Periodic solutions for a neutral delay predator-prey model with nonmonotonic functional response

By using a continuation theorem based on coincidence degree theory, some new sufficient conditions are obtained for the existence of positive periodic solutions of the following neutral delay predator-prey model with nonmonotonic functional response: \begin{equation*} \left\{\begin{array}{l} x'(t)=x(t)[r(t)-a(t)x(t-\sigma(t))-b(t)x'(t-\sigma(t))]-g(x(t))y(t),\\ y'(t)=y(t)[-d(t)+\mu(t)g(x(t-\tau(t))]. \end{array}\right. \end{equation*} Moreover, an example is employed to illustrate the main results

Comparison of Three Dimensional Selfdual Representations by Faltings-Serre Method

In this thesis, we prove that, a selfdual 3-dimensional Galois representation constructed by van Geemen and Top is isomorphic to a quadratic twist of the symmetric square of the Tate module of an elliptic curve. This is an application of our refinement of the Faltings-Serre method to 3-dimensional Galois representations with ground field not equal to Q. The proof makes use of the Faltings-Serre method, $\ell$-adic Lie algebra, and Burnside groups

Effect of 3D Roughness Patch on Instability Amplification in a Supersonic Boundary Layer

Surface roughness is known to have a substantial impact on the aerothermodynamic loading of high-speed vehicles, particularly via its influence on the laminar-turbulent transition process within the boundary layer. Numerical simulations are performed to investigate the effects of a distributed region of densely packed, sinusoidal shape roughness elements on a Mach 3.5 flat plate boundary layer for flow conditions corresponding to the planned conditions of an upcoming experiment in the Mach 3.5 Supersonic Low Disturbance Tunnel at the NASA Langley Research Center. Analysis of convective instabilities in the wake of the roughness patch was reported in a previous paper and the current work extends that analysis to instability amplification across the length of the roughness patch. Quasiparallel stability analysis of the modified boundary layer flow over the patch indicates two dominant families of unstable disturbances, namely, a group of high frequency modes that amplify in localized regions along the roughness patch and another group of low frequency modes that have smaller peak amplification rates but amplify steadily both above the roughness patch and in the wake region behind it. The results suggest that the amplification factors associated with the high-frequency modes are sufficiently low, at least for the roughness patches considered in this paper, so that these modes are unlikely to have a major influence on the transition process. The amplification of the low-frequency modes within the region of the roughness patch is further quantified via direct numerical simulations. Results confirm the strongly destabilizing influence of the roughness patch on the first mode instabilities, yielding an N-factor increment of N 3.6 for a roughness patch length of eight wavelengths

Identification and mechanical control of ferroelastic domain structure in rhombohedral CaMn7_7O12_{12}

We report on observation of ferroelastic domain structure in single crystals of multiferroic CaMn$_7$O$_{12}$ at room temperature. Two types of ferroelastic domain wall are found, consistent with the material's rhombohedral symmetry that is reduced from cubic symmetry at higher temperatures. Using Raman spectroscopy along with other measurements, we develop a systematic method to determine the microscopic domain orientation. Moreover, we find a switching behavior of the domains, which allows us to detwin the crystals conveniently at room temperature using a moderate uniaxial compression. Our result paves the way for further spectroscopic study and domain engineering in CaMn$_7$O$_{12}$.Comment: 7 pages, 4 figure