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We employ polarization tomography to characterize the modal properties of a dielectric nanocavity with sub-wavelength mode confinement. Our analysis of reflection spectra shows that the Fano-lineshape depends strongly on the polarization in a confocal configuration, and that the lineshape can be transformed into a Lorentzian-like peak for a certain polarization. For this polarization setting, the background is almost fully suppressed in a finite range of frequencies. This enables us to identify another resonance that has not yet been experimentally reported for these nanocavities. Lastly, we use symmetry-forbidden polarizations and show that, surprisingly, the modal resonance features of the system remain visible.

We propose a fully Bayesian approach to wideband, or broadband, direction-of-arrival (DoA) estimation and signal detection. Unlike previous works in wideband DoA estimation and detection, where the signals were modeled in the time-frequency domain, we directly model the time-domain representation and treat the non-causal part of the source signal as latent variables. Furthermore, our Bayesian model allows for closed-form marginalization of the latent source signals by leveraging conjugacy. To further speed up computation, we exploit the sparse ``stripe matrix structure'' of the considered system, which stems from the circulant matrix representation of linear time-invariant (LTI) systems. This drastically reduces the time complexity of computing the likelihood from $\mathcal{O}(N^3 k^3)$ to $\mathcal{O}(N k^3)$, where $N$ is the number of samples received by the array and $k$ is the number of sources. These computational improvements allow for efficient posterior inference through reversible jump Markov chain Monte Carlo (RJMCMC). We use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than the conventional reversible variant. Detection, estimation, and reconstruction of the latent source signals can then all be performed in a fully Bayesian manner through the samples drawn using NRJMCMC. We evaluate the detection performance of the procedure by comparing against generalized likelihood ratio testing (GLRT) and information criteria.

The remedian uses a $k\times b$ matrix to approximate the median of $n\leq b^{k}$ streaming input values by recursively replacing buffers of $b$ values with their medians, thereby ignoring its $200(\lceil b/2\rceil / b)^{k}%$ most extreme inputs. Rousseeuw & Bassett (1990) and Chao & Lin (1993); Chen & Chen (2005) study the remedian's distribution as $k\rightarrow\infty$ and as $k,b\rightarrow\infty$. The remedian's breakdown point vanishes as $k\rightarrow\infty$, but approaches $(1/2)^{k}$ as $b\rightarrow\infty$. We study the remedian's robust-regime distribution as $b\rightarrow\infty$, deriving a normal distribution for standardized (mean, median, remedian, remedian rank) as $b\rightarrow\infty$, thereby illuminating the remedian's accuracy in approximating the sample median. We derive the asymptotic efficiency of the remedian relative to the mean and the median. Finally, we discuss the estimation of more than one quantile at once, proposing an asymptotic distribution for the random vector that results when we apply remedian estimation in parallel to the components of i.i.d. random vectors., Comment: 34 pages, 3 figures, 3 tables, 2 algorithms

Motivated by the testing condition for Radon-Brascamp-Lieb multilinear functionals established in arXiv:2201.12201, this paper is concerned with identifying local conditions on smooth maps $u(t)$ with values in the space of decomposable p-forms on some real vector space V which guarantee uniform integrability of $||u(t)||^{-\tau}$ over a certain natural, noncompact family of norms. One can loosely regard this problem as a higher-dimensional analogue of establishing uniform bounds for the size of a sublevel set of a function in terms of the size of its derivatives. The resulting theorem relies extensively on ideas from Geometric Invariant Theory to understand what appropriate derivative bounds look like in this context. Several examples and applications are presented, including a new local characterization of so-called "model" Radon-like transforms in terms of the semistability of a natural curvature functional (giving an equivalent but rather different criterion than the one first established in arXiv:2303.03325)., Comment: 66 pages

Modern physics experiments rely on precise timing provided by programmable digital pulse generators. In many experimental control systems, this role is filled by custom devices built on Field Programmable Gate Arrays (FPGAs). While highly flexible and performant, these systems can be difficult to scale to very large systems due to cost and complexity. Recent advances in microcontroller systems allows these much simpler systems to fill the role of digital pulse generators. Here we demonstrate one such alternative based on the Raspberry Pi Pico microcontroller which allows for timing resolution down to 7.5 ns with a minimum pulse width of of 37.5 ns., Comment: 9 pages, 5 figures

Experiments were performed to study how rocket exhaust blows soil in lunar and Martian conditions. Jets of gas were blown downwardly at various granular materials while a camera recorded the formation of scour holes as the material was removed. The experiments were performed in a series of conditions ranging from ambient 101 kPa pressure down to 0.3 kPa. This includes the range that is relevant for lunar conditions, because it is not hard vacuum inside the rocket exhaust where soil is being eroded. Prior work in ambient conditions showed that erosion rate is proportional to the square of the densimetric Froude number. However, the prior work was not performed at low pressures. In the new work, preliminary results show that as the gas density is so low that gas flow around the sand grains is no longer in the continuum regime, then erosion rate is faster than predicted by the earlier results. The dependency of erosion rate on various parameters is determined, but it turns out to be more complex than expected so additional experimental work will be required to develop complete scaling relationships., Comment: 9 pages, 7 figures. ASCE Earth & Space 2016 conference

Exponential histograms, with bins of the form $\left\{ \left(\rho^{k-1},\rho^{k}\right]\right\} _{k\in\mathbb{Z}}$, for $\rho>1$, straightforwardly summarize the quantiles of streaming data sets (Masson et al. 2019). While they guarantee the relative accuracy of their estimates, they appear to use only $\log n$ values to summarize $n$ inputs. We study four aspects of exponential histograms -- size, accuracy, occupancy, and largest gap size -- when inputs are i.i.d. $\mathrm{Exp}\left(\lambda\right)$ or i.i.d. $\mathrm{Pareto}\left(\nu,\beta\right)$, taking $\mathrm{Exp}\left(\lambda\right)$ (or, $\mathrm{Pareto}\left(\nu,\beta\right)$) to represent all light- (or, heavy-) tailed distributions. We show that, in these settings, size grows like $\log n$ and takes on a Gumbel distribution as $n$ grows large. We bound the missing mass to the right of the histogram and the mass of its final bin and show that occupancy grows apace with size. Finally, we approximate the size of the largest number of consecutive, empty bins. Our study gives a deeper and broader view of this low-memory approach to quantile estimation., Comment: 43 pages, 8 figures, 4 tables

Say we have a collection of independent random variables $X_0, ... , X_n$, where $X_0 \sim \mathcal{N}(\mu_0, \sigma_0^2)$, but $X_i \sim \mathcal{N}(\mu, \sigma^2)$, for $1 \leq i \leq n$. We characterize the distribution of $R_0 := 1 + \sum_{i=1}^{n} \mathbf{1}\{X_i \leq X_0\}$, the rank of the random variable whose distribution potentially differs from that of the others -- the odd normal out. We show that $R_0 - 1$ is approximately beta-binomial, an approximation that becomes equality as $\sigma/\sigma_0$ or $(\mu-\mu_0)/\sigma_0$ become large or small. The intra-class correlation of the approximating beta-binomial depends on $\Pr(X_1 \leq X_0)$ and $\Pr(X_1 \leq X_0, X_2 \leq X_0)$. Our approach relies on the conjugacy of the beta distribution for the binomial: $\Phi((X_0-\mu)/\sigma)$ is approximately $\mathrm{Beta}(\alpha(\sigma/\sigma_0, (\mu-\mu_0)/\sigma_0), \beta(\sigma/\sigma_0, (\mu-\mu_0)/\sigma_0))$ for functions $\alpha, \beta > 0$. We study the distributions of the in-normal ranks. Throughout, simulations corroborate the formulae we derive., Comment: 81 pages, 14 figures

We present a comprehensive investigation of the light-matter interaction dynamics in two-dimensional materials coupled with a spectrally isolated cavity mode in the strong coupling regime. The interaction between light and matter breaks the translational symmetry of excitons in the two-dimensional lattice and results in the emergence of a localized polariton state. Employing a novel approach involving transformation to exciton reaction coordinates, we derive a Markovian master equation to describe the formation of a macroscopic population in the localized polariton state. Our study shows that the construction of a large-scale polariton population is affected by correction terms addressing the breakdown of translational symmetry. Increasing the spatial width of the cavity mode increases the Coulomb scattering rates while the correction terms saturate and affect the system's dynamics progressively less. Tuning the lattice temperature can induce bistability and hysteresis with different origins than those recognized for quantum wells in larger microcavities. We identify a limit temperature $T_{\mathrm{l}}$ as a key factor for stimulated emissions and forming a macroscopic population, enriching our understanding of strong coupling dynamics in systems with extreme confinement., Comment: 15 pages, 15 figures

The starting point for much of multivariate analysis (MVA) is an $n\times p$ data matrix whose $n$ rows represent observations and whose $p$ columns represent variables. Some multivariate data sets, however, may be best conceptualized not as $n$ discrete $p$-variate observations, but as $p$ curves or functions defined on a common time interval. Here we introduce a framework for extending techniques of multivariate analysis to such settings. The proposed continuous-time multivariate analysis (CTMVA) framework rests on the assumption that the curves can be represented as linear combinations of basis functions such as $B$-splines, as in the Ramsay-Silverman representation of functional data; but whereas functional data analysis extends MVA to the case of observations that are curves rather than vectors -- heuristically, $n\times p$ data with $p$ infinite -- we are instead concerned with what happens when $n$ is infinite. We present continuous-time extensions of the classical MVA methods of covariance and correlation estimation, principal component analysis, Fisher's linear discriminant analysis, and $k$-means clustering. We show that CTMVA can improve on the performance of classical MVA, in particular for correlation estimation and clustering, and can be applied in some settings where classical MVA cannot, including variables observed at disparate time points. CTMVA is illustrated with a novel perspective on a well-known Canadian weather data set, and with applications to data sets involving international development, brain signals, and air quality. The proposed methods are implemented in the publicly available R package \texttt{ctmva}.

Tools have been developed to model and simulate the effects of lunar landing vehicles on the lunar environment, mostly addressing the effects of regolith erosion by rocket plumes and the fate of the ejected lunar soil particles. The KSC Granular Mechanics and Regolith Operations Lab tools have now been expanded to address volatile contamination of the lunar surface (Stern, 1999). Landing nearby such a crater will result in the migration of significant exhaust plume gas into the cold trap of the crater, and will also create an unnatural atmosphere over the volatile reservoirs that are to be studied. Our calculations address: 1) the time for the plume-induced local atmosphere above cold traps to decay to normal levels, 2) the efficiency of gas migration into a permanently shadowed crater when the landing is outside it but nearby, and 3) reduction on contamination afforded by moving the landing site further from the crater or by topographically shielding the crater from the direct flux of a lander's ground jet. We also address plume volatiles adsorbed onto and driven inside soil ejecta particles from their residence in the high pressure stagnation region of the engine exhaust plume, and how their mechanical dispersal across the lunar surface contributes to the induced atmosphere. One additional question is whether the collection of soil ejecta along the base of a topographic feature will produce a measurable plume volatile release distinct from the background. We mostly address item 2). Item 3) is obvious from our results excepting that the removal distances may be large, but changes to landing strategy can improve the situation., Comment: 13 pages, 18 figures. Presented at Earth & Space 2014 conference

A physics-based computer model has been developed to support the development of volatile extraction from regolith of the Moon and asteroids. The model is based upon empirical data sets for extraterrestrial soils and simulants, including thermal conductivity of regolith and mixed composition ice, heat capacity of soil and mixed composition ice, hydrated mineral volatile release patterns, and sublimation of ice. A new thermal conductivity relationship is derived that generalizes cases of regolith with varying temperature, soil porosity, and pore vapor pressure. Ice composition is based upon measurements of icy ejecta from the Lunar CRater Observation and Sensing Satellite (LCROSS) impact and it is shown that thermal conductivity and heat capacity equations for water ice provide adequate accuracy at the present level of development. The heat diffusion equations are integrated with gas diffusion equations using multiple adaptive timesteps. The entire model is placed into a Crank-Nicholson framework where the finite difference formalism was extended to two dimensions in axisymmetry. The one-dimensional version of the model successfully predicts heat transfer that matches lunar and asteroid data sets. The axisymmetric model has been used to study heat dissipation around lunar drills and water extraction in asteroid coring devices., Comment: 50 pages, 23 figures

The first asteroid simulants workshop was held in late 2015. These materials are needed for tests of technologies and mission operational concepts, for training astronauts , for medical studies, and a variety of other purposes. The new program is based on lessons learned from the earlier lunar simulants program. It aims to deliver families of simulants for major spectral classes of asteroids both in cobble and regolith form, beginning with one type of carbonaceous chondrite and rapidly expanding to provide four to six more asteroid classes. These simulants will replicate a selected list of asteroid properties, but not all known properties, in order to serve the greatest number of users at an affordable price. They will be benchmarked by a variety of data sets including laboratory analysis of meteorites, observation of bolides, remote sensing of asteroids, data from asteroid missions, and scientific modeling. A variety of laboratory tests will verify the as-manufactured simulants are accurately and repeatedly providing the specified characteristics., Comment: 13 pages, no figures. Presented at Earth & Space 2016 conference

We have studied several field geotechnical test instruments for their applicability to lunar soil simulants and analog soils. Their performance was evaluated in a series of tests in lunar simulants JSC-1A, NU-LHT-2M, and CHENOBI each prepared in carefully controlled states of compaction through vibration on a shake table with overburden. In general, none of the instruments is adequate for a low-cohesion, frictional soil, but we find that a modified version of a shear vane tester allows us to extract several of the important soil parameters. This modified instrument may be useful for use on the lunar surface by astronauts or a robotic lander. We have also found that JSC-1A does not behave mechanically like the other lunar soil simulants, probably because its particle shapes are more rounded. Furthermore we have studied a soil material, BP-1, identified as very lunar-like at a lunar analog location. We find this material has a natural particle size distribution similar to that of lunar soil and arguably better than JSC-1A. We find that BP-1 behaves very similarly to the high fidelity lunar simulants NU-LHT-2M and CHENOBI., Comment: 15 pages, 14 figures. Presented at Earth & Space 2010 conference

The physical state of the lunar soil in the permanently shadowed craters of the moon is inferred from experimental investigation. The permanently shadowed craters do not undergo the same thermal cycling experienced by other parts of the moon and therefore could be slightly less compacted. This study is significant because excavating, roving, and landing interactions, along with the energy budgets and deployment schedules for associated technology, need to be scaled and designed properly. Results indicate that the degree of compaction due to thermal cycling is a function of the depth in the soil column., Comment: 6 pages, 3 figures. Presented at Earth & Space 2010 conference

A mathematical model and software implementation developed to predict trajectories of single lunar dust particles acted on by a high velocity gas flow is discussed. The model uses output from a computation fluid dynamics (CFD) or direct simulation Monte Carlo (DSMC) simulation of a rocket nozzle hot gas jet. The gas density, velocity vector field, and temperature predicted by the CFD/DSMC simulations, provide the data necessary to compute the forces and accelerations acting on a single particle of regolith. All calculations of trajectory assume that the duration of particle flight is much shorter than the change in gas properties, i.e., the particle trajectory calculations take into account the spatial variation of the gas jet, but not the temporal variation. This is a reasonable first-order assumption. Final results are compared to photogrammetry derived estimates of dust angles form Apollo landing videos., Comment: 9 pages, 9 figures. Presented at Earth & Space 2008 conference

This manuscript analyzes lunar lander soil erosion models and trajectory models to calculate how much damage will occur to spacecraft orbiting in the vicinity of the Moon. The soil erosion models have considerable uncertainty due to gaps in our understanding of the basic physics. The results for ~40 t landers show that the Lunar Orbital Gateway will be impacted by 1000s to 10,000s of particles per square meter but the particle sizes are very small and the impact velocity is low so the damage will be slight. However, a spacecraft in Low Lunar Orbit that happens to pass through the ejecta sheet will sustain extensive damage with hundreds of millions of impacts per square meter: although they are small, they are in the hypervelocity regime, and exposed glass on the spacecraft will sustain spallation over 4% of its surface., Comment: 10 pagers, 8 figures

We present a practical cell-centred volume-of-fluid method developed within a pure Eulerian setting for the simulation of compressible solid-fluid problems. The method builds on a previously published diffuse-interface Godunov-type scheme through the addition of a specialised mixed-cell update that is capable of maintaining sharp interfaces indefinitely. The mixed-cell update is local and may be viewed as an interface-sharpening extension to the underlying diffuse-interface scheme along the lines of other techniques such as Tangent of Hyperbola INterface Capturing (THINC), and hence the method can be straightforwardly extended to include other coupled physics. We validate the method on a range of challenging test problems including a collapsing metal shell, cylinder impacts and the three-dimensional simulation of a buried explosive charge. Finally we demonstrate the robustness of the method, and its use in a multi-physics context, by modelling the BRL 105mm unconfined shaped charge with reactive high-explosive burn and rate-sensitive plasticity., Comment: 34 pages, 15 figures, submitted to Journal of Computational Physics

This paper gives a complete geometric characterization in all dimensions and codimensions of those Radon-like transforms which, up to endpoints, satisfy the largest possible range of local $L^p \rightarrow L^q$ inequalities permitted by quadratic-type scaling. The necessary and sufficient curvature-type criterion is phrased in terms of an associated Newton-like diagram. In the case of averages over families of polynomial graphs, the curvature condition implies sharp endpoint estimates as well. The proof relies on the recently-developed multilinear Radon-Brascamp-Lieb testing criterion and a refined version of differential inequalities for polynomials first appearing in work on the Oberlin affine curvature condition., Comment: 58 pages

We provide a simple criterion on a family of functions that implies a square function estimate on $L^p$ for every even integer $p \geq 2$. This defines a new type of superorthogonality that is verified by checking a less restrictive criterion than any other type of superorthogonality that is currently known., Comment: 12 pages

This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of simulating a broad range of different multi-physics applications, including multi-material interaction, damage and void opening. The work at hand extends this method with a technique to model realistic material inhomogeneities, and examines the performance of the method on a selection of challenging problems. Material inhomogeneities are included by evolving a scalar field that perturbs a material's plastic yield stress. This perturbation results in non-uniform fragments with a measurable statistical distribution, allowing for underlying defects in a material to be modelled. As the underlying numerical scheme is three dimensional, parallelisable and multi-physics-capable, the scheme can be tested on a range of strenuous problems. These problems especially include a three-dimensional explosively driven fracture study, with an explicitly resolved condensed phase explosive. The new scheme compares well with both experiment and previous numerical studies.