William Wang

We study how the rigidity transition in a triangular lattice changes as a function of anisotropy by preferentially filling bonds on the lattice in one direction. We discover that the onset of rigidity in anisotropic spring networks on a regular triangular lattice arises in at least two steps, reminiscent of the two-step melting transition in two dimensional crystals. In particular, our simulations demonstrate that the percolation of stress-supporting bonds happens at different critical volume fractions along different directions. By examining each independent component of the elasticity tensor, we determine universal exponents and develop universal scaling functions to analyze isotropic rigidity percolation as a multicritical point. Our crossover scaling approach is applicable to anisotropic biological materials (e.g. cellular cytoskeletons, extracellular networks of tissues like tendons), and extensions to this analysis are important for the strain stiffening of these materials.

A new configuration is proposed for spherical hohlraums on OMEGA in which seven laser entrance holes (LEHs) are used—five around the equator and one at each pole [Farmer et al., Phys. Plasmas 26, 032701 (2019)]. This is known as the PEPR (pentagonal prism) hohlraum. A new view-factor code LORE is used to model the PEPR hohlraum and compare its performance with tetrahedral hohlraums shot on OMEGA. With optimization of beam pointings, the PEPR hohlraum produces a nonuniformity ranging from 1.1\% (rms) at low albedos to 0.6\% at high albedos. The tradeoffs between hohlraum-to-capsule ratio, uniformity, and background radiation temperature have been explored, and it has been shown that larger LEH radii on the poles can result in a modest improvement in uniformity. The seven-hole PEPR hohlraum is well matched to the OMEGA symmetry and promises to provide insight into the performance of spherical hohlraums including octahedral (six-LEH) hohlraums.

Spherical hohlraums, including tetrahedral hohlraums shot on OMEGA and octahedral hohlraums (with six laser entrance holes on the faces of a cube) proposed by Lan et al. promise significant uniformity advantages compared with conventional cylindrical hohlraums. This work advocates a minor rearrangement of the port locations of the 48 quads proposed for irradiating octahedral hohlraums on the SG4 laser. This will enable symmetric direct-drive implosions to be carried out in the same target chamber with minimal adjustments of the beam pointings (no more than about 12 degrees, in contrast to 35 degrees in typical National Ignition Facility direct-drive designs). View-factor calculations for octahedral hohlraums find essentially the same excellent performance as in Ref. 2, with the capsule nonuniformity ranging from 0.6% (rms) at early times to <0.1% at later times.