26,977 research outputs found
Permutations Containing Many Patterns
It is shown that the maximum number of patterns that can occur in a
permutation of length is asymptotically . This significantly improves
a previous result of Coleman
Kondo resonance narrowing in d- and f-electron systems
By developing a simple scaling theory for the effect of Hund's interactions
on the Kondo effect, we show how an exponential narrowing of the Kondo
resonance develops in magnetic ions with large Hund's interaction. Our theory
predicts an exponential reduction of the Kondo temperature with spin S of the
Hund's coupled moment, a little-known effect first observed in d-electron
alloys in the 1960's, and more recently encountered in numerical calculations
on multi-band Hubbard models with Hund's interactions. We discuss the
consequences of Kondo resonance narrowing for the Mott transition in d-band
materials, particularly iron pnictides, and the narrow ESR linewidth recently
observed in ferromagnetically correlated f-electron materials.Comment: 4 pages, 3 figure
Bounds on the Compactness of Neutron Stars from Brightness Oscillations
The discovery of high-amplitude brightness oscillations at the spin frequency
or its first overtone in six neutron stars in low-mass X-ray binaries during
type~1 X-ray bursts provides a powerful new way to constrain the compactness of
these stars, and hence to constrain the equation of state of the dense matter
in all neutron stars. Here we present the results of general relativistic
calculations of the maximum fractional rms amplitudes that can be observed
during bursts. In particular, we determine the dependence of the amplitude on
the compactness of the star, the angular dependence of the emission from the
surface, the rotational velocity at the stellar surface, and whether there are
one or two emitting poles. We show that if two poles are emitting, as is
strongly indicated by independent evidence in 4U 1636-536 and KS 1731-26, the
resulting limits on the compactness of the star can be extremely restrictive.
We also discuss the expected amplitudes of X-ray color oscillations and the
observational signatures necessary to derive convincing constraints on neutron
star compactness from the amplitudes of burst oscillations.Comment: 8 pages plus one figure, AASTeX v. 4.0, submitted to The
Astrophysical Journal Letter
Prediction of stable walking for a toy that cannot stand
Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658
(1998)] showed that a gravity-powered toy with no control and which has no
statically stable near-standing configurations can walk stably. We show here
that a simple rigid-body statically-unstable mathematical model based loosely
on the physical toy can predict stable limit-cycle walking motions. These
calculations add to the repertoire of rigid-body mechanism behaviors as well as
further implicating passive-dynamics as a possible contributor to stability of
animal motions.Comment: Note: only corrections so far have been fixing typo's in these
comments. 3 pages, 2 eps figures, uses epsf.tex, revtex.sty, amsfonts.sty,
aps.sty, aps10.sty, prabib.sty; Accepted for publication in Phys. Rev. E.
4/9/2001 ; information about Andy Ruina's lab (including Coleman's, Garcia's
and Ruina's other publications and associated video clips) can be found at:
http://www.tam.cornell.edu/~ruina/hplab/index.html and more about Georg
Bock's Simulation Group with whom Katja Mombaur is affiliated can be found at
http://www.iwr.uni-heidelberg.de/~agboc
Electric charge in the field of a magnetic event in three-dimensional spacetime
We analyze the motion of an electric charge in the field of a magnetically
charged event in three-dimensional spacetime. We start by exhibiting a first
integral of the equations of motion in terms of the three conserved components
of the spacetime angular momentum, and then proceed numerically. After crossing
the light cone of the event, an electric charge initially at rest starts
rotating and slowing down. There are two lengths appearing in the problem: (i)
the characteristic length , where and are the
electric charge and mass of the particle, and is the magnetic charge of the
event; and (ii) the spacetime impact parameter . For , after a time of order , the particle makes sharply a quarter of a
turn and comes to rest at the same spatial position at which the event happened
in the past. This jump is the main signature of the presence of the magnetic
event as felt by an electric charge. A derivation of the expression for the
angular momentum that uses Noether's theorem in the magnetic representation is
given in the Appendix.Comment: Version to appear in Phys. Rev.
Kondo effect and channel mixing in oscillating molecules
We investigate the electronic transport through a molecule in the Kondo
regime. The tunneling between the electrode and the molecule is asymmetrically
modulated by the oscillations of the molecule, i.e., if the molecule gets
closer to one of the electrodes the tunneling to that electrode will increase
while for the other electrode it will decrease. The system is described by a
two-channel Anderson model with phonon-assisted hybridization, which is solved
with the Wilson numerical renormalization group method. The results for several
functional forms of tunneling modulation are presented. For a linearized
modulation the Kondo screening of the molecular spin is caused by the even or
odd conduction channel. At the critical value of the electron-phonon coupling
an unstable two-channel Kondo fixed point is found. For a realistic modulation
the spin at the molecular orbital is Kondo screened by the even conduction
channel even in the regime of strong coupling. A universal consequence of the
electron-phonon coupling is the softening of the phonon mode and the related
instability to perturbations that break the left-right symmetry. When the
frequency of oscillations decreases below the magnitude of such perturbation,
the molecule is abruptly attracted to one of the electrodes. In this regime,
the Kondo temperature is enhanced and, simultaneously, the conductance through
the molecule is suppressed.Comment: published versio
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