Daniels Nonlinear Lab [NCSU Banner]

Dept of Physics


Most physical systems are not in equilibrium, but rather are subject to driving and/or dissipation. Far from equilibrium, where nonlinear effects become important, these systems display a rich array of complex behaviors. Systems can be dynamic, chaotic, or turbulent, and more remarkably can produce static patterns or exhibit persistent dynamics while remaining statistically stationary. Although there is typically no free-energy-like functional to minimize in a nonequilibrium system, quantities analogous to those used in equilibrium statistical mechanics can often elucidate the mean behavior.

Current experiments address:


Our research is supported by North Carolina State University, the National Science Foundation (DMS-0968258 and DMR-1206808), and the James S. McDonnell Foundation.

Acoustic Properties of Granular Materials

The acoustic properties of granular materials are inherently non-linear and complex, reflecting the highly heterogeneous structure and history-dependence of particle interactions. Of particular interest is the Density of Vibrational Modes, which has been shown to be related to the rigidity of jammed, disordered solids [1,2,3]. In [prior work] we've established a technique with which to measure the density of modes for static, granular systems without detailed knowledge of the particle interactions or structure.

We are now extending this methodology to characterize the acoustic emissions from granular systems which exhibit stick-slip behavior under shear. Our apparatus is an annular shear cell with a dozen acoustic probes, as well as precision stress and strain sensors. Our granular material is photoelastic, which facilitates the measurement of contact forces between grains. Examples of experimental images (top) of the contact force network, timestamped relative to the time of a slip event, along with the associated difference images (bottom) are provided above. Images such as these allow us to see the structure and dynamics of a given event. By studying the time evolution of the Density of Modes, we hope to better understand the mechanics that dictate wait times between slip events, as well as the duration and spatial extent of the associated deformation.

We've also begun to study the shape dependence of the Density of Modes (with undergraduates Alex Mauney [now a doctoral student at Cornell], and senior Rebekah Lee). Besides simply reducing the symmetry of the system or introducing rotational coupling between grains, particles with angular shape, or with concave faces can introduce qualitatively different modes of contact, as illustrated above. Understanding the effect shape has on the acoustic properties of granular packings may facilitate effective design of acoustic metamaterials.

Ted Brzinski, postdoc
see also an application to geophysics


  • Eli T. Owens and Karen E. Daniels. Acoustic measurement of a granular density of modes Soft Matter 9:1214 (2013) [Link] [PDF]

  • Danielle S. Bassett, Eli T. Owens, Karen E. Daniels, Mason A. Porter. Influence of Topology on Signal Propagation in Granular Force Networks. Physical Review E 86: 041306 (2012) [Link] [PDF]

  • Eli T. Owens and Karen E. Daniels. Sound propagation and force chains in granular materials. Europhysics Letters 94, 54005 (2011) [Link][and a movie]

Flow-Stabilized Solids

Particulate matter exhibits emergent mechanical properties that play central roles in many physical and biological systems. The bulk response of particulate matter has contributions from thermal fluctuations and geometric exclusion, but little is known about the interplay between the two aspects. To probe this regime, together with Robert Riehn, we have developed a novel in-situ technique for assembling flow-stabilized solids by hydrodynamically confining particles from a dilute Brownian suspension. Intriguingly, we find these solids assemble in heap-like shapes and we find their mechanical properties can be described as a solid-like elastic material.

Click here for more details.


  • Carlos P. Ortiz, Karen E. Daniels, Robert Riehn. Nonlinear Elasticity of Flow-Stabilized Solids. Physical Review E 90: 022304 (2014) [Link] [PDF]

  • Carlos P. Ortiz, Robert Riehn, and Karen E. Daniels. Flow-driven formation of solid-like microsphere heaps. Soft Matter, 2013,9, 543-549 [Link]

Folding Dynamics

Creased materials accommodate strain primarily at the folds. This feature allows for the construction of bellows-like objects which are much softer than the constituent material. An example of an origami-like Kapton bellows undergoing compression is shown at right. Such devices present a promising new design for actuators operating at low temperatures, but the implementation is hampered by nonlinear effects such as fracture, buckling, and hysteresis.

In a joint project with the NC State nuclear physics group and Frederic Lechenault at ENS Paris, we are studying the nonlinear elasticity of folded materials. Improvements in our ability to understand the dynamics of folds under strain will hopefully contribute to actuator design in an ultracold neutron experiment aimed at measuring the neutron's electric dipole moment.

Gel Fracture

The image at left was taken of a droplet of food coloring spreading within self-generated fractures at the surface of gel agar in a Petri dish. This is quite different from the circular way which surfactant-laden droplets spread on either solid or liquid surfaces, and is related to the fact that the gel substrate is a viscoelastic material which can fracture. We are studying how this instability arises from competition between the surface tension of the droplet and the elastic properties of the substrate. Such instabilities are important to understand in order to reliably work with non-Newtonian fluids in industrial and biomedical settings.

The image at right shows the photoelastic stress field present during crack-crack interactions. We have investigated the origin of the curved shapes made by pairs of interacting cracks, which occur in situations as diverse as dental enamel, cleaved silicon, geological faults, and planetary ice crusts. Through experiments on diverse materials (not just gels) we have quantified this universal shape and formulated a geometric model to understand how it arises. The work identifies an easily-measured shape parameter which could serve as a diagnostic tool for identifying the stress state under which cracks were formed in natural systems where history and dynamics are inaccessible.


  • Joshua B. Bostwick, Karen E. Daniels. Capillary Fracture of Soft Gels. Physical Review E 88: 042410 (2013) [Link] [PDF]

  • Melissa L. Fender, Frederic Lechenault, Karen E. Daniels. Universal shapes formed by two interacting cracks. Physical Review Letters 105: 125505 (2010) [Link]

  • K. E. Daniels, S. Mukhopadhyay, P. J. Houseworth, and R. P. Behringer. Instabilities in droplets spreading on gels. Physical Review Letters 99 124501 (2007) [Link]

Laboratory Models of Natural Faults

Geological faults ihave granular textures on many scales, from microscopic grains to macroscopic rocks. We seek to understand the extent to which granular interactions (interparticle, frictional slip) account for the range of geological observations & the inferred dynamic fault histories.

We conduct laboratory experiments using birefringent (photoelastic) particles in a simulated strike-slip fault. This movie of a laboratory fault experiment shows events in which the abrupt localization of the shear strain to the center of apparatus corresponds to little change in the force chain geometry away from the "fault." Bright particles are experiencing greater force than dark particles.

[This movie] shows an annular fault, and is representative of the pronounced stick-slip behavior we observe in the lab.

Ted Brzinski, postdoc


  • Nicholas W. Hayman, Lucie Ducloue, Kate L. Foco, Karen E. Daniels. Granular controls on periodicity of stick-slip events: kinematics and force-chains in an experimental fault. Pure and Applied Geophysics 168: 2239-2257 (2011) [Link] [PDF]

  • K. E. Daniels and N. W. Hayman. "Force chains in seismogenic faults visualized with photoelastic granular shear experiments." Journal of Geophysical Research. 113: B11411 (2008). [Link]

Rubble Pile Asteroids

Most Near-Earth Objects (NEOs) are composed of fracture rock, sometimes so fractured as to be nearer to a granular material than a solid body. These "rubble pile" asteroids are only weakly held together by gravitational forces: a child would be able to throw a ball above the escape velocity!


  • Karen E. Daniels. Rubble-Pile Near Earth Objects: Insights from Granular Physics Asteroids: Prospective Energy and Material Resources. Springer, 2013. [PDF]

Vegetation Patterns

[pattern formation on a golf course, courtesy Art Brunneau (NCSU Turf Science)]

Spatial patterns of 'dead' lawn grass have often been ascribed to Turing-type reaction-diffusion processes related to water scarcity. We have suggested an alternative hypothesis: that the air within the grass canopy is unstable to a convective instability, such that chill damage caused by falling cold air is responsible for the creation of brown and green bands of grass. This hypothesis is consistent with several features of small-scale vegetation patterns, including their length scale, rapid onset and transient nature. We find that the predictions of a porous medium convection model based are consistent with measurements made for a particular instance of lawn-patterning in North Carolina. In the image at left (courtesy Art Brunneau of the NCSU Turf Science program), it is clear that only the longer grass (taller fluid layer) is subject to this pattern-forming instability, as would be predicted by the convection model we propose.


  • Sally E. Thompson and Karen E. Daniels. A Porous Convection Model for Small-Scale Grass Patterns. The American Naturalist. 175: E10-E15 (2010) [Link]

  • Gopal G. Penny, Karen E. Daniels, and Sally E. Thompson. Local properties of patterned vegetation: quantifying endogenous and exogenous effects. Philosophical Transactions of the Royal Society A. 371: 20120359 (2013) [Link] [PDF]

Granular Materials

From avalanches and erosion to the transport of grain or pharmaceuticals, granular materials are all around us. When working with them, it rapidly becomes clear that these "simple" systems produce complex behavior: networks of force chains support the material, flowing motion is localized in shear bands, and particles segregate by size or shape when you try to mix them.

An important feature of granular materials is that the internal forces are not carried uniformly by the material, but instead through long chain-like strucutres whose density and orientation depend on the state and history of the sample. We are able to visualize these forces using a photoelastic disks and a polariscope, as seen in the image at right.

Research projects in the group address visualizing sound wave propagation, effects of order and anisotropy on material properties, phase transitions, and developing and testing statistical mechanical models.

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