Hydro-dynamical models for the chaotic dripping faucet

We give a hydrodynamical explanation for the chaotic behaviour of a dripping faucet using the results of the stability analysis of a static pendant drop and a proper orthogonal decomposition (POD) of the complete dynamics. We find that the only relevant modes are the two classical normal forms associated with a Saddle-Node-Andronov bifurcation and a Shilnikov homoclinic bifurcation. This allows us to construct a hierarchy of reduced order models including maps and ordinary differential equations which are able to qualitatively explain prior experiments and numerical simulations of the governing partial differential equations and provide an explanation for the complexity in dripping. We also provide a new mechanical analogue for the dripping faucet and a simple rationale for the transition from dripping to jetting modes in the flow from a faucet.Comment: 16 pages, 14 figures. Under review for Journal of Fluid Mechanic

Exact corrections for finite-time drift and diffusion coefficients

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on It\^o-Taylor expansions. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments, that furnish extra theoretical checks for that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series.Comment: 18 pages, 5 figure

Shock excitation of the knots of Hen 3-1475

We present new optical STIS HST spectroscopic observations of the jets of the proto-planetary nebula Hen 3-1475. The excitation conditions of the knots of Hen 3-1475 are derived from the observed optical spectra, confirming that the knots are shock excited. The shocked spectra are qualitatively reproduced by simple ``3/2''D bow shock models. We present a set of bow shock models devoted to planetary nebulae, and discuss the effects of the pre-ionization conditions, the bow shock velocity, the bow shock shape and the chemical abundances on the predicted spectra. To explore the reliability of the ``3/2''D bow shock models, we also compare the observed spectra of other three proto-planetary nebulae (M 1-92, M 2-56 and CRL 618) to the predicted spectra.Comment: 13 pages. A&A (in press

Spin dynamics of the spin-Peierls compound CuGeO_3 under magnetic field

The magnetic field--driven transition in the spin-Peierls system CuGeO_3 associated with the closing of the spin gap is investigated numerically. The field dependence of the spin dynamical structure factor (seen by inelastic neutron scattering) and of the momentum dependent static susceptibility are calculated. In the dimerized phase (H<H_c), we suggest that the strong field dependence of the transverse susceptibility could be experimentally seen from the low temperature spin-echo relaxation rate 1/T_{2G} or the second moment of the NMR spectrum. Above H_c low energy spin excitations appear at incommensurate wave vectors where the longitudinal susceptibility chi_{zz}(q) peaks.Comment: 4 pages, LaTeX, postscript figures include

Locality of temperature

This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of "intensivity of temperature" to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance, we prove exponential clustering of correlations above a universal critical temperature that upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature, local expectation values can be approximated efficiently in the error and the system size.Comment: 11 pages + 6 pages appendix, 6 figures; proof of the clustering theorem corrected, improved presentatio

Influence of the anion potential on the charge ordering in quasi-one dimensional charge transfer salts

We examine the various instabilities of quarter-filled strongly correlated electronic chains in the presence of a coupling to the underlying lattice. To mimic the physics of the (TMTTF)$_2$X Bechgaard-Fabre salts we also include electrostatic effects of intercalated anions. We show that small displacements of the anion can stabilize new mixed Charged Density Wave-Bond Order Wave phases in which central symmetry centers are suppressed. This finding is discussed in the context of recent experiments. We suggest that the recently observed charge ordering is due to a cooperative effect between the Coulomb interaction and the coupling of the electronic stacks to the anions. On the other hand, the Spin-Peierls instability at lower temperature requires a Peierls-like lattice coupling.Comment: Latex, 4 pages, 4 postscript figure

Time-dependent ejection velocity model for the outflow of Hen 3--1475

We present 2D axisymmetric and 3D numerical simulations of the proto-planetary nebula Hen 3-1475, which is characterized by a remarkably highly collimated optical jet, formed by a string of shock-excited knots along the axis of the nebula. It has recently been suggested that the kinematical and morphological properties of the Hen 3-1475 jet could be the result of an ejection variability of the central source (Riera et al. 2003). The observations suggest a periodic variability of the ejection velocity superimposed on a smoothly increasing ejection velocity ramp. From our numerical simulations, we have obtained intensity maps (for different optical emission lines) and position-velocity diagrams, in order to make a direct comparison with the HST observations of this object. Our numerical study allows us to conclude that a model of a precessing jet with a time-dependent ejection velocity, which is propagating into an ISM previously perturbed by an AGB wind, can succesfully explain both the morphological and the kinematical characteristics of this proto-planetary nebula.Comment: Astronomy and Astrophysics (accepted) (8 figures

Hole-Pairs in a Spin Liquid: Influence of Electrostatic Hole-Hole Repulsion

The stability of hole bound states in the t-J model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to $2 \times 30$ sites. For a nearest-neighbors (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange $J$. At $\sim 10$ hole doping the pairs break only for a NN-repulsion as large as $V \sim 4J$. Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper-oxides is remarked.Comment: Revised version with new figures. 4 pages, 5 figure

3-D Kinematics of the HH 110 jet

We present new results on the kinematics of the jet HH 110. New proper motion measurements have been calculated from [SII] CCD images obtained with a time baseline of nearly fifteen years. HH 110 proper motions show a strong asymmetry with respect to the outflow axis, with a general trend of pointing towards the west of the axis direction. Spatial velocities have been obtained by combining the proper motions and radial velocities from Fabry-Perot data. Velocities decrease by a factor ~3 over a distance of ~10$^{18}$ cm, much shorter than the distances expected for the braking caused by the jet/environment interaction. Our results show evidence of an anomalously strong interaction between the outflow and the surrounding environment, and are compatible with the scenario in which HH 110 emerges from a deflection in a jet/cloud collision.Comment: (1)Universitat de Barcelona; (2)UNAM; (3)UPC; (4)University of Hawaii; (5)Southern Astrophysical Research Telescope. 9 pages; 7 Figures Accepted by A&