Condensed Matter

When a crack propagate in a viscoelastic solid energy dissipation can occur very far from the crack tip where the stress field may be very different from the r −1/2 singular form expected close to the crack tip. Most theories of crack propagation focus on the near crack-tip region. Remarkable, here I show that a simple theory which does not account for the nature of the stress field in the near crack-tip region result in a crack propagation energy in semi-quantitative agreement with a theory based on the stress field in the near crack-tip region. I consider both opening and closing crack propagation, and show that for closing crack propagation in viscoelastic solids, some energy dissipation processes must occur in thecrack tip process zone.

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the work of [Nascimento et. al, Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free-energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined in [Le Roux et. al, Submitted, 2020].

We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl--von Kármán number Γ and the recently introduced Scriven--Love number SL , respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on Γ , whereas SL governs the absolute or convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance results in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ , the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions---reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher--Kolmogorov equations. This model possesses Lifshitz points, where the front dynamics undergo a steady-to-oscillatory bifurcation, thus shedding light on the pattern selection mechanism in neurons.

The influence of static stress and alternating loading direction on the potential energy and mechanical properties of amorphous alloys is investigated using molecular dynamics simulations. The model glass is represented via a binary mixture which is first slowly annealed well below the glass transition temperature and then subjected to elastostatic loading either along a single direction or along two and three alternating directions. We find that at sufficiently large values of the static stress, the binary glass becomes rejuvenated via collective, irreversible rearrangements of atoms. Upon including additional orientation of the static stress in the loading protocol, the rejuvenation effect is amplified and the typical size of clusters of atoms with large nonaffine displacements increases. As a result of prolonged mechanical loading, the elastic modulus and the peak value of the stress overshoot during startup continuous compression become significantly reduced, especially for loading protocols with alternating stress orientation. These findings are important for the design of novel processing methods to improve mechanical properties of metallic glasses.

The influence of variable-amplitude loading on the potential energy and mechanical properties of amorphous materials is investigated using molecular dynamics simulations. We study a binary mixture that is either rapidly or slowly cooled across the glass transition temperature and then subjected to a sequence of shear cycles with strain amplitudes above and below the yielding strain. It was found that well annealed glasses can be rejuvenated by small-amplitude loading if the strain amplitude is occasionally increased above the critical value. By contrast, poorly annealed glasses are relocated to progressively lower energy states when subyield cycles are alternated with large-amplitude cycles that facilitate exploration of the potential energy landscape. The analysis of nonaffine displacements revealed that in both cases, the typical size of plastic rearrangements varies depending on the strain amplitude and number of cycles, but remains smaller than the system size, thus preserving structural integrity of amorphous samples.

The seismic waves emitted during granular flows are generated by different sources: high frequencies by inter-particle shocks and low frequencies by global motion and large scale deformation. To unravel these different mechanisms, an experimental study has been performed on the seismic waves emitted by dry quasi steady granular flows. The emitted seismic waves were recorded using shock accelerometers and the flow dynamics were captured with a fast camera. The mechanical characteristics of the particle shocks were analyzed, along with the duration between shocks and the correlations in the particle motion. The high-frequency seismic waves (1-50 kHz) were found to originate from particle shocks and waves trapped in the flowing layer. The low-frequency waves (20-60 Hz) were generated by the oscillations of the particles along their trajectories, i.e. from cycles of dilation/compression during the shear. The profiles of granular temperature (i.e. the square of particle velocity fluctuations) and average velocity were measured and related to the average properties of the flow as well as to the slope angle and flow thickness. These profiles were then used in a simple steady granular flow model to predict the radiated seismic energy and the energetic efficiency, i.e. the fraction of the flow potential energy converted to seismic energy. Scaling laws relating the seismic power, the shear strain rate and the inertial number were derived. In particular, the emitted seismic power is proportional to the granular temperature, which is also related to the mean flow velocity.

We focus on cone-shaped nano- and microparticles, which have recently been found to show particularly strong propulsion when they are exposed to a traveling ultrasound wave, and study based on direct acoustofluidic computer simulations how their propulsion depends on the cones' aspect ratio. The simulations reveal that the propulsion velocity and even its sign are very sensitive to the aspect ratio, where short particles move forward whereas elongated particles move backward. Furthermore, we identify a cone shape that allows for a particularly large propulsion speed. Our results contribute to the understanding of the propulsion of ultrasound-propelled colloidal particles, suggest a method for separation and sorting of nano- and microcones concerning their aspect ratio, and provide useful guidance for future experiments and applications.

The conformational and dynamical properties of active self-propelled filaments/polymers are investigated in the presence of hydrodynamic interactions by both, Brownian dynamics simulations and analytical theory. Numerically, a discrete linear chain composed of active Brownian particles is considered, analytically, a continuous linear semiflexible polymer with active velocities changing diffusively. The force-free nature of active monomers is accounted for - no Stokeslet fluid flow induced by active forces - and higher order hydrodynamic multipole moments are neglected. The nonequilibrium character of the active process implies a dependence of the stationary-state properties on HI via the polymer relaxation times. In particular, at moderate activities, HI lead to a substantial shrinkage of flexible and semiflexible polymers to an extent far beyond shrinkage of comparable free-draining polymers; even flexible HI-polymers shrink, while active free-draining polymers swell monotonically. Large activities imply a reswelling, however, to a less extent than for non-HI polymers, caused by the shorter polymer relaxation times due to hydrodynamic interactions. The polymer mean square displacement is enhanced, and an activity-determined ballistic regime appears. Over a wide range of time scales, flexible active polymers exhibit a hydrodynamically governed subdiffusive regime, with an exponent significantly smaller than that of the Rouse and Zimm models of passive polymers. Compared to simulations, the approximate analytical approach predicts a weaker hydrodynamic effect.

Propelling microorganisms through fluids and moving fluids along cellular surfaces are essential biological functions accomplished by long, thin structures called motile cilia and flagella, whose regular, oscillatory beating breaks the time-reversal symmetry required for transport. Although top-down experimental approaches and theoretical models have allowed us to broadly characterize such organelles and propose mechanisms underlying their complex dynamics, constructing minimal systems capable of mimicking ciliary beating and identifying the role of each component remains a challenge. Here we report the bottom-up assembly of a minimal synthetic axoneme, which we call a synthoneme, using biological building blocks from natural organisms, namely pairs of microtubules and cooperatively associated axonemal dynein motors. We show that upon provision of energy by ATP, microtubules undergo rhythmic bending by cyclic association-dissociation of dyneins. Our simple and unique beating minimal synthoneme represents a self-organized nanoscale biomolecular machine that can also help understand the mechanisms underlying ciliary beating.

Active solids consume energy to allow for actuation, shape change, and wave propagation not possible in equilibrium. For two-dimensional active surfaces, powerful design principles exist that realise this phenomenology across systems and length scales. However, control of three-dimensional bulk solids remains a challenge. Here, we develop both a continuum theory and microscopic simulations that describe an active surface wrapped around a passive soft solid. The competition between active surface stresses and bulk elasticity leads to a broad range of previously unexplored phenomena, which we dub active elastocapillarity. In passive materials, positive surface tension rounds out corners and drives every shape towards a sphere. By contrast, activity can send the surface tension negative, which results in a diversity of stable shapes selected by elasticity. We discover that in these reconfigurable objects, material nonlinearity controls reversible switching and snap-through transitions between anisotropic shapes, as confirmed by a particle-based numerical model. These transition lines meet at a critical point, which allows for a classification of shapes based on universality. Even for stable surfaces, a signature of activity arises in the negative group velocity of surface Rayleigh waves. These phenomena offer insights into living cellular membranes and underpin universal design principles across scales from robotic metamaterials down to shape-shifting nanoparticles.