Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Role of interactions in ferrofluid thermal ratchets

Orientational fluctuations of colloidal particles with magnetic moments may be rectified with the help of external magnetic fields with suitably chosen time dependence. As a result a noise-driven rotation of particles occurs giving rise to a macroscopic torque per volume of the carrier liquid. We investigate the influence of mutual interactions between the particles on this ratchet effect by studying a model system with mean-field interactions. The stochastic dynamics may be described by a nonlinear Fokker-Planck equation for the collective orientation of the particles which we solve approximately by using the effective field method. We determine an interval for the ratio between coupling strength and noise intensity for which a self-sustained rectification of fluctuations becomes possible. The ratchet effect then operates under conditions for which it were impossible in the absence of interactions.Comment: 18 pages, 10 figure

Assessing the influence of one astronomy camp over 50 years

The International Astronomical Youth Camp has benefited thousands of lives during its 50-year history. We explore the pedagogy behind this success, review a survey taken by more than 300 previous participants, and discuss some of the challenges the camp faces in the future.Comment: 10 pages, 4 figure

Analysis of the shearing instability in nonlinear convection and magnetoconvection

Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced

A minimal model for chaotic shear banding in shear-thickening fluids

We present a minimal model for spatiotemporal oscillation and rheochaos in shear-thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modelled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium `phase diagram' of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, travelling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.Comment: Revised version (in particular, new section III.E. and Appendix A

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.Comment: 10 pages, 9 figure

Dilaton Domain Walls and Dynamical Systems

Domain wall solutions of $d$-dimensional gravity coupled to a dilaton field $\sigma$ with an exponential potential $\Lambda e^{-\lambda\sigma}$ are shown to be governed by an autonomous dynamical system, with a transcritical bifurcation as a function of the parameter $\lambda$ when $\Lambda<0$. All phase-plane trajectories are found exactly for $\lambda=0$, including separatrices corresponding to walls that interpolate between $adS_d$ and adS_{d-1} \times\bR, and the exact solution is found for $d=3$. Janus-type solutions are interpreted as marginal bound states of these ``separatrix walls''. All flat domain wall solutions, which are given exactly for any $\lambda$, are shown to be supersymmetric for some superpotential $W$, determined by the solution.Comment: 30 pp, 11 figs, significant revision of original. Minor additional corrections in version to appear in journa

PENGARUH VARIASI DOSIS ZEOLIT TERHADAP KADAR LOGAM TIMBAL (Pb) PADA AIR LINDI TPA JATIBARANG SEMARANG

Limbah berupa cairan akibat pembusukan sampah / air lindi di Tempat Pembuangan Akhir (TPA) Jatibarang Semarang mengandung logam berat Timbal (Pb) yang berasal dari sampah plastik, tinta pada kertas, batu baterai dll yang dapat mencemari lingkungan. Penggunaan zeolit merupakan salah satu teknologi yang dapat dimanfaatkan untuk menghilangkan bahan cemaran dalam air lindi. Tujuan dari penelitian ini adalah mengetahui pengaruh variasi dosis zeolit (5 gram, 10 gram, 15 gram, 20 gram, 25 gram) terhadap kadar logam timbal (Pb) pada air lindi TPA Jatibarang Semarang. Jenis penelitian ini adalah true eksperiment dengan rancangan pretest and posttest with control group design. Populasi dalam penelitian ini adalah seluruh air lindi TPA Jatibarang, kemudian diambil sampel pada bagian inlet IPAS TPA.Analisis data dengan uji one way ANOVA atau uji Kruskal-wallis (α= 0,05). Hasil penelitian menunjukkan kadar awal Pb adalah 0,1011 mg/l, hal ini menunjukkan kadar timbal masih diatas baku mutu (0,1 mg/l). Sedangkan rata-rata suhu dan pH air lindi sebelum perlakuan adalah 260C dan 8,31. Penurunan kadar Pb pada dosis 5 gram, 10 gram, 15 gram, 20 gram, dan 25 gram berturut-turut sebagai berikut: -16,12%, -10,97%, - 3,22%, -3,22% dan 0%.Uji Kruskal-Wallis menunjukkan nilai p=0,710 yang berarti tidak ada perbedaan penurunankadar Pb pada variasi dosis zeolit. Hal ini disebabkan karena terjadi desorpsi Pb dari zeolit dan zeolit mengadsorp logam lain yang lebih reaktif,sehingga dapat disimpulkan bahwa pemberian variasi dosis zeolit tidak berpengaruh terhadap kadar logam timbal (Pb) pada air lindi TPA Jatibarang Semarang. Kata Kunci: Air lindi, Kadar timbal (Pb),Zeolit,TPA Jatibarang Semaran

Scaling supernova hydrodynamics to the laboratory

Supernova (SN) 1987A focused attention on the critical role of hydrodynamic instabilities in the evolution of supernovae. To test the modeling of these instabilities, we are developing laboratory experiments of hydrodynamic mixing under conditions relevant to supernovae. Initial results were reported in J. Kane et al. [Astrophys. J. 478, L75 (1997) and B. A. Remington et al., Phys. Plasmas 4, 1994 (1997)]. The Nova laser is used to generate a 10–15 Mbar shock at the interface of a two-layer planar target, which triggers perturbation growth due to the Richtmyer–Meshkov instability, and to the Rayleigh–Taylor instability as the interface decelerates. This resembles the hydrodynamics of the He-H interface of a Type II supernova at intermediate times, up to a few ×103 s.×103s. The scaling of hydrodynamics on microscopic laser scales to the SN-size scales is presented. The experiment is modeled using the hydrodynamics codes HYADES [J. T. Larson and S. M. Lane, J. Quant. Spect. Rad. Trans. 51, 179 (1994)] and CALE [R. T. Barton, Numerical Astrophysics (Jones and Bartlett, Boston, 1985), pp. 482–497], and the supernova code PROMETHEUS [P. R. Woodward and P. Collela, J. Comp. Phys. 54, 115 (1984)]. Results of the experiments and simulations are presented. Analysis of the spike-and-bubble velocities using potential flow theory and Ott thin-shell theory is presented, as well as a study of 2D versus 3D differences in perturbation growth at the He-H interface of SN 1987A.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69672/2/PHPAEN-6-5-2065-1.pd

Potential For Power: A Symposium On The Prospects For Power From Currently Unconventional Energy Sources

The wave energy arriving on the west coast of the United Kingdom represents a very substantial energy resource, amounting on average to more than twice the present installed capacity of the CEGB. Recent, comprehensive, studies by the CEGB (1) (2) and the National Engineering Laboratory (3) suggest that although there is no obvious technical reason for being unable ultimately to harness much of this energy, and many methods have been proposed, there are still considerable uncertainties over the choice of wave power system and its economics. Wave power does show sufficient promise however to have been made the subject of serious studies supported by the CEGB and the Department of Energy (4). In this Paper the potential of wave power and some of the more promising methods of harnessing it are discussed, together with an appreciation of some of the many technical and engineering problems which still need to be examined, and a discussion of the impact of wave power on the environment. By considering the results of recent research and their impact on wave power economics it is argued that wave power could be exploited to conserve fossil fuels but is unlikely to be competitive with nuclear power