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A goal of computational studies of protein-protein interfaces (PPIs) is to predict the binding site between two monomers that form a heterodimer. The simplest version of this problem is to rigidly re-dock the bound forms of the monomers, which involves generating computational models of the heterodimer and then scoring them to determine the most native-like models. Scoring functions have been assessed previously using rank- and classification-based metrics, however, these methods are sensitive to the number and quality of models in the scoring function training set. We assess the accuracy of seven PPI scoring functions by comparing their scores to a measure of structural similarity to the x-ray crystal structure (i.e. the DockQ score) for a non-redundant set of heterodimers from the Protein Data Bank. For each heterodimer, we generate re-docked models uniformly sampled over DockQ and calculate the Spearman correlation between the PPI scores and DockQ. For some targets, the scores and DockQ are highly correlated; however, for many targets, there are weak correlations. Several physical features can explain the difference between difficult- and easy-to-score targets. For example, strong correlations exist between the score and DockQ for targets with highly intertwined monomers and many interface contacts. We also develop a new score based on only three physical features that matches or exceeds the performance of current PPI scoring functions. These results emphasize that PPI prediction can be improved by focusing on correlations between the PPI score and DockQ and incorporating more discriminating physical features into PPI scoring functions., Comment: 21 pages, 7 figures

Capillary droplets form due to surface tension when two immiscible fluids are mixed. We describe the motion of gravity-driven capillary droplets flowing through narrow constrictions and obstacle arrays in both simulations and experiments. Our new capillary deformable particle model recapitulates the shape and velocity of single oil droplets in water as they pass through narrow constrictions in microfluidic chambers. Using this experimentally validated model, we simulate the flow and clogging of single capillary droplets in narrow channels and obstacle arrays and find several important results. First, the capillary droplet speed profile is nonmonotonic as the droplet exits the narrow orifice, and we can tune the droplet properties so that the speed overshoots the terminal speed far from the constriction. Second, in obstacle arrays, we find that extremely deformable droplets can wrap around obstacles, which leads to decreased average droplet speed in the continuous flow regime and increased probability for clogging in the regime where permanent clogs form. Third, the wrapping mechanism causes the clogging probability in obstacle arrays to become nonmonotonic with surface tension $\Gamma$. At large $\Gamma$, the droplets are nearly rigid and the clogging probability is large since the droplets can not squeeze through the gaps between obstacles. With decreasing $\Gamma$, the clogging probability decreases as the droplets become more deformable. However, in the small-$\Gamma$ limit the clogging probability increases, since the droplets are extremely deformable and cause clogs as they wrap around the obstacles. The results from these studies are important for developing a predictive understanding of capillary droplet flows through complex and confined geometries.

Proteins fold to a specific functional conformation with a densely packed hydrophobic core that controls their stability. We develop a geometric, yet all-atom model for proteins that explains the universal core packing fraction of $\phi_c=0.55$ found in experimental measurements. We show that as the hydrophobic interactions increase relative to the temperature, a novel jamming transition occurs when the core packing fraction exceeds $\phi_c$. The model also recapitulates the global structure of proteins since it can accurately refold to native-like structures from partially unfolded states., Comment: 5 pages, 4 figures

Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on numerous biochemical and physical properties of cancer cells, adipocytes, and other key components of adipose tissue. We model breast cancer invasion into adipose tissue as a physical process by carrying out simulations of active, cohesive spherical particles (cancer cells) invading into confluent packings of deformable polyhedra (adipocytes). We quantify the degree of invasion by calculating the interfacial area $A_t$ between cancer cells and adipocytes. We determine the long-time value of $A_t$ versus the activity and strength of the cohesion between cancer cells, as well as mechanical properties of the adipocytes and extracellular matrix (ECM) in which the adipocytes are embedded. We show that the degree of invasion collapses onto a master curve by plotting it versus a dimensionless energy scale $E_c$, which grows linearly with mean-square fluctuations and persistence time of the cancer cell velocities, is inversely proportional to the pressure of the system, and has an offset that increases with the cancer cell cohesive energy. The condition, $E_c \gg 1$, indicates that cancer cells will invade the adipose tissue, whereas for $E_c \ll 1$, the cancer cells and adipocytes remain demixed. We also show that constraints on adipocyte positions by the ECM decrease $A_t$ relative to that obtained for unconstrained adipocytes. Finally, spatial heterogeneity in structural and mechanical properties of the adipocytes in the presence of ECM impedes invasion relative to adipose tissue with uniform properties.

Chromatin is a polymer complex of DNA and proteins that regulates gene expression. The three-dimensional structure and organization of chromatin controls DNA transcription and replication. High-throughput chromatin conformation capture techniques generate Hi-C maps that can provide insight into the 3D structure of chromatin. Hi-C maps can be represented as a symmetric matrix where each element represents the average contact probability or number of contacts between two chromatin loci. Previous studies have detected topologically associating domains (TADs), or self-interacting regions in Hi-C maps within which the contact probability is greater than that outside the region. Many algorithms have been developed to identify TADs within Hi-C maps. However, most TAD identification algorithms are unable to identify nested or overlapping TADs and for a given Hi-C map there is significant variation in the location and number of TADs identified by different methods. We develop a novel method, KerTAD, using a kernel-based technique from computer vision and image processing that is able to accurately identify nested and overlapping TADs. We benchmark this method against state-of-the-art TAD identification methods on both synthetic and experimental data sets. We find that KerTAD consistently has higher true positive rates (TPR) and lower false discovery rates (FDR) than all tested methods for both synthetic and manually annotated experimental Hi-C maps. The TPR for KerTAD is also largely insensitive to increasing noise and sparsity, in contrast to the other methods. We also find that KerTAD is consistent in the number and size of TADs identified across replicate experimental Hi-C maps for several organisms. KerTAD will improve automated TAD identification and enable researchers to better correlate changes in TADs to biological phenomena, such as enhancer-promoter interactions and disease states., Comment: 23 pages, 10 figures

The mechanical properties of Cu-Ti alloys have been characterized extensively through experimental studies. However, a detailed understanding of why the strength of Cu increases after a small fraction of Ti atoms is added to the alloy is still missing. In this work, we address this question using density functional theory (DFT) and molecular dynamics (MD) simulations with modified embedded atom method (MEAM) interatomic potentials. First, we performed calculations of uniaxial tension deformations of small bicrystalline Cu cells using DFT static simulations. We then carried out uniaxial tension deformations on much larger bicrystalline and polycrystalline Cu cells using MEAM MD simulations. In bicrystalline Cu, the inclusion of Ti increases the grain boundary separation energy and maximum tensile stress. The DFT calculations demonstrate that the increase in tensile stress can be attributed to an increase in the local charge density arising from Ti. MEAM simulations in larger bicrystalline systems have shown that increasing the Ti concentration decreases the density of stacking faults. This observation is enhanced in polycrystalline Cu, where the addition of Ti atoms, even at concentrations as low as 1.5 at.%, increases the yield strength and elastic modulus of the material compared to pure Cu. Under uniaxial tensile loading, the addition of small amounts of Ti hinders the formation of partial Shockley dislocations in the grain boundaries of Cu, leading to reduced local deformation. These results shed light on the role of Ti in determining the mechanical properties of polycrystalline Cu and will enable the engineering of grain boundaries and the inclusion of Ti to improve degradation resistance.

Previous studies have shown that the interiors of proteins are densely packed, reaching packing fractions that are as large as those found for static packings of individual amino-acid-shaped particles. How can the interiors of proteins take on such high packing fractions given that amino acids are connected by peptide bonds and many amino acids are hydrophobic with attractive interactions? We investigate this question by comparing the structural and mechanical properties of collapsed attractive disk-shaped bead-spring polymers to those of three reference systems: static packings of repulsive disks, of attractive disks, and of repulsive disk-shaped bead-spring polymers. We show that attractive systems quenched to temperatures below the glass transition $T \ll T_g$ and static packings of both repulsive disks and bead-spring polymers possess similar interior packing fractions. Previous studies have shown that static packings of repulsive disks are isostatic at jamming onset, i.e. the number of contacts $N_c$ matches the number of degrees of freedom, which strongly influences their mechanical properties. We find that repulsive polymers are hypostatic at jamming onset, but effectively isostatic when including quartic modes. While attractive disk and polymer packings are hyperstatic, we identify a definition for interparticle contacts for which they can also be considered as effectively isostatic. As a result, we show that the mechanical properties (e.g. scaling of the potential energy with excess contact number and low-frequency contribution to the density of vibrational modes) of weakly attractive disk and polymer packings are similar to those of ${\it isostatic}$ repulsive disk and polymer packings. Our results demonstrate that static packings generated via attractive collapse or compression of repulsive particles possess similar structural and mechanical properties., Comment: 17 pages, 16 figures, 2 appendices

During epithelial wound healing, cell morphology near the healed wound and the healing rate vary strongly among different developmental stages even for a single species like \textit{Drosophila}. We develop deformable particle (DP) model simulations to understand how variations in cell mechanics give rise to distinct wound closure phenotypes in the \textit{Drosophila} embryonic ectoderm and larval wing disc epithelium. We find that plastic deformation of the cell membrane can generate large changes in cell shape consistent with wound closure in the embryonic ectoderm. Our results show that the embryonic ectoderm is best described by cell membranes with an elasto-plastic response, whereas the larval wing disc is best described by cell membranes with an exclusively elastic response. By varying the mechanical response of cell membranes in DP simulations, we recapitulate the wound closure behavior of both the embryonic ectoderm and the larval wing disc.

Most granular packings possess shear moduli ($G$) that increase with the applied external pressure, and bulk moduli ($B$) that increase or remain constant with pressure. This paper presents "tessellated" granular metamaterials for which both $G$ and the ratio $G/B$ decrease with increasing pressure. The granular metamaterials are made from flexible tessellations forming a ring of closed cells, each containing a small number of solid particles. For under-constrained tessellations, the dominant contributions to $G$ and $B$ are the particle-particle and particle-cell interactions. With specific particle configurations in the cells, we limit the number of possible particle rearrangements to achieve decreasing $G$ as we increase the pressure difference between the inside and outside of the tessellation, leading to $G/B \ll 1$ at large pressures. We further study tessellated granular metamaterials with cells containing a single particle and many particles to determine the variables that control the mechanical response of particle-filled tessellations as a function of pressure., Comment: 16 pages, 6 figures

Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus $\left\langle G \right\rangle$ increases as a power-law in pressure $p$ for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase {\it or} decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct {\it tessellated} granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on $p$. We find that the slope of the shear modulus with pressure, $\lambda_c < 0$ for all packings in single cells with PBC where the number of particles per cell $N \ge 6$. In contrast, single cells with FXW and FLW can possess $\lambda_c > 0$, as well as $\lambda_c < 0$, for $N \le 16$. We show that we can force the mechanical properties of multi-cell granular metamaterials to possess those of single cells by constraining the endpoints of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a novel platform for the design of soft materials with specified mechanical properties.

Metallic glasses are frequently used as structural materials. Therefore, it is important to develop methods to predict their mechanical response as a function of the microstructure prior to loading. We develop a coarse-grained spring network model, which describes the mechanical response of metallic glasses using an equivalent series network of springs, which can break and re-form to mimic atomic rearrangements during deformation. To validate the model, we perform simulations of quasistatic, uniaxial tension of Lennard-Jones and embedded atom method (EAM) potentials for Cu$_{50}$Zr$_{50}$ metallic glasses. We consider samples prepared using a wide range of cooling rates and with different amounts of crystalline order. We show that both the Lennard-Jones and EAM models possess qualitatively similar stress $\sigma$ versus strain $\gamma$ curves. By specifying five parameters in the spring network model (ultimate strength, strain at ultimate strength, slopes of $\sigma(\gamma)$ at $\gamma=0$ and at large strain, and strain at fracture where $\sigma=0$), we can accurately describe the form of the stress-strain curves during uniaxial tension for the computational studies of Cu$_{50}$Zr$_{50}$, as well as recent experimental studies of several Zr-based metallic glasses. For the computational studies of Cu$_{50}$Zr$_{50}$, we find that the yield strain distribution is shifted to larger strains for slowly cooled glasses compared to rapidly cooled glasses. In addition, the average number of new springs and their rate of formation decreases with decreasing cooling rate. These effects offset each other at large strains, causing the stress-strain curve to become independent of the sample preparation protocol in this regime. In future studies, we will extract the parameters that define the spring network model directly from atomic rearrangements that occur during uniaxial deformation., Comment: 16 pages, 13 figures

The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the cells remain mechanically stable remains unknown. Here, we used computer simulations of deformable particles to develop a purely mechanical model for the development of the spongy mesophyll tissue. By stipulating that (1) cell perimeter grows only near voids, (2) cells both form and break adhesive bonds, and (3) the tissue pressure remains constant, the computational model was able to recapitulate the developmental trajectory of the microstructure of the spongy mesophyll observed in Arabidopsis thaliana leaves. Robust generation of pore space in the spongy mesophyll requires a balance of cell growth, adhesion, stiffness and tissue pressure to ensure cell networks remain both porous yet mechanically robust. The success of this mechanical model of tissue growth and porosity evolution suggests that simple physical principles can coordinate and drive the development of complex plant tissues like the spongy mesophyll., Comment: 28 pages, 6 figures, 1 table, 9 pages of supplementary information

Experimental data on the compressive strength $\sigma_{\rm max}$ versus strain rate ${\dot \varepsilon}_{\rm eng}$ for metallic glasses undergoing uniaxial compression shows significantly different behavior for different alloys. For some metallic glasses, $\sigma_{\rm max}$ decreases with increasing ${\dot \varepsilon}_{\rm eng}$, for others, $\sigma_{\rm max}$ increases with increasing ${\dot \varepsilon}_{\rm eng}$, and for others $\sigma_{\rm max}$ versus ${\dot \varepsilon}_{\rm eng}$ is nonmonotonic. Using numerical simulations of metallic glasses undergoing uniaxial compression at nonzero strain rate and temperature, we show that they obey a universal relation for the compressive strength versus temperature, which determines their mechanical response. At low ${\dot \varepsilon}_{\rm eng}$, increasing strain rate leads to increases in temperature and decreases in $\sigma^*_{\rm max}$, whereas at high ${\dot \varepsilon}_{\rm eng}$, increasing strain rate leads to decreases in temperature and increases in $\sigma^*_{\rm max}$. This non-monotonic behavior of $\sigma^*_{\rm max}$ versus temperature causes the nonmonotonic behavior of $\sigma^*_{\rm max}$ versus ${\dot \varepsilon}_{\rm eng}$. Variations in the internal dissipation change the characteristic strain rate at which the nonmonotonic behavior occurs. These results are general for a wide range of metallic glasses with different atomic interactions, damping coefficients, and chemical compositions., Comment: 5 pages, 3 figures

Granular metamaterials are a promising choice for the realization of mechanical computing devices. As preliminary evidence of this, we demonstrate here how to embed Boolean logic gates (AND and XOR) into a granular metamaterial by evolving where particular grains are placed in the material. Our results confirm the existence of gradients of increasing "AND-ness" and "XOR-ness" within the space of possible materials that can be followed by evolutionary search. We measure the computational functionality of a material by probing how it transforms bits encoded as vibrations with zero or non-zero amplitude. We compared the evolution of materials built from mass-contrasting particles and materials built from stiffness-contrasting particles, and found that the latter were more evolvable. We believe this work may pave the way toward evolutionary design of increasingly sophisticated, programmable, and computationally dense metamaterials with certain advantages over more traditional computational substrates., Comment: Accepted to the Genetic and Evolutionary Computation Conference 2022 (GECCO '22)

The glass-forming ability (GFA) of alloys, colloidal dispersions, and other particulate materials, as measured by the critical cooling rate $R_c$, can span more than ten orders of magnitude. Even after numerous previous studies, the physical features that control the GFA are still not well understood. For example, it is well-known that mixtures are better glass-formers than monodisperse systems and that particle size and cohesive energy differences among constituents improve the GFA, but it is not currently known how particle size differences couple to cohesive energy differences to determine the GFA. We perform molecular dynamics simulations to determine the GFA of equimolar, binary Lennard-Jones (LJ) mixtures versus the normalized cohesive energy difference $\epsilon_\_$ and mixing energy $\bar \epsilon_{AB}$ between particles A and B. We find several important results. First, the $\log_{10} R_c$ contours in the $\bar \epsilon_{AB}$-$\epsilon_\_$ plane are ellipsoidal for all diameter ratios, and thus $R_c$ is determined by the Mahalanobis distance $d_M$ from a given point in the $\bar \epsilon_{AB}$-$\epsilon_\_$ plane to the center of the ellipsoidal contours. Second, LJ systems for which the larger particles have larger cohesive energy are generally better glass formers than those for which the larger particles have smaller cohesive energy. Third, $d_M(\epsilon_\_,\bar \epsilon_{AB})$ is determined by the relative Voronoi volume difference between particles and local chemical order $S_{AB}$, which gives the average fraction of nearest-neighbor B particles surrounding an A particle and vice-versa. In particular, the shifted Mahalanobis distance $d_M - d^0_M$ versus the shifted chemical order $S_{AB}-S_{AB}^0$ collapses onto a hyperbolic master curve for all diameter ratios.

We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus $\langle G \rangle$ scales with pressure $P$ as $\langle G \rangle \sim P^{\beta}$, with $\beta \approx 0.75$ for jammed packings of deformable particles with zero bending energy. In contrast, $\beta \approx 0.5$ for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.

Soft, amorphous solids such as tissues, foams, and emulsions are composed of deformable particles. However, the effect of single-particle deformability on the collective behavior of soft solids is still poorly understood. We perform numerical simulations of two-dimensional jammed packings of explicitly deformable particles to study the mechanical response of model soft solids. We find that jammed packings of deformable particles with excess shape degrees of freedom possess low-frequency quartic vibrational modes that stabilize the packings even though they possess fewer interparticle contacts than the nominal isostatic value. Adding intra-particle constraints can rigidify the particles, but these particles undergo a buckling transition and gain an effective shape degree of freedom when their preferred perimeter is above a threshold value. We find that the mechanical response of jammed packings of deformable particles with shape degrees of freedom differs significantly from that of jammed packings of rigid-shape particles, which emphasizes the importance of particle deformability in modelling soft solids., Comment: 12 pages total, 6 main figures, 4 appendices, 5 appendix figures

We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power-law in the interparticle overlap with exponent $\alpha$, have found that the ensemble-averaged shear modulus $\langle G \rangle$ increases with pressure $P$ as $\sim P^{(\alpha-3/2)/(\alpha-1)}$ at large pressures. However, a deep theoretical understanding of this scaling behavior is lacking. We show that the shear modulus of jammed packings of frictionless, spherical particles has two key contributions: 1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and 2) discontinuous jumps during compression that arise from changes in the contact network. We show that the shear modulus of the first geometrical family for jammed packings can be collapsed onto a master curve: $G^{(1)}/G_0 = (P/P_0)^{(\alpha-2)/(\alpha-1)} - P/P_0$, where $P_0 \sim N^{-2(\alpha-1)}$ is a characteristic pressure that separates the two power-law scaling regions and $G_0 \sim N^{-2(\alpha-3/2)}$. Deviations from this form can occur when there is significant non-affine particle motion near changes in the contact network. We further show that $\langle G (P)\rangle$ is not simply a sum of two power-laws, but $\langle G \rangle \sim (P/P_c)^a$, where $a \approx (\alpha -2)/(\alpha-1)$ in the $P \rightarrow 0$ limit and $\langle G \rangle \sim (P/P_c)^b$, where $b \gtrsim (\alpha -3/2)/(\alpha-1)$ above a characteristic pressure $P_c$. In addition, the magnitudes of both contributions to $\langle G\rangle$ from geometrical families and changes in the contact network remain comparable in the large-system limit for $P >P_c$., Comment: 15 pages, 19 figures

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear with dissipative Newtonian dynamics at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction $\phi = 0.646 \pm 0.001$. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media., Comment: 5 pages, 4 figures

Prediction of the glass forming ability (GFA) of alloys remains a major challenge. We are not able to predict the composition dependence of the GFA of even binary alloys. To investigate the effect of each element's propensity to form particular crystal structures on glass formation, we focus on binary alloys composed of elements with the same size, but different atomic symmetries using the patchy-particle model. For mixtures with atomic symmetries that promote different crystal structures, the minimum critical cooling rate $R_c$ is only a factor of $5$ lower than that for the pure substances. For mixtures with different atomic symmetries that promote local crystalline and icosahedral order, the minimum $R_c$ is more than $3$ orders of magnitude lower than that for pure substances. Results for $R_c$ for the patchy-particle model are in agreement with those from embedded atom method simulations and sputtering experiments of NiCu, TiAl, and high entropy alloys., Comment: 6 pages, 5 figures

We carry out numerical studies of static packings of frictionless superellipsoidal particles in three spatial dimensions. We consider more than $200$ different particle shapes by varying the three shape parameters that define superellipsoids. We characterize the structural and mechanical properties of both disordered and ordered packings using two packing-generation protocols. We perform athermal quasi-static compression simulations starting from either random, dilute configurations (Protocol 1) or thermalized, dense configurations (protocol $2$), which allows us to tune the orientational order of the packings. In general, we find that the contact numbers at jamming onset for superellipsoid packings are hypostatic, with $z_J < z_{\rm iso}$, where $z_{\rm iso} = 2d_f$ and $d_f = 5$ or $6$ depending on whether the particles are axi-symmetric or not. Over the full range of orientational order, we find that the number of quartic modes of the dynamical matrix for the packings always matches the number of missing contacts relative to the isostatic value. This result suggests that there are no mechanically redundant contacts for ordered, yet hypostatic packings of superellipsoidal particles. Additionally, we find that the packing fraction at jamming onset for disordered packings of superellipsoidal particles can be collapsed using two particle shape parameters, e.g. the asphericity $\mathcal{A}$ and reduced aspect ratio $\beta$ of the particles., Comment: 10 pages, 14 figures

The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure $p$, the ensemble-averaged static shear modulus $\langle G-G_0 \rangle$ scales with $p^\alpha$, where $\alpha \approx 1$, but above a characteristic pressure $p^{**}$, $\langle G-G_0 \rangle \sim p^\beta$, where $\beta \approx 0.5$. However, we find that the shear modulus $G^i$ for an individual packing typically decreases linearly with $p$ along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, $\langle G \rangle$ also depends on a contribution from discontinuous jumps in $\langle G \rangle$ that occur at the transitions between geometrical families. For $p > p^{**}$, geometrical-family and rearrangement contributions to $\langle G \rangle$ are of opposite signs and remain comparable for all system sizes. $\langle G \rangle$ can be described by a scaling function that smoothly transitions between the two power-law exponents $\alpha$ and $\beta$. We also demonstrate the phenomenon of {\it compression unjamming}, where a jammed packing can unjam via isotropic compression., Comment: 6 pages, 4 pages

Micro- and nano-resonators have important applications including sensing, navigation, and biochemical detection. Their performance is quantified using the quality factor $Q$, which gives the ratio of the energy stored to the energy dissipated per cycle. Metallic glasses are a promising materials class for micro- and nano-scale resonators since they are amorphous and can be fabricated precisely into complex shapes on these lengthscales. To understand the intrinsic dissipation mechanisms that ultimately limit large $Q$-values in metallic glasses, we perform molecular dynamics simulations to model metallic glass resonators subjected to bending vibrations. We calculate the vibrational density of states, redistribution of energy from the fundamental mode of vibration, and $Q$ versus the kinetic energy per atom $K$ of the excitation. In the linear and nonlinear response regimes where there are no atomic rearrangements, we find that $Q \rightarrow \infty$ (since we do not consider coupling to the environment). We identify a characteristic $K_r$ above which atomic rearrangements occur, and there is significant energy leakage from the fundamental mode to higher frequencies, causing finite $Q$. Thus, $K_r$ is a critical parameter determining resonator performance. We show that $K_r$ decreases as a power-law, $K_r\sim N^{-k},$ with increasing system size $N$, where $k \approx 1.3$. We estimate the critical strain $\langle \gamma_r \rangle \sim 10^{-8}$ for micron-sized resonators below which atomic rearrangements do not occur, and thus large $Q$-values can be obtained when they are operated below $\gamma_r$. We find that $K_r$ for amorphous resonators is comparable to that for resonators with crystalline order., Comment: 12 pages, 13 figures

We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and the deformable particle (DP) model that we developed for compressed bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at fixed area to avoid overlap during compression. We directly compare the structural and mechanical properties of jammed particle packings generated using the SP and DP models as a function of the true packing fraction $\rho$, instead of the reduced number density $\phi$. We show that near jamming onset the excess contact number $\Delta z=z-z_J$ and shear modulus ${\cal G}$ scale as $\Delta \rho^{0.5}$ in the large system limit for both the SP and DP models, where $\Delta \rho = \rho-\rho_J$ and $z_J \approx 4$ and $\rho_J \approx 0.842$ are the values at jamming onset. $\Delta z$ and ${\cal G}$ for the SP and DP models begin to differ for $\rho \gtrsim 0.88$. In this regime, $\Delta z \sim {\cal G}$ can be described by a sum of two power-laws in $\Delta \rho$, i.e. $\Delta z \sim {\cal G} \sim C_0\Delta \rho^{0.5} +C_1\Delta \rho^{1.0}$ to lowest order. We show that the ratio $C_1/C_0$ is much larger for the DP model compared to to that for the SP model. We also characterize the void space in jammed packings as a function of $\rho$. We find that, unlike the SP model, the DP model is able to describe the formation of Plateau borders as the system approaches $\rho = 1$. We further show that the results for $z$ and the shape factor ${\cal A}$ versus $\rho$ for the DP model agree with recent experimental studies of compressed foams and emulsions., Comment: 12 pages, 11 figures, 9 main figures, and 2 supplemental figures

The design of multi-functional BMGs is limited by the lack of a quantitative understanding of the variables that control the glass-forming ability (GFA) of alloys. Both geometric frustration (e.g. differences in atomic radii) and energetic frustration (e.g. differences in the cohesive energies of the atomic species) contribute to the GFA. We perform molecular dynamics simulations of binary Lennard-Jones mixtures with only energetic frustration. We show that there is little correlation between the heat of mixing and critical cooling rate $R_c$, below which the system crystallizes, except that $\Delta H_{\rm mix} < 0$. By removing the effects of geometric frustration, we show strong correlations between $R_c$ and the variables $\epsilon_- = (\epsilon_{BB}-\epsilon_{AA})/(\epsilon_{AA}+\epsilon_{BB})$ and ${\overline \epsilon}_{AB} = 2\epsilon_{AB}/(\epsilon_{AA}+\epsilon_{BB})$, where $\epsilon_{AA}$ and $\epsilon_{BB}$ are the cohesive energies of atoms $A$ and $B$ and $\epsilon_{AB}$ is the pair interaction between $A$ and $B$ atoms. We identify a particular $f_B$-dependent combination of $\epsilon_-$ and ${\overline \epsilon}_{AB}$ that collapses the data for $R_c$ over nearly $4$ orders of magnitude in cooling rate.

We employ numerical simulations to study active transistor-like switches made from two-dimensional (2D) granular crystals containing two types of grains with the same size, but different masses. We tune the mass contrast and arrangement of the grains to maximize the width of the frequency band gap in the device. The input signal is applied to a single grain on one side of the device, and the output signal is measured from another grain on the other side of the device. Changing the size of one or many grains tunes the pressure, which controls the vibrational response of the device. Switching between the on and off states is achieved using two mechanisms: 1) pressure-induced switching where the interparticle contact network is the same in the on and off states, and 2) switching through contact breaking. In general, the performance of the acoustic switch, as captured by the gain ratio and switching time between the on and off states, is better for pressure-induced switching. We show that in these acoustic switches the gain ratio between the on and off states can be larger than $10^4$ and the switching time (multiplied by the driving frequency) is comparable to that obtained recently for sonic crystals and less than that for photonic transistor-like switches. Since the self-assembly of grains with different masses into 2D granular crystals is challenging, we describe simulations of circular grains with small circular knobs placed symmetrically around the perimeter mixed with circular grains without knobs. Using umbrella sampling techniques, we show that devices with grains with $3$ knobs most efficiently form the hexagonal crystals that yield the largest band gap., Comment: 16 pages, 23 figures

We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings. We focus on two protocols for generating MS packings: 1) isotropic compression and 2) applied simple or pure shear strain $\gamma$ at fixed packing fraction $\phi$. MS packings of frictionless disks occur as geometric families (i.e. parabolic segments with positive curvature) in the $\phi$-$\gamma$ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, $d\phi/d\gamma >0$ and $d\phi/d\gamma <0$. In contrast, MS packings from protocol 2 populate segments with $d\phi/d\gamma <0$ only. For both simple and pure shear, we derive a relationship between the stress anisotropy and dilatancy $d\phi/d\gamma$ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large-system limit. We also develop a framework to calculate the stress anisotropy distribution for packings generated via protocol 2 in terms of the stress anisotropy distribution for packings generated via protocol 1. These results emphasize that for repulsive frictionless disks, different packing-generation protocols give rise to different MS packing probabilities, which lead to differences in macroscopic properties of MS packings., Comment: 1. change the vertical axis label in Fig. 7 (b), fix the Eq. 13 in the revised manuscript; 2. Add new results of pure shear case in Appendix A; 3. page 3, fix typos, use d$\phi$ in the revised manuscript.; 4. define the pure shear strain as ${\gamma}=\ln (Lx'/Ly')$, which makes the relationship between the components of the stress tensor and dilatancy for simple and pure shear the same

There are two main classes of physics-based models for two-dimensional cellular materials: packings of repulsive disks and the vertex model. These models have several disadvantages. For example, disk interactions are typically a function of particle overlap, yet the model assumes that the disks remain circular during overlap. The shapes of the cells can vary in the vertex model, however, the packing fraction is fixed at $\phi=1$. Here, we describe the deformable particle model (DPM), where each particle is a polygon composed of a large number of vertices. The total energy includes three terms: two quadratic terms to penalize deviations from the preferred particle area $a_0$ and perimeter $p_0$ and a repulsive interaction between DPM polygons that penalizes overlaps. We performed simulations to study the onset of jamming in packings of DPM polygons as a function of asphericity, ${\cal A} = p_0^2/4\pi a_0$. We show that the packing fraction at jamming onset $\phi_J({\cal A})$ grows with increasing ${\cal A}$, reaching confluence at ${\cal A} \approx 1.16$. ${\cal A}^*$ corresponds to the value at which DPM polygons completely fill the cells obtained from a surface-Voronoi tessellation. Further, we show that DPM polygons develop invaginations for ${\cal A} > {\cal A}^*$ with excess perimeter that grows linearly with ${\cal A}-{\cal A}^*$. We confirm that packings of DPM polygons are solid-like over the full range of ${\cal A}$ by showing that the shear modulus is nonzero., Comment: 6 pages, 5 figures

We perform computational studies of static packings of a variety of nonspherical particles including circulo-lines, circulo-polygons, ellipses, asymmetric dimers, and dumbbells to determine which shapes form hypostatic versus isostatic packings and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from na\"ive constraint counting. To generate highly accurate force- and torque-balanced packings of circulo-lines and -polygons, we developed an interparticle potential that gives continuous forces and torques as a function of the particle coordinates. We show that the packing fraction and coordination number at jamming onset obey a master-like form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity ${\cal A}$, which is proportional to the ratio of the squared perimeter to the area of the particle. Further, the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same ${\cal A}$. For hypostatic packings of nonspherical particles, we verify that the number of "quartic" modes along which the potential energy increases as the fourth power of the perturbation amplitude matches the number of missing contacts relative to the isostatic value. In addition, we calculate the principal curvatures of the inequality constraints for each contact in circulo-line packings and identify specific types of contacts with inequality constraints that possess convex curvature. These contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable., Comment: 17 pages, 22 figures

We revisit the longstanding question of the onset of sediment transport driven by a turbulent fluid flow via laboratory measurements. We use particle tracking velocimetry to quantify the fluid flow as well as the motion of individual grains. As we increase the flow speed above the transition to sediment transport, we observe that an increasing fraction of grains are transported downstream, although the average downstream velocity of the transported grains remains roughly constant. However, we find that the fraction of mobilized grains does not vanish sharply at a critical flow rate. Additionally, the distribution of the fluctuating velocities of non-transported grains becomes broader with heavier tails, meaning that unambiguously separating mobile and static grains is not possible. As an alternative approach, we quantify the statistics of grain velocities by using a mixture model consisting of two forms for the grain velocities: a decaying-exponential tail, which represents grains transported downstream, and a peaked distribution centered at zero velocity, which represents grains that fluctuate due to the turbulent flow but remain in place. Our results suggest that more sophisticated statistical measures may be required to quantify grain motion near the onset of sediment transport, particularly in the presence of turbulence., Comment: 9 pages, 7 figures

We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low inertial number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress $\Sigma$ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied $\Sigma$, isotropically prepared states with size $L$ must undergo a total strain $\gamma_{\rm ms}(\Sigma,L)$. The number density of MS packings ($\propto \gamma_{\rm ms}^{-1}$) vanishes for $\Sigma > \Sigma_c \approx 0.11$ according to a critical scaling form with a length scale $\xi \propto |\Sigma - \Sigma_c|^{-\nu}$, where $\nu \approx 1.7-1.8$. Above the yield stress ($\Sigma>\Sigma_c$), no MS packings that can support $\Sigma$ exist in the large system limit, $L/\xi \gg 1$. MS packings generated via shear possess anisotropic force and contact networks, suggesting that $\Sigma_c$ is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.

Amorphous materials such as metallic, polymeric, and colloidal glasses, exhibit complex preparation-dependent mechanical response to applied shear. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate $R$ used to prepare them. The ensemble-averaged stress versus strain curve $\langle\sigma(\gamma)\rangle$ resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak at intermediate strain, and a plastic flow regime at large strains. In contrast, for each glass configuration in the ensemble, the stress-strain curve consists of many short nearly linear segments that are punctuated by particle-rearrangement-induced rapid stress drops. We quantify the shape of the small stress-strain segments, as well as the frequency and size of the stress drops in each glass configuration. We decompose the stress loss into the loss from particle rearrangements and from softening i.e., the reduction of the slopes of the linear segments in $\sigma(\gamma)$), and then compare the two contributions as a function of $R$ and $\gamma$. For the current studies, the rearrangement-induced stress loss is larger than the softening-induced stress loss, however, softening stress losses increase with decreasing cooling rate. We also characterize the structure of the potential energy landscape along the strain direction for glasses prepared with different $R$, and observe a dramatic change of the properties of the landscape near the yielding transition. We then show that the rearrangement-induced energy loss per strain can serve as an order parameter for the yielding transition, which sharpens for slow cooling rates and in the large system-size limit., Comment: 17 pages, 19 figures

Amorphous solids, such as metallic, polymeric, and colloidal glasses, display complex spatiotemporal response to applied deformations. In contrast to crystalline solids, during loading, amorphous solids exhibit a smooth crossover from elastic response to plastic flow. In this study, we investigate the mechanical response of binary Lennard-Jones glasses to athermal, quasistatic pure shear as a function of the cooling rate used to prepare them. We find several key results concerning the connection between strain-induced particle rearrangements and mechanical response. We show that more rapidly cooled glasses undergo more frequent and larger particle rearrangements than slowly cooled glasses. We find that the ratio of the shear to bulk moduli decreases with increasing cooling rate, which suggests that more rapidly cooled glasses are more ductile than slowly cooled samples. In addition, we characterized the degree of reversibility of particle motion during cyclic shear. We find that irreversible particle motion occurs even in the putative linear regime of stress versus strain. However, slowly cooled glasses, which undergo smaller rearrangements, are more reversible under cyclic shear than rapidly cooled glasses. Thus, we show that more ductile glasses are also less reversible., Comment: 6 pages, 5 figures

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We show that employing sparse representations provides more accurate ODE reconstruction compared to least-squares reconstruction techniques for a given amount of time series data. We test and validate the ODE reconstruction method on known 1D, 2D, and 3D systems of ODEs. The 1D system possesses two stable fixed points; the 2D system possesses an oscillatory fixed point with closed orbits; and the 3D system displays chaotic dynamics on a strange attractor. We determine the amount of data required to achieve an error in the reconstructed functions to less than $0.1\%$. For the reconstructed 1D and 2D systems, we are able to match the trajectories from the original ODEs even at long times. For the 3D system with chaotic dynamics, as expected, the trajectories from the original and reconstructed systems do not match at long times, but the reconstructed and original models possess similar Lyapunov exponents. Now that we have validated this ODE reconstruction method on known models, it can be employed in future studies to identify new systems of ODEs using time series data from deterministic systems for which there is no currently known ODE model., Comment: 15 pages, 20 figures

Sediment transport occurs when the nondimensional fluid shear stress $\Theta$ at the bed surface exceeds a minimum value $\Theta_c$. A large collection of data, known as the Shields curve, shows that $\Theta_c$ is primarily a function of the shear Reynolds number ${\rm{Re}}_*$. It is commonly assumed that $\Theta>\Theta_c({\rm{Re}}_*)$ occurs when the ${\rm Re}_*$-dependent fluid forces are too large to maintain static equilibrium for a typical surface grain. A complimentary approach, which remains relatively unexplored, is to identify $\Theta_c({\rm{Re}}_*)$ as the applied shear stress at which grains cannot stop moving. With respect to grain dynamics, ${\rm{Re}}_*$ can be viewed as the viscous time scale for a grain to equilibrate to the fluid flow divided by the typical time for the fluid force to accelerate a grain over the characteristic bed roughness. We performed simulations of granular beds sheared by a model fluid, varying only these two time scales. We find that the critical Shields number $\Theta_c({\rm Re}_*)$ obtained from the model mimics the Shields curve and is insensitive to the grain properties, the model fluid flow, and the form of the drag law. Quantitative discrepancies between the model results and the Shields curve are consistent with previous calculations of lift forces at varying ${\rm Re}_*$. Grains at low ${\rm Re}_*$ find more stable configurations than those at high ${\rm{Re}}_*$ due to differences in the grain reorganization dynamics. Thus, instead of focusing on mechanical equilibrium of a typical grain at the bed surface, $\Theta_c({\rm{Re}}_*)$ may be better described by the stress at which mobile grains cannot find a stable configuration and stop moving., Comment: to appear in Phys. Rev. Fluids

When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate $R_c$, the crystalline state is bypassed and an amorphous glassy state forms instead. $R_c$ (or the corresponding critical casting thickness $d_c$) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small $R_c<10^{-2}$ K/s, pure metals and most alloys are poor glass-formers with large $R_c>10^{10}$ K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with $R_c$ approaching that for silica. Recent simulations have shown that hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are many other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? We perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude., Comment: 12 pages, 10 figures

We performed molecular dynamics simulations of granular beds driven by a model hydrodynamic shear flow to elucidate general grain-scale mechanisms that determine the onset and cessation of sediment transport. By varying the Shields number (the nondimensional shear stress at the top of the bed) and particle Reynolds number (the ratio of particle inertia to viscous damping), we explore how variations of the fluid flow rate, particle inertia, and fluid viscosity affect the onset and cessation of bed motion. For low to moderate particle Reynolds numbers, a critical boundary separates mobile and static states. Transition times between these states diverge as this boundary is approached both from above and below. At high particle Reynolds number, inertial effects become dominant, and particle motion can be sustained well below flow rates at which mobilization of a static bed occurs. We also find that the onset of bed motion (for both low and high particle Reynolds numbers) is described by Weibullian weakest-link statistics, and thus is crucially dependent on the packing structure of the granular bed, even deep beneath the surface., Comment: 8 pages, 7 figures

Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a general class of mathematical models for the immune response to infection. However, accuracy can be increased at the expense of delayed prognosis. We investigate several systems of ordinary differential equations (ODEs) that model the host immune response to a pathogen load. Advantages of systems of ODEs for investigating the immune response to infection include the ability to collect data on large numbers of `virtual patients', each with a given set of model parameters, and obtain many time points during the course of the infection. We implement patient-to-patient variability $v$ in the ODE models by randomly selecting the model parameters from Gaussian distributions with variance $v$ that are centered on physiological values. We use logistic regression with one-versus-all classification to predict the discrete steady-state outcomes of the system. We find that the prediction algorithm achieves near $100\%$ accuracy for $v=0$, and the accuracy decreases with increasing $v$ for all ODE models studied. The fact that multiple steady-state outcomes can be obtained for a given initial condition, i.e. the basins of attraction overlap in the space of initial conditions, limits the prediction accuracy for $v>0$. Increasing the elapsed time of the variables used to train and test the classifier, increases the prediction accuracy, while adding explicit external noise to the ODE models decreases the prediction accuracy. Our results quantify the competition between early prognosis and high prediction accuracy that is frequently encountered by clinicians., Comment: 14 pages, 7 figures

We perform molecular dynamics (MD) simulations of the crystallization process in binary Lennard-Jones systems during heating and cooling to investigate atomic-scale crystallization kinetics in glass-forming materials. For the cooling protocol, we prepared equilibrated liquids above the liquidus temperature $T_l$ and cooled each sample to zero temperature at rate $R_c$. For the heating protocol, we first cooled equilibrated liquids to zero temperature at rate $R_p$ and then heated the samples to temperature $T > T_l$ at rate $R_h$. We measured the critical heating and cooling rates $R_h^*$ and $R_c^*$, below which the systems begin to form a substantial fraction of crystalline clusters during the heating and cooling protocols. We show that $R_h^* > R_c^*$, and that the asymmetry ratio $R_h^*/R_c^*$ includes an intrinsic contribution that increases with the glass-forming ability (GFA) of the system and a preparation-rate dependent contribution that increases strongly as $R_p \rightarrow R_c^*$ from above. We also show that the predictions from classical nucleation theory (CNT) can qualitatively describe the dependence of the asymmetry ratio on the GFA and preparation rate $R_p$ from the MD simulations and results for the asymmetry ratio measured in Zr- and Au-based bulk metallic glasses (BMG). This work emphasizes the need for and benefits of an improved understanding of crystallization processes in BMGs and other glass-forming systems., Comment: 8 pages, 7 figures

Bulk metallic glasses (BMGs) are amorphous alloys with desirable mechanical properties and processing capabilities. To date, the design of new BMGs has largely employed empirical rules and trial-and-error experimental approaches. Ab initio computational methods are currently prohibitively slow to be practically used in searching the vast space of possible atomic combinations for bulk glass formers. Here, we perform molecular dynamics simulations of a coarse-grained, anisotropic potential, which mimics interatomic covalent bonding, to measure the critical cooling rates for metal-metalloid alloys as a function of the atomic size ratio $\sigma_S/\sigma_L$ and number fraction $x_S$ of the metalloid species. We show that the regime in the space of $\sigma_S/\sigma_L$ and $x_S$ where well-mixed, optimal glass formers occur for patchy and LJ particle mixtures coincides with that for experimentally observed metal-metalloid glass formers. Our simple computational model provides the capability to perform combinatorial searches to identify novel glass-forming alloys., Comment: 6 pages, 5 figures

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate $R$, size ratio $\alpha$, and number fraction $x_S$ of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate $R_c$, below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with $\alpha \gtrsim 0.8$ that do not de-mix, $R_c$ decreases strongly with $\Delta \phi_J$, as $R_c \sim \exp(-1/\Delta \phi_J^2)$, where $\Delta \phi_J$ is the difference between the average packing fraction of the amorphous packings and random crystal structures at $R_c$. Systems with $\alpha \lesssim 0.8$ partially de-mix, which promotes crystallization, but we still find a strong correlation between $R_c$ and $\Delta \phi_J$. We show that known metal-metal BMGs occur in the regions of the $\alpha$ and $x_S$ parameter space with the lowest values of $R_c$ for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing $\alpha$ to increase packing efficiency, while maximizing $\alpha$ to prevent de-mixing., Comment: 5 pages, 4 figures

We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in frictional packings, $m=N_c^0-N_c$. The saddle order $m$ represents the number of unconstrained degrees of freedom that a static packing would possess if friction were removed. Using a novel numerical method that allows us to enumerate disk packings for each $m$, we show that the probability to obtain a packing with saddle order $m$ at a given static friction coefficient $\mu$, $P_m(\mu)$, can be expressed as a power-series in $\mu$. Using this form for $P_m(\mu)$, we quantitatively describe the dependence of the average contact number on friction coefficient for static disk packings obtained from direct simulations of the Cundall-Strack model for all $\mu$ and $N$., Comment: 4 pages, 4 figures

Contact breaking and Hertzian interactions between grains can both give rise to nonlinear vibrational response of static granular packings. We perform molecular dynamics simulations at constant energy in 2D of frictionless bidisperse disks that interact via Hertzian spring potentials as a function of energy and measure directly the vibrational response from the Fourier transform of the velocity autocorrelation function. We compare the measured vibrational response of static packings near jamming onset to that obtained from the eigenvalues of the dynamical matrix to determine the temperature above which the linear response breaks down. We compare packings that interact via single-sided (purely repulsive) and double-sided Hertzian spring interactions to disentangle the effects of the shape of the potential from contact breaking. Our studies show that while Hertzian interactions lead to weak nonlinearities in the vibrational behavior (e.g. the generation of harmonics of the eigenfrequencies of the dynamical matrix), the vibrational response of static packings with Hertzian contact interactions is dominated by contact breaking as found for systems with repulsive linear spring interactions., Comment: 8 pages, 6 figures