About

Professor Joshua Socolar is a faculty member of the Department of Physics at Duke University, where he has been serving as a Professor of Physics since 2011. His research interests include collective behavior in condensed matter and dynamical systems, with specific focus on limit-periodic structures, quasicrystals, packing problems, and tiling theory. He also investigates self-assembly and phases of designed colloidal particles, shear jamming and stick-slip behavior in dry granular materials, the organization and dynamics of complex networks, and the topological elasticity of mechanical lattices. His work encompasses a broad range of topics related to the physical properties and behaviors of complex systems, contributing to the understanding of exotic patterns in crystal structures, the jamming phenomena in granular materials, and the mathematical modeling of tiling and quasicrystalline structures. His research has been supported by various grants, including those from the Army Research Office, the National Institutes of Health, and the National Science Foundation. Professor Socolar holds a Ph.D. from the University of Pennsylvania and a B.A. from Haverford College.

Research topics

• Computer Science
• Materials science
• Physics
• Composite material
• Mechanics
• Condensed matter physics
• Acoustics
• Thermodynamics
• Structural engineering
• Engineering
• Telecommunications
• Optics

Selected publications

• Editorial: DSNP Dissertation Award 2025 – Pushing the limits of active metamaterials

  Physical review. E · 2026-03-09

  articleOpen accessSenior author
  PublisherDOI

• Dynamical Heterogeneity in Shear-Jammed Granular Systems

  EPJ Web of Conferences · 2025-01-01

  articleOpen accessSenior author

  Granular suspensions can jam into solids under shear at densities below the isotropic jamming density. At sufficiently large shear stress, these shear-jammed structures undergo plastic flow through small deformations of the particles, contact breaking or slipping, and associated particle rearrangements. Although the shear jamming phenomenon has been extensively studied in recent decades, little is known about how shearjammed states evolve under steady shear. In this work, we report on systematic experiments on the evolution of a shear-jammed system using a recently developed multi-ring Couette shear device. This device imposes a linear shear profile on a layer of photoelastic discs, mimicking a two-dimensional suspension with a small Stokes number. We find that the displacements of the particles exhibit strong spatio-temporal correlations within the range of packing fractions where shear jamming occurs. The particle dynamics are quantified using the fourpoint susceptibility, which grows significantly as the packing fraction approaches the isotropic jamming point from below.

  PublisherOA PDFDOI

• Quasicrystalline structure of the hat monotile tilings

  Physical review. B./Physical review. B · 2023-12-11 · 12 citations

  article1st authorCorresponding

  Tiling models can reveal unexpected ways in which local constraints give rise to exotic long-range spatial structure. The recently discovered hat monotile (and its mirror image) has been shown to be aperiodic [Smith et al., arXiv:2303.10798]; it can tile the plane with no holes or overlaps, but cannot do so periodically. We show that the structure enforced by the local space-filling constraints is quasiperiodic with hexagonal (C6) rotational symmetry. Although this symmetry is compatible with periodicity, the incommensurate ratio characterizing the quasiperiodicity stays locked to the golden mean as the tile parameters are continuously varied. We analyze a modification of the metatiles introduced by Smith et al. that yields a set of key tiles that can be constructed as projections of a subset of six-dimensional hypercubic lattice points onto the two-dimensional tiling plane. We analytically compute the diffraction pattern of a set of unit masses placed at the tiling vertices, establishing the quasiperiodic nature of the tiling. We point out several unusual features of the family of key tilings and associated hat tilings, including the tile rearrangements associated with the phason degree of freedom associated with incommensurate density waves, which exhibit novel features that may influence the elastic properties of a material in which atoms or larger particles spontaneously exhibit the symmetries of the hat tiling.

  PublisherDOI

• Evolution of force networks during stick-slip motion of an intruder in a granular material: Topological measures extracted from experimental data

  Physical review. E · 2023-11-15 · 8 citations

  article

  In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data do not include precise information about individual contact forces, we use an approach developed in our previous work [Basak et al., J. Eng. Mech. 147, 04021100 (2021)0733-939910.1061/(ASCE)EM.1943-7889.0002003] based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable slip precursors. In particular, the number of generators describing the structure and complexity of force networks increases consistently before slips. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams and, therefore, of the underlying networks, for systems of pentagonal particles.

  PublisherDOI

• Quasicrystalline structure of the Smith monotile tilings

  arXiv (Cornell University) · 2023-05-02 · 3 citations

  preprintOpen access1st authorCorresponding

  Tiling models can reveal unexpected ways in which local constraints give rise to exotic long-range spatial structure. The recently discovered Hat monotile (and its mirror image) has been shown to be aperiodic~[Smith et al., arXiv:2303.10798 (2023)]; it can tile the plane with no holes or overlaps, but cannot do so periodically. We show that the structure enforced by the local space-filling constraints is quasiperiodic with hexagonal (C6) rotational symmetry. Although this symmetry is compatible with periodicity, the incommensurate ratio characterizing the quasiperiodicity stays locked to the golden mean as the tile parameters are continuously varied. We analyze a modification of the metatiles introduced by Smith et al. that yields a set of ``Key tiles'' that can be constructed as projections of a subset of six-dimensional hypercubic lattice points onto the two-dimensional tiling plane. We analytically compute the diffraction pattern of a set of unit masses placed at the tiling vertices, establishing the quasiperiodic nature of the tiling. We point out several unusual features of the family of Key tilings and associated Hat tilings, including the tile rearrangements associated with the phason degree of freedom associated with incommensurate density waves, which exhibit novel features that may influence the elastic properties of a material in which atoms or larger particles spontaneously exhibit the symmetries of the Hat tiling.

  PublisherOA PDFDOI

• Microscopic reversibility and emergent elasticity in ultrastable granular systems

  Frontiers in Physics · 2022-11-28 · 4 citations

  articleOpen accessSenior authorCorresponding

  In a recent paper (Zhao et al., Phys Rev X, 2022, 12: 031,021), we reported experimental observations of “ultrastable” states in a shear-jammed granular system subjected to small-amplitude cyclic shear. In such states, all the particle positions and contact forces are reproduced after each shear cycle so that a strobed image of the stresses and particle positions appears static. In the present work, we report further analyses of data from those experiments to characterize both global and local responses of ultrastable states within a shear cycle, not just the strobed dynamics. We find that ultrastable states follow a power-law relation between shear modulus and pressure with an exponent β ≈ 0.5, reminiscent of critical scaling laws near jamming. We also examine the evolution of contact forces measured using photoelasticimetry. We find that there are two types of contacts: non-persistent contacts that reversibly open and close; and persistent contacts that never open and display no measurable sliding. We show that the non-persistent contacts make a non-negligible contribution to the emergent shear modulus. We also analyze the spatial correlations of the stress tensor and compare them to the predictions of a recent theory of the emergent elasticity of granular solids, the Vector Charge Theory of Granular mechanics and dynamics (VCTG) (Nampoothiri et al., Phys Rev Lett, 2020, 125: 118,002). We show that our experimental results can be fit well by VCTG, assuming uniaxial symmetry of the contact networks. The fits reveal that the response of the ultrastable states to additional applied stress is substantially more isotropic than that of the original shear-jammed states. Our results provide important insight into the mechanical properties of frictional granular solids created by shear.

  PublisherDOI

• Universal features of the stick-slip dynamics of an intruder moving through a confined granular medium

  Physical review. E · 2022-04-21 · 5 citations

  articleSenior author

  Experiments and simulations of an intruder dragged by a spring through a two-dimensional annulus of granular material exhibit robust force fluctuations. At low packing fractions (ϕ<ϕ_{0}), the intruder clears an open channel. Above ϕ_{0}, stick-slip dynamics develop, with an average energy release that is independent of the particle-particle and particle-base friction coefficients but does depend on the width W of the annulus and the diameter D of the intruder. A simple model predicts the dependence of ϕ_{0} on W and D, allowing for a data collapse for the average energy release as a function of ϕ/ϕ_{0}. These results pose challenges for theories of mechanical failure in amorphous materials.

  PublisherDOI

• Ultrastable Shear-Jammed Granular Material

  Physical Review X · 2022-08-01 · 17 citations

  articleOpen accessSenior author

  Dry granular materials, such as sand, gravel, pills, or agricultural grains, can become rigid when compressed or sheared. Under isotropic compression, the material reaches a certain jamming density and then resists further compression. Shear jamming occurs when resistance to shear emerges in a system at a density lower than the jamming density. Although shear jamming is prevalent in frictional granular materials, their stability properties are not well described by standard elasticity theory and thus call for experimental characterization. We report on experimental observations of changes in the mechanical properties of a shear-jammed granular material subjected to small-amplitude, quasistatic cyclic shear. We study a layer of plastic disks confined to a shear cell, using photoelasticimetry to measure all interparticle vector forces. For sufficiently small cyclic shear amplitudes and large enough initial shear, the material evolves to an unexpected "ultrastable" state in which all the particle positions and interparticle contact forces remain unchanged after each complete shear cycle for thousands of cycles. The stress response of these states to small imposed shear is nearly elastic, in contrast to the original shear-jammed state.

  PublisherOA PDFDOI

• Microscopic Reversibility and Emergent Elasticity in Ultrastable Granular Systems

  arXiv (Cornell University) · 2022-09-25

  preprintOpen accessSenior author

  In a recent paper [Phys. Rev. X 12, 031021], we reported experimental observations of ``ultrastable'' states in a shear-jammed granular system subjected to small-amplitude cyclic shear. In such states, all the particle positions and contact forces are reproduced after each shear cycle so that a strobed image of the stresses and particle positions appears static. In the present work, we report further analyses of data from those experiments to characterize both global and local responses of ultrastable states within a shear cycle, not just the strobed dynamics. We find that ultrastable states follow a power-law relation between shear modulus and pressure with an exponent $β\approx 0.5$, reminiscent of critical scaling laws near jamming. We also examine the evolution of contact forces measured using photoelasticimetry. We find that there are two types of contacts: non-persistent contacts that reversibly open and close; and persistent contacts that never open \yiqiu{and display no measurable sliding}. We show that the non-persistent contacts make a non-negligible contribution to the emergent shear modulus. We also analyze the spatial correlations of the stress tensor and compare them to the predictions of a recent theory of the emergent elasticity of granular solids, the Vector Charge Theory of Granular mechanics and dynamics (VCTG) [Phys. Rev. Lett. 125, 118002, arXiv:2204.11811]. We show that our experimental results can be fit well by VCTG, assuming uniaxial symmetry of the contact networks. The fits reveal that the response of the ultrastable states to additional applied stress is substantially more isotropic than that of the original shear-jammed states. Our results provide important insight into the mechanical properties of frictional granular solids created by shear.

  PublisherOA PDFDOI

• Stick-Slip Dynamics in a Granular Material With Varying Grain Angularity

  Frontiers in Physics · 2022-07-15 · 13 citations

  articleOpen accessSenior author

  Experiments, simulations, and theoretical treatments of granular materials typically feature circular or elliptical grains. However, grains found in natural systems often have flat faces that introduce local rotational constraints; these rotational constraints have been shown to affect, for example, the jamming transition, discontinuous shear thickening, and ordered states in colloids and thermalized grains. In this work, we experimentally investigate the effects of grain angularity on stick-slip dynamics. A weighted slider is pulled by a spring over a gravity-packed granular bed composed of polygonal grains with varying angularity. We find that packings of triangular or square grains have higher shear strengths than packings of pentagons, hexagons, heptagons, or disks. Additionally, as the number of sides increases, sticking periods, during which the slider remains motionless while the spring force on it increases, become shorter on average, with the material yielding at smaller applied stresses. Lastly, we find that dilation of the medium during sticking periods tends to be larger for grains with higher angularity, in part because of the presence of stilt-like columnar structures that prop the slider up. We report on measurements of the pulling force on the slider, particle dynamics during slip events, and properties of force-bearing contact networks identified via photoelasticity. Our findings indicate that high angularity of grains (pentagons, squares, triangles) leads to differences in grain-scale flow and macroscopic stick-slip dynamics of bulk granular materials. Our experiments also indicate a continuous change in dynamics with decreasing angularity as the circular grain limit is approached.

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: Dynamics of Boolean Networks and Gene Expression

  NSF · $420k · 2004–2009

• Structure, Response, and Flow of Dense Granular Materials

  NSF · $508k · 2018–2021

• The Dynamical Logic of Developmental Regulatory Networks

  NSF · $420k · 2011–2015

Frequent coauthors

• Hu Zheng

  China University of Mining and Technology

  34 shared

• Paul J. Steinhardt

  Princeton University

  23 shared

• C. Manuel Carlevaro

  Instituto de Fisica de Liquidos y Sistemas Biologicos

  19 shared

• Ryan Kozlowski

  College of the Holy Cross

  19 shared

• Luis A. Pugnaloni

  18 shared

• Xianrui Cheng

  University of Southern California

  17 shared

• Patrick Charbonneau

  Duke University

  17 shared

• Yuchen Zhao

  Nanyang Technological University

  14 shared

Education

• PhD, Physics

  University of Pennsylvania

  1987

• BA, Physics

  Haverford College

  1980