Condensed Matter

Despite their outstanding mechanical properties, with many industrial applications, a rational and systematic design of new and controlled auxetic materials remains poorly developed. Here a unified framework is established to describe bidimensional perfect auxetics with potential use in the design of new materials. Perfect auxetics are characterized by a Poisson's ratio ν=?? over a finite strain range and can be modeled as materials composed of rotating rigid units. Inspired by a natural connection between these rotating rigid units with an antiferromagnetic spin system, here are unveiled the conditions for the emergence of a non-trivial floppy mode responsible for the auxetic behavior. Furthermore, this model paves a simple pathway for the design of new auxetic materials, based on three simple steps, which set the sufficient connectivity and geometrical constraints for perfect auxetics. In particular, a new exotic crystal, a Penrose quasi-crystal and the long desired isotropic auxetic material are designed and constructed for the first time. Using 3D printed materials, finite element methods and this rigid unit model, the auxetic behavior of these designs is shown to be robust under small disturbances in the structure, though the Poisson's ratio value relies on system's details, approaching ?? close to the ideal case.

We investigate the radial thermocapillary flow driven by a laser-heated microbead in partial wetting at the water-air interface. Particular attention is paid to the evolution of the convective flow patterns surrounding the hot sphere as the latter is increasingly heated. The flow morphology is nearly axisymmetric at low laser power P. Increasing P leads to symmetry breaking with the onset of counter-rotating vortex pairs. The boundary condition at the interface, close to no-slip in the low-P regime, turns about stress-free between the vortex pairs in the high-P regime. These observations strongly support the view that surface-active impurities are inevitably adsorbed on the water surface where they form an elastic layer. The onset of vortex pairs is the signature of a hydrodynamic instability in the layer response to the centrifugal forced flow. Interestingly, our study paves the way for the design of active colloids able to achieve high-speed self-propulsion via vortex pair generation at a liquid interface.

Dense granular systems subjected to an imposed shear stress undergo stick-slip dynamics with systematic patterns of dilation-compaction. During each stick phase, as the frictional strength builds up, the granular system dilates to accommodate shear strain, developing stronger force networks. During each slip event, when the stored energy is released, particles experience large rearrangements and the granular network can significantly change. Here, we use numerical simulations of 3D, sheared frictional packings to show that the mean betweenness centrality -- a property of network of interparticle connections -- follows consistent patterns during the stick-slip dynamics, showing sharp spikes at each slip event. We identify the source of this behavior as arising from the connectivity and contact arrangements of granular network during dilation-compaction cycles, and find that a lower potential for connection between particles leads to an increase of mean betweenness centrality in the system. Furthermore, we show that at high confinements, few particles lose contact during slip events, leading to a smaller change in granular connectivity and betweenness centrality.

Traditionally, ion-selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1 - 10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk conductance, reaches values of hundreds of nanometers for typical surface charge densities and ionic concentrations, suggesting the possibility of designing large-nanopore (10 - 100 nm), high-conductance membranes exhibiting significant ion-selectivity. Such membranes would have potentially dramatic implications for the efficiency of osmotic energy conversion and separation techniques. Furthermore, we demonstrate that this mechanism of dynamic selectivity leads ultimately to the rectification of ionic current, rationalizing previous studies showing that Debye overlap is not a necessary condition for the occurrence of rectifying behavior in nanopores.

We study synchronization dynamics in binary mixtures of locally coupled Kuramoto oscillators which perform Brownian motion in a two-dimensional box. We introduce two models, where in model I there are two type of oscillators, say A and B , and any two similar oscillators tend to synchronize their phases, while any two dissimilar ones tend to be out of phase. In model J , in contrast, the oscillators in subpopulation A behave as in model I , while the oscillators in subpopulation B tend to be out of phase with all the others. In the real space all the oscillators in both models interact via a soft-core repulsive potential. Both subpopulations of model I and subpopulation A of model J , by their own, exhibit a phase coherent attractor in a certain region of model parameters. The approach to the attractor, after an initial transient regime, is exponential with some characteristic synchronization time scale ? . Numerical analysis reveals that the attractors of the two subpopulations survive within model I , regardless of the composition of the mixture ? and the strength of the cross-population negative coupling constant H , and that ? sensitively depends on ? , H and the packing fraction. In particular, the ability of the oscillators to move and exchange neighbours can significantly decrease ? . In contrast, model J predicts suppression of the synchronized state in subpopulation A and emergence of the coherent attractor in the "contrarians" subpopulation B for strong and weak cross-population coupling, respectively.

Collection of self-propelled particles (SPPs) exhibit coherent motion and show true long-range order in two-dimensions. Inhomogeneity, in general destroys the usual long-range order of the polar SPPs. We model a system of polar self-propelled particles with inhomogeneous interaction strength or bond disorder. The system is studied near the order-to-disorder transition for different strengths of the disorder. The nature of phase transition changes from discontinuous to continuous type by tuning the strength of the disorder. The bond disorder also enhances the ordering near the transition due to the formation of a homogeneous flock state for the large disorder. It leads to faster information transfer in the system and enhances the system information entropy. Our study gives a new understanding of the effect of intrinsic inhomogeneity in the self-propelled particle system.

We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of the mobility coefficient, Λ(r, r ′ ) , which relates the thermodynamic driving force on monomers at position r ′ to the motion of monomers at position r . A first approach based on the Green-Kubo formalism turns out to be impractical because of a severe plateau problem. Instead, we propose to extract the mobility coefficient from an effective characteristic relaxation time of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblock copolymer melts. The DDFT results are in very good agreement with the data from corresponding fine-grained simulations.

We present a growth model for special Cosserat rods that allows for induced rotation of cross-sections. The growth law considers two controls, one for lengthwise growth and other for rotations. This is explored in greater detail for straight rods with helical and hemitropic material symmetries by introduction of a symmetry preserving growth to account for the microstructure. The example of a guided-guided rod possessing a chiral microstructure is considered to study its deformation due to growth. We show the occurrence of growth induced out-of-plane buckling in such rods.

During morphogenesis, a featureless convex cerebellum develops folds. As it does so, the cortex thickness is thinnest at the crest (gyri) and thickest at the trough (sulci) of the folds. This observation cannot be simply explained by elastic theories of buckling. A recent minimal model explained this phenomenon by modeling the developing cortex as a growing fluid under the constraints of radially spanning elastic fibers, a plia membrane and a nongrowing sub-cortex (Engstrom, et. al., PRX 2019). In this minimal buckling without bending morphogenesis (BWBM) model, the elastic fibers were assumed to act linearly with strain. Here, we explore how nonlinear elasticity influences shape development within BWBM. The nonlinear elasticity generates a quadratic nonlinearity in the differential equation governing the system's shape and leads to sharper troughs and wider crests, which is an identifying characteristic of cerebellar folds at later stages in development. As developing organs are typically not in isolation, we also explore the effects of steric confinement, and observe flattening of the crests. Finally, as a paradigmatic example, we propose a hierarchical version of BWBM from which a novel mechanism of branching morphogenesis naturally emerges to qualitatively predict later stages of the morphology of the developing cerebellum.

We investigate CO 2 -driven diffusiophoresis of colloidal particles and bacterial cells in a Hele-Shaw geometry. Combining experiments and a model, we understand the characteristic length and time scales of CO 2 -driven diffusiophoresis in relation to system dimensions and CO 2 diffusivity. Directional migration of wild-type V. cholerae and a mutant lacking flagella, as well as S. aureus and P. aeruginosa, near a dissolving CO 2 source shows that diffusiophoresis of bacteria is achieved independent of cell shape and Gram stain. Long-time experiments suggest possible applications for bacterial diffusiophoresis to cleaning systems or anti-biofouling surfaces.