Stochastic methods for slip prediction in a sheared granular system.

We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional system of soft frictional particles sandwiched between solid walls, one of which is exposed to a shearing force. The slip events are detected using stochastic state space models applied to various measures describing the system. The amplitudes of the events spread over more than four decades and present two distinctive peaks, one for the microslips and the other for the slips. We show that the measures describing the forces between the particles provide earlier detection of an upcoming slip event than the measures based solely on the wall movement. By comparing the detection times obtained from the considered measures, we observe that a typical slip event starts with a local change in the force network. However, some local changes do not spread globally over the force network. For the changes that become global, we find that their size strongly influences the further behavior of the system. If the size of a global change is large enough, then it triggers a slip event; if it is not, then a much weaker microslip follows. Quantification of the changes in the force network is made possible by formulating clear and precise measures describing their static and dynamic properties.

Dielectrowetting of a thin nematic liquid crystal layer.

We consider a mathematical model that describes the flow of a nematic liquid crystal (NLC) film placed on a flat substrate, across which a spatially varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (nonuniform) electric field generated, leading to instability of a flat film. Implementation of the long wave scaling leads to a partial differential equation that predicts the subsequent time evolution of the thin film. This equation is coupled to a boundary value problem that describes the interaction between the local molecular orientation of the NLC (the director field) and the electric potential. We investigate numerically the behavior of an initially flat film for a range of film heights and surface anchoring conditions.

Director gliding in a nematic liquid crystal layer: Quantitative comparison with experiments.

The interaction between nematic liquid crystals and polymer-coated substrates may lead to slow reorientation of the easy axis (so-called "director gliding") when a prolonged external field is applied. We consider the experimental evidence of zenithal gliding observed by Joly et al. [Phys. Rev. E 70, 050701 (2004)PLEEE81539-375510.1103/PhysRevE.70.050701] and Buluy et al. [J. Soc. Inf. Disp. 14, 603 (2006)1071-092210.1889/1.2235686] as well as azimuthal gliding observed by S. Faetti and P. Marianelli [Liq. Cryst. 33, 327 (2006)LICRE60267-829210.1080/02678290500512227], and we present a simple, physically motivated model that captures the slow dynamics of gliding, both in the presence of an electric field and after the electric field is turned off. We make a quantitative comparison of our model results and the experimental data and conclude that our model explains the gliding evolution very well.

Granular response to impact: Topology of the force networks.

The impact of an intruder on granular matter leads to the formation of mesoscopic force networks, which were seen particularly clearly in the recent experiments carried out with photoelastic particles [Clark et al., Phys. Rev. Lett. 114, 144502 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.144502]. These force networks are characterized by complex structure and evolve on fast time scales. While it is known that total photoelastic activity in the granular system is correlated with the acceleration of the intruder, it is not known how the structure of the force network evolves during impact, and if there are dominant features in the networks that can be used to describe the intruder's dynamics. Here, we use topological tools, in particular persistent homology, to describe these features. Persistent homology allows quantification of both structure and time evolution of the resulting force networks. We find that there is a clear correlation of the intruder's dynamics and some of the topological measures implemented. This finding allows us to discuss which properties of the force networks are most important when attempting to describe the intruder's dynamics. In particular, we find that the presence of loops in the force network, quantified by persistent homology, is strongly correlated to the deceleration of the intruder. In some cases, particularly for the impact on soft particles, the measures derived from the persistence analysis describe the deceleration of the intruder even better than the total photoelastic activity. We are also able to define an upper bound on the relevant time scale over which the force networks evolve.

Exploiting the Marangoni Effect To Initiate Instabilities and Direct the Assembly of Liquid Metal Filaments.

Utilization of the Marangoni effect in a liquid metal is investigated, focusing on initiating instabilities to direct material assembly via the Rayleigh-Plateau instability. Thin (2 nm) copper (Cu) films are lithographically patterned onto thick (12 nm) nickel (Ni) strips to induce a surface energy gradient at the maximum wavelength of the filament instability predicted by Rayleigh-Plateau instability analysis. The pattern is irradiated with an 18 ns pulsed laser such that the pattern melts and the resultant Ni-Cu surface tension gradient induces Marangoni flows due to the difference in surface energies. The experimental results, supported by extensive direct numerical simulations, demonstrate that the Marangoni flow exceeds the capillary flow induced by the initial geometry, guiding instabilities such that final nanoparticle location is directed toward the regions of higher surface energy (Ni regions). Our work shows a route for manipulation, by means of the Marangoni effect, to direct the evolution of the surface instabilities and the resulting pattern formation.

Effects of flexoelectricity and weak anchoring on a Freedericksz transition cell.

We consider a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field is applied. We investigate how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions, and material properties of the nematic liquid crystal layer vary. In particular, we focus on how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.

Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops.

The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic et al., Phys. Rev. E 93, 062903 (2016)10.1103/PhysRevE.93.062903], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.

Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.

In the companion paper [Pugnaloni et al., Phys. Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.

Scaling properties of force networks for compressed particulate systems.

We consider, computationally and experimentally, the scaling properties of force networks in the systems of circular particles exposed to compression in two spatial dimensions. The simulations consider polydisperse and monodisperse particles, both frictional and frictionless, and in experiments we use monodisperse and bidisperse frictional particles. While for some of the considered systems we observe consistent scaling exponents describing the behavior of the force networks, we find that this behavior is not universal. In particular, we find that frictionless systems, independently of whether they partially crystallize under compression or not, show scaling properties that are significantly different compared to the frictional disordered ones. The findings of nonuniversality are confirmed by explicitly computing fractal dimension for the considered systems. The results of the physical experiments are consistent with the results obtained in simulations of frictional disordered systems.

Instability of Nano- and Microscale Liquid Metal Filaments: Transition from Single Droplet Collapse to Multidroplet Breakup.

We carry out experimental and numerical studies to investigate the collapse and breakup of finite size, nano- and microscale, liquid metal filaments supported on a substrate. We find the critical dimensions below which filaments do not break up but rather collapse to a single droplet. The transition from collapse to breakup can be described as a competition between two fluid dynamic phenomena: the capillary driven end retraction and the Rayleigh-Plateau type instability mechanism that drives the breakup. We focus on the unique spatial and temporal transition region between these two phenomena using patterned metallic thin film strips and pulsed-laser-induced dewetting. The experimental results are compared to an analytical model proposed by Driessen et al. and modified to include substrate interactions. In addition, we report the results of numerical simulations based on a volume-of-fluid method to provide additional insight and highlight the importance of liquid metal resolidification, which reduces inertial effects.

Percolation and jamming transitions in particulate systems with and without cohesion.

We consider percolation and jamming transitions for particulate systems exposed to compression. For the systems built of particles interacting by purely repulsive forces in addition to friction and viscous damping, it is found that these transitions are influenced by a number of effects, and in particular by the compression rate. In a quasistatic limit, we find that for the considered type of interaction between the particles, percolation and jamming transitions coincide. For cohesive systems, however, or for any system exposed to even slow dynamics, the differences between the considered transitions are found and quantified.

Fully nonlinear dynamics of stochastic thin-film dewetting.

The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times.

Substrate-induced gliding in a nematic liquid crystal layer.

We consider the interaction between nematic liquid crystals (NLCs) and polymer substrates. Such substrates can interact with NLCs, exhibiting a phenomenon known as director gliding: the preferred orientation of the NLC molecules at the interface changes on time scales that are slow relative to the elastic relaxation time scale of the NLC. We present two models for gliding, inspired by experiments that investigate the interaction between the NLC and a polymer substrate. These models, though simple, lead to nontrivial results, including loss of bistability under gliding. Perhaps surprisingly, we find that externally imposed switching between the steady states of a bistable system may reverse the effect of gliding, preventing loss of bistability if switching is sufficiently frequent. Our findings may be of relevance to a variety of technological applications involving liquid crystal devices, and particularly to a new generation of flexible liquid crystal displays that implement polymeric substrates.

Electric-field variations within a nematic-liquid-crystal layer.

A thin layer of nematic liquid crystal (NLC) across which an electric field is applied is a setup of great industrial importance in liquid crystal display devices. There is thus a large literature modeling this situation and related scenarios. A commonly used assumption is that an electric field generated by electrodes at the two bounding surfaces of the layer will produce a field that is uniform: that is, the presence of NLC does not affect the electric field. In this paper, we use calculus of variations to derive the equations coupling the electric potential to the orientation of the NLC's director field, and use a simple one-dimensional model to investigate the limitations of the uniform field assumption in the case of a steady applied field. The extension of the model to the unsteady case is also briefly discussed.

Hierarchical nanoparticle ensembles synthesized by liquid phase directed self-assembly.

A liquid metal filament supported on a dielectric substrate was directed to fragment into an ordered, mesoscale particle ensemble. Imposing an undulated surface perturbation on the filament forced the development of a single unstable mode from the otherwise disperse, multimodal Rayleigh-Plateau instability. The imposed mode paved the way for a hierarchical spatial fragmentation of the filament into particles, previously seen only at much larger scales. Ultimately, nanoparticle radius control is demonstrated using a micrometer scale switch.

Numerical simulation of ejected molten metal nanoparticles liquified by laser irradiation: interplay of geometry and dewetting.

Metallic nanoparticles, liquified by fast laser irradiation, go through a rapid change of shape attempting to minimize their surface energy. The resulting nanodrops may be ejected from the substrate when the mechanisms leading to dewetting are sufficiently strong, as in the experiments involving gold nanoparticles [Habenicht et al., Science 309, 2043 (2005)]. We use a direct continuum-level approach to accurately model the process of liquid nanodrop formation and the subsequent ejection from the substrate. Our computations show a significant role of inertial effects and an elaborate interplay of initial geometry and wetting properties: e.g., we can control the direction of ejection by prescribing appropriate initial shape and/or wetting properties. The basic insight regarding ejection itself can be reached by considering a simple effective model based on an energy balance. We validate our computations by comparing directly with the experiments specified above involving the length scales measured in hundreds of nanometers and with molecular dynamics simulations on much shorter scales measured in tens of atomic diameters, as by M. Fuentes-Cabrera et al. [Phys. Rev. E 83, 041603 (2011)]. The quantitative agreement, in addition to illustrating how to control particle ejection, shows utility of continuum-based simulation in describing dynamics on nanoscale quantitatively, even in a complex setting as considered here.

Bifurcation properties of nematic liquid crystals exposed to an electric field: switchability, bistability, and multistability.

Bistable liquid crystal displays (LCDs) offer the potential for considerable power savings compared with conventional (monostable) LCDs. The existence of two (or more) stable field-free states that are optically distinct means that contrast can be maintained in a display without an externally applied electric field. An applied field is required only to switch the device from one state to the other, as needed. In this paper we examine the basic physical principles involved in generating multiple stable states and the switching between these states. We consider a two-dimensional geometry in which variable surface anchoring conditions are used to control the steady-state solutions and explore how different anchoring conditions can influence the number and type of solutions and whether or not switching is possible between the states. We find a wide range of possible behaviors, including bistability, tristability, and tetrastability, and investigate how the solution landscape changes as the boundary conditions are tuned.

Persistence of force networks in compressed granular media.

We utilize the tools of persistent homology to analyze features of force networks in dense granular matter, modeled as a collection of circular, inelastic frictional particles. The proposed approach describes these networks in a precise and tractable manner, allowing us to identify features that are difficult or impossible to characterize by other means. In contrast to other techniques that consider each force threshold level separately, persistent homology allows us to consider all threshold levels at once to describe the force network in a complete and insightful manner. We consider continuously compressed system of particles characterized by varied polydispersity and friction in two spatial dimensions. We find significant differences between the force networks in these systems, suggesting that their mechanical response may differ considerably as well.

Microstructure evolution during impact on granular matter.

We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself.

Defect modeling in spreading nematic droplets.

Experiments by Poulard and Cazabat [Langmuir 21, 6270 (2005)] on spreading droplets of nematic liquid crystal (NLC) reveal a surprisingly rich variety of behavior, including at least two different emerging length scales resulting from a contact line instability. In earlier work [Cummings, Lin, and Kondic, Phys. Fluids 23, 043102 (2011)] we modified a lubrication model for NLCs due to Ben Amar and Cummings [Phys. Fluids 13, 1160 (2001)] and showed that, in a qualitative sense, it can account for two-dimensional (2D) versions of the observed behavior. In the present work we propose a different approach that allows us to explore the effect of anchoring variations on the substrate, again in a 2D geometry. This in turn gives a simple way to model the presence of defects, which are nearly always present in such flows. The present model leads to additional terms in the governing equation. We explore the influence of these additional terms for some simple flow scenarios to gain insight into their influence.