Rayleigh-B\'{e}nard convection in a homeotropically aligned nematic liquid crystal

We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference $\Delta T$ and the applied vertical magnetic field $H$ and compare them with theoretical calculations. The experiments cover the field range 8 \alt h \equiv H/ H_{F} \alt 80 ($H_F =$ is the Fr\'eedericksz field). For $h$ less than a codimension-two field $h_{ct} \simeq 46$ the bifurcation is subcritical and oscillatory, with travelling- and standing-wave transients. Beyond $h_{ct}$ the bifurcation is stationary and subcritical until a tricritical field $h_t= 57.2$ is reached, beyond which it is supercritical. The bifurcation sequence as a function of $h$ found in the experiment confirms the qualitative aspects of the theoretical predictions. However, the value of $h_{ct}$ is about 10% higher than the predicted value and the results for $k_c$ are systematically below the theory by about 2% at small $h$ and by as much as 7% near $h_{ct}$. At $h_{ct}$, $k_c$ is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field $h_t^{th} = 51$ is somewhat below the experimental one. The fully developed flow above $R_c$ for $h < h_{ct}$ is chaotic. For $h_{ct} < h < h_t$ the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below $R_c$, i.e. the bifurcation is hysteretic. Above the tricritical field $h_t$, we find a bifurcation to a time independent pattern which within our resolution is non-hysteretic.Comment: 15 pages incl. 23 eps figure

Singularity in the boundary resistance between superfluid 4^4He and a solid surface

We report new measurements in four cells of the thermal boundary resistance $R$ between copper and $^4$He below but near the superfluid-transition temperature $T_\lambda$. For $10^{-7} \leq t \equiv 1 - T/T_\lambda \leq 10^{-4}$ fits of $R = R_0 t^{x_b} + B_0$ to the data yielded $x_b \simeq 0.18$, whereas a fit to theoretical values based on the renormalization-group theory yielded $x_b = 0.23$. Alternatively, a good fit of the theory to the data could be obtained if the {\it amplitude} of the prediction was reduced by a factor close to two. The results raise the question whether the boundary conditions used in the theory should be modified.Comment: 4 pages, 4 figures, revte

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures

Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection

We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number of approximately 1. We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.Comment: Preprint of experimental paper submitted to Phys. Rev. Lett. May 12 1993. Text is preceeded by many TeX macros. Figures 1 and 2 are rather lon

Pattern Formation and Dynamics in Rayleigh-B\'{e}nard Convection: Numerical Simulations of Experimentally Realistic Geometries

Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic situations. Rectangular and cylindrical geometries of varying aspect ratios for experimental boundary conditions, including fins and spatial ramps in plate separation, are examined with particular attention paid to the role of the mean flow. A small cylindrical convection layer bounded laterally either by a rigid wall, fin, or a ramp is investigated and our results suggest that the mean flow plays an important role in the observed wavenumber. Analytical results are developed quantifying the mean flow sources, generated by amplitude gradients, and its effect on the pattern wavenumber for a large-aspect-ratio cylinder with a ramped boundary. Numerical results are found to agree well with these analytical predictions. We gain further insight into the role of mean flow in pattern dynamics by employing a novel method of quenching the mean flow numerically. Simulations of a spiral defect chaos state where the mean flow is suddenly quenched is found to remove the time dependence, increase the wavenumber and make the pattern more angular in nature.Comment: 9 pages, 10 figure

Long, Bellows-Free Vertical Helium Transfer Lines for the LHC Cryogenic System

The cryogenic system for the Large Hadron Collider (LHC) under construction at CERN will include four new vertical helium transfer lines connecting the new helium refrigerators to the underground areas. These four transfer lines will be installed between a refrigerator on the surface and an interconnection box located 80 m to 145 m underground. They consist of a vacuum jacket, a thermal screen and four internal helium pipes. Due to space and accessibility limitations, the lines have been specified without bellows or bends of any kind in the long vertical part; the thermal contractions must be compensated at the surface only. The displacement due to these contractions amounts to more than 35 cm in one case, and all four internal pipes, as well as the thermal screen, must be able to contract and expand independently. The lines will be built and installed by a consortium of Linde AG and Babcock Noell Nuclear GmbH. Their technical design choices are presented together with expected performance

Weak interactions and quasi-stable particle energy loss

We discuss the interplay between electromagnetic energy loss and weak interactions in the context of quasistable particle particle propagation through materials. As specific examples, we consider staus, where weak interactions may play a role, and taus, where they don't.Comment: 4 pages, 4 figures, to appear in the proceedings of the Second Workshop on TeV Particle Astrophysics (August 2006, Madison, WI

Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-B\'enard convection

In turbulent thermal convection in cylindrical samples of aspect ratio \Gamma = D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis, because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number 1/\Ro_c, with 1/\Ro_c \propto 1/\Gamma. We present a Ginzburg-Landau like model that explains the existence of a bifurcation at finite 1/\Ro_c as a finite-size effect. The model yields the proportionality between 1/\Ro_c and $1/\Gamma$ and is consistent with several other measured or computed system properties.Comment: 4 pages, 4 figure

From multiplicative noise to directed percolation in wetting transitions

A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line changes from a directed-percolation to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions, Mean-field arguments and the mapping on a yet simpler model provide some further insight on the overall scenario.Comment: 4 pages, 3 figure

Quantized charge pumping through a quantum dot by surface acoustic waves

We present a realization of quantized charge pumping. A lateral quantum dot is defined by metallic split gates in a GaAs/AlGaAs heterostructure. A surface acoustic wave whose wavelength is twice the dot length is used to pump single electrons through the dot at a frequency f=3GHz. The pumped current shows a regular pattern of quantization at values I=nef over a range of gate voltage and wave amplitude settings. The observed values of n, the number of electrons transported per wave cycle, are determined by the number of electronic states in the quantum dot brought into resonance with the fermi level of the electron reservoirs during the pumping cycle.Comment: 8 page