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

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

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

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

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

Count three for wear able computers

This paper is a postprint of a paper submitted to and accepted for publication in the Proceedings of the IEE Eurowearable 2003 Conference, and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at the IET Digital Library. A revised version of this paper was also published in Electronics Systems and Software, also subject to Institution of Engineering and Technology Copyright. The copy of record is also available at the IET Digital Library.A description of 'ubiquitous computer' is presented. Ubiquitous computers imply portable computers embedded into everyday objects, which would replace personal computers. Ubiquitous computers can be mapped into a three-tier scheme, differentiated by processor performance and flexibility of function. The power consumption of mobile devices is one of the most important design considerations. The size of a wearable system is often a design limitation

Neutron and X-ray diffraction study of cubic [111] field cooled Pb(Mg1/3Nb2/3)O3

Neutron and x-ray diffraction techniques have been used to study the competing long and short-range polar order in the relaxor ferroelectric Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) under a [111] applied electric field. Despite reports of a structural transition from a cubic phase to a rhombohedral phase for fields E $>$ 1.7 kV/cm, we find that the bulk unit cell remains cubic (within a sensitivity of 90$^{\circ}$-$\alpha$ =0.03$^{\circ}$)for fields up to 8 kV/cm. Furthermore, we observe a structural transition confined to the near surface volume or `skin' of the crystal where the cubic cell is transformed to a rhombohedral unit cell at T$_{c}$=210 K for E $>$ 4 kV/cm, for which 90$^{\circ}$-$\alpha$=0.08 $\pm$ 0.03$^{\circ}$ below 50 K. While the bulk unit cell remains cubic, a suppression of the diffuse scattering and concomitant enhancement of the Bragg peak intensity is observed below T$_{c}$=210 K, indicating a more ordered structure with increasing electric field yet an absence of a long-range ferroelectric ground state in the bulk. The electric field strength has little effect on the diffuse scattering above T$_{c}$, however below T$_{c}$ the diffuse scattering is reduced in intensity and adopts an asymmetric lineshape in reciprocal space. The absence of hysteresis in our neutron measurements (on the bulk) and the presence of two distinct temperature scales suggests that the ground state of PMN is not a frozen glassy phase as suggested by some theories but is better understood in terms of random fields introduced through the presence of structural disorder. Based on these results, we also suggest that PMN represents an extreme example of the two-length scale problem, and that the presence of a distinct skin maybe necessary for a relaxor ground state.Comment: 12 pages, 9 figure

Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection

Explicit formulas for the rotation frequency and the long-wavenumber diffusion coefficients of global spirals with $m$ arms in Rayleigh-Benard convection are obtained. Global spirals and parallel rolls share exactly the same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals seem not to have a characteristic frequency $\omega_m$ or a typical size $R_m$, but their product $\omega_m R_m$ is a constant under given experimental conditions. The ratio $R_i/R_j$ of the radii of any two dislocations ($R_i$, $R_j$) inside a multi-armed spiral is also predicted to be constant. Some of these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication

Stability of Quasicrystals Composed of Soft Isotropic Particles

Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate to this day, we argue that the stability of certain soft-matter quasicrystals can be directly explained by examining a coarse-grained free energy for a system of soft isotropic particles. We show, both theoretically and numerically, that the stability can be attributed to the existence of two natural length scales in the pair potential, combined with effective three-body interactions arising from entropy. Our newly gained understanding of the stability of soft quasicrystals allows us to point at their region of stability in the phase diagram, and thereby may help control the self-assembly of quasicrystals and a variety of other desired structures in future experimental realizations.Comment: Revised abstract, more detailed explanations, and better images of the numerical minimization of the free energ

A Passive Phase Noise Cancellation Element

We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the output of a conventional oscillator at a frequency close to the sum of the linear mode frequencies. Above the threshold for parametric response, the coupled resonators exhibit self-oscillation at an inherent frequency. We find operating points of the device for which this periodic signal is immune to frequency noise in the driving oscillator, providing a way to clean its phase noise. We present results for the effect of thermal noise to advance a broader understanding of the overall noise sensitivity and the fundamental operating limits