Condensed Matter

Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destablizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, such as emerging wavelengths, may not be influenced by the imposed substrate anchoring. Going further into the nonlinear regime, considered via large-scale GPU-based simulations, shows however that nonlinear effects may play an important role, in particular in the case of strong substrate anchoring anisotropy. Our simulations show that instability of the film develops in two stages: the first stage involves formation of ridges that are perpendicular to the local anchoring direction; and the second involves breakup of these ridges and formation of drops, whose final distribution is influenced by the anisotropy imposed by the substrate. Finally, we show that imposing more complex substrate anisotropy patterns allows us to reach basic understanding of the influence of substrate-imposed defects in director orientation on the instability evolution.

Granular intrusion is commonly observed in natural and man-made settings. Unlike single-phase media like solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios. This trans-phase behavior increases the difficulty of accurately modeling these and other yielding (or flowable) materials. Micro-scale modeling methods, such as DEM (Discrete Element Method), capture this multiphase behavior by modeling the media at the grain scale, but interest often lies in the macro-scale characterizations of such systems. We examine the efficacy of a macro-scale continuum approach in modeling and understanding the physics and macroscopic phenomena behind a variety of granular intrusions cases using two basic frictional yielding constitutive models. We compare predicted granular force response and material flow to data in four 2D intrusion cases: (1) depth-dependence forces responses in horizontal submerged-intruder motion; (2) separation-dependent drag variation in parallel-plate vertical-intrusion; (3) initial-density-dependent drag fluctuations in free surface plowing, and (4) flow zone development in vertical plate intrusions in under-compacted granular media. Our continuum modeling approach captures the flow process and drag forces in each of these cases compared to experimental data while providing key meso- and macro-scopic insights. Our study highlights how continuum modeling approaches provide an alternative for efficient modeling as well as conceptual understanding of various granular intrusion phenomena

We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the square container. The search for these configurations is carried out with the help of two algorithms that we have devised: a first algorithm is in charge of obtaining sufficiently dense configurations starting from a random guess, while a second algorithm improves the configurations obtained in the first stage. The algorithms can be used sequentially or independently. The performance of these algorithms is assessed by carrying out numerical tests for configurations with a large number of circles.

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first order phase transitions and the continuation of triple points. To illustrate the method we apply it to a binary Phase-Field-Crystal model for the crystallisation of a mixture of two types of particles. The resulting phase diagram is determined for one- and two-dimensional domains. In the former case it is compared to the diagram obtained from a one-mode approximation. The various observed liquid and crystalline phases and their stable and metastable coexistence are discussed as well as the temperature-dependence of the phase diagrams. This includes the (dis)appearance of critical points and triple points. We also relate bifurcation diagrams for finite-size systems to the thermodynamics of phase transitions in the infinite-size limit.

Equilibration of polymer melts containing highly entangled long polymer chains in confinement or with free surfaces is a challenge for computer simulations. We approach this problem by first studying polymer melts based on the soft-sphere coarse-grained model confined between two walls with periodic boundary conditions in two directions parallel to the walls. Then we apply backmapping to reinsert the microscopic details of the underlying bead-spring model. Tuning the strength of the wall potential, the monomer density of confined polymer melts in equilibrium is kept at the bulk density even near the walls. In a weak confining regime, we observe the same conformational properties of chains as in the bulk melt showing that our confined polymer melts have reached their equilibrated state. Our methodology provides an efficient way of equilibrating large polymer films with different thicknesses and is not confined to a specific underlying microscopic model. Switching off the wall potential in the direction perpendicular to the walls, enables to study free-standing highly entangled polymer films or polymer films with one supporting substrate.

A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non=invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.

We study the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length L . We specifically compare straight rod-like particles to bent and branched wire frames. In dense suspensions the wire frames are frozen in a disordered state by the topological entanglements between their arms. We present a simple, geometric method to find the scaling of the elastic stress with concentration in these glassy systems. We apply this method to a simple 2D model system where a test particle is placed on a plane and constrained by a random distribution of points with number density ν . Two striking differences between wire frame and rod suspensions are found: 1) The linear elasticity per particle for wire frames is very large, scaling like ν 2 L 4 , whereas for rods it much smaller and independent of concentration. 2) Rods always shear thin but wire frames shear harden for densities less than ??K/ k B T L 4 ??????????????????, where K is the bending modulus of the particles. The deformation of wire frames is found to be important even for small strains, with the proportion of deformed particles at a particular strain, γ , being given by (ν L 2 ) 2 γ 2 . Our results agree well with a simple simulation of the 2D system.

We study the elastic response of rigid, wire frame particles in concentrated, glassy suspensions to a step strain by applying the simple, geometric methods developed in part I. The wire frame particles are comprised of thin, rigid rods of length L and their number density, ? , is such that ? L 3 ?? . We specifically compare rigid rods to L-shapes made of two equal length rods joined at right angles. The behaviour of wire frames is found to be strikingly different from that of rods. The linear elasticity scales like ? 3 L 6 for L-shaped particles, whereas it scales proportional to ? for rods and the non-linear response shows a transition from shear hardening to shear softening at a critical density ? c ??K/ k B T L 6 ??????????????????, where K is the bending modulus of the particles. For realistic particles made of double stranded DNA, this transition occurs at densities of about ? L 3 ??0 . The reason for these differences is that wire frames can be forced to bend by the entanglements with their surroundings, whereas rods always remain straight. This is found to be very important even for small strains, with most particles being bent above a critical strain γ c ??? L 3 ) ?? .

We report evidence of irregular unsteady flow of two-dimensional polymer solutions in the absence of inertia in cross-slot geometry using numerical simulations of Oldroyd-B model. By exploring the transition to time-dependent flow versus both the fluid elasticity and the polymer concentration, we find periodic behaviour close to the instability threshold and more complex flows at larger elasticity, in agreement with experimental findings. For high enough elasticity we obtain dynamics pointing to elastic turbulence, with temporal spectra of velocity fluctuations showing a power-law decay, of exponent in between -3 and -2, and probability density functions of velocity fluctuations that weakly deviate from Gaussianity while high non-Gaussian tails characterise those of local accelerations.

Elastic wave velocity in a soft fiber that varies depending on material constitution and axial stress level is an essential measure of mechanical signals in many technical applications. In this work, based on the small-on-large theory, we establish a model of linear elastic wave propagation in a finitely pre-stretched soft fiber. The formulas of longitudinal (Primary, P-) and transverse (Secondary, S-) wave velocities are provided and validated by numerical simulations as well as by experimental data on spider silk. The influences of material constitution, compressibility, and pre-stress on the wave propagation are investigated. We found that with increasing pre-stress, the variation of P-wave velocity highly relies on the concavity of the stress-strain curve. In contrast, an increase of S-wave velocity exhibits regardless of any constitutive model. For both P- and S-waves, the variation of the velocities is more significant in a compressible fiber than that in a nearly-incompressible one. Moreover, for minuscule pre-stress, we propose a modified formula for S-wave velocity based on the Rayleigh beam theory, which reveals the competition mechanism between "string vibration" and "beam vibration." This may provide a reliable theoretical basis for precise mechanical characterization of soft fibers and open a route for lightweight, tunable wave manipulation devices.