2,629 research outputs found
SO(3) vortices and disorder in the 2d SU(2) chiral model
We study the correlation function of the 2d SU(2) principal chiral model on
the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled
to SO(3) vortices we show that the vortices play a crucial role in disordering
the correlations at low temperature. Using a series of exact transformations we
prove that, if satisfied, certain inequalities between vortex correlations
imply exponential fall-off of the correlation function at arbitrarily low
temperatures. We also present some Monte Carlo evidence that these correlation
inequalities are indeed satisfied. Our method can be easily translated to the
language of 4d SU(2) gauge theory to establish the role of corresponding SO(3)
monopoles in maintaining confinement at small couplings.Comment: 13 pages LaTe
Chaotic Explosions
We investigate chaotic dynamical systems for which the intensity of
trajectories might grow unlimited in time. We show that (i) the intensity grows
exponentially in time and is distributed spatially according to a fractal
measure with an information dimension smaller than that of the phase space,(ii)
such exploding cases can be described by an operator formalism similar to the
one applied to chaotic systems with absorption (decaying intensities), but
(iii) the invariant quantities characterizing explosion and absorption are
typically not directly related to each other, e.g., the decay rate and fractal
dimensions of absorbing maps typically differ from the ones computed in the
corresponding inverse (exploding) maps. We illustrate our general results
through numerical simulation in the cardioid billiard mimicking a lasing
optical cavity, and through analytical calculations in the baker map.Comment: 7 pages, 5 figure
Unjamming of Granular Packings due to Local Perturbations: Stability and Decay of Displacements
We study the mechanical response generated by local deformations in jammed
packings of rigid disks. Based on discrete element simulations we determine the
critical force of the local perturbation that is needed to break the mechanical
equilibrium and examine the generated displacement field. Displacements decay
as a power law of the distance from the perturbation point. The decay exponent
and the critical force exhibit nontrivial dependence on the friction: Both
quantities are nonmonotonic and have a sharp maximum at the friction
coefficient 0.1. We find that the mechanical response properties are closely
related to the problem of force-indeterminacy where similar nonmonotonic
behavior was observed previously. We establish direct connection between the
critical force and the ensemble of static force networks.Comment: 4 pages, 4 figure
To make a nanomechanical Schr\"{o}dinger-cat mew
By an explicite calculation of Michelson interferometric output intensities
in the optomechanical scheme proposed by Marshall et al. (2003), an oscillatory
factor is obtained that may go down to zero just at the time a visibility
revival ought to be observed. Including a properly tuned phase shifter offers a
simple amendment to the situation. By using a Pockels phase shifter with fast
time-dependent modulation in one arm, one may obtain further possibilities to
enrich the quantum state preparation and reconstruction abilities of the
original scheme, thereby improving the chances to reliably detect genuine
quantum behaviour of a nanomechanical oscillator.Comment: For Proc. DICE-2010 (Castiglioncello), to be published in J. Phys.
Conf. Ser., 201
Universality in active chaos
Many examples of chemical and biological processes take place in large-scale
environmental flows. Such flows generate filamental patterns which are often
fractal due to the presence of chaos in the underlying advection dynamics. In
such processes, hydrodynamical stirring strongly couples into the reactivity of
the advected species and might thus make the traditional treatment of the
problem through partial differential equations difficult. Here we present a
simple approach for the activity in in-homogeneously stirred flows. We show
that the fractal patterns serving as skeletons and catalysts lead to a rate
equation with a universal form that is independent of the flow, of the particle
properties, and of the details of the active process. One aspect of the
universality of our appraoch is that it also applies to reactions among
particles of finite size (so-called inertial particles).Comment: 10 page
BANGO SEA XLOC/HMBC-H2OBC: complete heteronuclear correlation within minutes from one NMR pulse sequence
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Force indeterminacy in the jammed state of hard disks
Granular packings of hard discs are investigated by means of contact dynamics
which is an appropriate technique to explore the allowed force-realizations in
the space of contact forces. Configurations are generated for given values of
the friction coefficient, and then an ensemble of equilibrium forces is found
for fixed contacts. We study the force fluctuations within this ensemble. In
the limit of zero friction the fluctuations vanish in accordance with the
isostaticity of the packing. The magnitude of the fluctuations has a
non-monotonous friction dependence. The increase for small friction can be
attributed to the opening of the angle of the Coulomb cone, while the decrease
as friction increases is due to the reduction of connectivity of the
contact-network, leading to local, independent clusters of indeterminacy. We
discuss the relevance of indeterminacy to packings of deformable particles and
to the mechanical response properties.Comment: 4 pages, 3 figures. Minor changes, journal reference adde
Rapid granular flows on a rough incline: phase diagram, gas transition, and effects of air drag
We report experiments on the overall phase diagram of granular flows on an
incline with emphasis on high inclination angles where the mean layer velocity
approaches the terminal velocity of a single particle free falling in air. The
granular flow was characterized by measurements of the surface velocity, the
average layer height, and the mean density of the layer as functions of the
hopper opening, the plane inclination angle and the downstream distance x of
the flow. At high inclination angles the flow does not reach an x-invariant
steady state over the length of the inclined plane. For low volume flow rates,
a transition was detected between dense and very dilute (gas) flow regimes. We
show using a vacuum flow channel that air did not qualitatively change the
phase diagram and did not quantitatively modify mean flow velocities of the
granular layer except for small changes in the very dilute gas-like phase.Comment: 10 pages, 16 figures, accepted to Phys. Rev.
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