Dynamic pilot wave bound states.

Motivated by recent parallels between classical bouncing droplet experiments and quantum bound states, we explore the lessons that droplet experiments might teach us about the dynamics of quantum solutions. Since the classical experiment is periodically driven, we examine periodic driving of the integer spin Klein-Gordon equation. We find that an exact solution can be obtained, and surprisingly this solution necessarily produces "half-integer" orbital angular momentum. We stress that these findings are strictly mathematical; nevertheless, this and other physical implications are intriguing and suggest further study.

Effects of Polarization on Particle-Laden Flows.

Simulations of particle-laden flow with dielectric particles are carried out with varying levels of electrical charging and particle polarization. Simulation results reveal three distinct flow regions. For low particle charge and polarizability, flow is nearly symmetric and nonmeandering. For strong charging and polarization, particles form a continuous and tightly clustered sheet close to one of the walls. Between these extremes, particles form localized particle-rich regions, around which the gas executes a meandering flow. These results indicate that polarization can lead to qualitative changes in the characteristics of particle-laden flows subject to tribocharging.

Size Sorting on the Rubble-Pile Asteroid Itokawa.

Photographs of the asteroid Itokawa reveal unexpectedly strong size segregation between lowlands populated almost entirely by small pebbles and highlands consisting of larger boulders. We propose that this segregation may be caused by a simple and unexplored effect: pebbles accreting onto the asteroid rebound from boulders, but sink into pebbly regions. By number, overwhelmingly more particles on Itokawa are pebbles, and collisions involving these pebbles must unavoidably cause pebbly regions to grow. We carry out experiments and simulations that demonstrate that this mechanism of size sorting based on simple counting of grains produces strong lateral segregation that reliably obeys an analytic formula.

Surface contact charging.

Experiments in several laboratories have demonstrated that identical materials brought into repeated contact generate unexplained and growing surface charge domains. Here we show that the growth of charge from these experiments can be fitted to a previously developed first-principles model for contact charging based on feedback of random surface polarizations. Surprisingly this mechanism, which leads to exponential growth in colliding granular beds, can also explain nonexponential growth of surface charging, as well as predicting spatiotemporal growth of charge domains and their dependencies on material parameters.

Granular chaos and mixing: Whirled in a grain of sand.

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

Self-sustaining charging of identical colliding particles.

Recent experiments have demonstrated that identical material samples can charge one another after being brought into symmetric contact. The mechanism for this charging is not known. In this article, we use a simplified one-dimensional lattice model to analyze charging in the context of agitated particles. We find that the electric field from a single weakly polarized grain can feed back on itself by polarizing its neighbors, leading to an exponential growth in polarization. We show that, by incorporating partial neutralization between neighboring polarized particles, either uniform alignment of dipoles or complex charge and polarization waves can be produced. We reproduce a polarized state experimentally using identical colliding particles and raise several issues for future study.

AFM study of hydrophilicity on acetaminophen crystals.

Pharmaceutical powder processing is notoriously subject to unpredictable jamming, sticking and charging disturbances. To unveil the material science underlying these effects, we use atomic force microscopy (AFM) on a common pharmaceutical, acetaminophen (APAP). Specifically, we study surface adhesion and morphology as a function of relative humidity (RH) for monoclinic acetaminophen, using both plain AFM tips and tips functionalized to be hydrophobic or hydrophilic. Results indicate that the (001) crystal face exhibits significantly higher adhesion (surface potential) than the other crystal faces. For all the faces clear peaks in adhesion occur at 50-60% RH when they are examined using hydrophilic tips. The surface morphology of some facets showed a strong dependence on RH while others showed little or no significant change. In particular, the morphology of the (1-10) faces developed large terraces at high humidity, possibly due to deliquescence followed by recrystallization. These results confirm the hypothesis that different crystal facets exhibit distinct surface potentials and morphology that change with environmental exposure. The work suggests that future studies of powder behaviors would benefit from a more detailed modeling of crystal surface contact mechanics.

Automated reconstruction algorithm for identification of 3D architectures of cribriform ductal carcinoma in situ.

Ductal carcinoma in situ (DCIS) is a pre-invasive carcinoma of the breast that exhibits several distinct morphologies but the link between morphology and patient outcome is not clear. We hypothesize that different mechanisms of growth may still result in similar 2D morphologies, which may look different in 3D. To elucidate the connection between growth and 3D morphology, we reconstruct the 3D architecture of cribriform DCIS from resected patient material. We produce a fully automated algorithm that aligns, segments, and reconstructs 3D architectures from microscopy images of 2D serial sections from human specimens. The alignment algorithm is based on normalized cross correlation, the segmentation algorithm uses histogram equilization, Otsu's thresholding, and morphology techniques to segment the duct and cribra. The reconstruction method combines these images in 3D. We show that two distinct 3D architectures are indeed found in samples whose 2D histological sections are similarly identified as cribriform DCIS. These differences in architecture support the hypothesis that luminal spaces may form due to different mechanisms, either isolated cell death or merging fronds, leading to the different architectures. We find that out of 15 samples, 6 were found to have 'bubble-like' cribra, 6 were found to have 'tube-like' criba and 3 were 'unknown.' We propose that the 3D architectures found, 'bubbles' and 'tubes', account for some of the heterogeneity of the disease and may be prognostic indicators of different patient outcomes.

Electrostatic precursors to granular slip events.

It has been known for over a century that electrical signals are produced by material failure, for example during crack formation of crystals and glasses, or stick-slip motion of liquid mercury on glass. We describe here new experiments revealing that slip events in cohesive powders also produce electrical signals, and remarkably these signals can appear significantly in advance of slip events. We have confirmed this effect in two different experimental systems and using two common powdered materials, and in a third experiment we have demonstrated that similar voltage signals are produced by crack-like defects in several powdered materials.

The interplay between branching and pruning on neuronal target search during developmental growth: functional role and implications.

Regenerative strategies that facilitate the regrowth and reconnection of neurons are some of the most promising methods in spinal cord injury research. An essential part of these strategies is an increased understanding of the mechanisms by which growing neurites seek out and synapse with viable targets. In this paper, we use computational and theoretical tools to examine the targeting efficiency of growing neurites subject to limited resources, such as maximum total neural tree length. We find that in order to efficiently reach a particular target, growing neurites must achieve balance between pruning and branching: rapidly growing neurites that do not prune will exhaust their resources, and frequently pruning neurites will fail to explore space effectively. We also find that the optimal branching/pruning balance must shift as the target distance changes: different strategies are called for to reach nearby vs. distant targets. This suggests the existence of a currently unidentified higher-level regulatory factor to control arborization dynamics. We propose that these findings may be useful in future therapies seeking to improve targeting rates through manipulation of arborization behaviors.

Engineered in vitro/in silico models to examine neurite target preference.

Research on spinal cord injury (SCI) repair focuses on developing mechanisms to allow neurites to grow past an injury site. In this article, we observe that numerous divergent paths (i.e., spinal roots) are present along the spinal column, and hence guidance strategies must be devised to ensure that regrowing neurites reach viable targets. Therefore, we have engineered an in vitro micropatterned model in which cultured E7 dorsal root ganglia (DRG) explants may enter alternate pathways (?roots?) along a branching micropattern. Alongside this in vitro model, we have developed an in silico simulation that we validate by comparison with independent experiments. We find in both in silico and in vitro models that the probability of a neurite entering a given root decreases exponentially with respect to the number of roots away from the DRG; consequently, the likelihood of neurites reaching a distant root can be vanishingly small. This result represents a starting point for future strategies to optimize the likelihood that neurites will reach appropriate targets in the regenerating nervous system, and provides a new computational tool to evaluate the feasibility and expected success of neurite guidance in complex geometries.

Shape-mediated ordering in granular blends.

Many industries mix granular materials of different sizes and shapes. Product quality and consistency are often compromised by demixing of constituent components. Not only is this practically problematic but it is also philosophically unsettling, for on smaller colloidal scales, systems consisting of particles differing by size and shape display quantitatively predictable transitions between mixed and separated phases. We report here that patterns and segregation transitions analogous to those seen in colloidal systems can be found in granular blends differing in shape, concentration, and temperature. This provides insights into the mechanisms of granular segregation.

Alpha5beta1 integrin-fibronectin interactions specify liquid to solid phase transition of 3D cellular aggregates.

BACKGROUND: Tissue organization during embryonic development and wound healing depends on the ability of cells on the one hand to exchange adhesive bonds during active rearrangement and on the other to become fixed in place as tissue homeostasis is reached. Cells achieve these contradictory tasks by regulating either cell-cell adhesive bonds, mediated by cadherins, or cell-extracellular matrix (ECM) connections, regulated by integrins. Integrin alpha5beta1 and soluble fibronectin (sFN) are key players in cell-ECM force generation and in ECM polymerization. Here, we explore the interplay between integrin alpha5beta1 and sFN and its influence on tissue mechanical properties and cell sorting behavior. METHODOLOGY/PRINCIPAL FINDINGS: We generated a series of cell lines varying in alpha5beta1 receptor density. We then systematically explored the effects of different sFN concentrations on aggregate biomechanical properties using tissue surface tensiometry. We found previously unreported complex behaviors including the observation that interactions between fibronectin and integrin alpha5beta1 generates biphasic tissue cohesion profiles. Specifically, we show that at constant sFn concentration, aggregate cohesion increases linearly as alpha5beta1 receptor density is increased from low to moderate levels, producing a transition from viscoelastic-liquid to pseudo viscoelastic-solid behavior. However, further increase in receptor density causes an abrupt drop in tissue cohesion and a transition back to viscoelastic-liquid properties. We propose that this may be due to depletion of sFn below a critical value in the aggregate microenvironment at high alpha5beta1 levels. We also show that differential expression of alpha5beta1 integrin can promote phase-separation between cells. CONCLUSIONS/SIGNIFICANCE: The interplay between alpha5-integrin and sFn contributes significantly to tissue cohesion and, depending on their level of expression, can mediate a shift from liquid to elastic behavior. This interplay represents a tunable level of control between integrins and the ECM that can influence tissue cohesion and other mechanical properties, which may translate to the specification of tissue structure and function. These studies provide insights into important biological processes such as embryonic development, wound healing, and for tissue engineering applications.

A 2D mechanistic model of breast ductal carcinoma in situ (DCIS) morphology and progression.

Ductal carcinoma in situ (DCIS) of the breast is a non-invasive tumor in which cells proliferate abnormally, but remain confined within a duct. Although four distinguishable DCIS morphologies are recognized, the mechanisms that generate these different morphological classes remain unclear, and consequently the prognostic strength of DCIS classification is not strong. To improve the understanding of the relation between morphology and time course, we have developed a 2D in silico particle model of the growth of DCIS within a single breast duct. This model considers mechanical effects such as cellular adhesion and intra-ductal pressure, and biological features including proliferation, apoptosis, necrosis, and cell polarity. Using this model, we find that different regions of parameter space generate distinct morphological subtypes of DCIS, so elucidating the relation between morphology and time course. Furthermore, we find that tumors with similar architectures may in fact be produced through different mechanisms, and we propose future work to further disentangle the mechanisms involved in DCIS progression.

Swimming in granular media.

A class of reptiles known as sand swimmers adapts to hot environments by submerging beneath desert sands during the day and so provide a unique probe into the dynamics of intruders in granular beds. To understand the mechanism for swimming in an otherwise solid bed, we study a simple model of periodic contraction and extension of large intruders in a granular bed. Using an event-driven simulation, we find optimal conditions that idealized swimmers must use to critically fluidize a sand bed so that it is rigid enough to support a load when needed, but fluid enough to permit motion with minimal resistance. Swimmers-or other intruders-that agitate the bed too rapidly produce large voids that prevent traction from being achieved, while swimmers that move too slowly cannot travel before the bed resolidifies around them, i.e., the swimmers locally probe the fundamental time scale in a granular packing.

Cellular morphogenesis in silico.

We describe a model that simulates spherical cells of different types that can migrate and interact either attractively or repulsively. We find that both expected morphologies and previously unreported patterns spontaneously self-assemble. Among the newly discovered patterns are a segmented state of alternating discs, and a "shish-kebab" state, in which one cell type forms a ring around a second type. We show that these unique states result from cellular attraction that increases with distance (e.g., as membranes stretch viscoelastically), and would not be seen in traditional, e.g., molecular, potentials that diminish with distance. Most of the states found computationally have been observed in vitro, and it remains to be established what role these self-assembled states may play in in vivo morphogenesis.

Use of a static eliminator to improve powder flow.

Glidants and lubricants have long been used to improve the flow and processing of pharmaceutical and other powder blends. In this letter, we find that similar improvements can be attained, without additives, by using a simple static eliminator. These results indicate, first, that electrostatic effects on powder blends may be a significant cause of powder aggregation and flow instabilities, and second, that common additives such as magnesium stearate, colloidal silica, and talc may have as their chief effect the reduction of static. This suggests both that intelligent placement of static eliminators can eliminate the need for some of these additives and that judicious engineering of ionic and cationic additives may be effective in improving flow of "clingy" materials.

Why decussate? Topological constraints on 3D wiring.

Many vertebrate motor and sensory systems "decussate" or cross the midline to the opposite side of the body. The successful crossing of millions of axons during development requires a complex of tightly controlled regulatory processes. Because these processes have evolved in many distinct systems and organisms, it seems reasonable to presume that decussation confers a significant functional advantage--yet if this is so, the nature of this advantage is not understood. In this article, we examine constraints imposed by topology on the ways that a three-dimensional processor and environment can be wired together in a continuous, somatotopic, way. We show that as the number of wiring connections grows, decussated arrangements become overwhelmingly more robust against wiring errors than seemingly simpler same-sided wiring schemes. These results provide a predictive approach for understanding how 3D networks must be wired if they are to be robust, and therefore have implications both for future large-scale computational networks and for complex biomedical devices.