The Plane of the Kuiper Belt

We present a robust method for measuring the effective plane of the Kuiper belt. The derived plane has an inclination with respect to the ecliptic of 1º.86 and an ascending node of 81º.6, with a 1 σ error in pole position of the plane of 0º.37. The plane of the Kuiper belt is inconsistent with the invariable plane, the plane of Jupiter, and the plane of Neptune at the greater than 3 σ level. Using linear secular perturbation theory, we show that the plane of the Kuiper belt is expected to oscillate about the position of the invariable plane with a period of 1.9 million years and an amplitude of 1º.2. The present predicted position of the plane of the Kuiper belt has an inclination with respect to the ecliptic of 1º.74 and an ascending node of 86º.7, within 0º.20 of our measured position

Self-consistent size and velocity distributions of collisional cascades

The standard theoretical treatment of collisional cascades derives a steady-state size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently for the bodies' steady-state size and size-dependent velocity distributions. Specifically, we account for viscous stirring, dynamical friction, and collisional damping of the bodies' random velocities in addition to the mass conservation requirement typically applied to find the size distribution in a steady-state cascade. The resulting size distributions are significantly steeper than those derived without velocity evolution. For example, accounting self-consistently for the velocities can change the standard q=3.5 power-law index of the Dohnanyi (1969) differential size spectrum to an index as large as q=4. Similarly, for bodies held together by their own gravity, the corresponding power-law index range 2.88<q<3.14 of Pan & Sari (2005) can steepen to values as large as q=3.26. Our velocity results allow quantitative predictions of the bodies' scale heights as a function of size. Together with our predictions, observations of the scale heights for different sized bodies for the Kuiper belt, the asteroid belt, and extrasolar debris disks may constrain the mass and number of large bodies stirring the cascade as well as the colliding bodies' internal strengths.Comment: 23 pages, 3 figures, 1 table; submitted to Ap

The effect of electromechanical coupling on the strain in AlGaN/GaN heterojunction field effect transistors

The strain in AlGaN/GaN heterojunction field-effect transistors (HFETs) is examined theoretically in the context of the fully-coupled equation of state for piezoelectric materials. Using a simple analytical model, it is shown that, in the absence of a two-dimensional electron gas (2DEG), the out-of-plane strain obtained without electromechanical coupling is in error by about 30% for an Al fraction of 0.3. This result has consequences for the calculation of quantities that depend directly on the strain tensor. These quantities include the eigenstates and electrostatic potential in AlGaN/GaN heterostructures. It is shown that for an HFET, the electromechanical coupling is screened by the 2DEG. Results for the electromechanical model, including the 2DEG, indicate that the standard (decoupled) strain model is a reasonable approximation for HFET calculataions. The analytical results are supported by a self-consistent Schr\"odinger-Poisson calculation that includes the fully-coupled equation of state together with the charge-balance equation.Comment: 6 figures, revte

Rotational correlation and dynamic heterogeneity in a kinetically constrained lattice gas

We study dynamical heterogeneity and glassy dynamics in a kinetically constrained lattice gas model which has both translational and rotational degrees of freedom. We find that the rotational diffusion constant tracks the structural relaxation time as density is increased whereas the translational diffusion constant exhibits a strong decoupling. We investigate distributions of exchange and persistence times for both the rotational and translational degrees of freedom and compare our results on the distributions of rotational exchange times to recent single molecule studies.Comment: 7 pages, 5 figure

State-of-the-art and gaps for deep learning on limited training data in remote sensing

Deep learning usually requires big data, with respect to both volume and variety. However, most remote sensing applications only have limited training data, of which a small subset is labeled. Herein, we review three state-of-the-art approaches in deep learning to combat this challenge. The first topic is transfer learning, in which some aspects of one domain, e.g., features, are transferred to another domain. The next is unsupervised learning, e.g., autoencoders, which operate on unlabeled data. The last is generative adversarial networks, which can generate realistic looking data that can fool the likes of both a deep learning network and human. The aim of this article is to raise awareness of this dilemma, to direct the reader to existing work and to highlight current gaps that need solving.Comment: arXiv admin note: text overlap with arXiv:1709.0030

Frequency analysis via the method of moment functionals

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters

Search for surviving companions in type Ia supernova remnants

The nature of the progenitor systems of type~Ia supernovae is still unclear. One way to distinguish between the single-degenerate scenario and double-degenerate scenario for their progenitors is to search for the surviving companions. Using a technique that couples the results from multi-dimensional hydrodynamics simulations with calculations of the structure and evolution of main-sequence- and helium-rich surviving companions, the color and magnitude of main-sequence- and helium-rich surviving companions are predicted as functions of time. The surviving companion candidates in Galactic type~Ia supernova remnants and nearby extragalactic type~Ia supernova remnants are discussed. We find that the maximum detectable distance of main-sequence surviving companions (helium-rich surviving companions) is $0.6-4$~Mpc ($0.4-16$~Mpc), if the apparent magnitude limit is 27 in the absence of extinction, suggesting that the Large and Small Magellanic Clouds and the Andromeda Galaxy are excellent environments in which to search for surviving companions. However, only five Ia~SNRs have been searched for surviving companions, showing little support for the standard channels in the singe-degenerate scenario. To better understand the progenitors of type Ia supernovae, we encourage the search for surviving companions in other nearby type Ia supernova remnants.Comment: 25 pages, 5 figures, and 2 tables. Accepted for publication in Ap