Mixing, heating and ion-neutral decoupling induced by Rayleigh-Taylor instability in prominence-corona transition regions

This study explores nonlinear development of the magnetized Rayleigh-Taylor instability (RTI) in a prominence-corona transition region. Using a two-fluid model of a partially ionized plasma, we compare RTI simulations for several different magnetic field configurations. We follow prior descriptions of the numerical prominence model (Popescu Braileanu et al. 2021 Astron. Astrophys. 646, A93 (doi:10.1051/0004-6361/202039053), Popescu Braileanu et al. 2021 Astron. Astrophys. 650, A181 (doi:10.1051/0004-6361/202140425) and Popescu Braileanu et al. 2023 Astron. Astrophys. 670, A31 (doi:10.1051/0004-6361/202142996)) and explore the charged-neutral fluid coupling and plasma heating in a two-dimensional mixing layer for different magnetic field configurations. We also investigate how the shear in magnetic field surrounding a prominence may impact the release of the gravitational potential energy of the prominence material. We show that the flow decoupling is strongest in the plane normal to the direction of the magnetic field, where neutral pressure gradients drive ion-neutral drifts and frictional heating is balanced by adiabatic cooling of the expanding prominence material. We also show that magnetic field within the mixing plane can lead to faster nonlinear release of the gravitational energy driving the RTI, while more efficiently heating the plasma via viscous dissipation of associated plasma flows. We relate the computational results to potential observables by highlighting how integrating over under-resolved two-fluid sub-structure may lead to misinterpretation of observational data. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

The influence of thermal pressure gradients and ionization (im)balance on the ambipolar diffusion and charge-neutral drifts

Solar partially ionized plasma is frequently modelled using single-fluid (1F) or two-fluid (2F) approaches. In the 1F case, charge-neutral interactions are often described through ambipolar diffusion, while the 2F model fully considers charge-neutral drifts. Here, we expand the definition of the ambipolar diffusion coefficient to include inelastic collisions (ion/rec) in two cases: a VAL3C one-dimensional model and a 2F simulation of the Rayleigh-Taylor instability (RTI) in a solar prominence thread based on [Lukin et al. 2024 Phil. Trans. R. Soc. A 382, 20230417. (doi:10.1098/rsta.2023.0417)]. On one side, we evaluate the relative importance of the inelastic contribution, compared to elastic and charge-exchange collisions. On the other side, we compare the contributions of ion/rec, thermal pressure, viscosity and magnetic forces to the charge-neutral drift velocity of the turbulent flow of the RTI. Our analysis reveals that the contribution of inelastic collisions to the ambipolar diffusion coefficient is negligible across the chromosphere, allowing the classical definition of this coefficient to be safely used in 1F modelling. However, in the transition region, the contribution of inelastic collisions can become as significant as that of elastic collisions. Furthermore, we ascertain that the thermal pressure force predominantly influences the charge-neutral drifts in the RTI model, surpassing the impact of the magnetic force. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

Parametric resonance of Alfvén waves driven by ionization-recombination waves in the weakly ionized solar atmosphere

Parametric coupling of waves is one of the most efficient mechanisms of energy transfer that can lead to the growth or decay of waves. This transfer occurs at frequencies close to their natural frequencies. In partially ionized solar plasma, there are a multitude of waves that can undergo this process. Here, we study the parametric coupling of Alfvén waves propagating in a partially ionized solar plasma with ionization-recombination waves identified by our study to appear in a plasma in ionization non-equilibrium. Depending on the parameters that describe the plasma (density, temperature), coupling can lead to a parametric resonance. Our study determines the occurrence conditions of parametric resonance, by finding the boundaries between stable and unstable regions in the parameter space. Our results show that collisions and non-equilibrium recombination can both contribute to the onset of unstable behaviour of parametrically resonant Alfvén waves. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

Radiative loss and ion-neutral collisional effects in astrophysical plasmas

In this paper, we study the role of radiative cooling (RC) in a two-fluid model consisting of coupled neutrals and charged particles. We first analyse the linearized two-fluid equations where we include radiative losses in the energy equation for the charged particles. In a one-dimensional geometry for parallel propagation and in the limiting cases of weak and strong coupling, it can be shown analytically that the instability conditions for the thermal mode and the sound waves, the isobaric and isentropic criteria, respectively, remain unchanged with respect to one-fluid radiative plasmas. For the parameters considered in this paper, representative for the solar corona, the RC produces growth of the thermal mode and damping of the sound waves. In the weak coupling limit, the growth of the thermal instability and the damping of the sound waves is as derived in Field (Field 1965 Astrophys. J. 142, 531 (doi:10.1086/148317)) using the charged fluid properties. When neutrals are included and are sufficiently coupled to the charges, the thermal mode growth rate and the wave damping both reduce by the same factor, which depends on the ionization fraction only. For a heating function that is constant in time, we find that the growth of the thermal mode and the damping of the sound waves are slightly larger. The numerical calculation of the eigenvalues of the general system of equations in a three-dimensional geometry confirm the analytic results. We then run two-dimensional fully nonlinear simulations that give consistent results: a higher ionization fraction or lower coupling will increase the growth rate. The magnetic field contribution is negligible in the linear phase. Ionization-recombination effects might play an important role because the RC produces a large range of temperatures in the system. In the numerical simulation, after the first condensation phase, when the minimum temperature is reached, the fraction of neutrals increases four orders of magnitude because of the recombination. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

Viscoelastic instabilities of Taylor-Couette flows with different rotation regimes

The critical modes of the instabilities of viscoelastic Taylor-Couette flow are investigated using both experiments and linear stability analysis when only one cylinder rotates and the other is fixed. A viscoelastic Rayleigh circulation criterion highlights that the elasticity of the polymer solution can induce a flow instability even if the Newtonian counterpart is stable. When the inner cylinder solely rotates, experimental results show three critical modes: stationary axisymmetric vortices or Taylor vortices for small elasticity, standing waves, also called ribbons for intermediate values of elasticity, and disordered vortices (DV) for large elasticity values. When the outer cylinder rotates and the inner cylinder is fixed and for large values of elasticity, the critical modes appear in the form of DV. There is a good agreement between experimental and theoretical results provided that the elasticity of the polymer solution is accurately determined. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Hoop compression driven instabilities in spontaneously formed multilayer graphene blisters over a polymeric substrate

The blistering of elastic membranes is prone to elastic-solid as well as substrate-based mechanical instabilities. The solid-based instabilities have been well-explored in the mechanically indented blisters of elastic membranes over the rigid/solid substrates, but an integrated study illustrating the underlying mechanism for the onset of solid as well as substrate-based instabilities in the spontaneous blistering of a 2D material is still lacking in the literature. In this article, an extensive experimental as well as analytical analysis of the spontaneous blister-formation in the multilayer graphene (MLG) flakes over a polymeric substrate is reported, which elucidates the involved mechanism and the governing parameters behind the development of elastic-solid as well as viscoelastic-substrate based instabilities. Herein, a 'blister-collapse model' is proposed, which infers that the suppression of the hoop compression, resulting from the phase-transition of the confined matter, plays a crucial role in the development of the instabilities. The ratio of blister-height to flake-thickness is a direct consequence of the taper-angle of the MLG blister and the thickness-dependent elasticity of the upper-bounding MLG flake, which shows a significant impact on the growth-dynamics of the viscous fingering pattern (viscoelastic-substrate based instability) under the MLG blister.

A review on octenyl succinic anhydride modified starch-based Pickering-emulsion: Instabilities and ingredients interactions

Pickering emulsions endow attractive features and a wide versatility in both food and nonfood fields. In the last decades, a noticeable interest has emerged toward the use of octenyl succinic anhydride (OSA)-starch to improve the long-term stability in such systems. In this review, instabilities were pointed out, where a new kinetic equilibrium was observed in Pickering emulsions assigned to migration and size variations of particles. These features were monitored using rheological measurements to understand microstructure and droplets mobility. The elastic modulus (G'), the viscous modulus (G″), and tan(δ) values were attributed to the transition from solid to fluid and assigned to the instability of the formulation regardless of the type of the system configuration. The novelties in using OSA-modified starch, were also exposed. The chemical modification of starch decreased creaming for months. Interaction between OSA-modified starches and some ionic components (potassium, magnesium, and calcium) as well as hydrocolloids and proteins reduced creaming and coalescence due to dense interfacial film. Furthermore, the key parameters (oil fraction, fatty acids composition, oxidative stress oil polarity, and oil viscosity) that govern oil phase in Pickering emulsion, were analyzed. These parameters were found to be positively correlated to the stability of Pickering emulsions.

Investigation of the Polymer Coextrusion Process: A Review

A review of the different coextrusion processes and the related processing problems is presented. A one-dimensional bilayer coextrusion Poiseuille flow model is first developed with Newtonian and shear-thinning rheological behaviors. A transitory computation at the convergence between the two independent polymer layers shows that stationary interface position and velocity profile are established after a short distance of the order of the die gap which justifies the validity of the 1D stationary model. This model is then applied to multilayer temperature dependent coextrusion flows which correspond to realistic industrial coextrusion conditions. Marked interface instabilities may be observed depending on the rheology of the coextruded polymers and of their flow rate ratios. Experiments point clearly out that these instabilities may be amplified along the die land. Convective stability analysis as well as direct numerical computation discriminate flow situations which amplify or damp down instabilities. These 1D models are unable to account for the complex feedblock coat-hanger die geometries. A thin layer coextrusion model is then developed, based on the Hele-Shaw lubrication approximations already used for single layer extrusion problems. It allows to predict the location of the interfaces between the different layers in the whole die, and especially at die exit. This represents a major issue in feedblock die coextrusion. These thin layer approaches are unable to address the encapsulation of one polymer by the other in these complex die geometries with important gap thicknesses. Experiments conducted in dies of square section allow identifying the dynamics of encapsulation. 3D models are required to account for this phenomenon but the management of the sticking contact at the die wall poses difficult numerical problems.

Multiscale Soft Surface Instabilities for Adhesion Enhancement

Soft polymeric gels are susceptible to buckling-induced instabilities due to their great compliance to surface deformations. The instability patterns at soft interfaces have great potential in engineering functional materials with unique surface properties. In this work, we systematically investigated how swelling-induced instability patterns effectively improved the adhesive properties of soft polydimethylsiloxane (PDMS) gels. We directly imaged the formations of the surface instability features during the relaxation process of a swollen gel substrate. The features were found to greatly increase the adhesion energy of soft gels across multiple length scales, and the adhesion enhancement was associated with the variations of contact lines both inside the contact region and along the contact periphery. We expect that these studies of instability patterns due to swelling will further benefit the design of functional interfaces in various engineering applications.

The Emergence of Sequential Buckling in Reconfigurable Hexagonal Networks Embedded into Soft Matrix

The extreme and unconventional properties of mechanical metamaterials originate in their sophisticated internal architectures. Traditionally, the architecture of mechanical metamaterials is decided on in the design stage and cannot be altered after fabrication. However, the phenomenon of elastic instability, usually accompanied by a reconfiguration in periodic lattices, can be harnessed to alter their mechanical properties. Here, we study the behavior of mechanical metamaterials consisting of hexagonal networks embedded into a soft matrix. Using finite element analysis, we reveal that under specific conditions, such metamaterials can undergo sequential buckling at two different strain levels. While the first reconfiguration keeps the periodicity of the metamaterial intact, the secondary buckling is accompanied by the change in the global periodicity and formation of a new periodic unit cell. We reveal that the critical strains for the first and the second buckling depend on the metamaterial geometry and the ratio between elastic moduli. Moreover, we demonstrate that the buckling behavior can be further controlled by the placement of the rigid circular inclusions in the rotation centers of order 6. The observed sequential buckling in bulk metamaterials can provide additional routes to program their mechanical behavior and control the propagation of elastic waves.

Van der Waals interaction affects wrinkle formation in two-dimensional materials

Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer "bubbles" in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical "Winkler foundation" model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.

Electro-Hydrodynamics of Emulsion Droplets: Physical Insights to Applications

The field of droplet electrohydrodynamics (EHD) emerged with a seminal work of G.I. Taylor in 1966, who presented the so-called leaky dielectric model (LDM) to predict the droplet shapes undergoing distortions under an electric field. Since then, the droplet EHD has evolved in many ways over the next 55 years with numerous intriguing phenomena reported, such as tip and equatorial streaming, Quincke rotation, double droplet breakup modes, particle assemblies at the emulsion interface, and many more. These phenomena have a potential of vast applications in different areas of science and technology. This paper presents a review of prominent droplet EHD studies pertaining to the essential physical insight of various EHD phenomena. Here, we discuss the dynamics of a single-phase emulsion droplet under weak and strong electric fields. Moreover, the effect of the presence of particles and surfactants at the emulsion interface is covered in detail. Furthermore, the EHD of multi-phase double emulsion droplet is included. We focus on features such as deformation, instabilities, and breakups under varying electrical and physical properties. At the end of the review, we also discuss the potential applications of droplet EHD and various challenges with their future perspectives.

Melt-Spun Fibers for Textile Applications

Textiles have a very long history, but they are far from becoming outdated. They gain new importance in technical applications, and man-made fibers are at the center of this ongoing innovation. The development of high-tech textiles relies on enhancements of fiber raw materials and processing techniques. Today, melt spinning of polymers is the most commonly used method for manufacturing commercial fibers, due to the simplicity of the production line, high spinning velocities, low production cost and environmental friendliness. Topics covered in this review are established and novel polymers, additives and processes used in melt spinning. In addition, fundamental questions regarding fiber morphologies, structure-property relationships, as well as flow and draw instabilities are addressed. Multicomponent melt-spinning, where several functionalities can be combined in one fiber, is also discussed. Finally, textile applications and melt-spun fiber specialties are presented, which emphasize how ongoing research efforts keep the high value of fibers and textiles alive.

A Björling representation for Jacobi fields on minimal surfaces and soap film instabilities

We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal surface. When the amplitude vanishes, the curve forms part of the boundary to a critically stable domain, while when the gradient vanishes the Jacobi field is maximal along the curve. In the latter case, we show that the Jacobi field is maximally localized if its amplitude is taken to be the lowest eigenfunction of a one-dimensional Schrödinger operator. We present examples for the helicoid, catenoid, circular helicoids and planar Enneper minimal surfaces, and emphasize that the geometric nature of the Björling representation allows direct connection with instabilities observed in soap films.

Capillary-Based Microfluidics-Coflow, Flow-Focusing, Electro-Coflow, Drops, Jets, and Instabilities

Capillary-based microfluidics is a great technique to produce monodisperse and complex emulsions and particulate suspensions. In this review, the current understanding of drop and jet formation in capillary-based microfluidic devices for two primary flow configurations, coflow and flow-focusing is summarized. The experimental and theoretical description of fluid instabilities is discussed and conditions for controlled drop breakup in different modes of drop generation are provided. Current challenges in drop breakup with low interfacial tension systems and recent progress in overcoming drop size limitations using electro-coflow are addressed. In each scenario, the physical mechanisms for drop breakup are revisited, and simple scaling arguments proposed in the literature are introduced.

Particle-in-cell Simulations of the Whistler Heat-flux Instability in Solar Wind Conditions

In collision-poor plasmas from space, e.g., solar wind or stellar outflows, the heat flux carried by the strahl or beaming electrons is expected to be regulated by the self-generated instabilities. Recently, simultaneous field and particle observations have indeed revealed enhanced whistler-like fluctuations in the presence of counter-beaming populations of electrons, connecting these fluctuations to the whistler heat-flux instability (WHFI). This instability is predicted only for limited conditions of electron beam-plasmas, and has not yet been captured in numerical simulations. In this Letter we report the first simulations of WHFI in particle-in-cell setups, realistic for the solar wind conditions, and without temperature gradients or anisotropies to trigger the instability in the initiation phase. The velocity distributions have a complex reaction to the enhanced whistler fluctuations conditioning the instability saturation by a decrease of the relative drifts combined with induced (effective) temperature anisotropies (heating the core electrons and pitch-angle and energy scattering the strahl). These results are in good agreement with a recent quasilinear approach, and support therefore a largely accepted belief that WHFI saturates at moderate amplitudes. In the anti-sunward direction the strahl becomes skewed with a pitch-angle distribution decreasing in width as electron energy increases, which seems to be characteristic of self-generated whistlers and not to small-scale turbulence.

Growth and remodelling of living tissues: perspectives, challenges and opportunities

One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

Shearing-box simulations of MRI-driven turbulence in weakly collisional accretion discs

We present a systematic shearing-box investigation of MRI-driven turbulence in a weakly collisional plasma by including the effects of an anisotropic pressure stress, i.e. anisotropic (Braginskii) viscosity. We constrain the pressure anisotropy (Δp) to lie within the stability bounds that would be otherwise imposed by kinetic microinstabilities. We explore a broad region of parameter space by considering different Reynolds numbers and magnetic-field configurations, including net vertical flux, net toroidal-vertical flux and zero net flux. Remarkably, we find that the level of turbulence and angular-momentum transport are not greatly affected by large anisotropic viscosities: the Maxwell and Reynolds stresses do not differ much from the MHD result. Angular-momentum transport in Braginskii MHD still depends strongly on isotropic dissipation, e.g., the isotropic magnetic Prandtl number, even when the anisotropic viscosity is orders of magnitude larger than the isotropic diffusivities. Braginskii viscosity nevertheless changes the flow structure, rearranging the turbulence to largely counter the parallel rate of strain from the background shear. We also show that the volume-averaged pressure anisotropy and anisotropic viscous transport decrease with increasing isotropic Reynolds number (Re); e.g., in simulations with net vertical field, the ratio of anisotropic to Maxwell stress (α _A/α _M) decreases from ~ 0.5 to ~ 0.1 as we move from Re ~ 10³ to Re ~ 10⁴, while 〈4πΔp/B ²〉 → 0. Anisotropic transport may thus become negligible at high Re. Anisotropic viscosity nevertheless becomes the dominant source of heating at large Re, accounting for ≳50% of the plasma heating. We conclude by briefly discussing the implications of our results for RIAFs onto black holes.

Microspheres Formation in a Glass-Metal Hybrid Fiber System: Application in Optical Microwires

Multicomponent optical fibers with incorporated metals are promising photonic platforms for engineering of tailored plasmonic structures by laser micromachining or thermal processing. It has been observed that during thermal processing microfluidic phenomena lead to the formation of embedded micro- and nanostructures and spheres, thus triggering the technological motivation for their theoretical investigation, especially in the practical case of noble metal/glass composites that have not yet been investigated. Implemented microwires of gold core and glass cladding, recently studied experimentally, are considered as a reference validation platform. The Plateau-Rayleigh instability in such hybrid fibers is theoretically investigated by inducing surface tension perturbations and by comparing them to the Tomotika instability theory. The continuous-core breakup time was calculated via Finite Element Method (FEM) simulations for different temperatures and was found to be considerably higher to Tomotika’s model, while the final sphere diameter is a linear function of the initial core radius. Different sinusoidal perturbation parameters were considered, showing significant impact in the characteristics of formed spherical features. The theoretical results were in close agreement with previous experimental observations expected to assist in the understanding of the processes involved, providing insight into the engineering of fibers, both in the initial drawing process and post processing.

Gravitational instabilities in binary granular materials

The motion and mixing of granular media are observed in several contexts in nature, often displaying striking similarities to liquids. Granular dynamics occur in geological phenomena and also enable technologies ranging from pharmaceuticals production to carbon capture. Here, we report the discovery of a family of gravitational instabilities in granular particle mixtures subject to vertical vibration and upward gas flow, including a Rayleigh-Taylor (RT)-like instability in which lighter grains rise through heavier grains in the form of "fingers" and "granular bubbles." We demonstrate that this RT-like instability arises due to a competition between upward drag force increased locally by gas channeling and downward contact forces, and thus the physical mechanism is entirely different from that found in liquids. This gas channeling mechanism also generates other gravitational instabilities: the rise of a granular bubble which leaves a trail of particles behind it and the cascading branching of a descending granular droplet. These instabilities suggest opportunities for patterning within granular mixtures.

Domain Formations and Pattern Transitions via Instabilities in Soft Heterogeneous Materials

Experimental observations of domain formations and pattern transitions in soft particulate composites under large deformations are reported herein. The system of stiff inclusions periodically distributed in a soft elastomeric matrix experiences dramatic microstructure changes upon the development of elastic instabilities. In the experiments, the formation of microstructures with antisymmetric domains and their geometrically tailored evolution into a variety of patterns of cooperative particle rearrangements are observed. Through experimental and numerical analyses, it is shown that these patterns can be tailored by tuning the initial microstructural periodicity and concentration of the inclusions. Thus, these fully determined new patterns can be achieved by fine tuning of the initial microstructure.

The origin of compression influences geometric instabilities in bilayers

Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite-element set-up and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch. We find that the origin of compression determines the substrate stretch state at the primary instability point and thus significantly affects the critical buckling conditions. Similarly, it leads to different post-buckling evolutions and secondary instability patterns when the load further increases. Our results emphasize that future phase diagrams of geometric instabilities should incorporate not only the film thickness but also the origin of compression. Thoroughly understanding the influence of the origin of compression on geometric instabilities is crucial to solving real-life problems such as the engineering of smart surfaces or the diagnosis of neuronal disorders, which typically involve temporally or spatially combined origins of compression.

Fluid dynamic instabilities: theory and application to pattern forming in complex media

In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'.

Tailored Buckling Microlattices as Reusable Light-Weight Shock Absorbers

Structures and materials absorbing mechanical (shock) energy commonly exploit either viscoelasticity or destructive modifications. Based on a class of uniaxial light-weight geometrically nonlinear mechanical microlattices and using buckling of inner elements, either a sequence of snap-ins followed by irreversible hysteretic - yet repeatable - self-recovery or multistability is achieved, enabling programmable behavior. Proof-of-principle experiments on three-dimensional polymer microstructures are presented.

Collision velocity of dust grains in self-gravitating protoplanetary discs

We have conducted the first comprehensive numerical investigation of the relative velocity distribution of dust particles in self-gravitating protoplanetary discs with a view to assessing the viability of planetesimal formation via direct collapse in such environments. The viability depends crucially on the large sizes that are preferentially collected in pressure maxima produced by transient spiral features (Stokes numbers, St ∼ 1); growth to these size scales requires that collision velocities remain low enough that grain growth is not reversed by fragmentation. We show that, for a single-sized dust population, velocity driving by the disc's gravitational perturbations is only effective for St > 3, while coupling to the gas velocity dominates otherwise. We develop a criterion for understanding this result in terms of the stopping distance being of the order of the disc scaleheight. Nevertheless, the relative velocities induced by differential radial drift in multi-sized dust populations are too high to allow the growth of silicate dust particles beyond St ∼ 10^{- 2} or 10^-1 (10 cm to m sizes at 30 au), such Stokes numbers being insufficient to allow concentration of solids in spiral features. However, for icy solids (which may survive collisions up to several 10 m s^-1), growth to St ∼ 1 (10 m size) may be possible beyond 30 au from the star. Such objects would be concentrated in spiral features and could potentially produce larger icy planetesimals/comets by gravitational collapse. These planetesimals would acquire moderate eccentricities and remain unmodified over the remaining lifetime of the disc.

Ion-driven instabilities in the solar wind: Wind observations of 19 March 2005

Intervals of enhanced magnetic fluctuations have been frequently observed in the solar wind. But it remains an open question as to whether these waves are generated at the Sun and then transported outward by the solar wind or generated locally in the interplanetary medium. Magnetic field and plasma measurements from the Wind spacecraft under slow solar wind conditions on 19 March 2005 demonstrate seven events of enhanced magnetic fluctuations at spacecraft-frame frequencies somewhat above the proton cyclotron frequency and propagation approximately parallel or antiparallel to the background magnetic field B_o. The proton velocity distributions during these events are characterized by two components: a more dense, slower core and a less dense, faster beam. Observed plasma parameters are used in a kinetic linear dispersion equation analysis for electromagnetic fluctuations at k x B_o = 0; for two events the most unstable mode is the Alfvén-cyclotron instability driven by a proton component temperature anisotropy T_⊥/T_|| > 1 (where the subscripts denote directions relative to B_o), and for three events the most unstable mode is the right-hand polarized magnetosonic instability driven primarily by ion component relative flows. Thus, both types of ion anisotropies and both types of instabilities are likely to be local sources of these enhanced fluctuation events in the solar wind.

Statistical characterization of the growth and spatial scales of the substorm onset arc

We present the first multievent study of the spatial and temporal structuring of the aurora to provide statistical evidence of the near-Earth plasma instability which causes the substorm onset arc. Using data from ground-based auroral imagers, we study repeatable signatures of along-arc auroral beads, which are thought to represent the ionospheric projection of magnetospheric instability in the near-Earth plasma sheet. We show that the growth and spatial scales of these wave-like fluctuations are similar across multiple events, indicating that each sudden auroral brightening has a common explanation. We find statistically that growth rates for auroral beads peak at low wave number with the most unstable spatial scales mapping to an azimuthal wavelength λ≈ 1700-2500 km in the equatorial magnetosphere at around 9-12 R_E . We compare growth rates and spatial scales with a range of theoretical predictions of magnetotail instabilities, including the Cross-Field Current Instability and the Shear Flow Ballooning Instability. We conclude that, although the Cross-Field Current instability can generate similar magnitude of growth rates, the range of unstable wave numbers indicates that the Shear Flow Ballooning Instability is the most likely explanation for our observations.

Short-wavelength plasma turbulence and temperature anisotropy instabilities: recent computational progress

Plasma turbulence consists of an ensemble of enhanced, broadband electromagnetic fluctuations, typically driven by multi-wave interactions which transfer energy in wavevector space via non- linear cascade processes. Temperature anisotropy instabilities in collisionless plasmas are driven by quasi-linear wave-particle interactions which transfer particle kinetic energy to field fluctuation energy; the resulting enhanced fluctuations are typically narrowband in wavevector magnitude and direction. Whatever their sources, short-wavelength fluctuations are those at which charged particle kinetic, that is, velocity-space, properties are important; these are generally wavelengths of the order of or shorter than the ion inertial length or the thermal ion gyroradius. The purpose of this review is to summarize and interpret recent computational results concerning short-wavelength plasma turbulence, short-wavelength temperature anisotropy instabilities and relationships between the two phenomena.

Period-doubling and period-tripling in growing bilayered systems

Growing layers on elastic substrates are capable of creating a wide variety of surface morphologies. Moderate growth generates a regular pattern of sinusoidal wrinkles with a homogeneous energy distribution. While the critical conditions for periodic wrinkling have been extensively studied, the rich pattern formation beyond this first instability point remains poorly understood. Here we show that upon continuing growth, the energy progressively localizes and new complex morphologies emerge. Previous studies have often overlooked these secondary bifurcations; they have focused on large stiffness ratios between layer and substrate, where primary instabilities occur early, long before secondary instabilities emerge. We demonstrate that secondary bifurcations are particularly critical in the low stiffness ratio regime, where the critical conditions for primary and secondary instabilities move closer together. Amongst all possible secondary bifurcations, the mode of period-doubling plays a central role - it is energetically favorable over all other modes. Yet, we can numerically suppress period-doubling, by choosing boundary conditions, which favor alternative higher order modes. Our results suggest that in the low stiffness regime, pattern formation is highly sensitive to small imperfections: surface morphologies emerge rapidly, change spontaneously, and quickly become immensely complex. This is a common paradigm in developmental biology. Our results have significantly applications in the morphogenesis of living systems where growth is progressive and stiffness ratios are low.

The role of mechanics during brain development

Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated to neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl-von-Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

Dense, viscous brine behavior in heterogeneous porous medium systems

The behavior of dense, viscous calcium bromide brine solutions used to remediate systems contaminated with dense nonaqueous phase liquids (DNAPLs) is considered in laboratory and field porous medium systems. The density and viscosity of brine solutions are experimentally investigated and functional forms fit over a wide range of mass fractions. A density of 1.7 times, and a corresponding viscosity of 6.3 times, that of water is obtained at a calcium bromide mass fraction of 0.53. A three-dimensional laboratory cell is used to investigate the establishment, persistence, and rate of removal of a stratified dense brine layer in a controlled system. Results from a field-scale experiment performed at the Dover National Test Site are used to investigate the ability to establish and maintain a dense brine layer as a component of a DNAPL recovery strategy, and to recover the brine at sufficiently high mass fractions to support the economical reuse of the brine. The results of both laboratory and field experiments show that a dense brine layer can be established, maintained, and recovered to a significant extent. Regions of unstable density profiles are shown to develop and persist in the field-scale experiment, which we attribute to regions of low hydraulic conductivity. The saturated-unsaturated, variable-density groundwater flow simulation code SUTRA is modified to describe the system of interest, and used to compare simulations to experimental observations and to investigate certain unobserved aspects of these complex systems. The model results show that the standard model formulation is not appropriate for capturing the behavior of sharp density gradients observed during the dense brine experiments.

The effect of protein-precipitant interfaces and applied shear on the nucleation and growth of lysozyme crystals

This paper is concerned with the effect of protein-precipitant interfaces and externally applied shear on the nucleation and growth kinetics of hen egg-white lysozyme crystals. The early stages of microbatch crystallization of lysozyme were explored using both optical and confocal fluorescence microscopy imaging. Initially, an antisolvent (precipitant) was added to a protein drop and the optical development of the protein-precipitant interface was followed with time. In the presence of the water-soluble polymer poly(ethylene glycol) (PEG) a sharp interface was observed to form immediately within the drop, giving an initial clear separation between the lighter protein solution and the heavier precipitant. This interface subsequently became unstable and quickly developed within a few seconds into several unstable 'fingers' that represented regions of high concentration-gradient interfaces. Confocal microscopy demonstrated that the subsequent nucleation of protein crystals occurred preferentially in the region of these interfaces. Additional experiments using an optical shearing system demonstrated that oscillatory shear significantly decreased nucleation rates whilst extending the growth period of the lysozyme crystals. The experimental observations relating to both nucleation and growth have relevance in developing efficient and reliable protocols for general crystallization procedures and the controlled crystallization of single large high-quality protein crystals for use in X-ray crystallography.