887 research outputs found
A characteristic free criterion of birationality
One develops {\em ab initio} the theory of rational/birational maps over
reduced, but not necessarily irreducible, projective varieties in arbitrary
characteristic. A numerical invariant of a rational map is introduced, called
the Jacobian dual rank. It is proved that a rational map in this general setup
is birational if and only if the Jacobian dual rank attains its maximal
possible value. Even in the "classical" case where the source variety is
irreducible there is some gain for this invariant over the degree of the map as
it is, on one hand, intrinsically related to natural constructions in
commutative algebra and, on the other hand, is effectively straightforwardly
computable. Applications are given to results so far only known in
characteristic zero. In particular, the surprising result of Dolgachev
concerning the degree of a plane polar Cremona map is given an alternative
conceptual angle.Comment: 24 page
Power spectrum of many impurities in a d-wave superconductor
Recently the structure of the measured local density of states power spectrum
of a small area of the \BSCCO (BSCCO) surface has been interpreted in terms of
peaks at an "octet" of scattering wave vectors determined assuming weak,
noninterfering scattering centers. Using analytical arguments and numerical
solutions of the Bogoliubov-de Gennes equations, we discuss how the
interference between many impurities in a d-wave superconductor alters this
scenario. We propose that the peaks observed in the power spectrum are not the
features identified in the simpler analyses, but rather "background" structures
which disperse along with the octet vectors. We further consider how our
results constrain the form of the actual disorder potential found in this
material.Comment: 5 pages.2 figure
Kondo effect of non-magnetic impurities and the co-existing charge order in the cuprate superconductors
We present a theory of Kondo effect caused by an induced magnetic moment near
non-magnetic impurities such as Zn and Li in the cuprate superconductors. Based
on the co-existence of charge order and superconductivity, a natural
description of the induced moment and the resulting Kondo effect is obtained in
the framework of bond-operator theory of microscopic t-J-V Hamiltonian. The
local density of state near impurities is computed in a self-consistent
Bogoliubov-de Gennes theory which shows a low-energy peak in the middle of
superconducting gap. Our theory also suggests that the charge order can be
enhanced near impuries.Comment: 5 pages, 4 figure
Ground State and Spectral Properties of a Quantum Impurity in d-Wave Superconductors
The variational approach of Gunnarsson and Sch\"onhammer to the Anderson
impurity model is generalized to study d-wave superconductors in the presence
of dilute spin-1/2 impurities. We show that the local moment is screened when
the hybridization exceeds a nonzero critical value at which the ground state
changes from a spin doublet to a spin singlet. The electron spectral functions
are calculated in both phases. We find that while a Kondo resonance develops
above the Fermi level in the singlet phase, the spectral function exhibits a
low-energy spectral peak below the Fermi level in the spin doublet phase. The
origin of such a ``virtual Kondo resonance'' is the existence of low-lying
collective excitations in the spin-singlet sector. We discuss our results in
connection to recent spectroscopic experiments on Zn doped high-T
superconductors.Comment: 5 pages, 4figures, revised versio
Zeeman effects on the impurity-induced resonances in d-wave superconductors
It is shown how the resonant states induced by a single spinless impurity in
a d-wave superconductor evolve under the effect of an applied Zeeman magnetic
field. Moreover, it is demonstrated that the spin-orbit coupling to the
impurity potential can have important and characteristic effects on the
resonant states and their response to the Zeeman field, especially when the
impurity is close to the unitary limit. For zero or very small spin-orbit
interaction, the resonant states becomes Zeeman splitted by the magnetic field
while when the spin-orbit coupling is important, new low-lying resonances arise
which do not show any Zeeman splitting.Comment: 5 pages with 5 eps figures embedded. To appear on Phys. Rev.
Impurity state in the vortex core of d-wave superconductors: Anderson impurity model versus unitary impurity model
Using an extended Anderson/Kondo impurity model to describe the magnetic
moments around an impurity doped in high- d-wave cuprates and in
the framework of the slave-boson meanfield approach, we study numerically the
impurity state in the vortex core by exact diagonalization of the
well-established Bogoliubov-de Gennes equations. The low-energy impurity state
is found to be good agreement with scanning tunnelingmicroscopy observation.
After pinning a vortex on the impurity site, we compare the unitary impurity
model with the extended Anderson impurity model by examining the effect of the
magnetic field on the impurity state. We find that the impurity resonance in
the unitary impurity model is strongly suppressed by the vortex; while it is
insensitive to the field in the extended Anderson impurity model.Comment: 8 pages, 3 figure
Impurity induced resonant state in a pseudogap state of a high temperature superconductor
We predict a resonance impurity state generated by the substitution of one Cu
atom with a nonmagnetic atom, such as Zn, in the pseudogap state of a high-T_c
superconductor. The precise microscopic origin of the pseudogap is not
important for this state to be formed, in particular this resonance will be
present even in the absence of superconducting fluctuations in the normal
state. In the presence of superconducting fluctuations, we predict the
existence of a counterpart impurity peak on a symmetric bias.
The nature of impurity resonance is similar to the previously studied
resonance in the d-wave superconducting state.Comment: 4 pages, 2 figure
Quantum interference between non-magnetic impurities in d_x2-y2-wave superconductors
We study quantum interference of electronic waves that are scattered by
multiple non-magnetic impurities in a d_x2-y2-wave superconductor. We show that
the number of resonance states in the density-of-states (DOS), as well as their
frequency and spatial dependence change significantly as the distance between
the impurities or their orientation relative to the crystal lattice is varied.
Since the latter effect arises from the momentum dependence of the
superconducting gap, we argue that quantum interference is a novel tool to
identify the symmetry of unconventional superconductors.Comment: 4 pages, 4 figure
Intermittent applied mechanical loading induces subchondral bone thickening that may be intensified locally by contiguous articular cartilage lesions
Objectives: Changes in subchondral bone (SCB) and cross-talk with articular cartilage (AC) have been linked to osteoarthritis (OA). Using micro-computed tomography (micro-CT) this study: (1) examines changes in SCB architecture in a non-invasive loading mouse model in which focal AC lesions are induced selectively in the lateral femur, and (2) determines any modifications in the contralateral knee, linked to changes in gait, which might complicate use of this limb as an internal control. Methods: Right knee joints of CBA mice were loaded: once with 2weeks of habitual use (n=7), for 2weeks (n=8) or for 5weeks (n=5). Both left (contralateral) and right (loaded) knees were micro-CT scanned and the SCB and trabecular bone analysed. Gait analysis was also performed. Results: These analyses showed a significant increase in SCB thickness in the lateral compartments in joints loaded for 5weeks, which was most marked in the lateral femur; the contralateral non-loaded knee also showed transient SCB thickening (loaded once and repetitively). Epiphyseal trabecular bone BV/TV and trabecular thickness were also increased in the lateral compartments after 5 weeks of loading, and in all joint compartments in the contralateral knee. Gait analysis showed that applied loading only affected gait in the contralateral himd-limb in all groups of mice from the second week after the first loading episode. Conclusions: These data indicate a spatial link between SCB thickening and AC lesions following mechanical trauma, and the clear limitations associated with the use of contralateral joints as controls in such OA models, and perhaps in OA diagnosis
Molecular dynamics study of accelerated ion-induced shock waves in biological media
We present a molecular dynamics study of the effects of carbon- and iron-ion induced shock waves in DNA duplexes in liquid water. We use the CHARMM force field implemented within the MBN Explorer simulation package to optimize and equilibrate DNA duplexes in liquid water boxes of different sizes and shapes. The translational and vibrational degrees of freedom of water molecules are excited according to the energy deposited by the ions and the subsequent shock waves in liquid water are simulated. The pressure waves generated are studied and compared with an analytical hydrodynamics model which serves as a benchmark for evaluating the suitability of the simulation boxes. The energy deposition in the DNA backbone bonds is also monitored as an estimation of biological damage, something which is not possible with the analytical model
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