Correlation kernels for sums and products of random matrices

Let $X$ be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared singular values of $GX$ and $TX$, where $G$ is a complex Ginibre matrix and $T$ is a truncated unitary matrix. We also consider the product of $X$ and several complex Ginibre/truncated unitary matrices. As an application, we derive the precise condition for the squared singular values of the product of several truncated unitary matrices to follow a polynomial ensemble. We also consider the sum $H + M$ where $H$ is a GUE matrix and $M$ is a random matrix whose eigenvalue density is a polynomial ensemble. We show that the eigenvalues of $H + M$ follow a polynomial ensemble whose correlation kernel can be expressed as a double contour integral. As an application, we point out a connection to the two-matrix model.Comment: 33 pages, some changes suggested by the referee is made and some references are adde

Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement

Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used the method of lines to discretize the SRHD equations spatially and a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third order convex essentially non-oscillatory (CENO) and third and fifth order weighted essentially non-oscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code {\sl enzo}. We discuss the coupling of the AMR framework with the relativistic solvers. Via various test problems, we emphasize the importance of resolution studies in relativistic flow simulations because extremely high resolution is required especially when shear flows are present in the problem. We also present the results of two 3d simulations of astrophysical jets: AGN jets and GRB jets. Resolution study of those two cases further highlights the need of high resolutions to calculate accurately relativistic flow problems.Comment: 14 pages, 23 figures. A section on 3D GRB jet simulation added. Accepted by ApJ

Metasurface Near-field Measurements with Incident Field Reconstruction using a Single Horn Antenna

A simple method of superimposing multiple near field scans using a single horn antenna in different configurations to characterize a planar electromagnetic metasurface is proposed and numerically demonstrated. It can be used to construct incident fields for which the metasurface is originally designed for, which may otherwise be difficult or not possible to achieve in practice. While this method involves additional effort by requiring multiple scans, it also provides flexibility for the incident field to be generated, simply by changing the objective of a numerical optimization which is used to find the required horn configurations for the different experiments. The proposed method is applicable to all linear time-invariant metasurfaces including space-time modulated structures.Comment: 7 pages, 4 figure

SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm

The evolution of antiferromagnetic susceptibility to uniaxial pressure in Ba(Fe{1-x}Co{x})2As2

Neutron diffraction measurements are presented measuring the responses of both magnetic and structural order parameters of parent and lightly Co-doped Ba(Fe{1-x}Co{x})2As2 under the application of uniaxial pressure. We find that the uniaxial pressure induces a thermal shift in the onset of antiferromagnetic order that grows as a percentage of T_N as Co-doping is increased and the superconducting phase is approached. Additionally, as uniaxial pressure is increased within parent and lightly-doped Ba(Fe{1-x}Co{x})2As2 on the first order side of the tricritical point, we observe a decoupling between the onsets of the orthorhombic structural distortion and antiferromagnetism. Our findings place needed constraints on models exploring the nematic susceptibility of the bilayer pnictides in the tetragonal, paramagnetic regime.Comment: 10 pages, 7 figure

Modeling sediment movement and channel response to rainfall variability after a major earthquake

© 2018 Elsevier B.V. The 2008 Wenchuan Ms 8.0 earthquake caused severe destruction in the mountainous areas of Sichuan Province, China. Landslips and mass movements led to substantial amounts of loose sediment accumulating in valleys that subsequently led to widespread riverbed aggradation. In addition to erosion and deposition hazards, this aggradation produced rivers in earthquake affected areas that were more susceptible to flash floods under extreme rainfall events. However, fluvial processes and sediment movement after a major earthquake, as well as the re-working of sediments in future events, are not well studied. In this paper, we investigate the response of sediment and river channel evolution due to different rainfall scenarios after the Wenchuan earthquake by using the CAESAR-Lisflood model. This is the first time that this landscape evolution model has been employed to explore material migration processes in a post-earthquake area, and to test its applicability to real landform changes in the studied catchment. The CAESAR-Lisflood model is well suited to simulate sediment movement, particularly the fluvial processes driven by severe rainfall after an earthquake. We calibrated the model parameters to the 2013 extreme rainfall event using high-resolution satellite images. Under rainfall scenarios of different intensity and frequency over a 10-yr period, landform evolution and sediment migration in the post-earthquake area were simulated. The results showed that the sediment yield could be significantly increased under enhanced and intensified rainfall scenarios compared to a normal rainfall scenario. These findings are of importance for the planning of post-earthquake rehabilitation and regional sustainable development, which considers risk prevention and mitigation

Multiple mechanisms determine ER network morphology during the cell cycle in Xenopus egg extracts

In metazoans the endoplasmic reticulum (ER) changes during the cell cycle, with the nuclear envelope (NE) disassembling and reassembling during mitosis and the peripheral ER undergoing extensive remodeling. Here we address how ER morphology is generated during the cell cycle using crude and fractionated Xenopus laevis egg extracts. We show that in interphase the ER is concentrated at the microtubule (MT)-organizing center by dynein and is spread by outward extension of ER tubules through their association with plus ends of growing MTs. Fusion of membranes into an ER network is dependent on the guanosine triphosphatase atlastin (ATL). NE assembly requires fusion by both ATL and ER-soluble N-ethyl-maleimide–sensitive factor adaptor protein receptors. In mitotic extracts, the ER converts into a network of sheets connected by ER tubules and loses most of its interactions with MTs. Together, these results indicate that fusion of ER membranes by ATL and interaction of ER with growing MT ends and dynein cooperate to generate distinct ER morphologies during the cell cycle