Aaron Keys | University of Michigan (original) (raw)

Papers by Aaron Keys

Aps Meeting Abstracts, Mar 1, 2007

On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range ... more On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range periodic ordering. However, it is also possible to form quasicrystals, ordered solids with long-range aperiodicity. Although quasicrystals have been observed in many materials, their formation is poorly understood. We present the results of a molecular simulation study to elucidate the process by which quasicrystals form from supercooled liquids. We show that, as has been speculated in previous theoretical and experimental works, icosahedral clusters play a significant role in quasicrystal formation. Specifically, icosahedral clusters facilitate the formation of the so-called quasicrystal ``critical'' nucleus, and, together with phasons, facilitate the complicated mechanism that allows quasicrystals to grow aperiodic structures via local interactions. Our findings suggest that direct correlations between liquid ordering and solid structure may be a requisite property for quaiscrystal-forming systems, and is consistent with the class of systems that are known to form quasicrystals experimentally.

Nature, 2010

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a m... more All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of {\phi} = {\pi}/\sqrt18 ~ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with {\phi} = 0.7786, which was subsequently compressed numerically to {\phi} = 0.7820. Here we show that tetrahedra pack much better than this, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of {\phi} = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is {\phi} = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams, and compresses to {\phi} = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Bulletin of the American Physical Society, Mar 1, 2010

Arbor -We present HOOMD-blue, a new, open source code for performing molecular dynamics and relat... more Arbor -We present HOOMD-blue, a new, open source code for performing molecular dynamics and related many-body dynamics simulations on graphics processing units (GPUs). All calculations are fully implemented on the GPU, enabling large performance speedups over traditional CPUs. On typical benchmarks, HOOMD-blue is about 60 times faster on a current generation GPU compared to running on a single CPU core. Next generation chips are due for release in early 2010 and are expected to nearly double performance. Efficient execution is achieved without any lack of generality and thus a wide variety of capabilities are present in the code, including standard bond, pair, angle, dihedral and improper potentials, along with the common NPT, NVE, NVT, and Brownian dynamics integration routines. The code is object-oriented, well documented, and easy to modify. We are constantly adding new features and looking for new developers to contribute to this fast maturing, open-source code [1]. In this talk, we present an overview of HOOMD-blue and give examples of its current and planned capabilities and speed over traditional CPU-based codes.

Anomalous behaviour known as ``spatially heterogeneous dynamics'' (SHD) has been observed in supe... more Anomalous behaviour known as ``spatially heterogeneous dynamics'' (SHD) has been observed in supercooled liquids, dense colloids, and, more recently, in confined granular packings. Dynamics in these systems may be governed by proximity to a generic ``jamming transition,'' beyond which rearrangements cease and the viscosity diverges. However, the universality of this jamming hypothesis has not yet been tested in terms of variation in the hallmark dynamical heterogeneities as a function of control parameter. Here, we report measurement of SHD in systems of air-driven granular beads, as a simultaneous function of both density and effective temperature. On approach to jamming, the dynamics are found to become progressively slower and more heterogeneous. The measured dynamical time and length scales appear to diverge, and can be modeled both by mode-coupling theory and by the Vogel Tammann-Fulcher (VFT) equation, in quantitative analogy with glass-forming liquids. The Vogel temperature arising from the VFT fit, which corresponds to an ideal glass transition temperature in liquids, coincides with point-J, the volume fraction corresponding to a random close-packed structure. Our findings provide a significant step forward in the quest for a unified theory of ``jamming'' in disparate systems.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

From length scale distributions characterizing frozen amorphous domains, we relate the s ensemble... more From length scale distributions characterizing frozen amorphous domains, we relate the s ensemble method with standard cooling and aging protocols for forming glass. We show that in a class of models where space-time scaling is in harmony with that of experiment, the spatial distributions of excitations obtained with the s ensemble are identical to those obtained through cooling or aging, but the computational effort for applying the s ensemble is generally many orders of magnitude smaller than that of straightforward numerical simulation of cooling or aging. We find that in contrast to the equilibrium ergodic state, a nonequilibrium length scale characterizes the anticorrelation between excitations and encodes the preparation history of glass states.

The densest packing of tetrahedra remains an unsolved problem, and there has been much recent deb... more The densest packing of tetrahedra remains an unsolved problem, and there has been much recent debate. We simulate dense packings of mathematically smooth, hard regular tetrahedra using NPT Monte Carlo simulations and determine the density- pressure equation of state. We find disordered and ordered packings with densities that significantly exceed the hard-sphere FCC packing density of 0.740480490. Our findings thus demonstrate that tetrahedra obey Ulam's conjecture that spheres pack with a lower maximum packing density than any other hard convex object, despite recent conjecture to the contrary. We show that the system is able to achieve such high packing densities by the local ordering of tetrahedra into certain favorable motifs, forming larger structures that pack efficiently but are overall jammed.

Characterization of Materials, 2002

Physical Review Letters, 2007

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by ... more Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal 'nucleus' to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.

Physical Review E, 2007

We present results of molecular simulations that predict the phases formed by the selfassembly of... more We present results of molecular simulations that predict the phases formed by the selfassembly of model nanospheres functionalized with a single polymer "tether", including double gyroid, perforated lamella and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that stabilizes the gyroid and perforated lamella phases. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints", which we use to quantify the extent of icosahedral ordering.

Physical Review E, 2012

By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we ... more By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we explore the different ways in which dynamical facilitation manifests itself within the local dynamics of glassy materials. Dynamical facilitation is characterized both by a mobility transfer function, the propensity for highly-mobile regions to arise near regions that were previously mobile, and by a facilitation volume, the effect of an initial dynamical event on subsequent dynamics within a region surrounding it. Sustained bursts of dynamical activity -avalanches -are shown to occur in kinetically constrained models, but, contrary to recent claims, we find that the decreasing spatiotemporal extent of avalanches with increased supercooling previously observed in granular experiments does not imply diminishing facilitation. Viewed within the context of existing simulation and experimental evidence, our findings show that dynamical facilitation plays a significant role in the dynamics of systems investigated over the range of state points accessible to molecular simulations and granular experiments. arXiv:1202.5527v3 [cond-mat.stat-mech]

Nature, 2009

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres [1], which have... more All hard, convex shapes are conjectured by Ulam to pack more densely than spheres [1], which have a maximum packing fraction of φ = π/√18 ≈ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction [2][3]. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with φ = 0.7786 [4], which was subsequently compressed numerically to φ = 0.7820 [5][6]. Here we show that tetrahedra pack much better than this, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal [7][8][9][10], which can be compressed to a packing fraction of φ = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is φ = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams, and compresses to φ = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles.

Langmuir, 2005

Fabrication of diamond structures by self-assembly is a fundamental challenge in making three-dim... more Fabrication of diamond structures by self-assembly is a fundamental challenge in making three-dimensional photonic crystals. We simulate a system of model hard particles with attractive patches and show that they can self-assemble into a diamond structure from an initially disordered state. We quantify the extent to which the formation of the diamond structure can be facilitated by "seeding" the system with small diamond crystallites or by introducing a rotation interaction to mimic a carbon-carbon antibonding interaction. Our results suggest patchy particles may serve as colloidal "atoms" and "molecules" for the bottom-up self-assembly of three-dimensional crystals.

On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range ... more On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range periodic ordering. However, it is also possible to form quasicrystals, ordered solids with long-range aperiodicity. Although quasicrystals have been observed in many materials, their formation is poorly understood. We present the results of a molecular simulation study to elucidate the process by which quasicrystals form from

... 8:00 AM–10:48 AM, Wednesday, March 7, 2007. Colorado Convention Center Room: 108 Sponsoring U... more ... 8:00 AM–10:48 AM, Wednesday, March 7, 2007. Colorado Convention Center Room: 108 Sponsoring Unit: GSNP Chair: Jennifer Schwarz, Syracuse University Abstract ID: BAPS.2007.MAR.N22.7. ... Adam Abate Douglas Durian (Department of Physics, University of ...

Computer simulation is a critical tool to aid in the understanding of complex phenomena in chemic... more Computer simulation is a critical tool to aid in the understanding of complex phenomena in chemical engineering, yet its inclusion in the curriculum has often been limited. As the field becomes increasingly more diverse, simulation becomes even more important because it can effectively communicate new and difficult material to students. Technology, and in particular cyberinfrastructure, has now advanced sufficiently to allow students to investigate complex phenomena simulationally in short periods of time. As such, virtual laboratory ...

Aps Meeting Abstracts, Mar 1, 2007

On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range ... more On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range periodic ordering. However, it is also possible to form quasicrystals, ordered solids with long-range aperiodicity. Although quasicrystals have been observed in many materials, their formation is poorly understood. We present the results of a molecular simulation study to elucidate the process by which quasicrystals form from supercooled liquids. We show that, as has been speculated in previous theoretical and experimental works, icosahedral clusters play a significant role in quasicrystal formation. Specifically, icosahedral clusters facilitate the formation of the so-called quasicrystal ``critical'' nucleus, and, together with phasons, facilitate the complicated mechanism that allows quasicrystals to grow aperiodic structures via local interactions. Our findings suggest that direct correlations between liquid ordering and solid structure may be a requisite property for quaiscrystal-forming systems, and is consistent with the class of systems that are known to form quasicrystals experimentally.

Nature, 2010

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a m... more All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of {\phi} = {\pi}/\sqrt18 ~ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with {\phi} = 0.7786, which was subsequently compressed numerically to {\phi} = 0.7820. Here we show that tetrahedra pack much better than this, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of {\phi} = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is {\phi} = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams, and compresses to {\phi} = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Bulletin of the American Physical Society, Mar 1, 2010

Arbor -We present HOOMD-blue, a new, open source code for performing molecular dynamics and relat... more Arbor -We present HOOMD-blue, a new, open source code for performing molecular dynamics and related many-body dynamics simulations on graphics processing units (GPUs). All calculations are fully implemented on the GPU, enabling large performance speedups over traditional CPUs. On typical benchmarks, HOOMD-blue is about 60 times faster on a current generation GPU compared to running on a single CPU core. Next generation chips are due for release in early 2010 and are expected to nearly double performance. Efficient execution is achieved without any lack of generality and thus a wide variety of capabilities are present in the code, including standard bond, pair, angle, dihedral and improper potentials, along with the common NPT, NVE, NVT, and Brownian dynamics integration routines. The code is object-oriented, well documented, and easy to modify. We are constantly adding new features and looking for new developers to contribute to this fast maturing, open-source code [1]. In this talk, we present an overview of HOOMD-blue and give examples of its current and planned capabilities and speed over traditional CPU-based codes.

Anomalous behaviour known as ``spatially heterogeneous dynamics'' (SHD) has been observed in supe... more Anomalous behaviour known as ``spatially heterogeneous dynamics'' (SHD) has been observed in supercooled liquids, dense colloids, and, more recently, in confined granular packings. Dynamics in these systems may be governed by proximity to a generic ``jamming transition,'' beyond which rearrangements cease and the viscosity diverges. However, the universality of this jamming hypothesis has not yet been tested in terms of variation in the hallmark dynamical heterogeneities as a function of control parameter. Here, we report measurement of SHD in systems of air-driven granular beads, as a simultaneous function of both density and effective temperature. On approach to jamming, the dynamics are found to become progressively slower and more heterogeneous. The measured dynamical time and length scales appear to diverge, and can be modeled both by mode-coupling theory and by the Vogel Tammann-Fulcher (VFT) equation, in quantitative analogy with glass-forming liquids. The Vogel temperature arising from the VFT fit, which corresponds to an ideal glass transition temperature in liquids, coincides with point-J, the volume fraction corresponding to a random close-packed structure. Our findings provide a significant step forward in the quest for a unified theory of ``jamming'' in disparate systems.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

From length scale distributions characterizing frozen amorphous domains, we relate the s ensemble... more From length scale distributions characterizing frozen amorphous domains, we relate the s ensemble method with standard cooling and aging protocols for forming glass. We show that in a class of models where space-time scaling is in harmony with that of experiment, the spatial distributions of excitations obtained with the s ensemble are identical to those obtained through cooling or aging, but the computational effort for applying the s ensemble is generally many orders of magnitude smaller than that of straightforward numerical simulation of cooling or aging. We find that in contrast to the equilibrium ergodic state, a nonequilibrium length scale characterizes the anticorrelation between excitations and encodes the preparation history of glass states.

The densest packing of tetrahedra remains an unsolved problem, and there has been much recent deb... more The densest packing of tetrahedra remains an unsolved problem, and there has been much recent debate. We simulate dense packings of mathematically smooth, hard regular tetrahedra using NPT Monte Carlo simulations and determine the density- pressure equation of state. We find disordered and ordered packings with densities that significantly exceed the hard-sphere FCC packing density of 0.740480490. Our findings thus demonstrate that tetrahedra obey Ulam's conjecture that spheres pack with a lower maximum packing density than any other hard convex object, despite recent conjecture to the contrary. We show that the system is able to achieve such high packing densities by the local ordering of tetrahedra into certain favorable motifs, forming larger structures that pack efficiently but are overall jammed.

Characterization of Materials, 2002

Physical Review Letters, 2007

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by ... more Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal 'nucleus' to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.

Physical Review E, 2007

We present results of molecular simulations that predict the phases formed by the selfassembly of... more We present results of molecular simulations that predict the phases formed by the selfassembly of model nanospheres functionalized with a single polymer "tether", including double gyroid, perforated lamella and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that stabilizes the gyroid and perforated lamella phases. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints", which we use to quantify the extent of icosahedral ordering.

Physical Review E, 2012

By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we ... more By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we explore the different ways in which dynamical facilitation manifests itself within the local dynamics of glassy materials. Dynamical facilitation is characterized both by a mobility transfer function, the propensity for highly-mobile regions to arise near regions that were previously mobile, and by a facilitation volume, the effect of an initial dynamical event on subsequent dynamics within a region surrounding it. Sustained bursts of dynamical activity -avalanches -are shown to occur in kinetically constrained models, but, contrary to recent claims, we find that the decreasing spatiotemporal extent of avalanches with increased supercooling previously observed in granular experiments does not imply diminishing facilitation. Viewed within the context of existing simulation and experimental evidence, our findings show that dynamical facilitation plays a significant role in the dynamics of systems investigated over the range of state points accessible to molecular simulations and granular experiments. arXiv:1202.5527v3 [cond-mat.stat-mech]

Nature, 2009

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres [1], which have... more All hard, convex shapes are conjectured by Ulam to pack more densely than spheres [1], which have a maximum packing fraction of φ = π/√18 ≈ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction [2][3]. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with φ = 0.7786 [4], which was subsequently compressed numerically to φ = 0.7820 [5][6]. Here we show that tetrahedra pack much better than this, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal [7][8][9][10], which can be compressed to a packing fraction of φ = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is φ = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams, and compresses to φ = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles.

Langmuir, 2005

Fabrication of diamond structures by self-assembly is a fundamental challenge in making three-dim... more Fabrication of diamond structures by self-assembly is a fundamental challenge in making three-dimensional photonic crystals. We simulate a system of model hard particles with attractive patches and show that they can self-assemble into a diamond structure from an initially disordered state. We quantify the extent to which the formation of the diamond structure can be facilitated by "seeding" the system with small diamond crystallites or by introducing a rotation interaction to mimic a carbon-carbon antibonding interaction. Our results suggest patchy particles may serve as colloidal "atoms" and "molecules" for the bottom-up self-assembly of three-dimensional crystals.

On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range ... more On cooling, liquids ordinarily solidify into glasses or into crystalline phases with long- range periodic ordering. However, it is also possible to form quasicrystals, ordered solids with long-range aperiodicity. Although quasicrystals have been observed in many materials, their formation is poorly understood. We present the results of a molecular simulation study to elucidate the process by which quasicrystals form from

... 8:00 AM–10:48 AM, Wednesday, March 7, 2007. Colorado Convention Center Room: 108 Sponsoring U... more ... 8:00 AM–10:48 AM, Wednesday, March 7, 2007. Colorado Convention Center Room: 108 Sponsoring Unit: GSNP Chair: Jennifer Schwarz, Syracuse University Abstract ID: BAPS.2007.MAR.N22.7. ... Adam Abate Douglas Durian (Department of Physics, University of ...

Computer simulation is a critical tool to aid in the understanding of complex phenomena in chemic... more Computer simulation is a critical tool to aid in the understanding of complex phenomena in chemical engineering, yet its inclusion in the curriculum has often been limited. As the field becomes increasingly more diverse, simulation becomes even more important because it can effectively communicate new and difficult material to students. Technology, and in particular cyberinfrastructure, has now advanced sufficiently to allow students to investigate complex phenomena simulationally in short periods of time. As such, virtual laboratory ...