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

Partially APN Boolean functions and classes of functions that are not APN infinitely often

In this paper we define a notion of partial APNness and find various characterizations and constructions of classes of functions satisfying this condition. We connect this notion to the known conjecture that APN functions modified at a point cannot remain APN. In the second part of the paper, we find conditions for some transformations not to be partially APN, and in the process, we find classes of functions that are never APN for infinitely many extensions of the prime field \F_2, extending some earlier results of Leander and Rodier.Comment: 24 pages; to appear in Cryptography and Communication

Recent progress in the truncated Lanczos method : application to hole-doped spin ladders

The truncated Lanczos method using a variational scheme based on Hilbert space reduction as well as a local basis change is re-examined. The energy is extrapolated as a power law function of the Hamiltonian variance. This systematic extrapolation procedure is tested quantitatively on the two-leg t-J ladder with two holes. For this purpose, we have carried out calculations of the spin gap and of the pair dispersion up to size 2x15.Comment: 5 pages, 4 included eps figures, submitted to Phys. Rev. B; revised versio

Anderson impurity in the one-dimensional Hubbard model on finite size systems

An Anderson impurity in a Hubbard model on chains with finite length is studied using the density-matrix renormalization group (DMRG) technique. In the first place, we analyzed how the reduction of electron density from half-filling to quarter-filling affects the Kondo resonance in the limit of Hubbard repulsion U=0. In general, a weak dependence with the electron density was found for the local density of states (LDOS) at the impurity except when the impurity, at half-filling, is close to a mixed valence regime. Next, in the central part of this paper, we studied the effects of finite Hubbard interaction on the chain at quarter-filling. Our main result is that this interaction drives the impurity into a more defined Kondo regime although accompanied in most cases by a reduction of the spectral weight of the impurity LDOS. Again, for the impurity in the mixed valence regime, we observed an interesting nonmonotonic behavior. We also concluded that the conductance, computed for a small finite bias applied to the leads, follows the behavior of the impurity LDOS, as in the case of non-interacting chains. Finally, we analyzed how the Hubbard interaction and the finite chain length affect the spin compensation cloud both at zero and at finite temperature, in this case using quantum Monte Carlo techniques.Comment: 9 pages, 9 figures, final version to be published in Phys. Rev.

Quantum dot with ferromagnetic leads: a density-matrix renormalization group study

A quantum dot coupled to ferromagnetically polarized one-dimensional leads is studied numerically using the density matrix renormalization group method. Several real space properties and the local density of states at the dot are computed. It is shown that this local density of states is suppressed by the parallel polarization of the leads. In this case we are able to estimate the length of the Kondo cloud, and to relate its behavior to that suppression. Another important result of our study is that the tunnel magnetoresistance as a function of the quantum dot on-site energy is minimum and negative at the symmetric point.Comment: 4 pages including 5 figures. To be published as a Brief Report in Phys. Rev.

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

From spinons to magnons in explicit and spontaneously dimerized antiferromagnetic chains

We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of compiting spontaneous and explicit dimerization relevant for Spin-Peierls compounds. The bosonized theory is a two frequency Sine-Gordon field theory. We analize the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverge for vanishing dimerization. The internal oscilations of the magnon give rise to a series of excited state until another magnon is emited and a two magnon continuum is reached. We discuss, for weak dimerization, in which way the magnon forms as a result of a spinon-spinon interaction potential.Comment: 5 pages, latex, 3 figures embedded in the tex

Riemann Surfaces of genus g with an automorphism of order p prime and p>g

The present work completes the classification of the compact Riemann surfaces of genus g with an analytic automorphism of order p (prime number) and p > g. More precisely, we construct a parameteriza- tion space for them, we compute their groups of uniformization and we compute their full automorphism groups. Also, we give affine equations for special cases and some implications on the components of the singular locus of the moduli space of smooth curves of genus g.Comment: 28 pages, 5 figure