The fundamental instability responsible for the shear localization which results in bands amorphous solids remains unknown despite an enormous amount of research, both experimental and theoretical. As this is main mechanism failure metallic glasses, understanding invaluable finding how to stabilize such materials against tendency localize. In Letter we explain under shear, appearance highly correlated lines Eshelby-like quadrupolar singularities organize nonaffine plastic flow solid into a...

Gravito–capillary waves at free surfaces are ubiquitous in several natural and industrial processes involving quiescent liquid pools bounded by cylindrical walls. These emanate from the relaxation of initial interface distortions, which often take form a cavity (depression) centred on symmetry axis container. The surface reflect container walls leading to radially inward propagating wavetrain converging (focussing) onto axis. Under inviscid approximation for sufficiently shallow cavities, is...

In recent research it was found that the fundamental shear-localizing instability of amorphous solids under external strain, which eventually results in a shear band and failure, consists highly correlated array Eshelby quadrupoles all having same orientation some density $\ensuremath{\rho}$. this paper we calculate analytically energy $E(\ensuremath{\rho},\ensuremath{\gamma})$ associated with such structures as function $\ensuremath{\rho}$ strain $\ensuremath{\gamma}$. We show for strains...

By comparing the response to external strains in metallic glasses and Lennard-Jones we find a quantitative universality of fundamental plastic instabilities athermal, quasistatic limit. Microscopically these two types are as different one can imagine, latter being determined by binary interactions, whereas former is multiple interactions due effect electron gas that cannot be disregarded. In spite this enormous difference instability same saddle-node bifurcation. As result, statistics stress...

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids address controversy concerning energy spectrum that is associated with these excitations. Finding correct important because play a major role dissipation superfluid turbulence at near-zero temperatures. In this paper, we show analytically solution proposed by [L'vov Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, regularity prefactor. Furthermore,...

In this paper we extend the recent theory of shear localization in two-dimensional (2D) amorphous solids to three dimensions. two dimensions fundamental instability is related appearance a line displacement quadrupoles that makes an angle 45${}^{\ensuremath{\circ}}$ with principal stress axis. plastic also explained by formation lattice anisotropic elastic inclusions. case pure external stress, demonstrate 2D triangular similar elementary events. It shown arranged on plane that, similarly...

We study axisymmetric, free oscillations driven by gravity and surface tension at the interface of two viscous, immiscible, radially unbounded fluids, analytically numerically. The is perturbed as a zeroth-order Bessel function (in space) its evolution obtained time. In linearised approximation, we solve initial value problem (IVP) to obtain an analytic expression for time wave amplitude. It shown that mode temporally evolves in exactly same manner Fourier planar geometry. novel analytical...

We show numerically that large amplitude, shape deformations imposed on a spherical-cap, incompressible, sessile gas bubble pinned rigid wall can produce sharp, wall-directed jet. For such filled with permanent gas, the temporal spectrum for surface-tension-driven, linearized perturbations has been studied recently in D. Ding and J. Bostwick [“Oscillations of partially wetting bubble,” Fluid Mech. 945, A24 (2022)]. potential flow limit. reformulate this as an initial-value problem analogous...

Numerical studies of dimple and jet formation from a collapsing cavity often model the initial shape as truncated sphere, mimicking bursting bubble. In this study, we present minimal containing only nonlinear inertial capillary forces, which produces dimples jets wave trough. The trough in our simulation develops smooth perturbation, chosen to be an eigenmode linearised ${O}(\epsilon )$ problem ( $\epsilon$ is non-dimensional amplitude). We explain physical mechanism demonstrate that, for...

Abstract

Metallic Glasses are prone to fail mechanically via a shear-banding instability. In remarkable paper Johnson and Samwer demonstrated that this failure enjoys high degree of universality in the sense large group metallic glasses appears possess yield-strain decreases with temperature following $-T^{2/3}$ law up logarithmic corrections. Letter we offer theoretical derivation law. We show our formula fits very well simulational data on typical amorphous solids.

The steady viscous shallow water equations are often used for the study of hydraulic jumps. We cast these as a single parametric ordinary differential equation with global continuity constraint. solution provides both local velocity profile and downstream evolution film height. Moreover this is an exact approach, in contrast existing approaches which encounter closure problem need modeling. There only one supercritical initially. This shows jumplike behavior at Froude number close to unity,...

Hydraulic jumps created by gravity are seen everyday in the kitchen sink. We show that at small scales a circular hydraulic jump can be absence of surface tension. The theory is motivated our experimental finding height discontinuity spreading submicron molten metal droplets pulsed-laser ablation. By careful control initial conditions, this leads to solid femtoliter cups gold, silver, copper, niobium, and tin.

We perform linear stability analysis of an interface separating two immiscible, inviscid, quiescent fluids subject to a time-periodic body force. In generalised, orthogonal coordinate system, the time-dependent amplitude interfacial perturbations, in form standing waves, is shown be governed by generalised Mathieu equation. For zero forcing, equation reduces (generalised) simple harmonic oscillator The govern Faraday waves on four base states. use this demonstrate that and instabilities can...

Amorphous solids, confined on the nanoscale, are studied using molecular dynamics computer simulation. Unlike in bulk samples, failure patterns such systems strongly affected by confinement geometry and interfacial effects sample. We study a model glass, subjected to uniaxial loading, for varying aspect ratios of sample geometry. While small ratio, breaks forming neck, above critical value cavitation is seen. The ratio associated with strain-rate- temperature-dependent curvature which free...

Earlier studies on the circular hydraulic jump have shown that radial position of depends flow rate, gravity, and fluid viscosity. In this study, results from numerical simulations experiments jumps are presented through analysis, it is momentum flux an additional controlling parameter in determining location. Apart location, variation film thickness with parameters also obtained simulations. By including dependence dissipation along other parameters, data radius simulation (including...

The usefulness of glasses, and particularly metallic in technological applications is often limited by their toughness, (which defined as the area under stress vs. strain curve before plastic yielding). Recently, toughness was found to increase significantly addition small concentrations foreign atoms that act pinning centers. We model this phenomenon at zero temperature quasi-static straining with randomly positioned particles participate elastic deformation, but are pinned non-affine...

We present results of atomistic simulations a new model magnetic amorphous solid subjected to external mechanical strains and fields. The employed offers perspectives on important effects like Barkhausen noise magnetostriction. It is shown that the plastic response in such systems exhibit singularities characterized by unexpected exponents requiring careful theoretical reasoning. spatial structure events requires coarse grained elasto-magnetic theory which provided here.

We demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh-Plateau (RP) instability on a liquid cylinder by subjecting it radial oscillatory body force. Viscosity is found play crucial role in this stabilisation. Linear stability predictions are obtained via Floquet analysis demonstrating that RP unstable can be stabilised using forcing. also solve linearised, viscous initial-value problem for free-surface deformation obtaining an equation...

We demonstrate that gravity acting alone at large length scales (compared to the capillary length) can produce a jet from sufficiently steep, axisymmetric surface deformation imposed on quiescent, deep pool of liquid. Mechanistically, owes it origin focusing concentric, wave towards axis symmetry, quite analogous such waves and resultant formation observed during bubble collapse small scales. A weakly nonlinear theory based method multiple in potential flow limit is presented for modal...

We report simulations of undular hydraulic jumps occuring in a two-phase flow. Unlike bores (in rivers), where the inter- face remains horizontal low Reynolds show linear increase height incoming flow due to viscosity. Consequently, presence or absence undulations depends both on inlet Froude and number unlike criterion is traditionally considered sufficient. In our simulations, these display separated vortex underneath every crest. Despite strong influence viscosity, we that theory Benjamin...