No abstract

The coefficient of thermal expansion (CTE) of architected materials, as opposed to that of conventional solids, can be tuned to zero by intentionally altering the geometry of their structural layout. Existing material architectures, however, achieve CTE tunability only with a sacrifice in structural efficiency, i.e. a drop in both their stiffness to mass ratio and strength to mass ratio. In this work, we elucidate how to resolve the trade-off between CTE tunability and structural efficiency and present a lightweight bi-material architecture that not only is stiffer and stronger than other 3D architected materials, but also has a highly tunable CTE. Via a combination of physical experiments on 3D fabricated prototypes and numeric simulations, we demonstrate how two distinct mechanisms of thermal expansion appearing in a tetrahedron, can be exploited in an Octet lattice to generate a large range of CTE values, including negative, zero, or positive, with no loss in structural efficiency. The novelty and simplicity of the proposed design as well as the ease in fabrication, make this bi-material architecture well-suited for a wide range of applications, including satellite antennas, space optical systems, precision instruments, thermal actuators, and MEMS.

No abstract

No abstract

Abstract. We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the kth tensor powers of a positive line bundle L in a 1 √ kneighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential kϕ in a 1 √ k -neighborhood of a given point, the potential becomes an asymptotic perturbation of the Bargmann-Fock metric. We then prove that the Bergman kernel is also an asymptotic perturbation of the Bargmann-Fock Bergman kernel.

No abstract

We show that, for odd d, the L d+2 2 bounds of Sogge [10] and Xi [13] for the Nikodym maximal function over manifolds of constant sectional curvature, are unstable with respect to metric perturbation, in the spirit of the work of Sogge and Minicozzi [7]. A direct consequence is the instability of the bounds for the corresponding oscillatory integral operator. Furthermore, we extend our construction to show that the same phenomenon appears for any d-dimensional Riemannian manifold with a local totally geodesic submanifold of dimension ⌈ d+1 2 ⌉ if d ≥ 3. In contrast, Sogge's L 7 3 bound for the Nikodym maximal function on 3-dimensional variably curved manifolds is stable with respect to metric perturbation.

This paper presents thermally actuated hierarchical metamaterials with large linear and rotational motion made of passive solids. Their working principle relies on the definition of a triangular bi-material unit that uses temperature changes to locally generate in its internal members distinct rates of expansion that translate into anisotropic motions at the unit level and large deployment at the global scale. Obtained from solid mechanics theory, thermal experiments on fabricated proof-of-concepts and numerical analysis, the results show that introducing recursive patterns of just two orders of the hierarchy is highly effective in amplifying linear actuation at levels of nearly nine times the initial height, and rotational actuation of almost 18.5 times the initial skew angle.