drive sources

Spontaneous formation of densely packed shear bands of rotating fragments

Appearance of self-similar space-filling ball bearings has been suggested to provide the explanation for seismic gaps, shear weakness, and lack of detectable frictional heat formation in mature tectonic faults (shear zones). As the material in a shear zone fractures and grinds, it could be thought to eventually form a conformation that allows fragments to largely roll against each other without much sliding. This type of space-filling “ball bearing” can be constructed artificially, but so far how such delicate structures may appear spontaneously has remained unexplained. It is demonstrated here that first-principles simulations of granular packing with fragmenting grains indeed display spontaneous formation of shear bands with fragment conformations very similar to those of densely packed ball bearings

Cell aggregation : packing soft grains

Cellular aggregates may be considered as collections of membrane enclosed units with a pressure difference between the internal and external liquid phases. Cells are kept together by membrane adhesion and/or confined space compression. Pattern formation and, in particular, intercellular spacing have important roles in controlling solvent diffusion within such aggregates. A physical approach is used to study generic aspects of cellular packings in a confined space. Average material properties are derived from the free energy. The appearance of penetrating intercellular void channels is found to be critically governed by the cell wall adhesion mechanisms during the formation of dense aggregates. A fully relaxed aggregate efficiently hinders solvent diffusion at high hydrostatic pressures, while a small fraction (~0.1) of adhesion related packing frustration is sufficient for breaking such a blockage even at high a pressure

Cell aggregation : packing soft grains

Cellular aggregates may be considered as collections of membrane enclosed units with a pressure difference between the internal and external liquid phases. Cells are kept together by membrane adhesion and/or confined space compression. Pattern formation and, in particular, intercellular spacing have important roles in controlling solvent diffusion within such aggregates. A physical approach is used to study generic aspects of cellular packings in a confined space. Average material properties are derived from the free energy. The appearance of penetrating intercellular void channels is found to be critically governed by the cell wall adhesion mechanisms during the formation of dense aggregates. A fully relaxed aggregate efficiently hinders solvent diffusion at high hydrostatic pressures, while a small fraction (~0.1) of adhesion related packing frustration is sufficient for breaking such a blockage even at high a pressure

Fragmentation dynamics within shear bands-a model for aging tectonic faults?

A numerical model for packing of fragmenting blocks in a shear band is introduced, and its dynamics is compared with that of a tectonic fault. The shear band undergoes a slow aging process in which the blocks are being grinded by the shear motion and the compression. The dynamics of the model have the same statistical characteristics as the seismic activity in faults. The characteristic magnitude distribution of earthquakes appears to result from frictional slips at small and medium magnitudes, and from fragmentation of blocks at the largest magnitudes. Aftershocks to large-magnitude earthquakes are local recombinations of the fragments before they reach a new quasi-static equilibrium. The aftershocks satisfy Omori's law. Local precursor activity at a few times the normal background level appears at a short time before a major earthquake. Seismic gaps appear as a natural consequence of the aging process of a fault. Explanation of the heat flux and principal stress direction anomalies at the faults both involve the value of fracture stress of the blocks in the gouge. The final form of a tectonic fault is predicted to involve a gouge dominated by fine-grained and rather rounded blocks so that it cannot withstand large shear stresses

Aster formation and rupture transition in semi-flexible fiber networks with mobile cross-linkers

Fibrous active network structures whose properties are regulated by motor proteins, or simply motors, are fundamental to life. Here, a full elastic and three dimensional model for such networks and motors is presented. The effects of surface anchoring are accounted for and we demonstrate that for unidirectional motors two basic contractile phases emerge in these systems. The transition is governed by a single parameter (tb/tc) which is the ratio of the breaking strain (tb) and the motility limiting strain (tc) of the motors. For tb/tc [less, similar] 2 and clamped boundaries, the network ruptures and formation of local asters occurs with a high density of motors at the centre and the fibers radially spanning out. This phase displays contraction strain during the formation of asters but the network stress is relaxed once the asters have emerged, demonstrating that the formation of aster-like structures provides a mechanism for stress relaxation. For 2.7 [less, similar] tb/tc the network remains intact, but reaches a force equilibrium with a high contraction strain in the case of clamped boundaries. Between these two limits the network is partly ruptured. Experimental measurements (e.g. J. T. Nishizaka, H. Miyata, H. Yoshikawa, S. Ishiwata and K. Kinosita Jr., Nature, 1995, 377, 251 and J. F. Finer, R. M. Simmons, J. A. Spudich, Nature, 1994, 368, 113) indicate that actin filament and myosin motors interact with tb/tc ˜ 2.7 which is right at the limit of motor induced fracture for a random network, indicating that e.g. a cytoskeleton with active myosin is susceptible to rupture. This is perhaps not a coincidence and may well be an important factor contributing to cellular dynamics. In the case of free boundaries the network collapses onto one single aster. We also show that the distribution of energy on the motors is a power-law, below the motility limit energy, with the exponent -0.5