arXiv subjects

Corey S. O'Hern

Publications and source records attributed to Corey S. O'Hern.

At least 109 records · Page 6Linked to original sources

arXiv2009

Geometrical families of mechanically stable granular packings

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N < 16), we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16, we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady-state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.

cond-mat.soft↗

arXiv2009

Protein folding on rugged energy landscapes: Conformational diffusion on fractal networks

We employ simulations of model proteins to study folding on rugged energy landscapes. We construct ``first-passage'' networks as the system transitions from unfolded to native states. The nodes and bonds in these networks correspond to basins and transitions between them in the energy landscape. We find power-laws between the folding time and number of nodes and bonds. We show that these scalings are determined by the fractal properties of first-passage networks. Reliable folding is possible in systems with rugged energy landscapes because first passage networks have small fractal dimension.

cond-mat.soft↗

arXiv2009

Entropic origin of stress correlations in granular materials

We study the response of granular materials to external stress using experiment, simulation, and theory. We derive an entropic, Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively.

cond-mat.stat-mech↗

arXiv2009

Experimental Demonstration of Nonuniform Frequency Distributions of Granular Packings

We developed a novel experimental technique to generate mechanically stable (MS) packings of frictionless granular disks. We performed a series of coordinated experiments and numerical simulations to enumerate the MS packings in small 2D systems composed of bidisperse disks. We find that frictionless MS packings occur as discrete, well-separated points in configuration space and obtain excellent quantitative agreement between MS packings generated in experiments and simulations. In addition, we observe that MS packing probabilities can vary by many orders of magnitude and are robust with respect to the packing-generation procedure. These results suggest that the most frequent MS packings may dominate the structural and mechanical properties of granular systems. We argue that these results for small systems represent a crucial first-step in constructing a statistical description for large granular systems from the `bottom-up'.

cond-mat.soft↗

arXiv2008

Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles

We study the structural and mechanical properties of jammed ellipse packings, and find that the nature of the jamming transition in these systems is fundamentally different from that for spherical particles. Ellipse packings are generically hypostatic with more degrees of freedom than constraints. The spectra of low energy excitations possess two gaps and three distinct branches over a range of aspect ratios. In the zero compression limit, the energy of the modes in the lowest branch increases {\it quartically} with deformation amplitude, and the density of states possesses a $δ$-function at zero frequency. We identify scaling relations that collapse the low-frequency part of the spectra for different aspect ratios. Finally, we find that the degree of hypostaticity is determined by the number of quartic modes of the packing.

cond-mat.soft↗

arXiv2008

A percolation model for slow dynamics in glass-forming materials

We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq β\leq 1$ and the functional dependence of the structural relaxation time $τ_α$ and exponent $β$ on temperature, density, and wave number.

cond-mat.stat-mech↗

arXiv2008

Non-random coil behavior as a consequence of extensive PPII structure in the denatured state

Unfolded proteins may contain native or non-native residual structure, which has important implications for the thermodynamics and kinetics of folding as well as for misfolding and aggregation diseases. However, it has been universally accepted that residual structure should not affect the global size scaling of the denatured chain, which obeys the statistics of random coil polymers. Here we use a single-molecule optical technique, fluorescence correlation spectroscopy, to probe the denatured state of set of repeat proteins containing an increasing number of identical domains, from two to twenty. The availability of this set allows us to obtain the scaling law for the unfolded state of these proteins, which turns out to be unusually compact, strongly deviating from random-coil statistics. The origin of this unexpected behavior is traced to the presence of extensive non-native polyproline II helical structure, which we localize to specific segments of the polypeptide chain. We show that the experimentally observed effects of PPII on the size scaling of the denatured state can be well-described by simple polymer models. Our findings suggest an hitherto unforeseen potential of non-native structure to induce significant compaction of denatured proteins, affecting significantly folding pathways and kinetics.

q-bio.BM↗

arXiv2008

A minimal model for kinetic arrest

To elucidate slow dynamics in glassy materials, we introduce the {\it Figure-8 model} in which $N$ hard blocks undergo Brownian motion around a circuit in the shape of a figure-8. This system undergoes kinetic arrest at a critical packing fraction $ϕ=ϕ_g < 1$, and for $ϕ\approxϕ_g$ long-time diffusion is controlled by rare, cooperative `junction-crossing' particle rearrangements. We find that the average time between junction crossings $τ_{JC}$, and hence the structural relaxation time, does not simply scale with the configurational volume $\OmegaLow$ of transition states, because $τ_{JC}$ also depends on the time to complete a junction crossing. The importance of these results in understanding cage-breaking dynamics in glassy systems is discussed.

cond-mat.stat-mech↗

arXiv2008

Reliable protein folding on non-funneled energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant or pH, are adjusted to induce folding. A theory based on this insight predicts that (1) proteins with non-funneled energy landscapes can fold reliably to their native state, (2) reliable folding can occur as an equilibrium or out-of-equilibrium process, and (3) reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.

q-bio.BM↗

arXiv2007

The jamming transition and new percolation universality classes in particulate systems with attraction

We numerically study the jamming transition in particulate systems with attraction by investigating their mechanical response at zero temperature. We find three regimes of mechanical behavior separated by two critical transitions--connectivity and rigidity percolation. The transitions belong to different universality classes than their lattice counterparts, due to force balance constraints. We also find that these transitions are unchanged at low temperatures and resemble gelation transitions in experiments on colloidal and silica gels.

cond-mat.soft↗

arXiv2007

Entropy and Temperature of a Static Granular Assembly

Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a statistical framework. In molecular matter, equilibrium statistical mechanics, which is founded on the principle of conservation of energy, provides this framework. Grains, however, are small but macroscopic objects whose interactions are dissipative since energy can be lost through excitations of the internal degrees of freedom. In this work, we construct a statistical framework for static, mechanically stable packings of grains, which parallels that of equilibrium statistical mechanics but with conservation of energy replaced by the conservation of a function related to the mechanical stress tensor. Our analysis demonstrates the existence of a state function that has all the attributes of entropy. In particular, maximizing this state function leads to a well-defined granular temperature for these systems. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks. Our demonstration that a statistical ensemble can be constructed through the identification of conserved quantities other than energy is a new approach that is expected to open up avenues for statistical descriptions of other non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2006

Understanding the Frequency Distribution of Mechanically Stable Disk Packings

Relative frequencies of mechanically stable (MS) packings of frictionless bidisperse disks are studied numerically in small systems. The packings are created by successively compressing or decompressing a system of soft purely repulsive disks, followed by energy minimization, until only infinitesimal particle overlaps remain. For systems of up to 14 particles most of the MS packings were generated. We find that the packings are not equally probable as has been assumed in recent thermodynamic descriptions of granular systems. Instead, the frequency distribution, averaged over each packing-fraction interval $Δϕ$, grows exponentially with increasing $ϕ$. Moreover, within each packing-fraction interval MS packings occur with frequencies $f_k$ that differ by many orders of magnitude. Also, key features of the frequency distribution do not change when we significantly alter the packing-generation algorithm--for example frequent packings remain frequent and rare ones remain rare. These results indicate that the frequency distribution of MS packings is strongly influenced by geometrical properties of the multidimensional configuration space. By adding thermal fluctuations to a set of the MS packings, we were able to examine a number of local features of configuration space near each packing including the time required for a given packing to break to a distinct one, which enabled us to estimate the energy barriers that separate one packing from another. We found a positive correlation between the packing frequencies and the heights of the lowest energy barriers $ε_0$. We also examined displacement fluctuations away from the MS packings to correlate the size and shape of the local basins near each packing to the packing frequencies.

cond-mat.stat-mech↗

arXiv2006

Enumeration of distinct mechanically stable disk packings in small systems

We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small systems because this enables us to enumerate nearly all distinct MS packings. We measure the probability to obtain a MS packing at packing fraction $ϕ$ and find several notable results. First, the probability is highly nonuniform. When averaged over narrow packing fraction intervals, the most probable MS packing occurs at the highest $ϕ$ and the probability decays exponentially with decreasing $ϕ$. Even more striking, within each packing-fraction interval, the probability can vary by many orders of magnitude. By using two different packing-generation protocols, we show that these results are robust and the packing frequencies do not change qualitatively with different protocols.

cond-mat.stat-mech↗

arXiv2005

Measurements of the Yield Stress in Frictionless Granular Systems

We perform extensive molecular dynamics simulations of 2D frictionless granular materials to determine whether these systems can be characterized by a single static yield shear stress. We consider boundary-driven planar shear at constant volume and either constant shear force or constant shear velocity. Under steady flow conditions, these two ensembles give similar results for the average shear stress versus shear velocity. However, near jamming it is possible that the shear stress required to initiate shear flow can differ substantially from the shear stress required to maintain flow. We perform several measurements of the shear stress near the initiation and cessation of flow. At fixed shear velocity, we measure the average shear stress $Σ_{yv}$ in the limit of zero shear velocity. At fixed shear force, we measure the minimum shear stress $Σ_{yf}$ required to maintain steady flow at long times. We find that in finite-size systems $Σ_{yf} > Σ_{yv}$, which implies that there is a jump discontinuity in the shear velocity from zero to a finite value when these systems begin flowing at constant shear force. However, our simulations show that the difference $Σ_{yf} - Σ_{yv}$, and thus the discontinuity in the shear velocity, tend to zero in the infinite system size limit. Thus, our results indicate that in the large system limit, frictionless granular systems are characterized by a single static yield shear stress. We also monitor the short-time response of these systems to applied shear and show that the packing fraction of the system and shape of the velocity profile can strongly influence whether or not the shear stress at short times overshoots the long-time average value.

cond-mat.soft↗

arXiv2005

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

We perform molecular dynamics simulations of model granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time $t_l$ required for the velocity profiles to become linear and find that $t_l$ increases as a power-law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.

cond-mat.soft↗

arXiv2005

Random close packing revisited: How many ways can we pack frictionless disks?

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in 2d using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2d and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability $P(ϕ)$ for obtaining a collectively jammed state at a particular packing fraction $ϕ$ into two composite functions: 1) the density of CJ packing fractions $ρ(ϕ)$, which only depends on geometry and 2) the frequency distribution $β(ϕ)$, which depends on the particular algorithm used to create them. We find that the function $ρ(ϕ)$ is sharply peaked and that $β(ϕ)$ depends exponentially on $ϕ$. We predict that in the infinite system-size limit the behavior of $P(ϕ)$ in these systems is controlled by the density of CJ packing fractions--not the frequency distribution. These results suggest that the location of the peak in $P(ϕ)$ when $N \to \infty$ can be used as a protocol-independent definition of random close packing.

cond-mat.stat-mech↗

arXiv2004

Effective Temperatures in Athermal Systems Sheared at Fixed Normal Load

We perform molecular dynamics simulations of repulsive athermal systems sheared at fixed normal load to study the effective temperature $T_L$ defined from time-dependent fluctuation-dissipation relations for density. We show that these systems possess two distinct regimes as a function of the ratio $T_S/V$ of the granular temperature to the potential energy per particle. At small $T_S/V$, these systems are pressure-controlled and $T_L$ is set by the normal load. In contrast, they behave as quasi-equilibrium systems with $T_L \approx T_S$ that increases with shear rate at large $T_S/V$. These results point out several problems with using $T_L$ in thermodynamic descriptions of slowly sheared athermal systems.

cond-mat.soft↗

arXiv2004

Velocity Profiles in Repulsive Athermal Systems under Shear

We conduct molecular dynamics simulations of athermal systems undergoing boundary-driven planar shear flow in two and three spatial dimensions. We find that these systems possess nonlinear mean velocity profiles when the velocity $u$ of the shearing wall exceeds a critical value $u_c$. Above $u_c$, we also show that the packing fraction and mean-square velocity profiles become spatially-dependent with dilation and enhanced velocity fluctuations near the moving boundary. In systems with overdamped dynamics, $u_c$ is only weakly dependent on packing fraction $ϕ$. However, in systems with underdamped dynamics, $u_c$ is set by the speed of shear waves in the material and tends to zero as $ϕ$ approaches $ϕ_c$. In the small damping limit, $ϕ_c$ approaches values for random close-packing obtained in systems at zero temperature. For underdamped systems with $ϕ<ϕ_c$, $u_c$ is zero and thus they possess nonlinear velocity profiles at any nonzero boundary velocity.

cond-mat.soft↗