Disorder-induced zero-energy spectral singularity for random matrices with correlations

A zero-energy mid-band singularity has been found in the energy spectrum of random matrices with correlations between diagonal and off-diagonal elements typical of vibrational problems. Two representative classes of matrices, characterizing the instantaneous configurations in liquids and mechanically unstable lattices (which mimic the former) have been analysed. At least for disordered lattice models, the singularity is universal and its origin can be explained within the mean-field treatment.Comment: 4 pages, 3 figures. to appear in Phys. Rev.

Solutions of Backward Stochastic Differential Equations on Markov Chains

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We do not require the generating functions to be monotonic, instead using only an appropriate Lipschitz continuity condition.Comment: To appear in Communications on Stochastic Analysis, August 200

Many-body localization and mobility edge in a disordered Heisenberg spin ladder

We examine the interplay of interaction and disorder for a Heisenberg spin ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the quantum phase transition at a critical random field strength $h_c \sim 8.5\pm 0.5$, where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuation of the bipartite magnetization show distinct probability distributions which characterize different quantum phases. Furthermore, we show that for weaker $h$, energy eigenstates with higher energy density are delocalized while states at lower energy density are localized. This defines a mobility edge and a mobility gap separating these two phases. By following the evolution of low energy eigenstates, we observe that the mobility gap grows with increasing the random field strength, which drives the system to the phase of the full many-body localization with increasing disorder strength.Comment: 6 pages, 4 figure

Aphidophagous Coccinellids in Alfalfa, Small Grains, and Maize in Eastern South Dakota

In a 13-year study of aphidophagous coccinellids associated with alfalfa (Medicago sativa), maize (Zea mays), and small grain crops in eastern South Dakota, the following species were consistently associated with the crops: Hippodamia convergens, H. tredecimpunctata tibialis, H. parenthesis, Coleomegilla maculata lengi, Coccinella transversoguttata richardsoni, Cycloneda munda, and Adalia bipunctata. All species except A. bipunctata were associated with each of the three crops, while A. bipunctata occurred only in maize. Relative abundances of each species varied among crops and among years. Although only seven species were associated with the crops, additional species were captured on sticky traps stationed adjacent to sampled fields. The species diversity of immature coccinellids did not differ among crops but did differ among years. The diversity of adults differed among crops and years. The site from which samples were taken had no influence on the diversity of immatures or adults. Species relative abundances in alfalfa and small grains were more similar to each other than they were to relative abundances in maize

Filters and smoothers for self-exciting Markov modulated counting processes

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework

Rotor performance characteristics from an aeroacoustic helicopter wind-tunnel test program

An investigation of helicopter rotor noise at model scale was conducted in the Langley 4 by 7 meter tunnel. The program described was the first of a planned three-phase project whose purpose was to examine the characteristic noise mechanism involved in main rotor/tail rotor interaction noise. This first phase was conducted with a main rotor only, in order to identify the characteristic noise generated by only the main rotor. The aerodynamic operating conditions of the rotor system were defined during the test. The acoustic data were properly referenced