Wound opening in a thin incompressible viscoelastic tissue.

We develop a model to investigate analytically and numerically the mechanics of wound opening made in a viscoelastic, isotropic, homogeneous, and incompressive thin tissue. This process occurs just immediately after the wound infliction. Before any active biological action has taken place, the tissue relaxes, and the wound opens mostly due to the initial homeostatic tension of the tissue, its elastic and viscous properties, and the existing friction between the tissue and its substrate. We find that for a circular wound the regimes of deformation are defined by a single adimensional parameter λ, which characterizes the relative importance of viscosity over friction.

Lattice model for self-folding at the microscale.

Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process and folding occurs through a sequence of binding events, where pairs of panels meet at a specific closing angle. Here, we propose a lattice model to describe the dynamics of self-folding. As an example, we study the folding of a pyramid of N lateral faces. We combine analytical and numerical Monte Carlo simulations to find how the folding time depends on the number of faces, closing angle, and initial configuration. Implications for the study of more complex structures are discussed.

Modeling of Cell-Mediated Self-Assembled Colloidal Scaffolds.

A critical step in tissue engineering is the design and synthesis of 3D biocompatible matrices (scaffolds) to support and guide the proliferation of cells and tissue growth. The most existing techniques rely on the processing of scaffolds under controlled conditions and then implanting them in vivo, with questions related to biocompatibility and implantation that are still challenging. As an alternative, it was proposed to assemble the scaffolds in loco through the self-organization of colloidal particles mediated by cells. To overcome the difficulty to test experimentally all the relevant parameters, we propose the use of large-scale numerical simulation as a tool to reach useful predictive information and to interpret experimental results. Thus, in this study, we combine experiments, particle-based simulations, and mean-field calculations to show that, in general, the size of the self-assembled scaffold scales with the cell-to-particle ratio. However, we have found an optimal value of this ratio, for which the size of the scaffold is maximal when the cell-cell adhesion is suppressed. These results suggest that the size and structure of the self-assembled scaffolds may be designed by tuning the adhesion between cells in the colloidal suspension.

Smoluchowski equations for linker-mediated irreversible aggregation.

We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.

Optimal number of linkers per monomer in linker-mediated aggregation.

We study the dynamics of diffusion-limited irreversible aggregation of monomers, where bonds are mediated by linkers. We combine kinetic Monte Carlo simulations of a lattice model with a mean-field theory to study the dynamics when the diffusion of aggregates is negligible and only monomers diffuse. We find two values of the number of linkers per monomer which maximize the size of the largest aggregate. We explain the existence of the two maxima based on the distribution of linkers per monomer. This observation is well described by a simple mean-field model. We also show that a relevant parameter is the ratio of the diffusion coefficients of monomers and linkers. In particular, when this ratio is close to ten, the two maxima merge at a single maximum.

Crossover from three- to six-fold symmetry of colloidal aggregates in circular traps.

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap.

Finding the Optimal Nets for Self-Folding Kirigami.

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search, and thus, they do not guarantee the optimal solution. Here, we propose a deterministic procedure. We map the connectivity of the shell into a shell graph, where the nodes and links of the graph represent the vertices and edges of the shell, respectively. Identifying the nets that maximize the number of vertex connections corresponds to finding the set of maximum leaf spanning trees of the shell graph. This method allows us not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the maximum leaf spanning trees is obtained.

Dynamics of a network fluid within the liquid-gas coexistence region.

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class. We show that the slow dynamics is universal, being also observed outside the coexistence region at low temperatures in the single phase region.

Interaction anisotropy and the KPZ to KPZQ transition in particle deposition at the edges of drying drops.

The deposition process at the edge of evaporating colloidal drops varies with the shape of suspended particles. Experiments with prolate ellipsoidal particles suggest that the spatiotemporal properties of the deposit depend strongly on particle aspect ratio. As the aspect ratio increases, the particles form less densely-packed deposits and the statistical behavior of the deposit interface crosses over from the Kardar-Parisi-Zhang (KPZ) universality class to another universality class which was suggested to be consistent with the KPZ plus quenched disorder. Here, we numerically study the effect of particle interaction anisotropy on deposit growth. In essence, we model the ellipsoids, at the interface, as disk-like particles with two types of interaction patches that correspond to specific features at the poles and equator of the ellipsoid. The numerical results corroborate experimental observations and further suggest that the deposition transition can stem from interparticle interaction anisotropy. Possible extensions of our model to other systems are also discussed.

Dynamics of Patchy Particles in and out of Equilibrium.

We combine particle-based simulations, mean-field rate equations, and Wertheim's theory to study the dynamics of patchy particles in and out of equilibrium, at different temperatures and densities. We consider an initial random distribution of nonoverlapping three-patch particles, with no bonds, and analyze the time evolution of the breaking and bonding rates of a single bond. We find that the asymptotic (equilibrium) dynamics differs from the initial (out of equilibrium) one. These differences are expected to depend on the initial conditions, temperature, and density.

Dynamics of network fluids.

Network fluids are structured fluids consisting of chains and branches. They are characterized by unusual physical properties, such as, exotic bulk phase diagrams, interfacial roughening and wetting transitions, and equilibrium and nonequilibrium gels. Here, we provide an overview of a selection of their equilibrium and dynamical properties. Recent research efforts towards bridging equilibrium and non-equilibrium studies are discussed, as well as several open questions.

Dynamic Design of Spatial Patterns of Colloidal Suspensions.

We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential by means of dynamic density functional theory. We consider a nonlinear diffusion equation for the density and show that spatial patterns emerge from a sinusoidal external potential with a time-dependent wavelength. These patterns are characterized by a sinusoidal density with the average wavelength and a Bessel-function envelope with an induced wavelength that depends only on the amplitude of the temporal oscillations. As a generalization of this result, we propose a design strategy to obtain a family of spatial patterns using time-dependent potentials of practically arbitrary shape.

How the site degree influences quantum probability on inhomogeneous substrates.

We investigate the effect of the node degree and energy E on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependency of the quantum probability for each site on its degree. For a class of biregular structures formed by two disjoint subsets of sites sharing the same degree, the probability P_{k}(E) of finding the electron on any site with k neighbors is independent of E≠0, a consequence of an exact analytical result that we prove for any bipartite lattice. For more general nonbipartite structures, P_{k}(E) may depend on E as illustrated by an exact evaluation of a one-dimensional semiregular lattice: P_{k}(E) is large for small values of E when k is also small, and its maximum values shift towards large values of |E| with increasing k. Numerical evaluations of P_{k}(E) for two different types of percolation clusters and the Apollonian network suggest that this observed feature might be generally valid.

Self-charging of identical grains in the absence of an external field.

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Thermal gas rectification using a sawtooth channel.

We study the rectification of a two-dimensional thermal gas in a channel of asymmetric dissipative walls. For an ensemble of smooth Lennard-Jones particles, our numerical simulations reveal a nonmonotonic dependence of the flux on the thermostat temperature, channel asymmetry, and particle density, with three distinct regimes. Theoretical arguments are developed to shed light on the functional dependence of the flux on the model parameters.

How detrimental are seed galls to their hosts? Plant performance, germination, developmental instability and tolerance to herbivory in Inga laurina, a leguminous tree.

Gall inducers use these structures as shelters and sources of nutrition. Consequently, they cause multiple physiological changes in host plants. We studied the impact caused by seed coat galls of a braconid wasp on the performance of fruits, seeds and seedlings of tree Inga laurina. We tested whether these seed galls are 'nutrient sinks' with respect to the fruit/seed of host plant, and so constrain the reproductive ability and reduce seedling longevity. We measured the influence of such galls on the secondary compounds, fruit and seed parameters, seed viability and germination and seedling performance. Inga laurina has indehiscent legumes with polyembryonic seeds surrounded by a fleshy sarcotesta rich in sugars. The galls formed inside the seed coat and galled tissues presented higher phenol concentrations, around 7-fold that of ungalled tissues. Galls caused a significant reduction in parameters such as fruit and seed size, seed weight and the number of embryos. Fluctuating asymmetry (a stress indicator) was 31% higher in leaves of galled seed plants in comparison to ungalled seed plants. However, the negative effects on fruit and seed parameters were not sufficient to reduce seed germination (except the synchronization index) or seedling performance (except leaf area and chlorophyll content). We attributed these results to the ability of I. laurina to tolerate gall attack on seeds without a marked influence on seedling performance. Moreover, because of the intensity of seed galling on host plant, we suggest that polyembryony may play a role in I. laurina reproduction increasing tolerance to seed damage.

Field driven charging dynamics of a fluidized granular bed.

A simplified model has previously described the inductive charging of colliding identical grains in the presence of an external electric field. Here we extend that model by including heterogeneous surface charge distributions, grain rotations and electrostatic interactions between grains. We find from this more realistic model that strong heterogeneities in charging can occur in agitated granular beds, and we predict that shielding due to these heterogeneities can dramatically alter the charging rate in such beds.

Prediction and Control of Slip-Free Rotation States in Sphere Assemblies.

We study fixed assemblies of touching spheres that can individually rotate. From any initial state, sliding friction drives an assembly toward a slip-free rotation state. For bipartite assemblies, which have only even loops, this state has at least four degrees of freedom. For exactly four degrees of freedom, we analytically predict the final state, which we prove to be independent of the strength of sliding friction, from an arbitrary initial one. With a tabletop experiment, we show how to impose any slip-free rotation state by only controlling two spheres, regardless of the total number.

Critical Fragmentation Properties of Random Drilling: How Many Holes Need to Be Drilled to Collapse a Wooden Cube?

A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical and probabilistic behavior that is discussed here. Combining numerical simulations and rigorous results, we find off-critical scale-free behavior and a continuous transition at a critical density of holes that significantly differs from classical percolation.