Quasi-static and Dynamic Behavior of Additively Manufactured Metallic Lattice Cylinders

Lattice structures have tailorable mechanical properties which allows them to exhibit superior mechanical properties (per unit weight) beyond what is achievable through natural materials. In this paper, quasi-static and dynamic behavior of additively manufactured stainless steel lattice cylinders is studied. Cylindrical samples with internal lattice structure are fabricated by a laser powder bed fusion system. Equivalent hollow cylindrical samples with the same length, outer diameter, and mass (larger wall thickness) are also fabricated. Split Hopkinson bar is used to study the behavior of the specimens under high strain rate loading. It is observed that lattice cylinders reduce the transmitted wave amplitude up to about 21% compared to their equivalent hollow cylinders. However, the lower transmitted wave energy in lattice cylinders comes at the expense of a greater reduction in their stiffness, when compared to their equivalent hollow cylinder. In addition, it is observed that increasing the loading rate by five orders of magnitude leads to up to about 36% increase in the peak force that the lattice cylinder can carry, which is attributed to strain rate hardening effect in the bulk stainless steel material. Finite element simulations of the specimens under dynamic loads are performed to study the effect of strain rate hardening, thermal softening, and the failure mode on dynamic behavior of the specimens. Numerical results are compared with experimental data and good qualitative agreement is observed.Comment: 20th Biennial Conference of the APS Topical Group on Shock Compression of Condensed Matte

Constraining the Minimum Mass of High-Redshift Galaxies and Their Contribution to the Ionization State of the IGM

We model the latest HST WFPC3/IR observations of > 100 galaxies at redshifts z=7-8 in terms of a hierarchical galaxy formation model with starburst activity. Our model provides a distribution of UV luminosities per dark matter halo of a given mass and a natural explanation for the fraction of halos hosting galaxies. The observed luminosity function is best fit with a minimum halo mass per galaxy of 10^{9.4+0.3-0.9} Msun, corresponding to a virial temperature of 10^{4.9+0.2-0.7} K. Extrapolating to faint, undetected galaxies, the total production rate of ionizing radiation depends critically on this minimum mass. Future measurements with JWST should determine whether the entire galaxy population can comfortably account for the UV background required to keep the intergalactic medium ionized.Comment: 9 pages, 6 figures, submitted to ApJ, comments welcom

Lower Bounds on Implementing Robust and Resilient Mediators

We consider games that have (k,t)-robust equilibria when played with a mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by coalitions of size up to k and deviations by up to $t$ players with unknown utilities. We prove lower bounds that match upper bounds on the ability to implement such mediators using cheap talk (that is, just allowing communication among the players). The bounds depend on (a) the relationship between k, t, and n, the total number of players in the system; (b) whether players know the exact utilities of other players; (c) whether there are broadcast channels or just point-to-point channels; (d) whether cryptography is available; and (e) whether the game has a $k+t)-punishment strategy; that is, a strategy that, if used by all but at most$k+t$ players, guarantees that every player gets a worse outcome than they do with the equilibrium strategy