Homoclinic snaking in bounded domains

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of “snaking without bistability”, recently observed in simulations of binary fluid convection by Mercader, Batiste, Alonso and Knobloch (preprint)

Generation of finite wave trains in excitable media

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.Comment: 6 pages, 6 figure

Residual Oil Aerosol Measurements on Refridgerators and Liquefiers

The purity of the process gas is essential for the reliability of refrigerators and liquefiers. Filtration and adsorption of impurities like water, nitrogen, and oil result in a major effort, cost, and maintenance in the helium process. Expensive impurity monitors for moisture, nitrogen, and hydrocarbon contents are required to identify filter failures and leakage immediately during the operation. While water and nitrogen contaminants can be detected reliably, the measurement of oil aerosols at the ppb level is challenging. We present a novel diagnostic oil aerosol measurement system able to measure particles in the sub amp; 956;m range. This unit enabled us to evaluate and improve the oil separation system on a LINDE TCF 50 helium liquefie

In-situ synchrotron x-ray photoelectron spectroscopy study of medium-temperature baking of niobium for SRF application

In order to determine optimal parameters of vacuum thermal processing of superconducting radiofrequency niobium cavities exhaustive information on the initial chemical state of niobium and its modification upon a vacuum heat treatment is required. In the present work the chemical composition of the niobium surface upon ultra-high vacuum baking at 200 C-degrees-400 C-degrees similar to 'medium-temperature baking' and 'furnace baking' of cavities is explored in-situ by synchrotron x-ray photoelectron spectroscopy (XPS). Our findings imply that below the critical thickness of the Nb2O5 layer (approximate to 1nm) niobium starts to interact actively with surface impurities, such as carbon and phosphorus. By studying the kinetics of the native oxide reduction, the activation energy and the rate-constant relation have been determined and used for the calculation of the oxygen-concentration depth profiles. It has been established that the controlled diffusion of oxygen is realized at temperatures 200 C-degrees-300 C-degrees, and the native-oxide layer represents an oxygen source, while at 400 C-degrees the pentoxide is completely reduced and the doping level is determined by an ambient oxygen partial pressure. Fluorine (F to Nb atomic ratio is 0.2) after the buffered chemical polishing was found to be incorporated into the surface layer probed by XPS (approximate to 4.6nm), and its concentration increased during the low-temperature baking (F/Nb = 0.35 at 230 C-degrees) and depleted at higher temperatures (F/Nb = 0.11 at 400 C-degrees). Thus, the influence of fluorine on the performance of mid-T baked, nitrogen-doped and particularly mild-baked (120 C-degrees/48 h) cavities must be considered. The possible role of fluorine in the educed Nb+5 -> Nb+4 reaction under the impact of an x-ray beam at room temperature and during the thermal treatment is also discussed. The range of temperature and duration parameters of the thermal treatment at which the niobium surface would not be contaminated with impurities is determined

On the validity of mean-field amplitude equations for counterpropagating wavetrains

We rigorously establish the validity of the equations describing the evolution of one-dimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic model equation, namely the sine-Gordon equation. We consider both periodic amplitude functions and localized wavepackets. For the localized case, the wavetrains are completely decoupled at leading order, while in the periodic case the amplitude equations take the form of mean-field (nonlocal) Schr\"odinger equations rather than locally coupled partial differential equations. The origin of this weakened coupling is traced to a hidden translation symmetry in the linear problem, which is related to the existence of a characteristic frame traveling at the group velocity of each wavetrain. It is proved that solutions to the amplitude equations dominate the dynamics of the governing equations on asymptotically long time scales. While the details of the discussion are restricted to the class of model equations having a leading cubic nonlinearity, the results strongly indicate that mean-field evolution equations are generic for bimodal disturbances in dispersive systems with \O(1) group velocity.Comment: 16 pages, uuencoded, tar-compressed Postscript fil

Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability

A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - Bénard convection

An hydrodynamic shear instability in stratified disks

We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity $\Omega$ decreases outwards with radius $r$. At not too small stratification, its growth rate is a fraction of $\Omega$. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when $d \ln \Omega / d \ln r =-3/2$ (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.Comment: 19 pages, 13 figures, to appear in A&

Bistability of Slow and Fast Traveling Waves in Fluid Mixtures

The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically. The bifurcation behavior and the significantly different spatiotemporal properties of the different wave states - e.g. frequency, flow structure, and concentration distribution - are determined and related to each other and to a convenient measure of their nonlinearity. This allows to derive a limit for the applicability of small amplitude expansions. Additionally an universal scaling behavior of frequencies and mixing properties is found. PACS: 47.20.-k, 47.10.+g, 47.20.KyComment: 4 pages including 5 Postscript figure