A Superhydrophobicity-Slipperiness Switchable Surface with Magneto- and Thermo-responsive Wires for Repelling Complex Droplets.

The inefficacy of repelling water droplets laden with macromolecules (complex droplets or diluted polymer solution) is a long-standing shortcoming of superhydrophobic surfaces, which severely limits their reliability in practical applications. Here, we design a surface termed the superhydrophobicity-slipperiness switchable surface (3S surface), which demonstrates superhydrophobicity at room temperature and slipperiness when heated. The 3S surface is composed of magneto-responsive wires coated with superhydrophobic nanoparticles and impregnated with thermoresponsive paraffin, exhibiting lotus leaf-inspired passive water repellency and respiratory cilia-inspired active water repellency at room temperature. When heated, the impregnated paraffin melts and forms a lubricant layer atop the surface structures, exhibiting the pitcher-plant-inspired removal of complex droplets that remain pinned on conventional superhydrophobic surfaces. The counterintuitive integration of superhydrophobicity (a liquid-solid-gas composite system) and slipperiness (a liquid-lubricant-gas system) into a surface and the on-demand switch between them are not only important to the applicability of self-cleaning surfaces to real-world environments, where complex liquids are inevitable, but also provide insights into various interface-related applications.

Apple-like Shape of Freezing Paraffin Wax Droplets and Its Origin.

Paraffin wax stores energy in the form of latent heat at a nearly constant temperature during melting and releases this energy during solidification. This effect is used in industrial energy storage. At the same time, the possible deformation of even small volumes of material as a result of phase change is insufficiently studied. In this paper, the physical nature of such deformation, probably for the first time, is studied on the example of a droplet of paraffin wax. An unusual change in the shape of a melted droplet of paraffin wax placed on a relatively cold glass plate was observed in the laboratory experiments. As the droplet solidifies, its upper surface becomes nearly flat, and a dimple is formed in the center of this surface, making the droplet look like a fruit (pumpkins are more commonly shaped like this, but the authors prefer apples). A series of experiments, as well as physical and numerical modeling of the droplet's thermal state, taking into account the formation of a mushy zone between liquidus and solidus, made it possible to understand the role of gravity and gradual increase in viscosity and density of paraffin wax on changing the droplet shape and, in particular, to clarify the mechanism of formation of the dimple on its upper. It was shown that the mushy zone between the liquidus and solidus of the paraffin wax is responsible for the dimple formation.

Nonlinear dynamics and bifurcations of a planar undulating magnetic microswimmer.

Swimming microorganisms such as flagellated bacteria and sperm cells have fascinating locomotion capabilities. Inspired by their natural motion, there is an ongoing effort to develop artificial robotic nanoswimmers for potential in-body biomedical applications. A leading method for actuation of nanoswimmers is by applying a time-varying external magnetic field. Such systems have rich and nonlinear dynamics that call for simple fundamental models. A previous work studied forward motion of a simple two-link model with a passive elastic joint, assuming small-amplitude planar oscillations of the magnetic field about a constant direction. In this work, we found that there exists a faster, backward motion of the swimmer with very rich dynamics. By relaxing the small-amplitude assumption, we analyze the multiplicity of periodic solutions, as well as their bifurcations, symmetry breaking, and stability transitions. We have also found that the net displacement and/or mean swimming speed are maximized for optimal choices of various parameters. Asymptotic calculations are performed for the bifurcation condition and the swimmer's mean speed. The results may enable significantly improving the design aspects of magnetically actuated robotic microswimmers.

Resonant escape induced by a finite time harmonic excitation.

The purpose of this paper is twofold. First, we obtain the critical forcing needed for a resonant escape in finite time in the presence of damping. Second, we adapt the isolated resonance approximation (AIR) method to find the escaping time and analyze the escape in finite time. Approximations of the escape time on both the phase and the parameter planes were obtained. In particular, a peculiar fractal-like boundary of the finite-time escape region was revealed. This discovery helps to better understand the limitations of AIR and explains the sensitivity of the numerical experiments to the integration time.

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns.

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.

Effect of asymmetric cooling of sessile droplets on orientation of the freezing tip.

HYPOTHESIS: The shape of the "freezing tip" formed by the crystallization of water droplets demonstrated remarkable universality - no dependence on the cooling rate and physico-chemical properties of the substrate has been observed. At the same time, the spatial orientation of the freezing cone may be varied. We hypothesized that the orientation of the freezing tip is determined by the direction of heat flux at the base of the sessile droplet. This direction is expected to be changed when the substrate with a low thermal diffusivity is not cooled uniformly. EXPERIMENTS: We studied the freezing of water droplets placed on the inclined surface of wedges made from a variety of materials (polymers: Polymethylmethacrylate, Polytetrafluoroethylene, Polyurethane and metal: Titanium), which were cooled from below. The shape of the frozen droplets was controlled in situ. COMPUTATIONS: The computational model was suggested for the transient temperature field in the polymer wedge to determine a time variation of the local heat flux under the droplets. A comparison of numerical results and the measurements enabled us to confirm the aforementioned hypothesis relating the orientation of the freezing tips to the direction of the heat flux. FINDINGS: It was established that the orientation of the freezing cone axis depends on the location of the frozen droplet on the inclined surface of the wedge. Calculations of the transient temperature field of the wedge confirmed our hypothesis about the physical reason of the various spatial orientations of the freezing cones.

Giant amplification of small perturbations in frictional amorphous solids.

Catastrophic events in nature can be often triggered by small perturbations, with "remote triggering" of earthquakes being an important example. Here we present a mechanism for the giant amplification of small perturbations that is expected to be generic in systems whose dynamics is not derivable from a Hamiltonian. We offer a general discussion of the typical instabilities involved (being oscillatory with an exponential increase of noise) and examine in detail the normal forms that determine the relevant dynamics. The high sensitivity to external perturbations is explained for systems with and without dissipation. Numerical examples are provided using the dynamics of frictional granular matter. Finally, we point out the relationship of the presently discussed phenomenon to the highly topical issue of "exceptional points" in quantum models with non-Hermitian Hamiltonians.

Cherenkov-Like Surface Thermal Waves Emerging from Self-Propulsion of a Liquid Marble.

We explore the thermal field related to the self-propulsion of floating liquid marbles filled with aqueous ethanol. Cherenkov-like thermal waves arising from self-propulsion are registered. The opening angle of the thermal field Cherenkov triangle is governed by the inter-relation between the velocity of self-propulsion and the phase velocity of the capillary waves. The self-propulsion is driven by soluto-capillarity accompanied by thermo-capillarity. A semiquantitative analysis of the effect is presented. The empirical selection rule for capillary waves responsible for the mass, momentum, and heat transfer is outlined. The soluto-capillarity leads to much stronger spatial variations of the surface tension than the thermo-capillarity.

Noise amplification in frictional systems: Oscillatory instabilities.

It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e., the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential growth of small perturbations which are tamed by dynamical nonlinearities. The amplification can be giant, many orders of magnitude, and it ends with a catastrophic system-spanning plastic event. Here we follow up on this discovery, explore the scaling laws characterizing the onset of the instability, the scenarios of the development of the instability with and without damping, and the nature of the eventual system-spanning events. The possible relevance to earthquake physics and to the transition from static to dynamic friction is discussed.

Mixed global dynamics of forced vibro-impact oscillator with Coulomb friction.

This paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In the vast majority of the existing studies, this model included also viscous friction, and its global dynamics in the state space is governed by periodic, quasiperiodic, or chaotic attractors. We demonstrate that removal of the viscous friction leads to qualitative modification of the global dynamics, namely, the state space is divided into the regions with "regular" attraction to the aforementioned special solutions and the regions with profoundly Hamiltonian dynamics. The latter regions contain structures typical for forced Hamiltonian systems: stability islands, extended nonattractive chaotic regions, etc. We prove that such local Hamiltonian behavior should occur for phase trajectories with nonvanishing velocity. Stability analysis for the periodic orbits confirms the above statement. It is demonstrated that similar mixed global dynamics can be observed in a broader class of models.

Oscillatory Instabilities in Frictional Granular Matter.

Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to the vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e., the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations that are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the understanding of plasticity and failure in frictional granular materials. The possible relevance to earthquake physics is discussed.

Breather arrest, localization, and acoustic non-reciprocity in dissipative nonlinear lattices.

The effect of on-site damping on breather arrest, localization, and non-reciprocity in strongly nonlinear lattices is analytically and numerically studied. Breathers are localized oscillatory wavepackets formed by nonlinearity and dispersion. Breather arrest refers to breather disintegration over a finite "penetration depth" in a dissipative lattice. First, a simplified system of two nonlinearly coupled oscillators under impulsive excitation is considered. The exact relation between the number of beats (energy exchanges between oscillators), the excitation magnitude, and the on-site damping is derived. Then, these analytical results are correlated to those of the semi-infinite extension of the simplified system, where breather penetration depth is governed by a similar law to that of the finite beats in the simplified system. Finally, motivated by the experimental results of Bunyan, Moore, Mojahed, Fronk, Leamy, Tawfick, and Vakakis [Phys. Rev. E 97, 052211 (2018)], breather arrest, localization, and acoustic non-reciprocity in a non-symmetric, dissipative, strongly nonlinear lattice are studied. The lattice consists of repetitive cells of linearly grounded large-scale particles nonlinearly coupled to small-scale ones, and linear intra-cell coupling. Non-reciprocity in this lattice yields either energy localization or breather arrest depending on the position of excitation. The nonlinear acoustics governing non-reciprocity, and the surprising effects of existence of linear components in the coupling nonlinear stiffnesses, in the acoustics, are investigated.

Toward an Understanding of Magnetic Displacement of Floating Diamagnetic Bodies, I: Experimental Findings.

Diamagnetic objects (polymer and metallic plates and spheres, ceramic beads, and liquid marbles), floating on water, and a variety of organic liquids may be driven by a steady magnetic field of 0.1 T, registered at the water-vapor surface. Diamagnetic bodies are attracted to the magnet, when the apparent contact angle at the solid/liquid interface is obtuse and repelled from the magnet, when the angle is acute. Cold plasma-treated polyolefin rafts and spheres, demonstrating underwater floating, are repelled by a permanent magnet. Addition of a surfactant to the water, as well as cold plasma treatment of the polyolefin bodies, can turn the attraction into the repulsion. We conjecture that the observed effects are caused by the interplay of two main phenomena. The first is the gravity, which induces sliding of the particle on the deformed liquid/vapor interface (the Moses effect). The second cause is the hysteresis of the contact angle at the bodies' boundaries.

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy.

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales-a linear large-scale oscillator coupled to a small scale by a nonlinear spring-and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

Emergent interparticle interactions in thermal amorphous solids.

Amorphous media at finite temperatures, be them liquids, colloids, or glasses, are made of interacting particles that move chaotically due to thermal energy, continuously colliding and scattering off each other. When the average configuration in these systems relaxes only at long times, one can introduce effective interactions that keep the mean positions in mechanical equilibrium. We introduce a framework to determine the effective force laws that define an effective Hessian that can be employed to discuss stability properties and the density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these experience zero forces when not in contact and infinite forces when they touch. Close to jamming we recapture the effective interactions that at temperature T depend on the gap h between spheres as T/h [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006)EULEEJ0295-507510.1209/epl/i2006-10238-x]. For hard spheres at lower densities or for systems whose binary bare interactions are longer ranged (at any density), the emergent force laws include ternary, quaternary, and generally higher-order many-body terms, leading to a temperature-dependent effective Hessian.

Heat conduction in a chain of colliding particles with a stiff repulsive potential.

One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence-the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive-the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.

Localization in finite vibroimpact chains: Discrete breathers and multibreathers.

We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.

Determining the interparticle force laws in amorphous solids from a visual image.

We consider the problem of how to determine the force laws in an amorphous system of interacting particles. Given the positions of the centers of mass of the constituent particles we propose an algorithm to determine the interparticle force laws. Having n different types of constituents we determine the coefficients in the Laurent polynomials for the n(n+1)/2 possibly different force laws. A visual providing the particle positions in addition to a measurement of the pressure is all that is required. The algorithm proposed includes a part that can correct for experimental errors in the positions of the particles. Such a correction of unavoidable measurement errors is expected to benefit many experiments in the field.

What Determines the Static Force Chains in Stressed Granular Media?

The determination of the normal and transverse (frictional) interparticle forces within a granular medium is a long-standing, daunting, and yet unresolved problem. We present a new formalism that employs the knowledge of the external forces and the orientations of contacts between particles (of any given size), to compute all the interparticle forces. Having solved this problem, we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.