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A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This presents challenges to studying the existence of solutions to the wave equation via conventional energy methods. In this work, we show that semi-global forward solutions to the wave equation do nonetheless exist, but only in a microlocal sense. The main ingredient in this existence theorem is a propagation of singularities theorem that relates energy entering the string to energy leaving the string. The propagation theorem is localized in the fibers of a certain fibration of the blown-up string, but global in time, which means that energy entering the string at one time may emerge previously., Comment: 58 pgs; Lemma 9.3 has been updated

This work demonstrates a large area process for atomically thin 2D semiconductors to unlock the technological upscale required for their commercial uptake. The new atomic layer deposition (ALD) and conversion technique yields large area performance uniformity and tunability. Like graphene, 2D Transition Metal Dichalcogenides (TMDCs) are prone to upscaling challenges limiting their commercial uptake. They are challenging to grow uniformly on large substrates and to transfer on alternative substrates while they often lack in large area electrical performance uniformity. The scalable ALD process of this work enables uniform growth of 2D TMDCs on large area with independent control of layer thickness, stoichiometry and crystallinity while allowing chemical free transfers to application substrates. Field effect transistors (FETs) fabricated on flexible substrates using the process present a field effect mobility of up to 55 cm^2/Vs, subthreshold slope down to 80 mV/dec and on/off ratios of 10^7. Additionally, non-volatile memory transistors using ferroelectric FETs (FeFETs) operating at +-5 V with on/off ratio of 107 and a memory window of 3.25 V are demonstrated. These FeFETs demonstrate state-of-the-art performance with multiple state switching, suitable for one-transistor non-volatile memory and for synaptic transistors revealing the applicability of the process to flexible neuromorphic applications., Comment: 16 pages, 9 figures

The switchable optical and electrical properties of phase change materials (PCMs) are finding new applications beyond data storage in reconfigurable photonic devices. However, high power heat pulses are needed to melt-quench the material from crystalline to amorphous. This is especially true in silicon photonics, where the high thermal conductivity of the waveguide material makes heating the PCM energy inefficient. Here, we improve the energy efficiency of the laser-induced phase transitions by inserting a layer of two-dimensional (2D) material, either MoS2 or WS2, between the silica or silicon and the PCM. The 2D material reduces the required laser power by at least 40% during the amorphization (RESET) process, depending on the substrate. Thermal simulations confirm that both MoS2 and WS2 2D layers act as a thermal barrier, which efficiently confines energy within the PCM layer. Remarkably, the thermal insulation effect of the 2D layer is equivalent to a ~100 nm layer of SiO2. The high thermal boundary resistance induced by the van der Waals (vdW)-bonded layers limits the thermal diffusion through the layer interfaces. Hence, 2D materials with stable vdW interfaces can be used to improve the thermal efficiency of PCM-tuned Si photonic devices. Furthermore, our waveguide simulations show that the 2D layer does not affect the propagating mode in the Si waveguide, thus this simple additional thin film produces a substantial energy efficiency improvement without degrading the optical performance of the waveguide. Our findings pave the way for energy-efficient laser-induced structural phase transitions in PCM-based reconfigurable photonic devices., Comment: 34 pages, 12 figures

A static rotating cosmic string metric is singular along a timelike line and fails to be globally hyperbolic; these features make it difficult to solve the wave equation by conventional energy methods. Working on a single angular mode at a time, we use microlocal methods to construct forward parametrices for wave and Klein--Gordon equations on such backgrounds., Comment: 15 pages; improvements to exposition in response to referee comments

We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O(\lvert x \rvert^{-\kappa}),$ $\kappa \in (1,\infty) \backslash \mathbb{N}.$ Given suitably smooth and decaying initial data, we show a wave locally enjoys the decay rate $O(t^{-\kappa-2+\epsilon})$., Comment: 36 pages; updated with clarifying exposition and fixed typos

The current work considers solutions to the wave equation on asymptotically flat, stationary, Lorentzian spacetimes in (1+3) dimensions. We investigate the relationship between the rate at which the geometry tends to flat and the pointwise decay rate of solutions. The case where the spacetime tends toward flat at a rate of $|x|^{-1}$ was studied in \cite{tat2013}, where a $t^{-3}$ pointwise decay rate was established. Here we extend the result to geometries tending toward flat at a rate of $|x|^{-\kappa}$ and establish a pointwise decay rate of $t^{-\kappa-2}$ for $\kappa \in \mathbb{N}$ with $\kappa \ge 2$. We assume a weak local energy decay estimate holds, which restricts the geodesic trapping allowed on the underlying geometry. We use the resolvent to connect the time Fourier Transform of a solution to the Cauchy data. Ultimately the rate of pointwise wave decay depends on the low frequency behavior of the resolvent, which is sensitive to the rate at which the background geometry tends to flat.

Three-dimensional complete photonic bandgap materials or photonic crystals block light propagation in all directions. The rod-connected diamond structure exhibits the largest photonic bandgap known to date and supports a complete bandgap for the lowest refractive index contrast ratio down to $n_{high}/n_{low} \sim 1.9$. We confirm this threshold by measuring a complete photonic bandgap in the infrared region in Sn--S--O $(n\sim1.9)$ and Ge--Sb--S--O $(n\sim2)$ inverse rod-connected diamond structures. The structures were fabricated using a low-temperature chemical vapor deposition process via a single-inversion technique. This provides a reliable fabrication technique of complete photonic bandgap materials and expands the library of backfilling materials, leading to a wide range of future photonic applications.

H\"ormander proved global existence of solutions for sufficiently small initial data for scalar wave equations in $(1+4)-$dimensions of the form $\Box u = Q(u, u', u'')$ where $Q$ vanishes to second order and $(\partial_u^2 Q)(0,0,0)=0$. Without the latter condition, only almost global existence may be guaranteed. The first author and Sogge considered the analog exterior to a star-shaped obstacle. Both results relied on writing the lowest order terms $u\partial_\alpha u = \frac{1}{2}\partial_\alpha u^2$ and as such do not immediately generalize to systems. The current study remedies such and extends both results to the case of multiple speed systems., Comment: 21 pages