Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy

The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou, Capel and Quispel in 1992 as the family of partial difference equations generalizing to higher rank the lattice Korteweg-de Vries systems, and includes in particular the lattice Boussinesq system. We present a Lagrangian for the generic member of the lattice Gel'fand-Dikii hierarchy, and show that it can be considered as a Lagrangian 2-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus the multiform structure proposed in arXiv:0903.4086v2 [nlin.SI] is extended to a multi-component system.Comment: 12 page

An integrable multicomponent quad equation and its Lagrangian formulation

We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an elementary plaquette in the 2-dimensional lattice. The system is multidimensionally consistent and a Lagrangian which respects this feature, i.e., which has the desirable closure property, is obtained.Comment: 10 page

Discrete-time Calogero-Moser system and Lagrangian 1-form structure

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time as well as in continuous time, as a first example of a Lagrange 1-form structure in the sense of the recent paper [19]. The discrete-time model of the CM system was established some time ago arising as a pole-reduction of a semi-discrete version of the KP equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation as well as of the CM system, we establish the proper Lagrange 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in [19], for the simpler case of Lagrange 1-forms.Comment: 37 pages, 8 figure

Current-voltage characteristics of diluted Josephson-junction arrays: scaling behavior at current and percolation threshold

Dynamical simulations and scaling arguments are used to study the current-voltage (IV) characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where $p_c$ is the percolation threshold. For $p$ $>$ $p_c$ and zero temperature, the IV curves show power-law behavior above a disorder dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At $p_c$ and finite temperature $T$, the results show the scaling behavior of a T=0 superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to non-linearity appears at currents proportional to $$, with a thermal-correlation length exponent $\nu_T$ consistent with the corresponding value for the diluted XY model at $p_c$.Comment: Revtex, 9 postscript pages, to appear in Phys. Rev.

Current-voltage scaling of a Josephson-junction array at irrational frustration

Numerical simulations of the current-voltage characteristics of an ordered two-dimensional Josephson junction array at an irrational flux quantum per plaquette are presented. The results are consistent with an scaling analysis which assumes a zero temperature vortex glass transition. The thermal correlation length exponent characterizing this transition is found to be significantly different from the corresponding value for vortex-glass models in disordered two-dimensional superconductors. This leads to a current scale where nonlinearities appear in the current-voltage characteristics decreasing with temperature $T$ roughly as $T^2$ in contrast with the $T^3$ behavior expected for disordered models.Comment: RevTex 3.0, 12 pages with Latex figures, to appear in Phys. Rev. B 54, Rapid. Com

Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films

The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio

Geometrical Defects in Josephson Junction Arrays

Dislocations and disclinations in a lattice of Josephson junctions will affect the dynamics of vortex excitations within the array. These defects effectively distort the space in which the excitations move and interact. The interaction energy between such defects and excitations are determined and vortex trajectories in twisted lattices are calculated. Finally, possible experiments observing these effects are presented.Comment: 26 pages including 5 figure

Communication and information-giving in high-risk breast cancer consultations: influence on patient outcomes

This longitudinal study aimed to document (i) the information-giving and patient-communication styles of clinical geneticists and genetic counsellors (consultants) in familial breast cancer clinics and (ii) assess the effect of these styles on women`s knowledge, whether their expectations were met, satisfaction, risk perception and psychological status. A total of 158 women from high-risk breast cancer families completed self-report questionnaires at 2 weeks preconsultation and 4 weeks postconsultation. The consultations were audiotaped, transcribed and coded. Multivariate logistic regressions showed that discussing prophylactic mastectomy (P = 0.00) and oophorectomy (P = 0.01) led to women having significantly more expectations met; discussing genetic testing significantly decreased anxiety (P = 0.03) and facilitating understanding significantly decreased depression (P = 0,05). Receiving a summary letter of the consultation significantly lowered anxiety (P = 0.01) and significantly increased the accuracy of perceived risk (P = 0.02). Women whose consultant used more supportive communications experienced significantly more anxiety about breast cancer at the 4 weeks follow-up (P=0.00), These women were not significantly more anxious before genetic counselling. In conclusion, this study found that consultants vary in the amount of information they give and the way they communicate; and this variation can result in better or worse psychosocial outcomes. Greater use of supportive and counselling communications appeared to increase anxiety about breast cancer. Identifying methods to assist consultants to address emotional issues effectively may be helpful

Quantum Interference on the Kagom\'e Lattice

We study quantum interference effects due to electron motion on the Kagom\'e lattice in a perpendicular magnetic field. These effects arise from the interference between phase factors associated with different electron closed-paths. From these we compute, analytically and numerically, the superconducting-normal phase boundary for Kagom\'e superconducting wire networks and Josephson junction arrays. We use an analytical approach to analyze the relationship between the interference and the complex structure present in the phase boundary, including the origin of the overall and fine structure. Our results are obtained by exactly summing over one thousand billion billions ($\sim 10^{21}$) closed paths, each one weighted by its corresponding phase factor representing the net flux enclosed by each path. We expect our computed mean-field phase diagrams to compare well with several proposed experiments.Comment: 9 pages, Revtex, 3 figures upon reques

Phase transition in a chain of quantum vortices

We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore one can control the commensurability of the one-dimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex, and the long-range interaction between the vortices leads to the existence of a specific commensurate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton, with energy separated from the ground state by a finite gap. This gap vanishes in the incommensurate phase. Each soliton carries a fraction of a flux quantum; the propagation of solitons leads to a finite resistance of the array. We find the dependence of the resistance activation energy on the magnetic field and parameters of the Josephson array. This energy consists of the above-mentioned gap, and also of a boundary pinning term, which is different in the commensurate and incommensurate phases. The developed theory allows us to explain quantitatively the available experimental data.Comment: 14 pages, 7 eps figure