Oscillatory Doubly Diffusive Convection in a Finite Container

Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. Numerical simulations of the amplitude equations for experimental parameter values are presented and compared with the results of recent experiments by Predtechensky et al. [ Phys. Rev. Lett. 72, 218 (1994); Phys. Fluids 6, 3923 (1994)]

Oscillatory Bifurcation with Broken Translation Symmetry

The effect of distant endwalls on the bifurcation to traveling waves is considered. Previous approaches have treated the problem by assuming that it is a weak perturbation of the translation invariant problem. When the problem is formulated instead in a finite box of length L and the limit L--\u3e [infinity] is taken, one obtains amplitude equations that differ from the usual Ginzburg-Landau description by the presence of an additional nonlinear term. This formulation leads to a description in terms of the amplitudes of the primary box modes, which are odd and even parity standing waves. For large L, the equations that result take the form of a Hopf bifurcation with approximate D4 symmetry. These equations are able to describe, qualitatively, not only traveling and blinking states, but also asymmetrical blinking states and repeated transients, all of which have been observed in binary fluid convection experiments

Amplitude equations for a system with thermohaline convection

The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau equation, a Newell-Whitehead-type equation, and an equation of the $\phi^4$ type, respectively, were obtained. Analytic expressions for the coefficients of these equations and their various asymptotic forms are presented. In the case of Hopf bifurcation for low and high frequencies, the amplitude equation reduces to a perturbed nonlinear Schr\"odinger equation. In the high-frequency limit, structures of the type of "dark" solitons are characteristic of the examined physical system.Comment: 21 pages, 8 figure

Impact of Trapped Flux and Thermal Gradients on the SRF Cavity Quality Factor

The obtained Q0 value of a superconducting niobium cavity is known to depend on various factors like the RRR of the Niobium material, crystallinity, chemical treatment history, the high pressure rinsing process, or effectiveness of the magnetic shielding. We have observed that spatial thermal gradients over the cavity length during cool down appear to contribute to a degradation of Q0. Measurements were performed in the Horizontal Bi Cavity Test Facility HoBiCaT at HZB on TESLA type cavities as well as on disc and rod shaped niobium samples equipped with thermal, electrical and magnetic diagnostics. Possible explanations for the effect are discusse

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)

The Stability of Magnetized Rotating Plasmas with Superthermal Fields

During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper, we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the weak-field limit. We show that, when superthermal toroidal fields are considered, the effects of both compressibility and magnetic tension forces, which are related to the curvature of toroidal field lines, should be taken fully into account. We demonstrate that the presence of a strong toroidal component in the magnetic field plays a non-trivial role. When strong fields are considered, the strength of the toroidal magnetic field not only modifies the growth rates of the unstable modes but also determines which modes are subject to instabilities. We find that, for rotating configurations with Keplerian laws, the magnetorotational instability is stabilized at low wavenumbers for toroidal Alfven speeds exceeding the geometric mean of the sound speed and the rotational speed. We discuss the significance of our findings for the stability of cold, magnetically dominated, rotating fluids and argue that, for these systems, the curvature of toroidal field lines cannot be neglected even when short wavelength perturbations are considered. We also comment on the implications of our results for the validity of shearing box simulations in which superthermal toroidal fields are generated.Comment: 24 pages, 12 figures. Accepted for publication in ApJ. Sections 2 and 5 substantially expanded, added Appendix A and 3 figures with respect to previous version. Animations are available at http://www.physics.arizona.edu/~mpessah/research

Chaos in the Takens-Bogdanov bifurcation with O(2) symmetry

The Takens–Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation invariant in one spatial dimension with no left-right preference the imposition of periodic boundary conditions leads to the Takens–Bogdanov bifurcation with O(2) symmetry. This bifurcation, analyzed by G. Dangelmayr and E. Knobloch, Phil. Trans. R. Soc. London A 322, 243 (1987), describes the interaction between steady states and traveling and standing waves in the nonlinear regime and predicts the presence of modulated traveling waves as well. The analysis reveals the presence of several global bifurcations near which the averaging method (used in the original analysis) fails. We show here, using a combination of numerical continuation and the construction of appropriate return maps, that near the global bifurcation that terminates the branch of modulated traveling waves, the normal form for the Takens–Bogdanov bifurcation admits cascades of period-doubling bifurcations as well as chaotic dynamics of Shil’nikov type. Thus chaos is present arbitrarily close to the codimension two point