arXiv subjects

J. M. Schwarz

Publications and source records attributed to J. M. Schwarz.

At least 55 records · Page 3Linked to original sources

arXiv2018

Hyperuniformity with no fine tuning in sheared sedimenting suspensions

Particle suspensions, present in many natural and industrial settings, typically contain aggregates or other microstructures that can complicate macroscopic flow behaviors and damage processing equipment. Recent work found that applying uniform periodic shear near a critical transition can reduce fluctuations in the particle concentration across all length scales, leading to a hyperuniform state. However, this strategy for homogenization requires fine tuning of the strain amplitude. Here we show that in a model of sedimenting particles under periodic shear, there is a well-defined regime at low sedimentation speed where hyperuniform scaling automatically occurs. Our simulations and theoretical arguments show that the homogenization extends up to a finite lengthscale that diverges as the sedimentation speed approaches zero.

cond-mat.soft↗

arXiv2018

Frictional rigidity percolation and minimal rigidity proliferation: From a new universality class to superuniversality

We introduce two new concepts, frictional rigidity percolation and minimal rigidity proliferation, to help identify the nature of the frictional jamming transition as well as significantly broaden the scope of rigidity percolation. For frictional rigidity percolation, we construct rigid clusters in two different lattice models using a $(3,3)$ pebble game, while taking into account contacts below and at the Coulomb threshold. The first lattice is a honeycomb lattice with next-nearest neighbors, the second, a hierarchical lattice. For both, we generally find a continuous rigidity transition. Our numerical results suggest that, for the honeycomb lattice, the exponents associated with the transition found with the frictional $(3,3)$ pebble game are distinct from those of a central-force $(2,3)$ pebble game. We propose that localized motifs, such as hinges, connecting rigid clusters that are allowed only with friction could give rise to this new frictional universality class. However, the closeness of the order parameter exponent between the two cases hints at potential superuniversality. To explore this possibility, we construct a bespoke cluster generating algorithm invoking generalized Henneberg moves, dubbed minimal rigidity proliferation. The minimally rigid clusters the algorithm generates appear to be in the same universality class as connectivity percolation, suggesting superuniversality between all three types of transitions. Finally, the hierarchical lattice is analytically tractable and we find that the exponents depend both on the type of force and on the fraction of contacts at the Coulomb threshold. These combined results allow us to compare two universality classes on the same lattice via rigid clusters for the first time to highlight unifying and distinguishing concepts within the set of all possible rigidity transitions in disordered systems.

cond-mat.soft↗

arXiv2018

Compression stiffening in biological tissues: on the possibility of classic elasticity origins

Compression stiffening, or an increase in shear modulus with increasing compressive strain, has been observed in recent rheometry experiments on brain, liver, and fat tissues. Here, we extend the known types of biomaterials exhibiting this phenomenon to include agarose gel and fruit flesh. Further, we show that two different results from classic elasticity theory can account for the phenomenon of linear compression stiffening. One result is due to Barron and Klein, extended here to the relevant geometry and pre-stresses; the other is due to Birch. For incompressible materials, there are no adjustable parameters in either theory. Which one applies to a given situation is a matter of reference state, suggesting that the reference state is determined by the tendency of the material to develop, or not develop, axial stress (in excess of the applied pre-stress) when subjected to torsion at constant axial strain. Our experiments and analysis also strengthen the notion that seemingly distinct animal and plant tissues can have mechanically similar behavior under certain conditions.

cond-mat.soft↗

arXiv2017

Soft yet sharp interfaces in a vertex model of confluent tissue

How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the ability of cells to independently regulate adhesivity and tension, together with neighbor-based interaction rules, lets them support strikingly unusual interfaces. In particular, we show that mechanical- and fluctuation-based measurements of the effective surface tension of a cellular aggregate yield different results, leading to mechanically soft interfaces that are nevertheless extremely sharp.

cond-mat.soft↗

arXiv2017

Surface creasing of soft elastic continua as a Kosterlitz-Thouless transition

Harnessing a model from composite materials science, we show how point-like cusped surface features arise as quasi-particle excitations, termed "ghost fibers", on the surface of a homogeneous soft elastic material. These deformations appear above a critical compressive strain at which ghost fiber dipoles unbind, analogous to vortices in the Kosterlitz-Thouless transition. Finite-length creases can be described in the same framework. Our predictions for crease surface profiles and onset strain agree with previous experiments and simulations, and further experimental tests are proposed.

cond-mat.soft↗

arXiv2016

Chase-and-run dynamics in cell motility and the molecular rupture of interacting active elastic dimers

Cell migration in morphogenesis and cancer metastasis typically involves interplay between different cell types. We construct and study a minimal, one-dimensional model comprised of two different motile cells with each cell represented as an active elastic dimer. The interaction between the two cells via cadherins is modeled as a spring that can rupture beyond a threshold force as it undergoes dynamic loading via the attached motile cells. We obtain a phase diagram consisting of chase-and-run dynamics and clumping dynamics as a function of the stiffness of the interaction spring and the threshold force. We also find that while feedback between cadherins and cell-substrate interaction via integrins accentuates the chase-run behavior, feedback is not necessary for it.

cond-mat.soft↗

arXiv2015

Constraint percolation on hyperbolic lattices

Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices and are interesting in their own right with ordinary percolation exhibiting not one, but two, phase transitions. We study four constraint percolation models---$k$-core percolation (for $k=1,2,3$) and force-balance percolation---on several tessellations of the hyperbolic plane. By comparing these four different models, our numerical data suggests that all of the $k$-core models, even for $k=3$, exhibit behavior similar to ordinary percolation, while the force-balance percolation transition is discontinuous. We also provide a proof, for some hyperbolic lattices, of the existence of a critical probability that is less than unity for the force-balance model, so that we can place our interpretation of the numerical data for this model on a more rigorous footing. Finally, we discuss improved numerical methods for determining the two critical probabilities on the hyperbolic lattice for the $k$-core percolation models.

cond-mat.stat-mech↗

arXiv2015

Shape-shifting droplet networks

We consider a three-dimensional network of aqueous droplets joined by single lipid bilayers to form a cohesive, tissue-like material. The droplets in these networks can be programmed to have distinct osmolarities so that osmotic gradients generate internal stresses via local fluid flows to cause the network to change shape. We discover, using molecular dynamics simulations, a reversible folding-unfolding process by adding an osmotic interaction with the surrounding environment which necessarily evolves dynamically as the shape of the network changes. This discovery is the next important step towards osmotic robotics in this system. We also explore analytically and numerically how the networks become faceted via buckling and how quasi-one-dimensional networks become three-dimensional.

cond-mat.soft↗

arXiv2015

Rigid cluster decomposition reveals criticality in frictional jamming

We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.

cond-mat.soft↗

arXiv2015

A density-independent glass transition in biological tissues

Cell migration is important in many biological processes, including embryonic development, cancer metastasis, and wound healing. In these tissues, a cell's motion is often strongly constrained by its neighbors, leading to glassy dynamics. While self-propelled particle models exhibit a density-driven glass transition, this does not explain liquid-to-solid transitions in confluent tissues, where there are no gaps between cells and therefore the density is constant. Here we demonstrate the existence of a new type of rigidity transition that occurs in the well-studied vertex model for confluent tissue monolayers at constant density. We find the onset of rigidity is governed by a model parameter that encodes single-cell properties such as cell-cell adhesion and cortical tension, providing an explanation for a liquid-to-solid transitions in confluent tissues and making testable predictions about how these transitions differ from those in particulate matter.

physics.bio-ph↗

arXiv2014

The mechanics of anisotropic spring networks

We construct and analyze a model for a disordered linear spring network with anisotropy. The modeling is motivated by, for example, granular systems, nematic elastomers, and ultimately cytoskeletal networks exhibiting some underlying anisotropy. The model consists of a triangular lattice with two different bond occupation probabilities, $p_x$ and $p_y$, for the linear springs. We develop an effective medium theory (EMT) to describe the network elasticity as a function of $p_x$ and $p_y$. We find that the onset of rigidity in the EMT agrees with Maxwell constraint counting. We also find beyond linear behavior in the shear and bulk modulus as a function of occupation probability in the rigid phase for small strains, which differs from the isotropic case. We compare our EMT with numerical simulations to find rather good agreement. Finally, we discuss the implications of extending the reach of effective medium theory as well as draw connections with prior work on both anisotropic and isotropic spring networks.

cond-mat.soft↗

arXiv2014

On the modeling of endocytosis in yeast

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Experiments on endocytosis in yeast all agree that (i) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it and (ii) the large scale membrane deformation is tubular in shape. There are three competing proposals, in contrast, for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: (i) initiation, where clathrin interacts with the membrane via adaptor proteins, (ii) elongation, where the membrane is then further deformed by polymerizing actin filaments, followed by (iii) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could possibly be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed.

q-bio.CB↗

arXiv2014

Elastic instabilities in a layered cerebral cortex: A revised axonal tension model for cortex folding

We model the elasticity of the cerebral cortex as a layered material with bending energy along the layers and elastic energy between them in both planar and polar geometries. The cortex is also subjected to axons pulling from the underlying white matter. Above a critical threshold force, a "flat" cortex configuration becomes unstable and periodic unduluations emerge, i.e. a buckling instability occurs. These undulations may indeed initiate folds in the cortex. We identify analytically the critical force and the critical wavelength of the undulations. Both quantities are physiologically relevant values. Our model is a revised version of the axonal tension model for cortex folding, with our version taking into account the layered structure of the cortex. Moreover, our model draws a connection with another competing model for cortex folding, namely the differential growth-induced buckling model. For the polar geometry, we study the relationship between brain size and the critical force and wavelength to understand why small mice brains exhibit no folds, while larger human brains do, for example. Finally, an estimate of the bending rigidity constant for the cortex can be made based on the critical wavelength.

cond-mat.soft↗

arXiv2014

Active elastic dimers: Cells moving on rigid tracks

Experiments suggest that the migration of some cells in the three-dimensional extra cellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and alpha-actinin-driven extendability, while the friction coefficients of the two beads describe the catch/slip bond behavior of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch bond behavior of integrins at the front of the cell and slip bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch bond behavior and the dynamics of cross-linking, and the addition of active noise on the motion of the cell. Our model highlights the role of alpha-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion.

cond-mat.soft↗

arXiv2014

Energy barriers govern glassy dynamics in tissues

Recent observations demonstrate that densely packed tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here we develop numerical and theoretical models to calculate energy barriers to cell rearrangements, which help govern cell migration in cell monolayers. In contrast to work on sheared foams, we find that energy barrier heights are exponentially distributed and depend systematically on the cell's number of neighbors. Based on these results, we predict glassy two-time correlation functions for cell motion, with a timescale that increases rapidly as cell activity decreases. These correlation functions are used to construct simple random walks that reproduce the caging behavior observed for cell trajectories in experiments. This work provides a theoretical framework for predicting collective motion of cells in wound-healing, embryogenesis and cancer tumorigenesis.

cond-mat.soft↗

arXiv2013

Jamming graphs: A local approach to global mechanical rigidity

We revisit the concept of minimal rigidity as applied to soft repulsive, frictionless sphere packings in two-dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's theorem in two-dimensions. It constrains the global, average coordination number of the graph, for example. However, minimal rigidity does not address the geometry of local mechanical stability. The jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability. We demonstrate how jamming graphs can be constructed using local moves via the Henneberg construction such that these graphs fall under the jurisdiction of correlated percolation. We then probe how jamming graphs destabilize, or become unjammed, by deleting a bond and computing the resulting rigid cluster distribution. We also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra/redundant contacts destabilizes. The latter endeavor allows us to probe a disc packing in the rigid phase and uncover a potentially new diverging lengthscale associated with the random deletion of contacts as compared to the study of cut-out (or frozen in) subsystems.

cond-mat.soft↗

arXiv2013

Contact processes in crowded environments

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions/contacts between particles in the steady state limit, while in the active phase collisions persist. To investigate this system at higher densities, we construct and study a conserved-particle-number contact process with novel three-body interactions, which are potentially more likely than two-body interactions at higher densities. For example, consider one active (diffusing) particle colliding with two inactive (non-diffusing) particles such that they become active, in addition to spontaneous inactivation. In mean-field, this system exhibits a continuous dynamical phase transition belonging to the conserved directed percolation universality class. Simulations on square lattices support the mean field result. In contrast, the three-body interaction requiring two active particles to activate one inactive particle exhibits a discontinuous transition. Finally, inspired by kinetically-constrained models of the glass transition, we investigate the "caging effect" at even higher particle densities to look for a second dynamical phase transition back to an inactive phase. Square lattice simulations suggest a continuous transition with a new set of exponents differing from conserved directed percolation, i.e. a new universality class for contact processes with conserved particle number.

cond-mat.stat-mech↗

arXiv2013

Vicious accelerating walkers

A vicious walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. We numerically compute the survival probability exponent, α, for this system, which characterizes the probability for any two walkers not to meet. For example, for N = 3, α = 0.71 \pm 0.01. Based on our numerical data, we conjecture that 1/8N(N - 1) is an upper bound on α. We also numerically study N vicious Levy flights and find, for instance, for N = 3 and a Levy index μ = 1 that α = 1.31 \pm 0.03. Vicious accelerating walkers relate to no-crossing configurations of semiflexible polymer brushes and may prove relevant for a non-Markovian extension of Dyson's Brownian motion model.

cond-mat.stat-mech↗