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

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

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

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.

Switch on the engine: how the eukaryotic replicative helicase MCM2–7 becomes activated

© 2014, Springer-Verlag Berlin Heidelberg.A crucial step during eukaryotic initiation of DNA replication is the correct loading and activation of the replicative DNA helicase, which ensures that each replication origin fires only once. Unregulated DNA helicase loading and activation, as it occurs in cancer, can cause severe DNA damage and genomic instability. The essential mini-chromosome maintenance proteins 2–7 (MCM2–7) represent the core of the eukaryotic replicative helicase that is loaded at DNA replication origins during G1-phase of the cell cycle. The MCM2–7 helicase activity, however, is only triggered during S-phase once the holo-helicase Cdc45-MCM2–7-GINS (CMG) has been formed. A large number of factors and several kinases interact and contribute to CMG formation and helicase activation, though the exact mechanisms remain unclear. Crucially, upon DNA damage, this reaction is temporarily halted to ensure genome integrity. Here, we review the current understanding of helicase activation; we focus on protein interactions during CMG formation, discuss structural changes during helicase activation, and outline similarities and differences of the prokaryotic and eukaryotic helicase activation process

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.

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

Evolution of the Spin Gap Upon Doping a 2-Leg Ladder

The evolution of the spin gap of a 2-leg ladder upon doping depends upon the nature of the lowest triplet excitations in a ladder with two holes. Here we study this evolution using various numerical techniques for a t-t'-J ladder as the next-near-neighbor hopping t' is varied. We find that depending on the value of t', the spin gap can evolve continuously or discontinuously and the lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or two separate quasi-particles. Previous experimental results on the superconducting two-leg ladder Sr12Ca2Cu24O41 are discussed.Comment: 4 pages, latex, submitted to PR

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

Electron-lattice coupling and the broken symmetries of the molecular salt (TMTTF)2_2SbF6_6

(TMTTF)$_2$SbF$_6$ is known to undergo a charge ordering (CO) phase transition at $T_{CO}\approx156K$ and another transition to an antiferromagnetic (AF) state at $T_N\approx 8K$. Applied pressure $P$ causes a decrease in both $T_{CO}$ and $T_N$. When $P>0.5 GPa$, the CO is largely supressed, and there is no remaining signature of AF order. Instead, the ground state is a singlet. In addition to establishing an expanded, general phase diagram for the physics of TMTTF salts, we establish the role of electron-lattice coupling in determining how the system evolves with pressure.Comment: 4 pages, 5 figure