Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session K48: Athermal Systems and Statistical MechanicsFocus

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Sponsoring Units: GSNP Chair: Raphael Blumenfeld, Imperial College London Room: LACC 510 
Wednesday, March 7, 2018 8:00AM  8:36AM 
K48.00001: Percolation on correlated landscapes Invited Speaker: Hans Herrmann Random landscapes with powerlaw heightheight correlations are described by a Hurst exponent H and can be generated by the Fourier filtering method. The isoheight lines at the percolation threshold and their accessible perimeter as well as the shortest path on the percolation cluster are fractals for 1 < H < 0 with dimensions that depends on H. Exact results are recovered for H = 1 and H = 0. Analyzing numerically the winding angle, the left passage probability, and the driving function of these curves, it is found that for negative H there statistical properties are compatible with a SchrammLoewner evolution (SLE) and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. The watershed dividing drainage basins of the landscape can also be obtained from percolation by suppressing systematically the occupation of bridges, i.e. those sites or bonds which if occupied would create the spanning cluster. This delays the percolation threshold and produces at the end a connected line of bridges which is identical to the watershed, exhibiting trivially a first order percolation transition. At p_c, bridge percolation exhibits theta point scaling with a new tricritical exponent. Watersheds also are found to be compatible with SLE. For uncorrelated surfaces, i.e. H = 1, the corresponding diffusivities are κ = 1.734 +/ 0.005 for the watershed and κ = 1.04 +/ 0.02 for the shortest path, being the only examples known up to now with κ < 2. Both watershed and shortest path result from a global optimization process and identifying them, requires exploring an entire area. The perimeters of multilayered and directed percolation clusters at criticality are the scaling limits of the Loewner evolution of an anomalous Brownian motion, being superdiffusive and subdiffusive, respectively. 
Wednesday, March 7, 2018 8:36AM  8:48AM 
K48.00002: Equation of state in a model granular suspension Nariaki Sakaï , Sébastien Moulinet , Frederic Lechenault , Mokhtar AddaBedia We experimentally investigate the stationary sedimentation of an assembly of buoyant cylinders in a rotating HeleShaw cell. The resulting tunable centripetal force allows exploring various states of the system. We find that local density fluctuations are in onetoone correspondence with its mean, irrespective of the potential. From this relation, we derive a statistical pressure that appears to be proportional to a hydrodynamic pressure built from a mixture model over the whole range of explored packing fractions, allowing us to define an effective temperature in the medium. This quantity, which only depends on the density contrast between the grains and the liquid, entertains a simple relation to the dissipated energy. 
Wednesday, March 7, 2018 8:48AM  9:00AM 
K48.00003: Thermal Ensemble for Stresses in Dense Suspensions Jetin E Thomas , Kabir Ramola , Abhinendra Singh , Jeffrey Morris , Bulbul Chakraborty We develop a predictive framework for the macroscopic stress properties of dense suspensions 
Wednesday, March 7, 2018 9:00AM  9:12AM 
K48.00004: Memory in SolidSolid Interfaces Samuel Dillavou , Shmuel Rubinstein The interface between two solid, static bodies  your chair and the floor, your cup and the table, two books in a stack  is in fact continuously evolving. Due to smallscale roughness, ostensibly flat surfaces typically have a real area of contact several orders of magnitude smaller than apparent area. As a result, these contact points experience enormous pressures, and slowly deform in time. 
Wednesday, March 7, 2018 9:12AM  9:48AM 
K48.00005: Fragile Matter: Stress Networks and Stability of Athermal Solids Invited Speaker: Bulbul Chakraborty In this talk, I will discuss a theoretical framework for for understanding materials that are fragile. These are marginal solids that emerge out of thermal equilibrium in response to external stresses. Granular materials and nonBrownian colloidal suspensions are wellknown examples, however, reconfigurable pathways of force transmission also play an important role in biological systems. In granular materials, external forces such as gravity create rigid and flowing states. The mechanical integrity of these marginal solids is reliant on a filamentary network of stressbearing structures. An outstanding question in the field has been how the constraints of vectorial force balance influence the response of granular assemblies to stress, and create localized stress pathways. I will present results of recent work showing that the localized response is a consequence of the disorder in the underlying contact network, and can be mapped on to a ``localization'' problem. I will then discuss criterion for stability and yielding of these networks, based on a gaugepotential formalism that imposes all of the constraints of mechanical equilibrium. 
(Author Not Attending)

K48.00006: Field theory for athermal solids Eric DeGiuli Amorphous solids composed of macroscopic constituents, like granular media, foams, and emulsions, can be considered as zero temperature systems. Long ago, Edwards proposed that such systems could be treated by statistical mechanical methods by taking a flat average over all metastable states. Despite its attractive parsimony, this hypothesis has remained controversial and has led to conflicting results. I will present some new ideas that remove the ambiguity in Edwards' approach and make it a constructive, feasible route to derive macroscopic equations of state and field equations for athermal systems. In particular, I will show how shear strain can be included as a control parameter, explain the effect of preparation protocol, and show the utility of the renormalization group in this context. 
Wednesday, March 7, 2018 10:00AM  10:12AM 
K48.00007: Convex Force Polytopes as a Tool for Detecting Granular Plasticity Jishnu Nampoothiri , Kabir Ramola , Bulbul Chakraborty The response of athermal granular systems to external stresses, in the quasistatic regime, are governed by constraints of force and torque balance, along with Coulomb and positivity constraints. As the system undergoes shear, the violation of any of these constraints leads to plastic rearrangements of the system. For a given contact network of frictional jammed disks, we identify all valid force solutions to be within a ddimensional convex polytope, whose volume plays the role of an entropy. By investigating the behavior of the allowed solution space with increasing external shear, we identify the propensity of such packings to undergo a plastic event. We use this to investigate the nature of the yielding transition in frictional soft disks. 
Wednesday, March 7, 2018 10:12AM  10:24AM 
K48.00008: Emergent StrainStiffening in Interlocked Granular Chains Denis Dumont , Paul Rambach , Thomas Salez , Sylvain Patinet , Pascal Damman In nature and architecture, a wide variety of stable structures are formed from dense assemblies of randomlydistributed objects, as illustrated by the various shapes of bird nests. Most physical studies focus on highly anisotropic objects that ensure a solidlike collective behavior and thus the great stability of their assembly. In this presentation, we investigate the effective mechanical rigidity of granularchain assemblies from indentation experiments. Our observations show an exponential growth of the resistance force with the product of two factors: the indentation depth and the square root of the number of beads per chain. The first factor is reminiscent of the selfamplification of friction in a capstan, as well as in interleaved assemblies of sheets, where the increase in resistance is created by, and proportional to, the force exerted by the operator. The second factor points towards the central role played by topological constraints, in a way that is similar to polymer physics. We propose a novel interlocking model based on those two ingredients, and confront it to the experimental data. 
Wednesday, March 7, 2018 10:24AM  10:36AM 
K48.00009: Stress Tensor Measurements of Sheared Packings of NonSpherical Particles Barry Fitzgerald , Junaid Mehmood , Vinay Mahajan , Johan Padding In processing apparatus for dense gassolid flows, the motion of the constituent particles is dictated by interactions with the ambient gas and intercollisions with neighbouring particles. Typically, these particles are nonspherical in nature, such as the elongated biomass particles used in the production of biofuels in fluidised bed reactors. While experiments at both the laboratory and industrial scale can be used to study particle dynamics, information pertaining to particle contact neighbourhood and the interparticle forces in the bulk are difficult to ascertain, thus necessitating a numerical approach. 
Wednesday, March 7, 2018 10:36AM  10:48AM 
K48.00010: StickSlip Dynamics of an Intruder in a 2D Annular Bed of Photoelastic Disks Ryan Kozlowski , David Chen , Robert Behringer When a granular material is strained elastically, the system may resist granular rearrangement depending on interparticle friction, packing fraction, and surrounding boundary conditions. In these long timescale "stick" phases, stresses develop in the granular bed until the system yields in a fast timescale "slip" phase; an example is a slow buildup of stress between sliding tectonic plates and subsequent rapid unloading of stress in an earthquake. We investigate stickslip dynamics of an elastically driven intruder moving through a 2D annular bed of bidisperse photoelastic disks using high speed imaging of force chains on the grain scale. We analyze both the topology of force networks and the global pressure in the bed to understand force chain self organization and contact rearrangement in slip events once a steady state has been reached. In particular, ongoing work focuses on spatial extent of force chains in front of the intruder and local particle density in its wake at varying packing fraction, interparticle friction, and driving spring elastic constant. Parallel simulations are being studied by E. Goldberg, L. Pugnaloni, M. Carlevaro, and L. Kondic. 
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