Numerical study of laminar, standing hydraulic jumps in a planar geometry.

We solve the two-dimensional, planar Navier-Stokes equations to simulate a laminar, standing hydraulic jump using a Volume-of-Fluid method. The geometry downstream of the jump has been designed to be similar to experimental conditions by including a pit at the edge of the platform over which liquid film flows. We obtain jumps with and without separation.

Shear localization in three-dimensional amorphous solids.

In this paper we extend the recent theory of shear localization in two-dimensional (2D) amorphous solids to three dimensions. In two dimensions the fundamental instability of shear localization is related to the appearance of a line of displacement quadrupoles that makes an angle of 45^{∘} with the principal stress axis. In three dimensions the fundamental plastic instability is also explained by the formation of a lattice of anisotropic elastic inclusions.

Yield strain in shear banding amorphous solids.

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 of a highly correlated array of Eshelby quadrupoles all having the same orientation and some density ρ. In this paper we calculate analytically the energy E(ρ,γ) associated with such highly correlated structures as a function of the density ρ and the external strain γ. We show that for strains smaller than a characteristic strain γ(Y) the total strain energy initially increases as the quadrupole density increases, but that for strains larger than γ(Y) the energy monotonically decreases with quadrupole density.

Microscopic mechanism of shear bands in amorphous solids.

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

Universality of the plastic instability in strained amorphous solids.

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

Gravity-free hydraulic jumps and metal femtoliter cups.

Hydraulic jumps created by gravity are seen everyday in the kitchen sink. We show that at small scales a circular hydraulic jump can be created in the absence of gravity by surface tension. The theory is motivated by our experimental finding of a height discontinuity in spreading submicron molten metal droplets created by pulsed-laser ablation.