On separating a fixed point from zero by invariants

Assume a fixed point v in V^G can be separated from zero by a homogeneous invariant f ∈ k[V]^G of degree p^r d where p > 0 is the characteristic of the ground field k and p, d are coprime. We show that then v can also be separated from zero by an invariant of degree p^r , which we obtain explicitly from f . It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power

Dual Fronts Propagating into an Unstable State

The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into {\em two} fronts propagating with {\em different} velocities was observed numerically in a magnetic system. The intermediate state is unstable and grows linearly in time. We first establish rigorously the existence of this phenomenon, called ``dual front,'' for a class of structurally unstable one-component models. Then we use this insight to explain dual fronts for a generic two-component reaction-diffusion system, and for the magnetic system.Comment: 19 pages, Postscript, A

Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis

Many molecular glass forming liquids show a shift of the glass transition Tg to lower temperatures when the liquid is confined into mesoporous host matrices. Two contrary explanations for this effect are given in literature: First, confinement induced acceleration of the dynamics of the molecules leads to an effective downshift of Tg increasing with decreasing pore size. Secondly, due to thermal mismatch between the liquid and the surrounding host matrix, negative pressure develops inside the pores with decreasing temperature, which also shifts Tg to lower temperatures. Here we present novel dynamic mechanical analysis measurements of the glass forming liquid salol in Vycor and Gelsil with pore sizes of d = 2.6, 5.0 and 7.5 nm. The dynamic complex elastic susceptibility data can be consistently described with the assumption of two relaxation processes inside the pores: A surface induced slowed down relaxation due to interaction with rough pore interfaces and a second relaxation within the core of the pores. This core relaxation time is reduced with decreasing pore size d, leading to a downshift of Tg in perfect agreement with recent DSC measurements

A Northward Range Extension of the Hispid Cotton Rat (\u3ci\u3eSigmodon hispidus\u3c/i\u3e) in Missouri

The hispid cotton rat (Sigmodon hispidus) is a widely distributed rodent with a geographic range extending from north-central Mexico to southern Nebraska and central Virginia and from southeastern Arizona east to Florida (Carleton et al. 1999, Peppers and Bradley 2000, Wilson and Reeder 2005) with isolated populations in Arizona (Bradley et al. 2012) and California (Clark 1972). Range expansions for the species have been well documented (Clark 1972, Farney 1975, Benedict et al. 2000, Wright et al. 2010, Wills et al. 2011). The majority of these range expansions have occurred across the Central Plains during the 20th century and have been attributed to climate change (e.g., Benedict et al. 2000, Hoffman 2008). Bailey (1902) was the first to document movement of S. hispidus into the Central Plains by documenting individuals for the first time in Kansas that most likely moved northward from Oklahoma. By 1947, the species had reached the Kansas/Nebraska border (Cockrum 1948). Just over 10 years later, Jones (1960) reported 12 individuals near the Nemaha River in southeastern Nebraska, and by the late 1960s (Choate and Genoways 1967, Genoways and Schlitter 1967) and mid-1970s (Farney 1975), the species had been documented in several parts of the state

Motion of a Solitonic Vortex in the BEC-BCS Crossover

We observe a long-lived solitary wave in a superfluid Fermi gas of $^6$Li atoms after phase-imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known equation of state in the BEC-BCS crossover

Direct Hopf Bifurcation in Parametric Resonance of Hybridized Waves

We study parametric resonance of interacting waves having the same wave vector and frequency. In addition to the well-known period-doubling instability we show that under certain conditions the instability is caused by a Hopf bifurcation leading to quasiperiodic traveling waves. It occurs, for example, if the group velocities of both waves have different signs and the damping is weak. The dynamics above the threshold is briefly discussed. Examples concerning ferromagnetic spin waves and surface waves of ferro fluids are discussed.Comment: Appears in Phys. Rev. Lett., RevTeX file and three postscript figures. Packaged using the 'uufiles' utility, 33 k

In-situ spatially resolved x-ray diffraction mapping of the alpha to beta to alpha transformation in commercially pure titanium arc welds

Spatially Resolved X-Ray Diffraction (SRXRD) is used to map the {alpha}{r_arrow}{beta}{r_arrow}{alpha} phase transformation in the heat affected zone (HAZ) of commercially pure titanium gas tungsten arc welds. In-situ SRXRD experiments were conducted on arc welds using a 200 pm diameter x-ray beam at Stanford Synchrotron Radiation Laboratory (SSRL). A map was created which identifies six HAZ microstructural regions that exist between the liquid weld pool and the base metal during welding. The first region is single phase {beta}-Ti that forms in a 2- to 3-mm band adjacent to the liquid weld pool. The second region is back transformed {alpha}-Ti that forms behind the portion of the HAZ where {beta}-Ti was once present at higher temperatures. The third region is completely recrystallized {alpha}-Ti that forms in a 2- to 3-mm band surrounding the single phase {beta}-Ti region. Recrystallized {alpha}-Ti was observed by itself and also with varying amounts of {beta}-Ti. The fourth region of the weld is the partially transformed zone where {alpha}-Ti and {beta}-Ti coexist during welding. The fifth region is directly behind the partially transformed zone and consists of a mixture of recrystallized and back transformed {alpha}-Ti The sixth region is farthest from the weld pool and consists of {alpha}-Ti that is undergoing annealing and recrystallization. Annealing of the base metal was observed to some degree in all of the SRXRD patterns, showing that annealing exceeded 13 mm from the centerline of the weld. Although the microstructure consisted predominantly of {alpha}-Ti, both prior to the weld and after the weld, the (002) texture of the starting material was altered during welding to produce a predominantly (101) texture within the resulting HAZ

Time-delayed feedback control in astrodynamics

In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded