Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session J24: Crystallization, Jamming, and Glassy BehaviorFocus
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Sponsoring Units: GSNP DFD Chair: Mark Shattuck, The City College of New York Room: 401 |
Tuesday, March 3, 2020 2:30PM - 3:06PM |
J24.00001: Nucleation in Granular Media Undergoing Cyclic Shear Invited Speaker: Weiwei Jin Recent experiments have found that homogeneous nucleation occurs in dense granular materials undergoing cyclic shear from an initially disordered state. In the experiments, the mm-sized grains are under gravitational loading and interact via frictional contact forces. In this work, we carry out discrete element method simulations to determine the contributions of friction and gravity to crystallization of granular materials during cyclic shear. We show that cyclic shear of frictionless granular materials in the absence of gravity gives rise to a first-order-like phase transition from a disordered state to a polycrystalline state with domains of face-centered cubic and hexagonal close packed positional order. The polycrystalline ordering develops through homogeneous nucleation, i.e., spontaneous formation of crystalline clusters far from the boundaries of the system. The small crystalline clusters typically shrink before they reach a critical size, above which crystallites with no preferred orientation grow to reach the system size. Thus, gravitational loading and frictional forces are not necessary to induce crystallization in driven granular media. |
Tuesday, March 3, 2020 3:06PM - 3:18PM |
J24.00002: Structural and Mechanical Characteristics of the Disorded-Ordered Transition in Mechanically Stable Sphere Packings Hideyuki Mizuno, Kuniyasu Saitoh, Leo Silbert Using the discrete element method, we generate mechanically stable sphere packings in three dimensions that span a wide range in structural order, ranging from fully amorphous through to (quasi) ordered structures, as characterized by the globally averaged bond orientational order parameter. While amorphous systems exhibit features consistent with hyperuniformity – suppressed density fluctuations in the long-wavelength limit – as the packing structure becomes more ordered, the low-wavenumber limit of the static structure factor grows with increasing order. As the packing pressure, p, is varied from the marginally rigidity (p~0) to more robust systems (p>>0), the packing coordination number, z, follows a familiar scaling relation with pressure, Δz = z-z0 ~ p1/2, where z0 = z(p=0). While it has previously been noted that Δz is the control parameter that determines packing properties, here we show how packing structure plays an influential role on the mechanical properties of the packings. Specifically, we find that the elastic (bulk and shear) moduli, generically referred to as M, become functions of both Dz and structure, to the extent that, M – M0 ~ Δz. Here, M0 are the values of the elastic moduli in the zero-pressure limit, whose values depend on the structure of the packing. |
Tuesday, March 3, 2020 3:18PM - 3:30PM |
J24.00003: Isostatic, ordered disk packings Philip Tuckman, Kyle VanderWerf, Mark Shattuck, Corey Shane O'Hern Numerous studies have shown that disordered, jammed disk packings are |
Tuesday, March 3, 2020 3:30PM - 3:42PM |
J24.00004: Athermal fluctuations in disordered crystals Pappu Acharya, Surajit Sengupta, Bulbul Chakraborty, Kabir Ramola We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of the weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions. |
Tuesday, March 3, 2020 3:42PM - 3:54PM |
J24.00005: Mechanically stable sphere packings at arbitrarily low densities Robert Dennis, Eric Corwin Lightweight materials can be formed by creating mechanically rigid structures with a combination of compressive and tensile forces. By considering purely compressive forces in sphere packings, we determine the limits on creating low density rigid systems. An Apollonian packing proves that a rigid packing can completely fill space, but proof for the existence of a lowest density rigid packing was unknown. The previously known lowest density packings are constructed by diluting simple crystals, but we present a new construction based on rigid bridges. This new construction not only demonstrates that lower density packings can be achieved, but it can be used to create rigid packings with densities arbitrarily close to zero. We demonstrate the rigidity of these low density packings using both established and novel procedures and we explore the properties of these configurations to gain a deeper understanding of the limits of rigidity in repulsive systems. Such constructions not only lay an old puzzle to rest, but enable the development of new lightweight materials. |
Tuesday, March 3, 2020 3:54PM - 4:06PM |
J24.00006: Real-space renormalization of randomly vacated lattices: a renormalization group for jamming? Abe Clark Jamming occurs in granular materials, as well as in emulsions, dense suspensions, and other amorphous, particulate systems. When the pack- ing fraction φ, defined as the ratio of particle volume to system volume, is increased past a critical value φc, a liquid-solid phase transition occurs, and grains are no longer able to rearrange. Previous studies have shown evidence of spatial correlations that diverge near φ = φc, but there has been no explicit spatial renormalization group (RG) scheme that has captured this transition. Here, I present a candidate for such a scheme, using a block-spin-like transformation of a randomly vacated lattice of grains. I define a real-space RG transformation based on local mechanical stability. This model displays a critical packing fraction φc and gives estimates of critical exponents in two and three dimensions. |
Tuesday, March 3, 2020 4:06PM - 4:18PM |
J24.00007: Critical scaling for yield is independent of distance to isostaticity Jacob D Thompson, Abe Clark Granular materials, suspensions, foams, and emulsions can form amorphous jammed states. These states can yield when subjected to a shear stress τ. When μ = τ/p, where p is the system pressure, exceeds a critical value μc, jammed states become inaccessible and flow persists indefinitely. Near μ = μc, long-range cooperative effects become dominant, as shown by the success of recent nonlocal rheological models. Long-range cooperativity in these systems is often framed in terms of the isostatic jamming point, which occurs at p = 0. The relationship between isostatic jamming and yielding is not fully understood. Here, using simulations of quasi-statically sheared soft sphere packings, we observe critical behavior near μ=μc, with a diverging length scale ξ ~ |μ - μc |-ν, that is independent of distance to isostaticity over a wide range of p. The critical scaling functions and values of the scaling exponents are nearly independent of distance to isostaticity despite the large range of p. Our results demonstrate that yielding of jammed systems represents a critical transition that is distinct from the isostatic point. Our results may also be useful in deriving and improving nonlocal rheological models. |
Tuesday, March 3, 2020 4:18PM - 4:30PM |
J24.00008: The Influence of the Wall on Confined Random Packing of Rods Jason Jiang, Julian O Freeman, Eric Weeks We experimentally study the random packing of rods into small containers, and in particular, examine the influence of the container surface on the packing. Our experiments use cylindrical containers of different radii, and rods of aspect ratio 8. As previously seen, rods packed into smaller cylindrical containers yielded lower volume fractions than in larger containers. In this current work, we coat the inner vertical surface of the containers with sandpaper to change the enhance friction between the wall and the rods. We find a linear relationship between the volume fraction f and 1/R (using the radius R of the container). The intercept gives the infinite-radius container extrapolated volume fraction, and the slope quantifies how strongly the walls affect the packing. As might be expected, rougher sandpaper results in a stronger influence from the walls. Surprisingly, sandpaper also influences the infinite-radius extrapolation volume fraction. |
Tuesday, March 3, 2020 4:30PM - 4:42PM |
J24.00009: Two-stage jamming in semiflexible polymers and fibers Joseph Fox Dietz, Robert Hoy We find that jamming in model freely rotating polymers with bond angle θ0 occurs in two stages. The first, precursor stage occurs when the average number of unique interchain contacts Zchain jumps discontinuously as chains “entangle” at a packing fraction φe(θ0). Entanglement is a necessary but not a sufficient condition for mechanical rigidity; systems rigidify (i.e. jam) at φJ(θ0) > φe(θ0), and Zchain jumps discontinuously again at φJ(θ0). These discontinuities become sharper as polymers stiffen (as θ0 decreases). We find that φe(θ0) ~ .8φJ(θ0) despite the fact that both decrease by a factor of nearly two as polymers stiffen. Our results for small θ0 may also describe jamming phenomena in fiber networks. |
Tuesday, March 3, 2020 4:42PM - 4:54PM |
J24.00010: Low frequency vibrations of deformable particles Dong Wang, Arman Boromand, Michael Murrell, Mark Shattuck, Corey Shane O'Hern Disk packings at jamming onset exhibit an excess of low-frequency vibrational modes compared to the number predicted by Debye scaling. The excess number of modes, which controls the mechanical response of packings, decreases as the packings are compressed above jamming onset. In this work, we calculate the spectrum of vibrational modes from the eigenvalues of the dynamical matrix for truly deformable particles at jamming onset as a function of the shape parameter A = p2/(4πa), where p is the perimeter and a is the area of the particle. We show that there is an excess number of low frequency, collective modes in the density of vibrational modes for jammed packings of deformable particles over a wide range of particle shape both above and below the characteristic value A ≈ 1.15 at which the system is confluent. |
Tuesday, March 3, 2020 4:54PM - 5:06PM |
J24.00011: Structure and dynamics during training of memory in jammed packings Ian Graham, Andrea Jo-Wei Liu Jammed packings can be trained by intermediate-amplitude quasistatic oscillatory shear to fall into periodic trajectories in which the same multiple local minima are explored in each period. Here we ask how the rearrangement dynamics and stroboscopic snapshots of packing structure evolve during the training process. We use persistent homology to characterize the structure. We characterize rearrangements in terms of T1 events and classify them as reversible if they return to their initial configuration and irreversible if they do not. At the end of the training process, irreversible T1 events must vanish when the system falls into a periodic trajectory (develops a memory). We find that the structure varies continuously during the training, but that the nature and number of T1 events remains nearly constant until the last cycle or two before the system develops memory. Thus, observable changes in structure have relatively little effect on dynamics until near the end of the training process, in contrast with glassy dynamics, in which extremely subtle changes in structure lead to enormous changes in dynamics. |
Tuesday, March 3, 2020 5:06PM - 5:18PM |
J24.00012: Measuring the Granular Density of Modes in 3D via Impact Eli Owens, Sydney Blue, Salem C Wright The jamming transition is an important feature of granular materials, with prior work showing an excess of low frequency modes in the granular density of states (or modes). In this work, we present an experimental method for acoustically measuring the granular density of modes using a single impact event to excite vibrational modes in the granular material. We test three different granular materials, all of which are composed of spherical plastic beads. The first two systems are monodisperse collections of either 6 mm or 8 mm diameter beads. The third system is a bidisperse mixture of the previous two bead sizes. During data collection, the particles are confined to a 30x30x20 cm box; on top of this box, and resting on the granular material is a light, rigid sheet onto which weights can be placed. To excite the material, an impactor is dropped on top of the system. The response of the granular material to the impact pulse is recorded by piezoelectric sensors buried throughout the material, and the density of modes is computed from the spectrum of the velocity autocorrelation of these sensors. Our initial measurements of the density of modes differentiate between the three different systems and between different pressure states. |
Tuesday, March 3, 2020 5:18PM - 5:30PM |
J24.00013: Quenching to field-stabilized magnetization plateaus in the unfrustrated Ising antiferromagnet Adam Iaizzi, Ying-Jer Kao We study the square-lattice Ising antiferromagnet in a uniform field using single spin flip Metropolis algorithm dynamics. Starting from an infinite temperature state, we perform an instantaneous quench to finite T. Under this protocol, the field stabilizes two magnetization plateaus in a regime where the equilibrium magnetization is zero. This occurs despite the absence of intrinsic disorder or frustration. These metastable plateau states are extremely stable, even for small sizes and moderate temperatures. Ergodicity is restored near the edges of the plateaus. The plateaus can be understood as ‘tilings’ of stable local configurations. Once the system reaches one of these tiled states, the probability of flipping even a single spin is exponentially suppressed. Although the details of the plateaus will depend on the update scheme, the underlying principle causing the breakdown of ergodicity is quite general. This simple case can thus provide a paradigm for understanding ergodicity breakdown in Monte Carlo dynamics more generally. |
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