Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on P that avoid the pattern p is denoted A v _P (p). We extend a proof of Simion and Schmidt to show that A v _P (132)=A v _P (123) for any poset P, and we exactly classify the posets for which equality holds.     

Simplicity of lie module triple systems

We analyze how certain constructions of Lie module triple systems affect the structure theory, particularly simplicity. We are thus able to show that there is no upper bound on the number of summands in a direct sum decomposition of a simple Lie module triple system as a module for its inner derivation algebra.     

Inelastic phonon interactions at solid–graphite interfaces

The presented model predicts thermal boundary conductance at interfaces where one material comprising the junction is characterized by high elastic anisotropy. In contrast to previous approaches, the current methodology accounts for contributions from inelastic scattering through consideration of multiple-phonon interactions. Inelastic contributions become significant as the temperature, as well as the degree of acoustic mismatch between the materials, increases. Inclusion of the inelastic interactions is necessary for a variety of interfacial systems including the metal–graphite boundary examined here. Improvement is shown over existing approaches that address only elastic scattering as both three- and four-phonon interactions significantly augment the transport.     

Demonstration of the frequency upshifting of microwave radiation byrapid plasma creation

A technique for frequency-upshifting electromagnetic radiation is demonstrated. By ionizing azulene vapor contained in a resonant cavity using a laser pulse, the frequency of the incident RF wave at 33.3 GHz is upshifted by 5% with greater than 10% efficiency. Maximum frequency upshift of 2.3 times the source frequency is observed. There are two mechanisms thought to be operative in producing the observed frequency upshift: the time-dependent dielectric constant due to increasing plasma density, and rapid Q-switching of the cavity. This technique has the potential of being able to generate tunable and chirped radiation over a very broad (Δf/f≳1) frequency range     

Design,Synthesis, and Application of a Water-soluble Photocage for Aqueous Cyclopentadiene-based Diels-Alder Photoclick Chemistry in Hydrogels

Spatiotemporally functionalized hydrogels have exciting applications in tissue engineering, but their preparation often relies on radical-based strategies that can be deleterious in biological settings. Herein, the computationally guided design, synthesis, and application of a water-soluble cyclopentadienone-norbornadiene (CPD-NBD) adduct is disclosed as a diene photocage for radical-free Diels-Alder photopatterning. We show that this scalable CPD-NBD derivative is readily incorporated into hydrogel formulations, providing gels that can be patterned with dienophiles upon 365 nm uncaging of cyclopentadiene. Patterning is first visualized through conjugation of cyanine dyes, then biological utility is highlighted by patterning peptides to direct cellular adhesion. Finally, the ease of use and versatility of this CPD-NBD derivative is demonstrated by direct incorporation into a commercial 3D printing resin to enable the photopatterning of structurally complex, printed hydrogels.     

Harnessing Plasticity in an Amine-Borane as a Piezoelectric and Pyroelectric Flexible Film

We demonstrate that trimethylamine borane can exhibit desirable piezoelectric and pyroelectric properties. The material was shown to be able operate as a flexible film for both thermal sensing, thermal energy conversion and mechanical sensing with high open circuit voltages (>10 V). A piezoelectric coefficient of d₃₃≈10–16 pC N⁻¹, and pyroelectric coefficient of p≈25.8 μC m⁻² K⁻¹ were achieved after poling, with high pyroelectric figure of merits for sensing and harvesting, along with a relative permittivity of 6.3.     

Harnessing Plasticity in an Amine‐Borane as a Piezoelectric and Pyroelectric Flexible Film

We demonstrate that trimethylamine borane can exhibit desirable piezoelectric and pyroelectric properties. The material was shown to be able operate as a flexible film for both thermal sensing, thermal energy conversion and mechanical sensing with high open circuit voltages (>10 V). A piezoelectric coefficient of d₃₃≈10–16 pC N^?1, and pyroelectric coefficient of p≈25.8 μC m^?2 K^?1 were achieved after poling, with high pyroelectric figure of merits for sensing and harvesting, along with a relative permittivity of 6.3.