Search

While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework that reveals the topological origins of truncation resonances, elucidating formally the conditions that influence their existence and properties. Elastic beams with sinusoidal and step-wise property modulations are considered as classical examples of periodic structures. Their non-trivial topological characteristics stem from the consideration of a phason parameter that produces spatial shifts of the property modulation while continuously varying how the boundaries are truncated. In this context, non-trivial band gaps are characterized by an integer topological invariant, the Chern number, which is equal to the number of truncation resonances that traverse a band gap as the phason is varied. We highlight the existence of multiple chiral edge states that may be localized at opposite boundaries, and illustrate how these can be independently tuned by modified boundary-specific phason parameters. Furthermore, we show that the frequency location of a truncation resonance is influenced by the modulation volume fraction, boundary conditions, and number of cells comprising the finite structure, thus quantifying its robustness to these factors. Non-topological in-gap resonances induced by a defect are also demonstrated, showing that these can be coupled with topological modes when the defect is located at an edge. Finally, experimental investigations on bi-material phononic-crystal beams are conducted to support these findings. The tunability of truncation resonances by material-property modulation may be exploited in applications ranging from vibration attenuation and thermal conductivity reduction to filtering and flow control by phononic subsurfaces.

Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in good faith, however rarely is consideration given to whether a systemic failure has occurred. Taking this into account can cause certainty in a hypothesis to decrease as the evidence for it becomes apparently stronger. We perform a probabilistic Bayesian analysis of this effect with examples based on (i) archaeological evidence, (ii) weighing of legal evidence, and (iii) cryptographic primality testing. We find that even with surprisingly low systemic failure rates high confidence is very difficult to achieve and in particular we find that certain analyses of cryptographically-important numerical tests are highly optimistic, underestimating their false-negative rate by as much as a factor of $2^{80}$.

We present the concept of a locally resonant nanophononic metamaterial for thermoelectric energy conversion. Our configuration, which is based on a silicon thin-film with a periodic array of pillars erected on one or two of the free surfaces, qualitatively alters the base thin-film phonon spectrum due to a hybridization mechanism between the pillar local resonances and the underlying atomic lattice dispersion. Using an experimentally-fitted lattice-dynamics-based model, we conservatively predict a drop in the metamaterial thermal conductivity to as low as 50% of the corresponding uniform thin-film value despite the fact that the pillars add more phonon modes to the spectrum.

There is a limited amount of hypervelocity impact (HVI) data on pressurized composite overwrapped pressure vessels (COPV). In recent years, NASA has performed HVI tests to characterize impact conditions resulting in either leak or burst of the COPVs representative of spacecraft hardware. This paper reports on the results of 40 tests that have been conducted on several types of COPV configurations, pressurized by inert gas to near the vessels rated maximum expected operating pressure (MEOP). These tests were used to better understand COPV response under HVI conditions and develop ballistic limit equations (BLE) related to these tests.

Additive Construction is the process of building infrastructure such as habitats, garages, roads, berms, etcetera layer by layer (3D printing). The National Aeronautics and Space Administration (NASA) and the United States Army Corps of Engineers (USACE) are pursuing additive construction to build structures using resources available in-situ. Using materials available in-situ reduces the cost of planetary missions and operations in theater. The NASA team is investigating multiple binders that can be produced on planetary surfaces, including the magnesium oxide-based Sorel cement; the components required to make Ordinary Portland Cement (OPC), the common cement used on Earth, have been found on Mars. The availability of OPC-based concrete on Earth drove the USACE to pursue additive construction for base housing and barriers for military operations. Planetary and military base structures must be capable of resisting micrometeoroid impacts with velocities ranging from 11 to 72km/s for particle sizes 200 micrometers or more (depending on protection requirements) as well as bullets and shrapnel with a velocity of 1.036km/s with projectiles 5.66mm diameter and 57.40mm in length, respectively.