519 research outputs found
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
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
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
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
are considered, where is the percolation threshold. For
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 and finite temperature ,
the results show the scaling behavior of a T=0 superconducting transition. The
resistance is linear but vanishes for decreasing with an apparent
exponential behavior. Crossover to non-linearity appears at currents
proportional to , with a thermal-correlation length exponent
consistent with the corresponding value for the diluted XY model at
.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 roughly as in contrast with the 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 () 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
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