An absorption tube for the investigation of gases in the photographic infrared

An absorption cell of novel design is described, which combines the advantages of long path and relatively small volume

Pinning control of spatiotemporal chaos

Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented

Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection

A theory of the novel spiral chaos state recently observed in Rayleigh-Benard convection is proposed in terms of the importance of invasive defects i.e defects that through their intrinsic dynamics expand to take over the system. The motion of the spiral defects is shown to be dominated by wave vector frustration, rather than a rotational motion driven by a vertical vorticity field. This leads to a continuum of spiral frequencies, and a spiral may rotate in either sense depending on the wave vector of its local environment. Results of extensive numerical work on equations modelling the convection system provide some confirmation of these ideas.Comment: Revtex (15 pages) with 4 encoded Postscript figures appende

Grain boundary motion in layered phases

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as $\epsilon^{-1/2}$, where $\epsilon$ is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time dependent traveling velocity of the boundary, and especially their dependence on wavenumber. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain boundary motion through curved rolls is the dominant coarsening mechanism.Comment: 16 pages, 5 figure

Comment on ``The linear instability of magnetic Taylor-Couette flow with Hall effect''

In the paper we comment on (R\"udiger & Shalybkov, Phys. Rev. E. 69, 016303 (2004) (RS)), the instability of the Taylor--Couette flow interacting with a homogeneous background field subject to Hall effect is studied. We correct a falsely generalizing interpretation of results presented there which could be taken to disprove the existence of the Hall--drift induced magnetic instability described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103. It is shown that in contrast to what is suggested by RS, no additional shear flow is necessary to enable such an instability with a non--potential magnetic background field, whereas for a curl--free one it is. In the latter case, the instabilities found in RS in situations where neither a hydrodynamic nor a magneto--rotational instability exists are demonstrated to be most likely magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are clarified.Comment: 3 pages, 1 figure; accepted by Physical Review

Finite Size Scaling of Domain Chaos

Numerical studies of the domain chaos state in a model of rotating Rayleigh-Benard convection suggest that finite size effects may account for the discrepancy between experimentally measured values of the correlation length and the predicted divergence near onset

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

Effect of the Centrifugal Force on Domain Chaos in Rayleigh-B\'enard convection

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects rotating Rayleigh-B\'enard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly-stationary nearly-radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency $f\sim\epsilon^\mu$ with $\mu\simeq1$ as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, $\mu$ and the domain size closely agreed with experiment.Comment: 8 pages, 11 figure

Who Contributes to the Knowledge Sharing Economy?

Information sharing dynamics of social networks rely on a small set of influencers to effectively reach a large audience. Our recent results and observations demonstrate that the shape and identity of this elite, especially those contributing \emph{original} content, is difficult to predict. Information acquisition is often cited as an example of a public good. However, this emerging and powerful theory has yet to provably offer qualitative insights on how specialization of users into active and passive participants occurs. This paper bridges, for the first time, the theory of public goods and the analysis of diffusion in social media. We introduce a non-linear model of \emph{perishable} public goods, leveraging new observations about sharing of media sources. The primary contribution of this work is to show that \emph{shelf time}, which characterizes the rate at which content get renewed, is a critical factor in audience participation. Our model proves a fundamental \emph{dichotomy} in information diffusion: While short-lived content has simple and predictable diffusion, long-lived content has complex specialization. This occurs even when all information seekers are \emph{ex ante} identical and could be a contributing factor to the difficulty of predicting social network participation and evolution.Comment: 15 pages in ACM Conference on Online Social Networks 201

Aging in the Relaxor Ferroelectric PMN/PT

The relaxor ferroelectric (PbMn$_{1/3}$Nb$_{2/3}$O$_3$)$_{1-x}$(PbTiO$_3$)$_{x}$, $x=0.1$, (PMN/PT(90/10)) is found to exhibit several regimes of complicated aging behavior. Just below the susceptibility peak there is a regime exhibiting rejuvenation but little memory. At lower temperature, there is a regime with mainly cumulative aging, expected for simple domain-growth. At still lower temperature, there is a regime with both rejuvenation and memory, reminiscent of spin glasses. PMN/PT (88/12) is also found to exhibit some of these aging regimes. This qualitative aging behavior is reminiscent of that seen in reentrant ferromagnets, which exhibit a crossover from a domain-growth ferromagnetic regime into a reentrant spin glass regime at lower temperatures. These striking parallels suggest a picture of competition in PMN/PT (90/10) between ferroelectric correlations formed in the domain-growth regime with glassy correlations formed in the spin glass regime. PMN/PT (90/10) is also found to exhibit frequency-aging time scaling of the time-dependent part of the out-of-phase susceptibility for temperatures 260 K and below. The stability of aging effects to thermal cycles and field perturbations is also reported.Comment: 8 pages RevTeX4, 11 figures; submitted to Phys. Rev.