The realization of input-output maps using bialgebras

The theory of bialgebras is used to prove a state space realization theorem for input/output maps of dynamical systems. This approach allows for the consideration of the classical results of Fliess and more recent results on realizations involving families of trees. Two examples of applications of the theorum are given

Analytic solutions of the Rolie Poly model in time-dependent shear

We consider shear flows that comprise of step changes in the shear rate. For these flows, we derive analytic solutions of the Rolie-Poly constitutive equation. Our method involves piecing together solutions for constant rate shear in a variety of flow rate regimes. We obtain solutions for interrupted shear, recoverable strain and non-linear relaxation following cessation of flow. Whenever strong flow is present we neglect reptation, as other mechanisms dominate and for interrupted shear our solution is approximate as we neglect convective constraint release. Our analytic solutions provide new insight in several ways. These include revealing the mechanism of some experimental features of these flows; suggesting a method to extract the polymer contribution to the normal stress in the velocity gradient direction (σyy) from shear stress measurements alone; and a method to isolate the influence of convective constraint release (CCR) from damping function measurements. We also run complementary GLaMM model calculations to verify that insight from our analytic approach translates to this more detailed model

Discrimination History, Backlash Fear, and Ethnic Identity Among Arab Americans: Post-9/11 Snapshots

The authors examined discrimination history, backlash fear, and ethnic identity of Arab Americans nationally at 3 times, beginning shortly after September 11, 2001. Relations between variables were moderate, and discrimination history and backlash fear were statistically significant predictors of ethnic identity. Implications for acculturation and ethnic identity are discussed. Los autores examinaron la historia de la discriminación, el miedo a las reacciones violentas, y la identidad étnica de individuos Americanos de origen Árabe a nivel nacional en 3 momentos distintos, comenzando poco tiempo después del 11 de Septiembre de 2001. Las relaciones entre las variables fueron moderadas, y la historia de la discriminación y el miedo a las reacciones violentas pronosticaron con una fiabilidad estadísticamente significativa el nivel de identidad étnica. Se discuten las implicaciones para la aculturación y la identidad étnica

The Accidental Tide Gauge: A GPS Reflection Case Study from Kachemak Bay, Alaska

For the last decade, it has been known that reflected GPS signals observed with specialized instruments could be used to measure sea level. In this letter, data from an existing geodeticquality GPS site near Kachemak Bay, Alaska, are analyzed for a one-year time period. Daily sea-level variations are more than 7 m. Tidal coefficients have been estimated and compared with coefficients estimated from records from a traditional tide gauge at Seldovia Harbor, approximately 30 km away. The GPS and Seldovia estimates of M(sub 2) and S(sub 2) coefficients agree to better than 2%; much of this residual can be attributed to true differences in the tide over 30 km as it propagates up Kachemak Bay. For daily mean sea levels the agreement is 2.3 cm. Because a standard geodetic GPS receiver/antenna is used, this GPS instrument can measure long-term sea-level changes in a stable terrestrial reference frame

On the Hydrodynamic Interaction of Shock Waves with Interstellar Clouds. II. The Effect of Smooth Cloud Boundaries on Cloud Destruction and Cloud Turbulence

The effect of smooth cloud boundaries on the interaction of steady planar shock waves with interstellar clouds is studied using a high-resolution local AMR technique with a second-order accurate axisymmetric Godunov hydrodynamic scheme. A 3D calculation is also done to confirm the results of the 2D ones. We consider an initially spherical cloud whose density distribution is flat near the cloud center and has a power-law profile in the cloud envelope. When an incident shock is transmitted into a smooth cloud, velocity gradients in the cloud envelope steepen the smooth density profile at the upstream side, resulting in a sharp density jump having an arc-like shape. Such a ``slip surface'' forms immediately when a shock strikes a cloud with a sharp boundary. For smoother boundaries, the formation of slip surface and therefore the onset of hydrodynamic instabilities are delayed. Since the slip surface is subject to the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the shocked cloud is eventually destroyed in $\sim 3-10$ cloud crushing times. After complete cloud destruction, small blobs formed by fragmentation due to hydrodynamic instabilities have significant velocity dispersions of the order of 0.1 $v_b$, where $v_b$ is the shock velocity in the ambient medium. This suggests that turbulent motions generated by shock-cloud interaction are directly associated with cloud destruction. The interaction of a shock with a cold HI cloud should lead to the production of a spray of small HI shreds, which could be related to the small cold clouds recently observed by Stanimirovic & Heiles (2005). The linewidth-size relation obtained from our 3D simulation is found to be time-dependent. A possibility for gravitational instability triggered by shock compression is also discussed.Comment: 62 pages, 16 figures, submitted to Ap