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

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

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

On the soliton width in the incommensurate phase of spin-Peierls systems

We study using bosonization techniques the effects of frustration due to competing interactions and of the interchain elastic couplings on the soliton width and soliton structure in spin-Peierls systems. We compare the predictions of this study with numerical results obtained by exact diagonalization of finite chains. We conclude that frustration produces in general a reduction of the soliton width while the interchain elastic coupling increases it. We discuss these results in connection with recent measurements of the soliton width in the incommensurate phase of CuGeO_3.Comment: 4 pages, latex, 2 figures embedded in the tex

Rapid Suppression of the Spin Gap in Zn-doped CuGeO_3 and SrCu_2O_3

The influence of non-magnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO$_3$ is studied. A simple extension to Zn-doped ${\rm Sr Cu_2 O_3}$ is also discussed. Using Exact Diagonalization techniques and intuitive arguments we show that Zn-doping introduces states in the Spin-Peierls gap of CuGeO$_3$. This effect can beunderstood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn-doping according to the numerical data presented here. As recent numerical calculations have shown, similar arguments apply to ladders with non-magnetic impurities simply replacing the tendency to dimerization in CuGeO$_3$ by the tendency to form spin-singlets along the rungs in SrCu$_2$O$_3$.Comment: 7 pages, 8 postscript figures, revtex, addition of figure 8 and a section with experimental predictions, submmited to Phys. Rev. B in May 199

Calibration of the INCA model in a Mediterranean forested catchment: the effect of hydrological inter-annual variability in an intermittent stream

International audienceMediterranean regions are characterised by a stream hydrology with a marked seasonal pattern and high inter-annual variability. Accordingly, soil N processes and leaching of solutes in Mediterranean regions also show a marked seasonality, occurring in pulses as soils re-wet following rain. The Integrated Nitrogen Catchment model (INCA) was applied to Fuirosos, a Mediterranean catchment located in NE Spain using hydrological data and streamwater nitrate and ammonium concentrations collected from 1999 to 2002. This study tested the model under Mediterranean climate conditions and assessed the effect of the high inter-annual variability on the ability of INCA to simulate discharge and N fluxes. The model was calibrated for the whole three-year period and the n coefficients of determinion (r2) between simulated and observed data were 0.54 and 0.1 for discharge and nitrate temporal dynamics, respectively. Ammonium dynamics were simulated poorly and the linear regression between observed and simulated data was not significant statistically. To assess the effect of inter-annual variability on INCA simulations, the calibration process was run separately for two contrasting hydrological years: a dry year with a total rainfall of 525 mm and a wet year with a total of 871 mm. The coefficients of determination for the correlation between observed and simulated discharge for these two periods were 0.67 (p2 = 0.13 p2 = 0.56 p Keywords: environmental modelling, intermittent stream, Mediterranean climate, Fuirosos, hydrology, nitrat

Diagonalization in Reduced Hilbert Spaces using a Systematically Improved Basis: Application to Spin Dynamics in Lightly Doped Ladders

A method is proposed to improve the accuracy of approximate techniques for strongly correlated electrons that use reduced Hilbert spaces. As a first step, the method involves a change of basis that incorporates exactly part of the short distance interactions. The Hamiltonian is rewritten in new variables that better represent the physics of the problem under study. A Hilbert space expansion performed in the new basis follows. The method is successfully tested using both the Heisenberg model and the $t-J$ model with holes on 2-leg ladders and chains, including estimations for ground state energies, static correlations, and spectra of excited states. An important feature of this technique is its ability to calculate dynamical responses on clusters larger than those that can be studied using Exact Diagonalization. The method is applied to the analysis of the dynamical spin structure factor $S(q,\omega)$ on clusters with $2 \times 16$ sites and 0 and 2 holes. Our results confirm previous studies (M. Troyer, H. Tsunetsugu, and T. M. Rice, Phys. Rev. $B 53$, 251 (1996)) which suggested that the state of the lowest energy in the spin-1 2-holes subspace corresponds to the bound state of a hole pair and a spin-triplet. Implications of this result for neutron scattering experiments both on ladders and planes are discussed.Comment: 9 pages, 8 figures, Revtex + psfig; changed conten

Gas-plasma compressional wave coupling by momentum transfer

Pressure disturbances in a gas-plasma mixed fluid will result in a hybrid response, with magnetosonic plasma waves coupled to acoustic waves in the neutral gas. In the analytical and numerical treatment presented here, we demonstrate the evolution of the total fluid medium response under a variety of conditions, with the gas-plasma linkage achieved by additional coupling terms in the momentum equations of each species. The significance of this treatment lies in the consideration of density perturbations in such fluids: there is no 'pure' mode response, only a collective one in which elements of the characteristics of each component are present. For example, an initially isotropic gas sound wave can trigger an anisotropic magnetic response in the plasma, with the character of each being blended in the global evolution. Hence sound waves do not remain wholly isotropic, and magnetic responses are less constrained by pure magnetoplasma dynamics

Charge and spin ordering, and charge transport properties in a two-dimensional inhomogeneous t-J model

We study a two-dimensional t-J model close to the Ising limit in which charge inhomogeneity is stabilized by an on-site potential e_s, by using diagonalization in a restricted Hilbert space and finite temperature Quantum Monte Carlo. Both site and bond centered stripes are considered and their similitudes and differences are analyzed. The amplitude of charge inhomogeneity is studied as e_s -> 0. Moreover, we show that the anti-phase domain ordering occurs at a much lower temperature than the formation of charge inhomogeneities and charge localization. Hole-hole correlations indicate a metallic behavior of the stripes with no signs of hole attraction. Kinetic energies and current susceptibilities are computed and indications of charge localization are discussed. The study of the doping dependence in the range 0.083 < x < 0.167 suggests that these features are characteristic of the whole underdoped region.Comment: minor changes, to be published in Physical Review